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Physics

By

Aristotle



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http://classics.mit.edu//Aristotle/physics.html

PhysicsBy Aristotle

Translated by . P. !ardie and . ". #aye





B$$" I

Part %

&hen the ob'ects of an in(uiry) in any department) have principles)conditions) or elements) it is through ac(uaintance *ith these that+no*ledge) that is to say scientific +no*ledge) is attained. ,or *edo not thin+ that *e +no* a thing until *e are ac(uainted *ith itsprimary conditions or first principles) and have carried our analysisas far as its simplest elements. Plainly therefore in the scienceof -ature) as in other branches of study) our first tas+ *ill be totry to determine *hat relates to its principles.

The natural *ay of doing this is to start from the things *hich aremore +no*able and obvious to us and proceed to*ards those *hich areclearer and more +no*able by nature for the same things are not

+no*ablerelatively to us and +no*able *ithout (ualification. So in thepresent in(uiry *e must follo* this method and advance from *hat ismore obscure by nature) but clearer to us) to*ards *hat is more clearand more +no*able by nature.

-o* *hat is to us plain and obvious at first is rather confusedmasses)the elements and principles of *hich become +no*n to us later byanalysis.Thus *e must advance from generalities to particulars for it is a*hole that is best +no*n to sense0perception) and a generality isa +ind of *hole) comprehending many things *ithin it) li+e parts.1uch the same thing happens in the relation of the name to theformula.A name) e.g. round ) means vaguely a sort of *hole: its definitionanalyses this into its particular senses. Similarly a child beginsby calling all men father ) and all *omen mother ) but later ondistinguishes each of them.

Part 2

The principles in (uestion must be either 3a4 one or 3b4 more thanone. If 3a4 one) it must be either 3i4 motionless) as Parmenides and1elissus assert) or 3ii4 in motion) as the physicists hold) somedeclaringair to be the first principle) others *ater. If 3b4 more than one)then either 3i4 a finite or 3ii4 an infinite plurality. If 3i4 finite3but more than one4) then either t*o or three or four or some othernumber. If 3ii4 infinite) then either as 5emocritus believed one in+ind) but differing in shape or form or different in +ind and evencontrary.

A similar in(uiry is made by those *ho in(uire into the number ofe6istents: for they in(uire *hether the ultimate constituents ofe6isting



things are one or many) and if many) *hether a finite or an infiniteplurality. So they too are in(uiring *hether the principle or elementis one or many.

-o* to investigate *hether Being is one and motionless is not acontribution

to the science of -ature. ,or 'ust as the geometer has nothing moreto say to one *ho denies the principles of his science0this beinga (uestion for a different science or for or common to all0so a maninvestigating principles cannot argue *ith one *ho denies theire6istence.,or if Being is 'ust one) and one in the *ay mentioned) there is aprinciple no longer) since a principle must be the principle of something or things.

To in(uire therefore *hether Being is one in this sense *ould be li+earguing against any other position maintained for the sa+e of argument3such as the !eraclitean thesis) or such a thesis as that Being isone man4 or li+e refuting a merely contentious argument0a description*hich applies to the arguments both of 1elissus and of Parmenides:their premisses are false and their conclusions do not follo*. $rrather the argument of 1elissus is gross and palpable and offers nodifficulty at all: accept one ridiculous proposition and the restfollo*s0a simple enough proceeding.

&e physicists) on the other hand) must ta+e for granted that thethingsthat e6ist by nature are) either all or some of them) in motion *hichis indeed made plain by induction. 1oreover) no man of science isbound to solve every +ind of difficulty that may be raised) but onlyas many as are dra*n falsely from the principles of the science: itis not our business to refute those that do not arise in this *ay:'ust as it is the duty of the geometer to refute the s(uaring of thecircle by means of segments) but it is not his duty to refuteAntiphon sproof. At the same time the holders of the theory of *hich *e arespea+ing do incidentally raise physical (uestions) though -ature isnot their sub'ect: so it *ill perhaps be as *ell to spend a fe* *ordson them) especially as the in(uiry is not *ithout scientific interest.

The most pertinent (uestion *ith *hich to begin *ill be this: In *hatsense is it asserted that all things are one7 ,or is is used inmany senses. 5o they mean that all things are substance or(uantitiesor (ualities7 And) further) are all things one substance0one man)one horse) or one soul0or (uality and that one and the same0*hiteor hot or something of the +ind7 These are all very differentdoctrinesand all impossible to maintain.

,or if both substance and (uantity and (uality are) then) *hetherthese e6ist independently of each other or not) Being *ill be many.

If on the other hand it is asserted that all things are (uality or(uantity) then) *hether substance e6ists or not) an absurdity results)if the impossible can properly be called absurd. ,or none of theotherscan e6ist independently: substance alone is independent: foreverythingis predicated of substance as sub'ect. -o* 1elissus says that Being



is infinite. It is then a (uantity. ,or the infinite is in thecategoryof (uantity) *hereas substance or (uality or affection cannot beinfinitee6cept through a concomitant attribute) that is) if at the same timethey are also (uantities. ,or to define the infinite you must use

(uantity in your formula) but not substance or (uality. If then Beingis both substance and (uantity) it is t*o) not one: if only substance)it is not infinite and has no magnitude for to have that it *illhave to be a (uantity.

Again) one itself) no less than being ) is used in many senses)so *e must consider in *hat sense the *ord is used *hen it is saidthat the All is one.

-o* *e say that 3a4 the continuous is one or that 3b4 the indivisibleis one) or 3c4 things are said to be one ) *hen their essence isone and the same) as li(uor and drin+ .

If 3a4 their $ne is one in the sense of continuous) it is many) forthe continuous is divisible ad infinitum.

There is) indeed) a difficulty about part and *hole) perhaps notrelevantto the present argument) yet deserving consideration on its o*naccount0namely)*hether the part and the *hole are one or more than one) and ho* theycan be one or many) and) if they are more than one) in *hat sensethey are more than one. 3Similarly *ith the parts of *holes *hichare not continuous.4 ,urther) if each of the t*o parts is indivisiblyone *ith the *hole) the difficulty arises that they *ill beindivisiblyone *ith each other also.

But to proceed: If 3b4 their $ne is one as indivisible) nothing *illhave (uantity or (uality) and so the one *ill not be infinite) as1elissus says0nor) indeed) limited) as Parmenides says) for thoughthe limit is indivisible) the limited is not.

But if 3c4 all things are one in the sense of having the samedefinition)li+e raiment and dress ) then it turns out that they aremaintainingthe !eraclitean doctrine) for it *ill be the same thing to be goodand to be bad ) and to be good and to be not good ) and so thesame thing *ill be good and not good ) and man and horse in fact)their vie* *ill be) not that all things are one) but that they arenothing and that to be of such0and0such a (uality is the same as

to be of such0and0such a si8e .

9ven the more recent of the ancient thin+ers *ere in a pother lestthe same thing should turn out in their hands both one and many. Sosome) li+e ycophron) *ere led to omit is ) others to change themode of e6pression and say the man has been *hitened instead of

is *hite ) and *al+s instead of is *al+ing ) for fear that ifthey added the *ord is they should be ma+ing the one to be many0asif one and being *ere al*ays used in one and the same sense. &hat

is may be many either in definition 3for e6ample to be *hite isone thing) to be musical another) yet the same thing be both) sothe one is many4 or by division) as the *hole and its parts. $n this



point) indeed) they *ere already getting into difficulties andadmittedthat the one *as many0as if there *as any difficulty about the samething being both one and many) provided that these are not oppositesfor one may mean either potentially one or actually one .

Part ;

If) then) *e approach the thesis in this *ay it seems impossible forall things to be one. ,urther) the arguments they use to prove theirposition are not difficult to e6pose. ,or both of them reasoncontentiously0Imean both 1elissus and Parmenides. <Their premisses are false andtheir conclusions do not follo*. $r rather the argument of 1elissusis gross and palpable and offers no difficulty at all: admit oneridiculousproposition and the rest follo*s0a simple enough proceeding.= Thefallacy of 1elissus is obvious. ,or he supposes that the assumption

*hat has come into being al*ays has a beginning 'ustifies theassumption

*hat has not come into being has no beginning . Then this also isabsurd) that in every case there should be a beginning of the thing0notof the time and not only in the case of coming to be in the full sensebut also in the case of coming to have a (uality0as if change nevertoo+ place suddenly. Again) does it follo* that Being) if one) ismotionless7 &hy should it not move) the *hole of it *ithin itself)as parts of it do *hich are unities) e.g. this *ater7 Again) *hy is(ualitative change impossible7 But) further) Being cannot be one inform) though it may be in *hat it is made of. 39ven some of thephysicistshold it to be one in the latter *ay) though not in the former.4 1anobviously differs from horse in form) and contraries from each other.

The same +ind of argument holds good against Parmenides also) besidesany that may apply specially to his vie*: the ans*er to him beingthat this is not true and that does not follo* . !is assumptionthat one is used in a single sense only is false) because it is usedin several. !is conclusion does not follo*) because if *e ta+e only*hite things) and if *hite has a single meaning) none the less *hatis *hite *ill be many and not one. ,or *hat is *hite *ill not be oneeither in the sense that it is continuous or in the sense that itmust be defined in only one *ay. &hiteness *ill be different from

*hat has *hiteness . -or does this mean that there is anything thatcan e6ist separately) over and above *hat is *hite. ,or *hitenessand that *hich is *hite differ in definition) not in the sense thatthey are things *hich can e6ist apart from each other. But Parmenideshad not come in sight of this distinction.

It is necessary for him) then) to assume not only that being hasthe same meaning) of *hatever it is predicated) but further that itmeans 3%4 *hat 'ust is and 324 *hat is 'ust one.

It must be so) for 3%4 an attribute is predicated of some sub'ect)so that the sub'ect to *hich being is attributed *ill not be) asit is something different from being . Something) therefore) *hichis not *ill be. !ence substance *ill not be a predicate of anythingelse. ,or the sub'ect cannot be a being) unless being means severalthings) in such a *ay that each is something. But e6 hypothesi beingmeans only one thing.



If) then) substance is not attributed to anything) but other thingsare attributed to it) ho* does substance mean *hat is rather than*hat is not7 ,or suppose that substance is also *hite . Since thedefinition of the latter is different 3for being cannot even beattributedto *hite) as nothing is *hich is not substance 4) it follo*s that

*hite is not0being00and that not in the sense of a particular not0being)but in the sense that it is not at all. !ence substance is notfor it is true to say that it is *hite) *hich *e found to mean not0being.If to avoid this *e say that even *hite means substance) it follo*sthat being has more than one meaning.

In particular) then) Being *ill not have magnitude) if it issubstance.,or each of the t*o parts must he in a different sense.

324 Substance is plainly divisible into other substances) if *econsiderthe mere nature of a definition. ,or instance) if man is asubstance)

animal and biped must also be substances. ,or if not substances)they must be attributes0and if attributes) attributes either of 3a4man or of 3b4 some other sub'ect. But neither is possible.

3a4 An attribute is either that *hich may or may not belong to thesub'ect or that in *hose definition the sub'ect of *hich it is anattribute is involved. Thus sitting is an e6ample of a separableattribute) *hile snubness contains the definition of nose ) to*hich *e attribute snubness. ,urther) the definition of the *holeis not contained in the definitions of the contents or elements ofthe definitory formula that of man for instance in biped ) orthat of *hite man in *hite . If then this is so) and if bipedis supposed to be an attribute of man ) it must be either separable)so that man might possibly not be biped ) or the definition of

man must come into the definition of biped 0*hich is impossible)as the converse is the case.

3b4 If) on the other hand) *e suppose that biped and animal areattributes not of man but of something else) and are not each of thema substance) then man too *ill be an attribute of something else.But *e must assume that substance is not the attribute of anything)that the sub'ect of *hich both biped and animal and eachseparatelyare predicated is the sub'ect also of the comple6 biped animal .

Are *e then to say that the All is composed of indivisible substances7Some thin+ers did) in point of fact) give *ay to both arguments. Tothe argument that all things are one if being means one thing) theyconceded that not0being is to that from bisection) they yielded bypositing atomic magnitudes. But obviously it is not true that if beingmeans one thing) and cannot at the same time mean the contradictoryof this) there *ill be nothing *hich is not) for even if *hat is notcannot be *ithout (ualification) there is no reason *hy it shouldnot be a particular not0being. To say that all things *ill be one)if there is nothing besides Being itself) is absurd. ,or *hounderstands

being itself to be anything but a particular substance7 But if thisis so) there is nothing to prevent there being many beings) as hasbeen said.



It is) then) clearly impossible for Being to be one in this sense.

Part >

The physicists on the other hand have t*o modes of e6planation.

The first set ma+e the underlying body one either one of the threeor something else *hich is denser than fire and rarer than air thengenerate everything else from this) and obtain multiplicity bycondensationand rarefaction. -o* these are contraries) *hich may be generali8edinto e6cess and defect . 3Compare Plato s #reat and Small 0e6ceptthat he ma+e these his matter) the one his form) *hile the otherstreat the one *hich underlies as matter and the contraries asdifferentiae)i.e. forms4.

The second set assert that the contrarieties are contained in theone and emerge from it by segregation) for e6ample Ana6imander andalso all those *ho assert that *hat is is one and many) li+e9mpedoclesand Ana6agoras for they too produce other things from their mi6tureby segregation. These differ) ho*ever) from each other in that theformer imagines a cycle of such changes) the latter a single series.Ana6agoras again made both his homceomerous substances and hiscontrariesinfinite in multitude) *hereas 9mpedocles posits only the so0calledelements.

The theory of Ana6agoras that the principles are infinite in multitude*as probably due to his acceptance of the common opinion of thephysiciststhat nothing comes into being from not0being. ,or this is the reason*hy they use the phrase all things *ere together and the cominginto being of such and such a +ind of thing is reduced to change of(uality) *hile some spo+e of combination and separation. 1oreover)the fact that the contraries proceed from each other led them to theconclusion. The one) they reasoned) must have already e6isted in theother for since everything that comes into being must arise eitherfrom *hat is or from *hat is not) and it is impossible for it to arisefrom *hat is not 3on this point all the physicists agree4) theythoughtthat the truth of the alternative necessarily follo*ed) namely thatthings come into being out of e6istent things) i.e. out of thingsalready present) but imperceptible to our senses because of thesmallnessof their bul+. So they assert that everything has been mi6ed in every.thing) because they sa* everything arising out of everything. Butthings) as they say) appear different from one another and receivedifferent names according to the nature of the particles *hich arenumerically predominant among the innumerable constituents of themi6ture. ,or nothing) they say) is purely and entirely *hite or blac+or s*eet) bone or flesh) but the nature of a thing is held to be thatof *hich it contains the most.

-o* 3%4 the infinite (ua infinite is un+no*able) so that *hat isinfinitein multitude or si8e is un+no*able in (uantity) and *hat is infinitein variety of +ind is un+no*able in (uality. But the principles in(uestion are infinite both in multitude and in +ind. Therefore it



is impossible to +no* things *hich are composed of them for it is*hen *e +no* the nature and (uantity of its components that *e suppose*e +no* a comple6.

,urther 324 if the parts of a *hole may be of any si8e in thedirection

either of greatness or of smallness 3by parts I mean componentsinto *hich a *hole can be divided and *hich are actually present init4) it is necessary that the *hole thing itself may be of any si8e.Clearly) therefore) since it is impossible for an animal or plantto be indefinitely big or small) neither can its parts be such) orthe *hole *ill be the same. But flesh) bone) and the li+e are theparts of animals) and the fruits are the parts of plants. !ence itis obvious that neither flesh) bone) nor any such thing can be ofindefinite si8e in the direction either of the greater or of the less.

Again 3;4 according to the theory all such things are already presentin one another and do not come into being but are constituents *hichare separated out) and a thing receives its designation from its chiefconstituent. ,urther) anything may come out of anything0*ater bysegregationfrom flesh and flesh from *ater. !ence) since every finite body ise6hausted by the repeated abstraction of a finite body) it seemsobviouslyto follo* that everything cannot subsist in everything else. ,or letflesh be e6tracted from *ater and again more flesh be produced fromthe remainder by repeating the process of separation: then) eventhoughthe (uantity separated out *ill continually decrease) still it *illnot fall belo* a certain magnitude. If) therefore) the process comesto an end) everything *ill not be in everything else 3for there *illbe no flesh in the remaining *ater4 if on the other hand it doesnot) and further e6traction is al*ays possible) there *ill be aninfinitemultitude of finite e(ual particles in a finite (uantity0*hich isimpossible. Another proof may be added: Since every body must diminishin si8e *hen something is ta+en from it) and flesh is (uantitativelydefinite in respect both of greatness and smallness) it is clear thatfrom the minimum (uantity of flesh no body can be separated out forthe flesh left *ould be less than the minimum of flesh.

astly 3>4 in each of his infinite bodies there *ould be alreadypresentinfinite flesh and blood and brain0 having a distinct e6istence)ho*ever)from one another) and no less real than the infinite bodies) and eachinfinite: *hich is contrary to reason.

The statement that complete separation never *ill ta+e place iscorrectenough) though Ana6agoras is not fully a*are of *hat it means. ,oraffections are indeed inseparable. If then colours and states hadentered into the mi6ture) and if separation too+ place) there *ouldbe a *hite or a healthy *hich *as nothing but *hite or healthy)i.e. *as not the predicate of a sub'ect. So his 1ind is an absurdperson aiming at the impossible) if he is supposed to *ish to separatethem) and it is impossible to do so) both in respect of (uantity andof (uality0 of (uantity) because there is no minimum magnitude) andof (uality) because affections are inseparable.

-or is Ana6agoras right about the coming to be of homogeneous bodies.



It is true there is a sense in *hich clay is divided into pieces ofclay) but there is another in *hich it is not. &ater and air are)and are generated from each other) but not in the *ay in *hichbric+scome from a house and again a house from bric+s and it is betterto assume a smaller and finite number of principles) as 9mpedocles

does.

Part ?

All thin+ers then agree in ma+ing the contraries principles) boththose *ho describe the All as one and unmoved 3for even Parmenidestreats hot and cold as principles under the names of fire and earth4and those too *ho use the rare and the dense. The same is true of5emocritus also) *ith his plenum and void) both of *hich e6ist) besays) the one as being) the other as not0being. Again he spea+s ofdifferences in position) shape) and order) and these are genera of*hich the species are contraries) namely) of position) above andbelo*)before and behind of shape) angular and angle0less) straight andround.

It is plain then that they all in one *ay or another identify thecontraries *ith the principles. And *ith good reason. ,or firstprinciplesmust not be derived from one another nor from anything else) *hileeverything has to be derived from them. But these conditions arefulfilledby the primary contraries) *hich are not derived from anything elsebecause they are primary) nor from each other because they arecontraries.

But *e must see ho* this can be arrived at as a reasoned result) as*ell as in the *ay 'ust indicated.

$ur first presupposition must be that in nature nothing acts on) oris acted on by) any other thing at random) nor may anything come fromanything else) unless *e mean that it does so in virtue of aconcomitantattribute. ,or ho* could *hite come from musical ) unless musicalhappened to be an attribute of the not0*hite or of the blac+7 -o)

*hite comes from not0*hite 0and not from any not0*hite ) but fromblac+ or some intermediate colour. Similarly) musical comes to befrom not0musical ) but not from any thing other than musical) butfrom unmusical or any intermediate state there may be.

-or again do things pass into the first chance thing *hite doesnot pass into musical 3e6cept) it may be) in virtue of a concomitantattribute4) but into not0*hite 0and not into any chance thing *hichis not *hite) but into blac+ or an intermediate colour musicalpasses into not0musical 0and not into any chance thing other thanmusical) but into unmusical or any intermediate state there maybe.

The same holds of other things also: even things *hich are not simplebut comple6 follo* the same principle) but the opposite state hasnot received a name) so *e fail to notice the fact. &hat is in tunemust come from *hat is not in tune) and vice versa the tuned passesinto untunedness0and not into any untunedness) but into thecorrespondingopposite. It does not matter *hether *e ta+e attunement) order) or



composition for our illustration the principle is obviously the samein all) and in fact applies e(ually to the production of a house)a statue) or any other comple6. A house comes from certain thingsin a certain state of separation instead of con'unction) a statue3or any other thing that has been shaped4 from shapelessness0eachof these ob'ects being partly order and partly composition.

If then this is true) everything that comes to be or passes a*ay from)or passes into) its contrary or an intermediate state. But theintermediatesare derived from the contraries0colours) for instance) from blac+and *hite. 9verything) therefore) that comes to be by a naturalprocessis either a contrary or a product of contraries.

@p to this point *e have practically had most of the other *riterson the sub'ect *ith us) as I have said already: for all of themidentifytheir elements) and *hat they call their principles) *ith thecontraries)giving no reason indeed for the theory) but contrained as it *ereby the truth itself. They differ) ho*ever) from one another in thatsome assume contraries *hich are more primary) others contraries *hichare less so: some those more +no*able in the order of e6planation)others those more familiar to sense. ,or some ma+e hot and cold) oragain moist and dry) the conditions of becoming *hile others ma+eodd and even) or again ove and Strife and these differ from eachother in the *ay mentioned.

!ence their principles are in one sense the same) in anotherdifferentdifferent certainly) as indeed most people thin+) but the sameinasmuchas they are analogous for all are ta+en from the same table ofcolumns)some of the pairs being *ider) others narro*er in e6tent. In this*ay then their theories are both the same and different) some better)some *orse some) as I have said) ta+e as their contraries *hat ismore +no*able in the order of e6planation) others *hat is morefamiliarto sense. 3The universal is more +no*able in the order of e6planation)the particular in the order of sense: for e6planation has to do *iththe universal) sense *ith the particular.4 The great and the small )for e6ample) belong to the former class) the dense and the rareto the latter.

It is clear then that our principles must be contraries.

Part

The ne6t (uestion is *hether the principles are t*o or three or morein number.

$ne they cannot be) for there cannot be one contrary. -or can theybe innumerable) because) if so) Being *ill not be +no*able: and inany one genus there is only one contrariety) and substance is onegenus: also a finite number is sufficient) and a finite number) suchas the principles of 9mpedocles) is better than an infinite multitudefor 9mpedocles professes to obtain from his principles all thatAna6agorasobtains from his innumerable principles. astly) some contraries are



more primary than others) and some arise from others0for e6ample s*eetand bitter) *hite and blac+0*hereas the principles must al*ays remainprinciples.

This *ill suffice to sho* that the principles are neither one norinnumerable.

#ranted) then) that they are a limited number) it is plausible tosuppose them more than t*o. ,or it is difficult to see ho* eitherdensity should be of such a nature as to act in any *ay on rarityor rarity on density. The same is true of any other pair ofcontrariesfor ove does not gather Strife together and ma+e things out of it)nor does Strife ma+e anything out of ove) but both act on a thirdthing different from both. Some indeed assume more than one such thingfrom *hich they construct the *orld of nature.

$ther ob'ections to the vie* that it is not necessary to assume athird principle as a substratum may be added. 3%4 &e do not find thatthe contraries constitute the substance of any thing. But *hat isa first principle ought not to be the predicate of any sub'ect. Ifit *ere) there *ould be a principle of the supposed principle: forthe sub'ect is a principle) and prior presumably to *hat is predicatedof it. Again 324 *e hold that a substance is not contrary to anothersubstance. !o* then can substance be derived from *hat are notsubstances7$r ho* can non0substances be prior to substance7

If then *e accept both the former argument and this one) *e must)to preserve both) assume a third some*hat as the substratum of thecontraries) such as is spo+en of by those *ho describe the All asone nature0*ater or fire or *hat is intermediate bet*een them. &hatis intermediate seems preferable for fire) earth) air) and *aterare already involved *ith pairs of contraries. There is) therefore)much to be said for those *ho ma+e the underlying substance differentfrom these four of the rest) the ne6t best choice is air) aspresentingsensible differences in a less degree than the others and after air)*ater. All) ho*ever) agree in this) that they differentiate their$ne by means of the contraries) such as density and rarity and moreand less) *hich may of course be generali8ed) as has already beensaid into e6cess and defect. Indeed this doctrine too 3that the $neand e6cess and defect are the principles of things4 *ould appear tobe of old standing) though in different forms for the early thin+ersmade the t*o the active and the one the passive principle) *hereassome of the more recent maintain the reverse.

To suppose then that the elements are three in number *ould seem)from these and similar considerations) a plausible vie*) as I saidbefore. $n the other hand) the vie* that they are more than threein number *ould seem to be untenable.

,or the one substratum is sufficient to be acted on but if *e havefour contraries) there *ill be t*o contrarieties) and *e shall haveto suppose an intermediate nature for each pair separately. If) onthe other hand) the contrarieties) being t*o) can generate from eachother) the second contrariety *ill be superfluous. 1oreover) it isimpossible that there should be more than one primary contrariety.,or substance is a single genus of being) so that the principles candiffer only as prior and posterior) not in genus in a single genusthere is al*ays a single contrariety) all the other contrarieties



in it being held to be reducible to one.

It is clear then that the number of elements is neither one nor morethan t*o or three but *hether t*o or three is) as I said) a (uestionof considerable difficulty.

Part

&e *ill no* give our o*n account) approaching the (uestion first *ithreference to becoming in its *idest sense: for *e shall be follo*ingthe natural order of in(uiry if *e spea+ first of commoncharacteristics)and then investigate the characteristics of special cases.

&e say that one thing comes to be from another thing) and one sortof thing from another sort of thing) both in the case of simple andof comple6 things. I mean the follo*ing. &e can say 3%4 man becomesmusical ) 324 *hat is not0musical becomes musical ) or 3;4) the not0musicalman becomes a musical man . -o* *hat becomes in 3%4 and 3240 manand not musical 0I call simple) and *hat each becomes0 musical 0simplealso. But *hen 3;4 *e say the not0musical man becomes a musical man )both *hat becomes and *hat it becomes are comple6.

As regards one of these simple things that become *e say not onlythis becomes so0and0so ) but also from being this) comes to be so0

and0so )as from being not0musical comes to be musical as regards the other*e do not say this in all cases) as *e do not say 3%4 from beinga man he came to be musical but only the man became musical .

&hen a simple thing is said to become something) in one case 3%4it survives through the process) in the other 324 it does not. ,orman remains a man and is such even *hen he becomes musical) *hereas*hat is not musical or is unmusical does not continue to e6ist) eithersimply or combined *ith the sub'ect.

These distinctions dra*n) one can gather from surveying the variouscases of becoming in the *ay *e are describing that) as *e say) theremust al*ays be an underlying something) namely that *hich becomes)and that this) though al*ays one numerically) in form at least isnot one. 3By that I mean that it can be described in different *ays.4,or to be man is not the same as to be unmusical . $ne partsurvives)the other does not: *hat is not an opposite survives 3for mansurvives4)but not0musical or unmusical does not survive) nor does thecompoundof the t*o) namely unmusical man .

&e spea+ of becoming that from this instead of this becoming thatmore in the case of *hat does not survive the change0 becoming musicalfrom unmusical ) not from man 0but there are e6ceptions) as *esometimesuse the latter form of e6pression even of *hat survives *e spea+of a statue coming to be from bron8e ) not of the bron8e becominga statue . The change) ho*ever) from an opposite *hich does notsurviveis described indifferently in both *ays) becoming that from this



or this becoming that . &e say both that the unmusical becomesmusical )and that from unmusical he becomes musical . And so both forms areused of the comple6) becoming a musical man from an unmusical man )and unmusical man becoming a musical man .

But there are different senses of coming to be . In some cases *edo not use the e6pression come to be ) but come to be so0and0so .$nly substances are said to come to be in the un(ualified sense.

-o* in all cases other than substance it is plain that there mustbe some sub'ect) namely) that *hich becomes. ,or *e +no* that *hena thing comes to be of such a (uantity or (uality or in such arelation)time) or place) a sub'ect is al*ays presupposed) since substance aloneis not predicated of another sub'ect) but everything else ofsubstance.

But that substances too) and anything else that can be said to be*ithout (ualification) come to be from some substratum) *ill appearon e6amination. ,or *e find in every case something that underliesfrom *hich proceeds that *hich comes to be for instance) animalsand plants from seed.

#enerally things *hich come to be) come to be in different *ays: 3%4by change of shape) as a statue 324 by addition) as things *hichgro* 3;4 by ta+ing a*ay) as the !ermes from the stone 3>4 by puttingtogether) as a house 3?4 by alteration) as things *hich turn inrespect of their material substance.

It is plain that these are all cases of coming to be from asubstratum.

Thus) clearly) from *hat has been said) *hatever comes to be is al*ayscomple6. There is) on the one hand) 3a4 something *hich comes intoe6istence) and again 3b4 something *hich becomes that0the latter 3b4in t*o senses) either the sub'ect or the opposite. By the oppositeI mean the unmusical ) by the sub'ect man ) and similarly I callthe absence of shape or form or order the opposite ) and the bron8eor stone or gold the sub'ect .

Plainly then) if there are conditions and principles *hich constitutenatural ob'ects and from *hich they primarily are or have come tobe0have come to be) I mean) *hat each is said to be in its essentialnature) not *hat each is in respect of a concomitant attribute0plainly)I say) everything comes to be from both sub'ect and form. ,or musicalman is composed 3in a *ay4 of man and musical : you can analyseit into the definitions of its elements. It is clear then that *hatcomes to be *ill come to be from these elements.

-o* the sub'ect is one numerically) though it is t*o in form. 3,orit is the man) the gold0the matter generally0that is counted) forit is more of the nature of a this ) and *hat comes to be does notcome from it in virtue of a concomitant attribute the privation)on the other hand) and the contrary are incidental in the process.4And the positive form is one0the order) the ac(uired art of music)or any similar predicate.

There is a sense) therefore) in *hich *e must declare the principlesto be t*o) and a sense in *hich they are three a sense in *hich the



contraries are the principles0say for e6ample the musical and theunmusical) the hot and the cold) the tuned and the untuned0and a sensein *hich they are not) since it is impossible for the contraries tobe acted on by each other. But this difficulty also is solved by thefact that the substratum is different from the contraries) for itis itself not a contrary. The principles therefore are) in a *ay)

not more in number than the contraries) but as it *ere t*o) nor yetprecisely t*o) since there is a difference of essential nature) butthree. ,or to be man is different from to be unmusical ) and tobe unformed from to be bron8e .

&e have no* stated the number of the principles of natural ob'ects*hich are sub'ect to generation) and ho* the number is reached: andit is clear that there must be a substratum for the contraries) andthat the contraries must be t*o. 3 et in another *ay of putting itthis is not necessary) as one of the contraries *ill serve to effectthe change by its successive absence and presence.4

The underlying nature is an ob'ect of scientific +no*ledge) by ananalogy. ,or as the bron8e is to the statue) the *ood to the bed)or the matter and the formless before receiving form to any thing*hich has form) so is the underlying nature to substance) i.e. the

this or e6istent.

This then is one principle 3though not one or e6istent in the samesense as the this 4) and the definition *as one as *e agreed thenfurther there is its contrary) the privation. In *hat sense theseare t*o) and in *hat sense more) has been stated above. Briefly) *ee6plained first that only the contraries *ere principles) and laterthat a substratum *as indispensable) and that the principles *erethree our last statement has elucidated the difference bet*een thecontraries) the mutual relation of the principles) and the natureof the substratum. &hether the form or the substratum is the essentialnature of a physical ob'ect is not yet clear. But that the principlesare three) and in *hat sense) and the *ay in *hich each is aprinciple)is clear.

So much then for the (uestion of the number and the nature of theprinciples.

Part D

&e *ill no* proceed to sho* that the difficulty of the early thin+ers)as *ell as our o*n) is solved in this *ay alone.

The first of those *ho studied science *ere misled in their searchfor truth and the nature of things by their ine6perience) *hich asit *ere thrust them into another path. So they say that none of thethings that are either comes to be or passes out of e6istence) because*hat comes to be must do so either from *hat is or from *hat is not)both of *hich are impossible. ,or *hat is cannot come to be 3becauseit is already4) and from *hat is not nothing could have come to be3because something must be present as a substratum4. So too theye6aggeratedthe conse(uence of this) and *ent so far as to deny even the e6istenceof a plurality of things) maintaining that only Being itself is. Suchthen *as their opinion) and such the reason for its adoption.

$ur e6planation on the other hand is that the phrases something comesto be from *hat is or from *hat is not ) *hat is not or *hat is does



something or has something done to it or becomes some particularthing )are to be ta+en 3in the first *ay of putting our e6planation4 in thesame sense as a doctor does something or has something done to him )

is or becomes something from being a doctor. These e6pressions maybe ta+en in t*o senses) and so too) clearly) may from being ) and

being acts or is acted on . A doctor builds a house) not (ua doctor)but (ua housebuilder) and turns gray) not (ua doctor) but (ua dar+0haired.$n the other hand he doctors or fails to doctor (ua doctor. But *eare using *ords most appropriately *hen *e say that a doctor doessomething or undergoes something) or becomes something from beinga doctor) if he does) undergoes) or becomes (ua doctor. Clearly thenalso to come to be so0and0so from not0being means (ua not0being .

It *as through failure to ma+e this distinction that those thin+ersgave the matter up) and through this error that they *ent so muchfarther astray as to suppose that nothing else comes to be or e6istsapart from Being itself) thus doing a*ay *ith all becoming.

&e ourselves are in agreement *ith them in holding that nothing canbe said *ithout (ualification to come from *hat is not. Butnevertheless*e maintain that a thing may come to be from *hat is not 0that is)in a (ualified sense. ,or a thing comes to be from the privation)*hich in its o*n nature is not0being)0this not surviving as aconstituentof the result. et this causes surprise) and it is thought impossiblethat something should come to be in the *ay described from *hat isnot.

In the same *ay *e maintain that nothing comes to be from being) andthat being does not come to be e6cept in a (ualified sense. In that*ay) ho*ever) it does) 'ust as animal might come to be from animal)and an animal of a certain +ind from an animal of a certain +ind.Thus) suppose a dog to come to be from a horse. The dog *ould then)it is true) come to be from animal 3as *ell as from an animal of acertain +ind4 but not as animal) for that is already there. But ifanything is to become an animal) not in a (ualified sense) it *illnot be from animal: and if being) not from being0nor from not0beingeither) for it has been e6plained that by from not being *e meanfrom not0being (ua not0being.

-ote further that *e do not subvert the principle that everythingeither is or is not.

This then is one *ay of solving the difficulty. Another consists inpointing out that the same things can be e6plained in terms ofpotentialityand actuality. But this has been done *ith greater precisionelse*here.So) as *e said) the difficulties *hich constrain people to deny thee6istence of some of the things *e mentioned are no* solved. ,or it*as this reason *hich also caused some of the earlier thin+ers toturn so far aside from the road *hich leads to coming to be andpassinga*ay and change generally. If they had come in sight of this nature)all their ignorance *ould have been dispelled.

Part E



$thers) indeed) have apprehended the nature in (uestion) but notade(uately.

In the first place they allo* that a thing may come to be *ithout(ualification from not being) accepting on this point the statementof Parmenides. Secondly) they thin+ that if the substratum is one

numerically) it must have also only a single potentiality0*hich isa very different thing.

-o* *e distinguish matter and privation) and hold that one of these)namely the matter) is not0being only in virtue of an attribute *hichit has) *hile the privation in its o*n nature is not0being and thatthe matter is nearly) in a sense is) substance) *hile the privationin no sense is. They) on the other hand) identify their #reat andSmall ali+e *ith not being) and that *hether they are ta+en togetheras one or separately. Their triad is therefore of (uite a different+ind from ours. ,or they got so far as to see that there must be someunderlying nature) but they ma+e it one0for even if one philosopherma+es a dyad of it) *hich he calls #reat and Small) the effect isthe same) for he overloo+ed the other nature. ,or the one *hichpersistsis a 'oint cause) *ith the form) of *hat comes to be0a mother) asit *ere. But the negative part of the contrariety may often seem)if you concentrate your attention on it as an evil agent) not to e6istat all.

,or admitting *ith them that there is something divine) good) anddesirable) *e hold that there are t*o other principles) the onecontraryto it) the other such as of its o*n nature to desire and yearn forit. But the conse(uence of their vie* is that the contrary desiresits *te6tinction. et the form cannot desire itself) for it is notdefective nor can the contrary desire it) for contraries are mutuallydestructive. The truth is that *hat desires the form is matter) asthe female desires the male and the ugly the beautiful0only the uglyor the female not per se but per accidens.

The matter comes to be and ceases to be in one sense) *hile in anotherit does not. As that *hich contains the privation) it ceases to bein its o*n nature) for *hat ceases to be0the privation0is contained*ithin it. But as potentiality it does not cease to be in its o*nnature) but is necessarily outside the sphere of becoming and ceasingto be. ,or if it came to be) something must have e6isted as a primarysubstratum from *hich it should come and *hich should persist in itbut this is its o*n special nature) so that it *ill be before comingto be. 3,or my definition of matter is 'ust this0the primarysubstratumof each thing) from *hich it comes to be *ithout (ualification) and*hich persists in the result.4 And if it ceases to be it *ill passinto that at the last) so it *ill have ceased to be before ceasingto be.

The accurate determination of the first principle in respect of form)*hether it is one or many and *hat it is or *hat they are) is theprovince of the primary type of science so these (uestions may standover till then. But of the natural) i.e. perishable) forms *e shallspea+ in the e6positions *hich follo*.

The above) then) may be ta+en as sufficient to establish that thereare principles and *hat they are and ho* many there are. -o* let usma+e a fresh start and proceed.



0000000000000000000000000000000000000000000000000000000000000000000000

B$$" II

Part %

$f things that e6ist) some e6ist by nature) some from other causes.

By nature the animals and their parts e6ist) and the plants andthe simple bodies 3earth) fire) air) *ater40for *e say that theseand the li+e e6ist by nature .

All the things mentioned present a feature in *hich they differ fromthings *hich are not constituted by nature. 9ach of them has *ithinitself a principle of motion and of stationariness 3in respect ofplace) or of gro*th and decrease) or by *ay of alteration4. $n theother hand) a bed and a coat and anything else of that sort) (uareceivingthese designations i.e. in so far as they are products of art0haveno innate impulse to change. But in so far as they happen to becomposedof stone or of earth or of a mi6ture of the t*o) they do have suchan impulse) and 'ust to that e6tent *hich seems to indicate thatnatureis a source or cause of being moved and of being at rest in that to*hich it belongs primarily) in virtue of itself and not in virtueof a concomitant attribute.

I say not in virtue of a concomitant attribute ) because 3forinstance4a man *ho is a doctor might cure himself. -evertheless it is not inso far as he is a patient that he possesses the art of medicine: itmerely has happened that the same man is doctor and patient0and thatis *hy these attributes are not al*ays found together. So it is *ithall other artificial products. -one of them has in itself the sourceof its o*n production. But *hile in some cases 3for instance housesand the other products of manual labour4 that principle is insomethingelse e6ternal to the thing) in others those *hich may cause a changein themselves in virtue of a concomitant attribute0it lies in thethings themselves 3but not in virtue of *hat they are4.

-ature then is *hat has been stated. Things have a nature *hichhave a principle of this +ind. 9ach of them is a substance for itis a sub'ect) and nature al*ays implies a sub'ect in *hich it inheres.

The term according to nature is applied to all these things andalso to the attributes *hich belong to them in virtue of *hat theyare) for instance the property of fire to be carried up*ards0*hichis not a nature nor has a nature but is by nature or accordingto nature .

&hat nature is) then) and the meaning of the terms by nature andaccording to nature ) has been stated. That nature e6ists) it *ould

be absurd to try to prove for it is obvious that there are manythingsof this +ind) and to prove *hat is obvious by *hat is not is the mar+of a man *ho is unable to distinguish *hat is self0evident from *hatis not. 3This state of mind is clearly possible. A man blind frombirth might reason about colours. Presumably therefore such persons



must be tal+ing about *ords *ithout any thought to correspond.4

Some identify the nature or substance of a natural ob'ect *ith thatimmediate constituent of it *hich ta+en by itself is *ithoutarrangement)e.g. the *ood is the nature of the bed) and the bron8e the nature

of the statue.

As an indication of this Antiphon points out that if you planted abed and the rotting *ood ac(uired the po*er of sending up a shoot)it *ould not be a bed that *ould come up) but *ood0*hich sho*s thatthe arrangement in accordance *ith the rules of the art is merelyan incidental attribute) *hereas the real nature is the other) *hich)further) persists continuously through the process of ma+ing.

But if the material of each of these ob'ects has itself the samerelationto something else) say bron8e 3or gold4 to *ater) bones 3or *ood4to earth and so on) that 3they say4 *ould be their nature and essence.Conse(uently some assert earth) others fire or air or *ater or someor all of these) to be the nature of the things that are. ,or *hateverany one of them supposed to have this character0*hether one thingor more than one thing0this or these he declared to be the *hole ofsubstance) all else being its affections) states) or dispositions.9very such thing they held to be eternal 3for it could not pass intoanything else4) but other things to come into being and cease to betimes *ithout number.

This then is one account of nature ) namely that it is the immediatematerial substratum of things *hich have in themselves a principleof motion or change.

Another account is that nature is the shape or form *hich isspecifiedin the definition of the thing.

,or the *ord nature is applied to *hat is according to nature andthe natural in the same *ay as art is applied to *hat is artisticor a *or+ of art. &e should not say in the latter case that thereis anything artistic about a thing) if it is a bed only potentially)not yet having the form of a bed nor should *e call it a *or+ ofart. The same is true of natural compounds. &hat is potentially fleshor bone has not yet its o*n nature ) and does not e6ist until itreceives the form specified in the definition) *hich *e name indefining*hat flesh or bone is. Thus in the second sense of nature it *ouldbe the shape or form 3not separable e6cept in statement4 of things*hich have in themselves a source of motion. 3The combination of thet*o) e.g. man) is not nature but by nature or natural .4

The form indeed is nature rather than the matter for a thing ismore properly said to be *hat it is *hen it has attained to fulfilmentthan *hen it e6ists potentially. Again man is born from man) but notbed from bed. That is *hy people say that the figure is not the natureof a bed) but the *ood is0if the bed sprouted not a bed but *ood *ouldcome up. But even if the figure is art) then on the same principlethe shape of man is his nature. ,or man is born from man.

&e also spea+ of a thing s nature as being e6hibited in the processof gro*th by *hich its nature is attained. The nature in this senseis not li+e doctoring ) *hich leads not to the art of doctoring but



to health. 5octoring must start from the art) not lead to it. Butit is not in this *ay that nature 3in the one sense4 is related tonature 3in the other4. &hat gro*s (ua gro*ing gro*s from somethinginto something. Into *hat then does it gro*7 -ot into that from *hichit arose but into that to *hich it tends. The shape then is nature.

Shape and nature ) it should be added) are in t*o senses. ,or theprivation too is in a *ay form. But *hether in un(ualified comingto be there is privation) i.e. a contrary to *hat comes to be) *emust consider later.

Part 2

&e have distinguished) then) the different *ays in *hich the termnature is used.

The ne6t point to consider is ho* the mathematician differs from thephysicist. $bviously physical bodies contain surfaces and volumes)lines and points) and these are the sub'ect0matter of mathematics.

,urther) is astronomy different from physics or a department of it7It seems absurd that the physicist should be supposed to +no* thenature of sun or moon) but not to +no* any of their essentialattributes)particularly as the *riters on physics obviously do discuss theirshape also and *hether the earth and the *orld are spherical or not.

-o* the mathematician) though he too treats of these things)neverthelessdoes not treat of them as the limits of a physical body nor doeshe consider the attributes indicated as the attributes of such bodies.That is *hy he separates them for in thought they are separable frommotion) and it ma+es no difference) nor does any falsity result) ifthey are separated. The holders of the theory of ,orms do the same)though they are not a*are of it for they separate the ob'ects ofphysics) *hich are less separable than those of mathematics. Thisbecomes plain if one tries to state in each of the t*o cases thedefinitionsof the things and of their attributes. $dd and even ) straightand curved ) and li+e*ise number ) line ) and figure ) do notinvolve motion not so flesh and bone and man 0these are definedli+e snub nose ) not li+e curved .

Similar evidence is supplied by the more physical of the branchesof mathematics) such as optics) harmonics) and astronomy. These arein a *ay the converse of geometry. &hile geometry investigatesphysicallines but not (ua physical) optics investigates mathematical lines)but (ua physical) not (ua mathematical.

Since nature has t*o senses) the form and the matter) *e mustinvestigateits ob'ects as *e *ould the essence of snubness. That is) such thingsare neither independent of matter nor can be defined in terms ofmatteronly. !ere too indeed one might raise a difficulty. Since there aret*o natures) *ith *hich is the physicist concerned7 $r should heinvestigatethe combination of the t*o7 But if the combination of the t*o) thenalso each severally. 5oes it belong then to the same or to differentsciences to +no* each severally7



If *e loo+ at the ancients) physics *ould to be concerned *ith thematter. 3It *as only very slightly that 9mpedocles and 5emocritustouched on the forms and the essence.4

But if on the other hand art imitates nature) and it is the part of

the same discipline to +no* the form and the matter up to a point3e.g. the doctor has a +no*ledge of health and also of bile andphlegm)in *hich health is reali8ed) and the builder both of the form of thehouse and of the matter) namely that it is bric+s and beams) and soforth4: if this is so) it *ould be the part of physics also to +no*nature in both its senses.

Again) that for the sa+e of *hich ) or the end) belongs to the samedepartment of +no*ledge as the means. But the nature is the end or

that for the sa+e of *hich . ,or if a thing undergoes a continuouschange and there is a stage *hich is last) this stage is the end or

that for the sa+e of *hich . 3That is *hy the poet *as carried a*ayinto ma+ing an absurd statement *hen he said he has the end for thesa+e of *hich he *as born . ,or not every stage that is last claimsto be an end) but only that *hich is best.4

,or the arts ma+e their material 3some simply ma+e it) others ma+eit serviceable4) and *e use everything as if it *as there for oursa+e. 3&e also are in a sense an end. That for the sa+e of *hichhas t*o senses: the distinction is made in our *or+ $n Philosophy.4The arts) therefore) *hich govern the matter and have +no*ledge aret*o) namely the art *hich uses the product and the art *hich directsthe production of it. That is *hy the using art also is in a sensedirective but it differs in that it +no*s the form) *hereas the art*hich is directive as being concerned *ith production +no*s thematter.,or the helmsman +no*s and prescribes *hat sort of form a helm shouldhave) the other from *hat *ood it should be made and by means of *hatoperations. In the products of art) ho*ever) *e ma+e the material*ith a vie* to the function) *hereas in the products of nature thematter is there all along.

Again) matter is a relative term: to each form there corresponds aspecial matter. !o* far then must the physicist +no* the form oressence7@p to a point) perhaps) as the doctor must +no* sine* or the smithbron8e 3i.e. until he understands the purpose of each4: and thephysicistis concerned only *ith things *hose forms are separable indeed) butdo not e6ist apart from matter. 1an is begotten by man and by thesun as *ell. The mode of e6istence and essence of the separable itis the business of the primary type of philosophy to define.

Part ;

-o* that *e have established these distinctions) *e must proceed toconsider causes) their character and number. "no*ledge is the ob'ectof our in(uiry) and men do not thin+ they +no* a thing till they havegrasped the *hy of 3*hich is to grasp its primary cause4. So clearly*e too must do this as regards both coming to be and passing a*ayand every +ind of physical change) in order that) +no*ing theirprinciples)*e may try to refer to these principles each of our problems.



In one sense) then) 3%4 that out of *hich a thing comes to be and*hich persists) is called cause ) e.g. the bron8e of the statue)the silver of the bo*l) and the genera of *hich the bron8e and thesilver are species.

In another sense 324 the form or the archetype) i.e. the statement

of the essence) and its genera) are called causes 3e.g. of theoctavethe relation of 2:%) and generally number4) and the parts in thedefinition.

Again 3;4 the primary source of the change or coming to rest e.g.the man *ho gave advice is a cause) the father is cause of the child)and generally *hat ma+es of *hat is made and *hat causes change of*hat is changed.

Again 3>4 in the sense of end or that for the sa+e of *hich a thingis done) e.g. health is the cause of *al+ing about. 3 &hy is he*al+ingabout7 *e say. To be healthy ) and) having said that) *e thin+ *ehave assigned the cause.4 The same is true also of all theintermediatesteps *hich are brought about through the action of something elseas means to*ards the end) e.g. reduction of flesh) purging) drugs)or surgical instruments are means to*ards health. All these thingsare for the sa+e of the end) though they differ from one anotherin that some are activities) others instruments.

This then perhaps e6hausts the number of *ays in *hich the termcause

is used.

As the *ord has several senses) it follo*s that there are severalcauses of the same thing not merely in virtue of a concomitantattribute4)e.g. both the art of the sculptor and the bron8e are causes of thestatue. These are causes of the statue (ua statue) not in virtue ofanything else that it may be0only not in the same *ay) the one beingthe material cause) the other the cause *hence the motion comes. Somethings cause each other reciprocally) e.g. hard *or+ causes fitnessand vice versa) but again not in the same *ay) but the one as end)the other as the origin of change. ,urther the same thing is the causeof contrary results. ,or that *hich by its presence brings about oneresult is sometimes blamed for bringing about the contrary by itsabsence. Thus *e ascribe the *rec+ of a ship to the absence of thepilot *hose presence *as the cause of its safety.

All the causes no* mentioned fall into four familiar divisions. Theletters are the causes of syllables) the material of artificialproducts)fire) Fc.) of bodies) the parts of the *hole) and the premisses ofthe conclusion) in the sense of that from *hich . $f these pairsthe one set are causes in the sense of substratum) e.g. the parts)the other set in the sense of essence0the *hole and the combinationand the form. But the seed and the doctor and the adviser) andgenerallythe ma+er) are all sources *hence the change or stationarinessoriginates)*hile the others are causes in the sense of the end or the good ofthe rest for that for the sa+e of *hich means *hat is best andthe end of the things that lead up to it. 3&hether *e say the good



itself or the apparent good ma+es no difference.4

Such then is the number and nature of the +inds of cause.

-o* the modes of causation are many) though *hen brought under headsthey too can be reduced in number. ,or cause is used in many senses

and even *ithin the same +ind one may be prior to another 3e.g. thedoctor and the e6pert are causes of health) the relation 2:% andnumberof the octave4) and al*ays *hat is inclusive to *hat is particular.Another mode of causation is the incidental and its genera) e.g. inone *ay Polyclitus ) in another sculptor is the cause of a statue)because being Polyclitus and sculptor are incidentally con'oined.Also the classes in *hich the incidental attribute is included thus

a man could be said to be the cause of a statue or) generally) aliving creature . An incidental attribute too may be more or lessremote) e.g. suppose that a pale man or a musical man *ere saidto be the cause of the statue.

All causes) both proper and incidental) may be spo+en of either aspotential or as actual e.g. the cause of a house being built iseither

house0builder or house0builder building .

Similar distinctions can be made in the things of *hich the causesare causes) e.g. of this statue or of statue or of imagegenerally)of this bron8e or of bron8e or of material generally. So too*ith the incidental attributes. Again *e may use a comple6 e6pressionfor either and say) e.g. neither Polyclitus nor sculptor but

Polyclitus)sculptor .

All these various uses) ho*ever) come to si6 in number) under eachof *hich again the usage is t*ofold. Cause means either *hat isparticularor a genus) or an incidental attribute or a genus of that) and theseeither as a comple6 or each by itself and all si6 either as actualor as potential. The difference is this much) that causes *hich areactually at *or+ and particular e6ist and cease to e6istsimultaneously*ith their effect) e.g. this healing person *ith this being0healedperson and that house0building man *ith that being0built house butthis is not al*ays true of potential causes00the house and thehousebuilderdo not pass a*ay simultaneously.

In investigating the cause of each thing it is al*ays necessary tosee+ *hat is most precise 3as also in other things4: thus man buildsbecause he is a builder) and a builder builds in virtue of his artof building. This last cause then is prior: and so generally.

,urther) generic effects should be assigned to generic causes)particulareffects to particular causes) e.g. statue to sculptor) this statueto this sculptor and po*ers are relative to possible effects)actuallyoperating causes to things *hich are actually being effected.

This must suffice for our account of the number of causes and themodes of causation.



Part >

But chance also and spontaneity are rec+oned among causes: many thingsare said both to be and to come to be as a result of chance andspontaneity.

&e must in(uire therefore in *hat manner chance and spontaneity arepresent among the causes enumerated) and *hether they are the sameor different) and generally *hat chance and spontaneity are.

Some people even (uestion *hether they are real or not. They say thatnothing happens by chance) but that everything *hich *e ascribe tochance or spontaneity has some definite cause) e.g. coming by chanceinto the mar+et and finding there a man *hom one *anted but did note6pect to meet is due to one s *ish to go and buy in the mar+et.Similarlyin other cases of chance it is al*ays possible) they maintain) tofind something *hich is the cause but not chance) for if chance *erereal) it *ould seem strange indeed) and the (uestion might be raised)*hy on earth none of the *ise men of old in spea+ing of the causesof generation and decay too+ account of chance *hence it *ould seemthat they too did not believe that anything is by chance. But thereis a further circumstance that is surprising. 1any things both cometo be and are by chance and spontaneity) and although +no* that eachof them can be ascribed to some cause 3as the old argument said *hichdenied chance4) nevertheless they spea+ of some of these things ashappening by chance and others not. ,or this reason also they oughtto have at least referred to the matter in some *ay or other.

Certainly the early physicists found no place for chance among thecauses *hich they recogni8ed0love) strife) mind) fire) or the li+e.This is strange) *hether they supposed that there is no such thingas chance or *hether they thought there is but omitted to mentionit0and that too *hen they sometimes used it) as 9mpedocles does *henhe says that the air is not al*ays separated into the highest region)but as it may chance . At any rate he says in his cosmogony that

it happened to run that *ay at that time) but it often ranother*ise.!e tells us also that most of the parts of animals came to be bychance.

There are some too *ho ascribe this heavenly sphere and all the *orldsto spontaneity. They say that the vorte6 arose spontaneously) i.e.the motion that separated and arranged in its present order all thate6ists. This statement might *ell cause surprise. ,or they areassertingthat chance is not responsible for the e6istence or generation ofanimals and plants) nature or mind or something of the +ind beingthe cause of them 3for it is not any chance thing that comes froma given seed but an olive from one +ind and a man from another4 andyet at the same time they assert that the heavenly sphere and thedivinest of visible things arose spontaneously) having no such causeas is assigned to animals and plants. et if this is so) it is a fact*hich deserves to be d*elt upon) and something might *ell have beensaid about it. ,or besides the other absurdities of the statement)it is the more absurd that people should ma+e it *hen they see nothingcoming to be spontaneously in the heavens) but much happening bychanceamong the things *hich as they say are not due to chance *hereas*e should have e6pected e6actly the opposite.



$thers there are *ho) indeed) believe that chance is a cause) butthat it is inscrutable to human intelligence) as being a divine thingand full of mystery.

Thus *e must in(uire *hat chance and spontaneity are) *hether theyare the same or different) and ho* they fit into our division of

causes.

Part ?

,irst then *e observe that some things al*ays come to pass in thesame *ay) and others for the most part. It is clearly of neither ofthese that chance is said to be the cause) nor can the effect ofchance be identified *ith any of the things that come to pass bynecessity and al*ays) or for the most part. But as there is a thirdclass of events besides these t*o0events *hich all say are bychance 0itis plain that there is such a thing as chance and spontaneity for*e +no* that things of this +ind are due to chance and that thingsdue to chance are of this +ind.

But) secondly) some events are for the sa+e of something) others not.Again) some of the former class are in accordance *ith deliberateintention) others not) but both are in the class of things *hich arefor the sa+e of something. !ence it is clear that even among thethings*hich are outside the necessary and the normal) there are some inconne6ion *ith*hich the phrase for the sa+e of something isapplicable.39vents that are for the sa+e of something include *hatever may bedone as a result of thought or of nature.4 Things of this +ind) then)*hen they come to pass incidental are said to be by chance . ,or'ust as a thing is something either in virtue of itself orincidentally)so may it be a cause. ,or instance) the housebuilding faculty is invirtue of itself the cause of a house) *hereas the pale or the musicalis the incidental cause. That *hich is per se cause of the effectis determinate) but the incidental cause is indeterminable) for thepossible attributes of an individual are innumerable. To resume then*hen a thing of this +ind comes to pass among events *hich are forthe sa+e of something) it is said to be spontaneous or by chance.3The distinction bet*een the t*o must be made later0for the presentit is sufficient if it is plain that both are in the sphere of thingsdone for the sa+e of something.4

96ample: A man is engaged in collecting subscriptions for a feast.!e *ould have gone to such and such a place for the purpose of gettingthe money) if he had +no*n. !e actually *ent there for another purposeand it *as only incidentally that he got his money by going thereand this *as not due to the fact that he *ent there as a rule ornecessarily)nor is the end effected 3getting the money4 a cause present inhimself0itbelongs to the class of things that are intentional and the resultof intelligent deliberation. It is *hen these conditions are satisfiedthat the man is said to have gone by chance . If he had gone ofdeliberatepurpose and for the sa+e of this0if he al*ays or normally *ent there*hen he *as collecting payments0he *ould not be said to have gone

by chance .



It is clear then that chance is an incidental cause in the sphereof those actions for the sa+e of something *hich involve purpose.Intelligent reflection) then) and chance are in the same sphere) forpurpose implies intelligent reflection.

It is necessary) no doubt) that the causes of *hat comes to pass by

chance be indefinite and that is *hy chance is supposed to belongto the class of the indefinite and to be inscrutable to man) and *hyit might be thought that) in a *ay) nothing occurs by chance. ,orall these statements are correct) because they are *ell grounded.Things do) in a *ay) occur by chance) for they occur incidentallyand chance is an incidental cause. But strictly it is not the cause0*ithout(ualification0of anything for instance) a housebuilder is the causeof a house incidentally) a fluteplayer may be so.

And the causes of the man s coming and getting the money 3*hen hedid not come for the sa+e of that4 are innumerable. !e may have *ishedto see somebody or been follo*ing somebody or avoiding somebody) ormay have gone to see a spectacle. Thus to say that chance is a thingcontrary to rule is correct. ,or rule applies to *hat is al*aystrue or true for the most part) *hereas chance belongs to a thirdtype of event. !ence) to conclude) since causes of this +ind areindefinite)chance too is indefinite. 3 et in some cases one might raise the(uestion*hether any incidental fact might be the cause of the chanceoccurrence)e.g. of health the fresh air or the sun s heat may be the cause) buthaving had one s hair cut cannot for some incidental causes are morerelevant to the effect than others.4

Chance or fortune is called good *hen the result is good) evil*hen it is evil. The terms good fortune and ill fortune are used*hen either result is of considerable magnitude. Thus one *ho comes*ithin an ace of some great evil or great good is said to be fortunateor unfortunate. The mind affirms the essence of the attribute)ignoringthe hair s breadth of difference. ,urther) it is *ith reason thatgood fortune is regarded as unstable for chance is unstable) as noneof the things *hich result from it can be invariable or normal.

Both are then) as I have said) incidental causes0both chance andspontaneity0inthe sphere of things *hich are capable of coming to pass notnecessarily)nor normally) and *ith reference to such of these as might come topass for the sa+e of something.

Part

They differ in that spontaneity is the *ider term. 9very resultof chance is from *hat is spontaneous) but not everything that isfrom *hat is spontaneous is from chance.

Chance and *hat results from chance are appropriate to agents thatare capable of good fortune and of moral action generally. Thereforenecessarily chance is in the sphere of moral actions. This isindicatedby the fact that good fortune is thought to be the same) or nearlythe same) as happiness) and happiness to be a +ind of moral action)



since it is *ell0doing. !ence *hat is not capable of moral actioncannot do anything by chance. Thus an inanimate thing or a lo*eranimalor a child cannot do anything by chance) because it is incapable ofdeliberate intention nor can good fortune or ill fortune beascribed

to them) e6cept metaphorically) as Protarchus) for e6ample) said thatthe stones of *hich altars are made are fortunate because they areheld in honour) *hile their fello*s are trodden under foot. 9ven thesethings) ho*ever) can in a *ay be affected by chance) *hen one *hois dealing *ith them does something to them by chance) but notother*ise.

The spontaneous on the other hand is found both in the lo*er animalsand in many inanimate ob'ects. &e say) for e6ample) that the horsecame spontaneously ) because) though his coming saved him) he didnot come for the sa+e of safety. Again) the tripod fell of itself )because) though *hen it fell it stood on its feet so as to serve fora seat) it did not fall for the sa+e of that.

!ence it is clear that events *hich 3%4 belong to the general classof things that may come to pass for the sa+e of something) 324 donot come to pass for the sa+e of *hat actually results) and 3;4 havean e6ternal cause) may be described by the phrase from spontaneity .These spontaneous events are said to be from chance if they havethe further characteristics of being the ob'ects of deliberateintentionand due to agents capable of that mode of action. This is indicatedby the phrase in vain ) *hich is used *hen A *hich is for the sa+eof B) does not result in B. ,or instance) ta+ing a *al+ is for thesa+e of evacuation of the bo*els if this does not follo* after*al+ing)*e say that *e have *al+ed in vain and that the *al+ing *as vain .This implies that *hat is naturally the means to an end is in vain )*hen it does not effect the end to*ards *hich it *as the naturalmeans0forit *ould be absurd for a man to say that he had bathed in vain becausethe sun *as not eclipsed) since the one *as not done *ith a vie* tothe other. Thus the spontaneous is even according to its derivationthe case in *hich the thing itself happens in vain. The stone thatstruc+ the man did not fall for the purpose of stri+ing him thereforeit fell spontaneously) because it might have fallen by the actionof an agent and for the purpose of stri+ing. The difference bet*eenspontaneity and *hat results by chance is greatest in things thatcome to be by nature for *hen anything comes to be contrary tonature)*e do not say that it came to be by chance) but by spontaneity. etstrictly this too is different from the spontaneous proper for thecause of the latter is e6ternal) that of the former internal.

&e have no* e6plained *hat chance is and *hat spontaneity is) andin *hat they differ from each other. Both belong to the mode ofcausation

source of change ) for either some natural or some intelligent agentis al*ays the cause but in this sort of causation the number ofpossiblecauses is infinite.

Spontaneity and chance are causes of effects *hich though they mightresult from intelligence or nature) have in fact been caused bysomething



incidentally. -o* since nothing *hich is incidental is prior to *hatis per se) it is clear that no incidental cause can be prior to acause per se. Spontaneity and chance) therefore) are posterior tointelligence and nature. !ence) ho*ever true it may be that theheavensare due to spontaneity) it *ill still be true that intelligence and

nature *ill be prior causes of this All and of many things in itbesides.

Part

It is clear then that there are causes) and that the number of themis *hat *e have stated. The number is the same as that of the thingscomprehended under the (uestion *hy . The *hy is referredultimatelyeither 3%4) in things *hich do not involve motion) e.g. inmathematics)to the *hat 3to the definition of straight line or

commensurable )Fc.4) or 324 to *hat initiated a motion) e.g. *hy did they go to*ar70because there had been a raid or 3;4 *e are in(uiring forthe sa+e of *hat7 0 that they may rule or 3>4) in the case of thingsthat come into being) *e are loo+ing for the matter. The causes)therefore)are these and so many in number.

-o*) the causes being four) it is the business of the physicist to+no* about them all) and if he refers his problems bac+ to all ofthem) he *ill assign the *hy in the *ay proper to his science0thematter) the form) the mover) that for the sa+e of *hich . The lastthree often coincide for the *hat and that for the sa+e of *hichare one) *hile the primary source of motion is the same in speciesas these 3for man generates man4) and so too) in general) are allthings *hich cause movement by being themselves moved and such asare not of this +ind are no longer inside the province of physics)for they cause motion not by possessing motion or a source of motionin themselves) but being themselves incapable of motion. !ence thereare three branches of study) one of things *hich are incapable ofmotion) the second of things in motion) but indestructible) the thirdof destructible things.

The (uestion *hy ) then) is ans*ered by reference to the matter)to the form) and to the primary moving cause. ,or in respect of comingto be it is mostly in this last *ay that causes are investigated0 *hatcomes to be after *hat7 *hat *as the primary agent or patient7 andso at each step of the series.

-o* the principles *hich cause motion in a physical *ay are t*o) of*hich one is not physical) as it has no principle of motion in itself.$f this +ind is *hatever causes movement) not being itself moved)such as 3%4 that *hich is completely unchangeable) the primaryreality)and 324 the essence of that *hich is coming to be) i.e. the formfor this is the end or that for the sa+e of *hich . !ence sincenatureis for the sa+e of something) *e must +no* this cause also. &e muste6plain the *hy in all the senses of the term) namely) 3%4 thatfrom this that *ill necessarily result 3 from this either *ithout(ualification or in most cases4 324 that this must be so if thatis to be so 3as the conclusion presupposes the premisses4 3;4 thatthis *as the essence of the thing and 3>4 because it is better thus



3not *ithout (ualification) but *ith reference to the essential naturein each case4.

Part D

&e must e6plain then 3%4 that -ature belongs to the class of causes

*hich act for the sa+e of something 324 about the necessary and itsplace in physical problems) for all *riters ascribe things to thiscause) arguing that since the hot and the cold) Fc.) are of such andsuch a +ind) therefore certain things necessarily are and come tobe0and if they mention any other cause 3one his friendship andstrife )another his mind 4) it is only to touch on it) and then good0byeto it.

A difficulty presents itself: *hy should not nature *or+) not forthe sa+e of something) nor because it is better so) but 'ust as thes+y rains) not in order to ma+e the corn gro*) but of necessity7 &hatis dra*n up must cool) and *hat has been cooled must become *aterand descend) the result of this being that the corn gro*s. Similarlyif a man s crop is spoiled on the threshing0floor) the rain did notfall for the sa+e of this0in order that the crop might be spoiled0butthat result 'ust follo*ed. &hy then should it not be the same *iththe parts in nature) e.g. that our teeth should come up of necessity0thefront teeth sharp) fitted for tearing) the molars broad and usefulfor grinding do*n the food0since they did not arise for this end)but it *as merely a coincident result and so *ith all other partsin *hich *e suppose that there is purpose7 &herever then all the partscame about 'ust *hat they *ould have been if they had come be foran end) such things survived) being organi8ed spontaneously in afitting*ay *hereas those *hich gre* other*ise perished and continue toperish)as 9mpedocles says his man0faced o60progeny did.

Such are the arguments 3and others of the +ind4 *hich may causedifficultyon this point. et it is impossible that this should be the true vie*.,or teeth and all other natural things either invariably or normallycome about in a given *ay but of not one of the results of chanceor spontaneity is this true. &e do not ascribe to chance or merecoincidencethe fre(uency of rain in *inter) but fre(uent rain in summer *e donor heat in the dog0days) but only if *e have it in *inter. If then)it is agreed that things are either the result of coincidence or foran end) and these cannot be the result of coincidence or spontaneity)it follo*s that they must be for an end and that such things areall due to nature even the champions of the theory *hich is beforeus *ould agree. Therefore action for an end is present in things *hichcome to be and are by nature.

,urther) *here a series has a completion) all the preceding stepsare for the sa+e of that. -o* surely as in intelligent action) soin nature and as in nature) so it is in each action) if nothinginterferes.-o* intelligent action is for the sa+e of an end therefore the natureof things also is so. Thus if a house) e.g. had been a thing madeby nature) it *ould have been made in the same *ay as it is no* byart and if things made by nature *ere made also by art) they *ouldcome to be in the same *ay as by nature. 9ach step then in the series



is for the sa+e of the ne6t and generally art partly completes *hatnature cannot bring to a finish) and partly imitates her. If)therefore)artificial products are for the sa+e of an end) so clearly also arenatural products. The relation of the later to the earlier terms ofthe series is the same in both. This is most obvious in the animals

other than man: they ma+e things neither by art nor after in(uiryor deliberation. &herefore people discuss *hether it is byintelligenceor by some other faculty that these creatures *or+)spiders) ants)and the li+e. By gradual advance in this direction *e come to seeclearly that in plants too that is produced *hich is conducive tothe end0leaves) e.g. gro* to provide shade for the fruit. If thenit is both by nature and for an end that the s*allo* ma+es its nestand the spider its *eb) and plants gro* leaves for the sa+e of thefruit and send their roots do*n 3not up4 for the sa+e of nourishment)it is plain that this +ind of cause is operative in things *hich cometo be and are by nature. And since nature means t*o things) thematter and the form) of *hich the latter is the end) and since allthe rest is for the sa+e of the end) the form must be the cause inthe sense of that for the sa+e of *hich .

-o* mista+es come to pass even in the operations of art: thegrammarianma+es a mista+e in *riting and the doctor pours out the *rong dose.!ence clearly mista+es are possible in the operations of nature also.If then in art there are cases in *hich *hat is rightly producedservesa purpose) and if *here mista+es occur there *as a purpose in *hat*as attempted) only it *as not attained) so must it be also in naturalproducts) and monstrosities *ill be failures in the purposive effort.Thus in the original combinations the o60progeny if they failedto reach a determinate end must have arisen through the corruptionof some principle corresponding to *hat is no* the seed.

,urther) seed must have come into being first) and not straight*aythe animals: the *ords *hole0natured first... must have meant seed.

Again) in plants too *e find the relation of means to end) thoughthe degree of organi8ation is less. &ere there then in plants also

olive0headed vine0progeny ) li+e the man0headed o60progeny ) ornot7 An absurd suggestion yet there must have been) if there *eresuch things among animals.

1oreover) among the seeds anything must have come to be at random.But the person *ho asserts this entirely does a*ay *ith nature and*hat e6ists by nature . ,or those things are natural *hich) by acontinuous movement originated from an internal principle) arriveat some completion: the same completion is not reached from everyprinciple nor any chance completion) but al*ays the tendency in eachis to*ards the same end) if there is no impediment.

The end and the means to*ards it may come about by chance. &e say)for instance) that a stranger has come by chance) paid the ransom)and gone a*ay) *hen he does so as if he had come for that purpose)though it *as not for that that he came. This is incidental) forchanceis an incidental cause) as I remar+ed before. But *hen an event ta+esplace al*ays or for the most part) it is not incidental or by chance.In natural products the se(uence is invariable) if there is noimpediment.



It is absurd to suppose that purpose is not present because *e donot observe the agent deliberating. Art does not deliberate. If theship0building art *ere in the *ood) it *ould produce the same resultsby nature. If) therefore) purpose is present in art) it is presentalso in nature. The best illustration is a doctor doctoring himself:

nature is li+e that.

It is plain then that nature is a cause) a cause that operates fora purpose.

Part E

As regards *hat is of necessity ) *e must as+ *hether the necessityis hypothetical ) or simple as *ell. The current vie* places *hatis of necessity in the process of production) 'ust as if one *ereto suppose that the *all of a house necessarily comes to be because*hat is heavy is naturally carried do*n*ards and *hat is light tothe top) *herefore the stones and foundations ta+e the lo*est place)*ith earth above because it is lighter) and *ood at the top of allas being the lightest. &hereas) though the *all does not come to be*ithout these) it is not due to these) e6cept as its material cause:it comes to be for the sa+e of sheltering and guarding certain things.Similarly in all other things *hich involve production for an endthe product cannot come to be *ithout things *hich have a necessarynature) but it is not due to these 3e6cept as its material4 it comesto be for an end. ,or instance) *hy is a sa* such as it is7 To effectso0and0so and for the sa+e of so0and0so. This end) ho*ever) cannotbe reali8ed unless the sa* is made of iron. It is) therefore)necessaryfor it to be of iron) it *e are to have a sa* and perform theoperationof sa*ing. &hat is necessary then) is necessary on a hypothesis itis not a result necessarily determined by antecedents. -ecessity isin the matter) *hile that for the sa+e of *hich is in thedefinition.

-ecessity in mathematics is in a *ay similar to necessity in things*hich come to be through the operation of nature. Since a straightline is *hat it is) it is necessary that the angles of a triangleshould e(ual t*o right angles. But not conversely though if theanglesare not e(ual to t*o right angles) then the straight line is not *hatit is either. But in things *hich come to be for an end) the reverseis true. If the end is to e6ist or does e6ist) that also *hichprecedesit *ill e6ist or does e6ist other*ise 'ust as there) if0theconclusionis not true) the premiss *ill not be true) so here the end or thatfor the sa+e of *hich *ill not e6ist. ,or this too is itself astarting0point)but of the reasoning) not of the action *hile in mathematics thestarting0point is the starting0point of the reasoning only) as thereis no action. If then there is to be a house) such0and0such thingsmust be made or be there already or e6ist) or generally the matterrelative to the end) bric+s and stones if it is a house. But the endis not due to these e6cept as the matter) nor *ill it come to e6istbecause of them. et if they do not e6ist at all) neither *ill thehouse) or the sa*0the former in the absence of stones) the latterin the absence of iron0'ust as in the other case the premisses *illnot be true) if the angles of the triangle are not e(ual to t*o right



angles.

The necessary in nature) then) is plainly *hat *e call by the nameof matter) and the changes in it. Both causes must be stated by thephysicist) but especially the end for that is the cause of thematter)

not vice versa and the end is that for the sa+e of *hich ) and thebeginning starts from the definition or essence as in artificialproducts) since a house is of such0and0such a +ind) certain thingsmust necessarily come to be or be there already) or since health isthis) these things must necessarily come to be or be there already.Similarly if man is this) then these if these) then those. Perhapsthe necessary is present also in the definition. ,or if one definesthe operation of sa*ing as being a certain +ind of dividing) thenthis cannot come about unless the sa* has teeth of a certain +indand these cannot be unless it is of iron. ,or in the definition toothere are some parts that are) as it *ere) its matter.

0000000000000000000000000000000000000000000000000000000000000000000000

B$$" III

Part %

-ature has been defined as a principle of motion and change ) andit is the sub'ect of our in(uiry. &e must therefore see that *eunderstandthe meaning of motion for if it *ere un+no*n) the meaning of

naturetoo *ould be un+no*n.

&hen *e have determined the nature of motion) our ne6t tas+ *ill beto attac+ in the same *ay the terms *hich are involved in it. -o*motion is supposed to belong to the class of things *hich arecontinuousand the infinite presents itself first in the continuous0that is ho*it comes about that infinite is often used in definitions of thecontinuous 3 *hat is infinitely divisible is continuous 4. Besidesthese) place) void) and time are thought to be necessary conditionsof motion.

Clearly) then) for these reasons and also because the attributesmentionedare common to) and coe6tensive *ith) all the ob'ects of our science)*e must first ta+e each of them in hand and discuss it. ,or theinvestigationof special attributes comes after that of the common attributes.

To begin then) as *e said) *ith motion.&e may start by distinguishing 3%4 *hat e6ists in a state offulfilmentonly) 324 *hat e6ists as potential) 3;4 *hat e6ists as potential andalso in fulfilment0one being a this ) another so much ) a third

such ) and similarly in each of the other modes of the predicationof being.

,urther) the *ord relative is used *ith reference to 3%4 e6cessand defect) 324 agent and patient and generally *hat can move and*hat can be moved. ,or *hat can cause movement is relative to *hatcan be moved ) and vice versa.



Again) there is no such thing as motion over and above the things.It is al*ays *ith respect to substance or to (uantity or to (ualityor to place that *hat changes changes. But it is impossible) as *eassert) to find anything common to these *hich is neither this nor(uantum nor (uale nor any of the other predicates. !ence neither *illmotion and change have reference to something over and above the

thingsmentioned) for there is nothing over and above them.

-o* each of these belongs to all its sub'ects in either of t*o *ays:namely 3%4 substance0the one is positive form) the other privation324 in (uality) *hite and blac+ 3;4 in (uantity) complete andincomplete3>4 in respect of locomotion) up*ards and do*n*ards or light andheavy.!ence there are as many types of motion or change as there aremeaningsof the *ord is .

&e have no* before us the distinctions in the various classes of beingbet*een *hat is full real and *hat is potential.

5ef. The fulfilment of *hat e6ists potentially) in so far as it e6istspotentially) is motion0namely) of *hat is alterable (ua alterable)alteration: of *hat can be increased and its opposite *hat can bedecreased 3there is no common name4) increase and decrease: of *hatcan come to be and can pass a*ay) coming to he and passing a*ay: of*hat can be carried along) locomotion.

96amples *ill elucidate this definition of motion. &hen the buildable)in so far as it is 'ust that) is fully real) it is being built) andthis is building. Similarly) learning) doctoring) rolling) leaping)ripening) ageing.

The same thing) if it is of a certain +ind) can be both potentialand fully real) not indeed at the same time or not in the samerespect)but e.g. potentially hot and actually cold. !ence at once such things*ill act and be acted on by one another in many *ays: each of them*ill be capable at the same time of causing alteration and of beingaltered. !ence) too) *hat effects motion as a physical agent can bemoved: *hen a thing of this +ind causes motion) it is itself alsomoved. This) indeed) has led some people to suppose that every moveris moved. But this (uestion depends on another set of arguments) andthe truth *ill be made clear later. is possible for a thing to causemotion) though it is itself incapable of being moved.

It is the fulfilment of *hat is potential *hen it is already fullyreal and operates not as itself but as movable) that is motion. &hatI mean by as is this: Bron8e is potentially a statue. But it isnot the fulfilment of bron8e as bron8e *hich is motion. ,or to bebron8e and to be a certain potentiality are not the same.

If they *ere identical *ithout (ualification) i.e. in definition)the fulfilment of bron8e as bron8e *ould have been motion. But theyare not the same) as has been said. 3This is obvious in contraries.

To be capable of health and to be capable of illness are not thesame) for if they *ere there *ould be no difference bet*een beingill and being *ell. et the sub'ect both of health and of sic+ness0*hetherit is humour or blood0is one and the same.4



&e can distinguish) then) bet*een the t*o0'ust as) to give anothere6ample) colour and visible are different0and clearly it is thefulfilment of *hat is potential as potential that is motion. So this)precisely) is motion.

,urther it is evident that motion is an attribute of a thing 'ust*hen it is fully real in this *ay) and neither before nor after. ,oreach thing of this +ind is capable of being at one time actual) atanother not. Ta+e for instance the buildable as buildable. Theactualityof the buildable as buildable is the process of building. ,or theactuality of the buildable must be either this or the house. But *henthere is a house) the buildable is no longer buildable. $n the otherhand) it is the buildable *hich is being built. The process then ofbeing built must be the +ind of actuality re(uired But building isa +ind of motion) and the same account *ill apply to the other +indsalso.

Part 2

The soundness of this definition is evident both *hen *e considerthe accounts of motion that the others have given) and also from thedifficulty of defining it other*ise.

$ne could not easily put motion and change in another genus0this isplain if *e consider *here some people put it they identify motion*ith or ine(uality or not being but such things are notnecessarilymoved) *hether they are different or une(ual or non0e6istent-or is change either to or from these rather than to or from theiropposites.

The reason *hy they put motion into these genera is that it is thoughtto be something indefinite) and the principles in the second columnare indefinite because they are privative: none of them is either

this or such or comes under any of the other modes of predication.The reason in turn *hy motion is thought to be indefinite is thatit cannot be classed simply as a potentiality or as an actuality0athing that is merely capable of having a certain si8e is notundergoingchange) nor yet a thing that is actually of a certain si8e) and motionis thought to be a sort of actuality) but incomplete) the reason forthis vie* being that the potential *hose actuality it is isincomplete.This is *hy it is hard to grasp *hat motion is. It is necessary toclass it *ith privation or *ith potentiality or *ith sheer actuality)yet none of these seems possible. There remains then the suggestedmode of definition) namely that it is a sort of actuality) oractualityof the +ind described) hard to grasp) but not incapable of e6isting.

The mover too is moved) as has been said0every mover) that is) *hichis capable of motion) and *hose immobility is rest0*hen a thing issub'ect to motion its immobility is rest. ,or to act on the movableas such is 'ust to move it. But this it does by contact) so that atthe same time it is also acted on. !ence *e can define motion as thefulfilment of the movable (ua movable) the cause of the attributebeing contact *ith *hat can move so that the mover is also acted on.The mover or agent *ill al*ays be the vehicle of a form) either a

this or such ) *hich) *hen it acts) *ill be the source and cause



of the change) e.g. the full0formed man begets man from *hat ispotentiallyman.

Part ;

The solution of the difficulty that is raised about the motion0*hetherit is in the movable0is plain. It is the fulfilment of thispotentiality)and by the action of that *hich has the po*er of causing motion andthe actuality of that *hich has the po*er of causing motion is notother than the actuality of the movable) for it must be the fulfilmentof both. A thing is capable of causing motion because it can do this)it is a mover because it actually does it. But it is on the movablethat it is capable of acting. !ence there is a single actuality ofboth ali+e) 'ust as one to t*o and t*o to one are the same interval)and the steep ascent and the steep descent are one0for these are oneand the same) although they can be described in different *ays. Soit is *ith the mover and the moved.

This vie* has a dialectical difficulty. Perhaps it is necessary thatthe actuality of the agent and that of the patient should not be thesame. The one is agency and the other patiency and the outcomeand completion of the one is an action ) that of the other a

passion .Since then they are both motions) *e may as+: in *hat are they) ifthey are different7 9ither 3a4 both are in *hat is acted on and moved)or 3b4 the agency is in the agent and the patiency in the patient.3If *e ought to call the latter also agency ) the *ord *ould be usedin t*o senses.4

-o*) in alternative 3b4) the motion *ill be in the mover) for thesame statement *ill hold of mover and moved . !ence either everymover *ill be moved) or) though having motion) it *ill not be moved.

If on the other hand 3a4 both are in *hat is moved and acted on0boththe agency and the patiency 3e.g. both teaching and learning) thoughthey are t*o) in the learner4) then) first) the actuality of each*ill not be present in each) and) a second absurdity) a thing *illhave t*o motions at the same time. !o* *ill there be t*o alterationsof (uality in one sub'ect to*ards one definite (uality7 The thingis impossible: the actuali8ation *ill be one.

But 3some one *ill say4 it is contrary to reason to suppose that thereshould be one identical actuali8ation of t*o things *hich aredifferentin +ind. et there *ill be) if teaching and learning are the same)and agency and patiency. To teach *ill be the same as to learn) andto act the same as to be acted on0the teacher *ill necessarily belearning everything that he teaches) and the agent *ill be acted on.$ne may reply:

3%4 It is not absurd that the actuali8ation of one thing should bein another. Teaching is the activity of a person *ho can teach) yetthe operation is performed on some patient0it is not cut adrift froma sub'ect) but is of A on B.

324 There is nothing to prevent t*o things having one and the sameactuali8ation) provided the actuali8ations are not described in thesame *ay) but are related as *hat can act to *hat is acting.



3;4 -or is it necessary that the teacher should learn) even if toact and to be acted on are one and the same) provided they are notthe same in definition 3as raiment and dress 4) but are the samemerely in the sense in *hich the road from Thebes to Athens and theroad from Athens to Thebes are the same) as has been e6plained above.,or it is not things *hich are in a *ay the same that have all their

attributes the same) but only such as have the same definition. Butindeed it by no means follo*s from the fact that teaching is the sameas learning) that to learn is the same as to teach) any more thanit follo*s from the fact that there is one distance bet*een t*o things*hich are at a distance from each other) that the t*o vectors AB andBa) are one and the same. To generali8e) teaching is not the sameas learning) or agency as patiency) in the full sense) though theybelong to the same sub'ect) the motion for the actuali8ation ofG in and the actuali8ation of through the action of G differin definition.

&hat then 1otion is) has been stated both generally and particularly.It is not difficult to see ho* each of its types *ill be defined0alterationis the fulfillment of the alterable (ua alterable 3or) morescientifically)the fulfilment of *hat can act and *hat can be acted on) as such40generallyand again in each particular case) building) healing) Fc. A similardefinition *ill apply to each of the other +inds of motion.

Part >

The science of nature is concerned *ith spatial magnitudes and motionand time) and each of these at least is necessarily infinite orfinite)even if some things dealt *ith by the science are not) e.g. a (ualityor a point0it is not necessary perhaps that such things should beput under either head. !ence it is incumbent on the person *hospeciali8esin physics to discuss the infinite and to in(uire *hether there issuch a thing or not) and) if there is) *hat it is.

The appropriateness to the science of this problem is clearlyindicated.All *ho have touched on this +ind of science in a *ay *orthconsideringhave formulated vie*s about the infinite) and indeed) to a man) ma+eit a principle of things.

3%4 Some) as the Pythagoreans and Plato) ma+e the infinite a principlein the sense of a self0subsistent substance) and not as a mereattributeof some other thing. $nly the Pythagoreans place the infinite amongthe ob'ects of sense 3they do not regard number as separable fromthese4) and assert that *hat is outside the heaven is infinite. Plato)on the other hand) holds that there is no body outside 3the ,ormsare not outside because they are no*here4)yet that the infinite ispresent not only in the ob'ects of sense but in the ,orms also.

,urther) the Pythagoreans identify the infinite *ith the even. ,orthis) they say) *hen it is cut off and shut in by the odd) providesthings *ith the element of infinity. An indication of this is *hathappens *ith numbers. If the gnomons are placed round the one) and*ithout the one) in the one construction the figure that results is



al*ays different) in the other it is al*ays the same. But Plato hast*o infinites) the #reat and the Small.

The physicists) on the other hand) all of them) al*ays regard theinfinite as an attribute of a substance *hich is different from itand belongs to the class of the so0called elements0*ater or air or

*hat is intermediate bet*een them. Those *ho ma+e them limited innumber never ma+e them infinite in amount. But those *ho ma+e theelements infinite in number) as Ana6agoras and 5emocritus do) saythat the infinite is continuous by contact0compounded of thehomogeneousparts according to the one) of the seed0mass of the atomic shapesaccording to the other.

,urther) Ana6agoras held that any part is a mi6ture in the same *ayas the All) on the ground of the observed fact that anything comesout of anything. ,or it is probably for this reason that he maintainsthat once upon a time all things *ere together. 3This flesh and thisbone *ere together) and so of any thing: therefore all things: andat the same time too.4 ,or there is a beginning of separation) notonly for each thing) but for all. 9ach thing that comes to be comesfrom a similar body) and there is a coming to be of all things) thoughnot) it is true) at the same time. !ence there must also be an originof coming to be. $ne such source there is *hich he calls 1ind) and1ind begins its *or+ of thin+ing from some starting0point. Sonecessarilyall things must have been together at a certain time) and must havebegun to be moved at a certain time.

5emocritus) for his part) asserts the contrary) namely that no elementarises from another element. -evertheless for him the common bodyis a source of all things) differing from part to part in si8e andin shape.

It is clear then from these considerations that the in(uiry concernsthe physicist. -or is it *ithout reason that they all ma+e it aprincipleor source. &e cannot say that the infinite has no effect) and theonly effectiveness *hich *e can ascribe to it is that of a principle.9verything is either a source or derived from a source. But therecannot be a source of the infinite or limitless) for that *ould bea limit of it. ,urther) as it is a beginning) it is both uncreatableand indestructible. ,or there must be a point at *hich *hat has cometo be reaches completion) and also a termination of all passing a*ay.That is *hy) as *e say) there is no principle of this) but it is this*hich is held to be the principle of other things) and to encompassall and to steer all) as those assert *ho do not recogni8e) alongsidethe infinite) other causes) such as 1ind or ,riendship. ,urther theyidentify it *ith the 5ivine) for it is deathless and imperishableas Ana6imander says) *ith the ma'ority of the physicists.

Belief in the e6istence of the infinite comes mainly from fiveconsiderations:

3%4 ,rom the nature of time0for it is infinite.324 ,rom the division of magnitudes0for the mathematicians also usethe notion of the infinite.

3;4 If coming to be and passing a*ay do not give out) it is onlybecausethat from *hich things come to be is infinite.



3>4 Because the limited al*ays finds its limit in something) so thatthere must be no limit) if everything is al*ays limited by somethingdifferent from itself.

3?4 1ost of all) a reason *hich is peculiarly appropriate and presents

the difficulty that is felt by everybody0not only number but alsomathematical magnitudes and *hat is outside the heaven are supposedto be infinite because they never give out in our thought.

The last fact 3that *hat is outside is infinite4 leads people tosupposethat body also is infinite) and that there is an infinite number of*orlds. &hy should there be body in one part of the void rather thanin another7 #rant only that mass is any*here and it follo*s that itmust be every*here. Also) if void and place are infinite) there mustbe infinite body too) for in the case of eternal things *hat may bemust be. But the problem of the infinite is difficult: manycontradictionsresult *hether *e suppose it to e6ist or not to e6ist. If it e6ists)*e have still to as+ ho* it e6ists as a substance or as the essentialattribute of some entity7 $r in neither *ay) yet none the less isthere something *hich is infinite or some things *hich are infinitelymany7

The problem) ho*ever) *hich specially belongs to the physicist isto investigate *hether there is a sensible magnitude *hich isinfinite.

&e must begin by distinguishing the various senses in *hich the terminfinite is used.

3%4 &hat is incapable of being gone through) because it is not inits nature to be gone through 3the sense in *hich the voice is

invisible 4.

324 &hat admits of being gone through) the process ho*ever havingno termination) or *hat scarcely admits of being gone through.

3;4 &hat naturally admits of being gone through) but is not actuallygone through or does not actually reach an end.

,urther) everything that is infinite may be so in respect of additionor division or both.

Part ?

-o* it is impossible that the infinite should be a thing *hich isitself infinite) separable from sensible ob'ects. If the infiniteis neither a magnitude nor an aggregate) but is itself a substanceand not an attribute) it *ill be indivisible for the divisible mustbe either a magnitude or an aggregate. But if indivisible) then notinfinite) e6cept in the sense 3%4 in *hich the voice is invisible .But this is not the sense in *hich it is used by those *ho say thatthe infinite e6ists) nor that in *hich *e are investigating it) namelyas 324 that *hich cannot be gone through . But if the infinite e6istsas an attribute) it *ould not be) (ua infinite an element insubstances)any more than the invisible *ould be an element of speech) thoughthe voice is invisible.



,urther) ho* can the infinite be itself any thing) unless both numberand magnitude) of *hich it is an essential attribute) e6ist in that*ay7 If they are not substances) a fortiori the infinite is not.

It is plain) too) that the infinite cannot be an actual thing anda substance and principle. ,or any part of it that is ta+en *ill be

infinite) if it has parts: for to be infinite and the infiniteare the same) if it is a substance and not predicated of a sub'ect.!ence it *ill be either indivisible or divisible into infinites. Butthe same thing cannot be many infinites. 3 et 'ust as part of airis air) so a part of the infinite *ould be infinite) if it is supposedto be a substance and principle.4 Therefore the infinite must be*ithoutparts and indivisible. But this cannot be true of *hat is infinitein full completion: for it must be a definite (uantity.

Suppose then that infinity belongs to substance as an attribute. But)if so) it cannot) as *e have said) be described as a principle) butrather that of *hich it is an attribute0the air or the even number.

Thus the vie* of those *ho spea+ after the manner of the Pythagoreansis absurd. &ith the same breath they treat the infinite as substance)and divide it into parts.

This discussion) ho*ever) involves the more general (uestion *hetherthe infinite can be present in mathematical ob'ects and things *hichare intelligible and do not have e6tension) as *ell as among sensibleob'ects. $ur in(uiry 3as physicists4 is limited to its specialsub'ect0matter)the ob'ects of sense) and *e have to as+ *hether there is or is notamong them a body *hich is infinite in the direction of increase.

&e may begin *ith a dialectical argument and sho* as follo*s thatthere is no such thing. If bounded by a surface is the definitionof body there cannot be an infinite body either intelligible orsensible.-or can number ta+en in abstraction be infinite) for number or that*hich has number is numerable. If then the numerable can be numbered)it *ould also be possible to go through the infinite.

If) on the other hand) *e investigate the (uestion more in accordance*ith principles appropriate to physics) *e are led as follo*s to thesame result.

The infinite body must be either 3%4 compound) or 324 simple yetneither alternative is possible.

3%4 Compound the infinite body *ill not be) if the elements are finitein number. ,or they must be more than one) and the contraries mustal*ays balance) and no one of them can be infinite. If one of thebodies falls in any degree short of the other in potency0suppose fireis finite in amount *hile air is infinite and a given (uantity offire e6ceeds in po*er the same amount of air in any ratio providedit is numerically definite0the infinite body *ill obviously prevailover and annihilate the finite body. $n the other hand) it isimpossiblethat each should be infinite. Body is *hat has e6tension in alldirections and the infinite is *hat is boundlessly e6tended) so thatthe infinite body *ould be e6tended in all directions ad infinitum.

-or 324 can the infinite body be one and simple) *hether it is) as



some hold) a thing over and above the elements 3from *hich theygeneratethe elements4 or is not thus (ualified.

3a4 &e must consider the former alternative for there are some people*ho ma+e this the infinite) and not air or *ater) in order that the

other elements may not be annihilated by the element *hich isinfinite.They have contrariety *ith each other0air is cold) *ater moist) firehot if one *ere infinite) the others by no* *ould have ceased tobe. As it is) they say) the infinite is different from them and istheir source.

It is impossible) ho*ever) that there should be such a body notbecauseit is infinite on that point a general proof can be given *hichappliese(ually to all) air) *ater) or anything else0but simply because thereis) as a matter of fact) no such sensible body) alongside the so0calledelements. 9verything can be resolved into the elements of *hich itis composed. !ence the body in (uestion *ould have been present inour *orld here) alongside air and fire and earth and *ater: butnothingof the +ind is observed.

3b4 -or can fire or any other of the elements be infinite. ,orgenerally)and apart from the (uestion of ho* any of them could be infinite)the All) even if it *ere limited) cannot either be or become one ofthem) as !eraclitus says that at some time all things become fire.3The same argument applies also to the one *hich the physicistssupposeto e6ist alongside the elements: for everything changes from contraryto contrary) e.g. from hot to cold4.

The preceding consideration of the various cases serves to sho* us*hether it is or is not possible that there should be an infinitesensible body. The follo*ing arguments give a general demonstrationthat it is not possible.

It is the nature of every +ind of sensible body to be some*here) andthere is a place appropriate to each) the same for the part and forthe *hole) e.g. for the *hole earth and for a single clod) and forfire and for a spar+.

Suppose 3a4 that the infinite sensible body is homogeneous. Then eachpart *ill be either immovable or al*ays being carried along. etneitheris possible. ,or *hy do*n*ards rather than up*ards or in any otherdirection7 I mean) e.g) if you ta+e a clod) *here *ill it be movedor *here *ill it be at rest7 ,or e6 hypothesi the place of the bodya+in to it is infinite. &ill it occupy the *hole place) then7 Andho*7 &hat then *ill be the nature of its rest and of its movement)or *here *ill they be7 It *ill either be at home every*here0then it*ill not be moved or it *ill be moved every*here0then it *ill notcome to rest.

But if 3b4 the All has dissimilar parts) the proper places of theparts *ill be dissimilar also) and the body of the All *ill have nounity e6cept that of contact. Then) further) the parts *ill be either



finite or infinite in variety of +ind. 3i4 ,inite they cannot be)for if the All is to be infinite) some of them *ould have to beinfinite)*hile the others *ere not) e.g. fire or *ater *ill be infinite. But)as *e have seen before) such an element *ould destroy *hat is contraryto it. 3This indeed is the reason *hy none of the physicists made

fire or earth the one infinite body) but either *ater or air or *hatis intermediate bet*een them) because the abode of each of the t*o*as plainly determinate) *hile the others have an ambiguous placebet*een up and do*n.4

But 3ii4 if the parts are infinite in number and simple) their properplaces too *ill be infinite in number) and the same *ill be true ofthe elements themselves. If that is impossible) and the places arefinite) the *hole too must be finite for the place and the bodycannotbut fit each other. -either is the *hole place larger than *hat canbe filled by the body 3and then the body *ould no longer be infinite4)nor is the body larger than the place for either there *ould be anempty space or a body *hose nature it is to be no*here.

Ana6agoras gives an absurd account of *hy the infinite is at rest.!e says that the infinite itself is the cause of its being fi6ed.This because it is in itself) since nothing else contains it0on theassumption that *herever anything is) it is there by its o*n nature.But this is not true: a thing could be some*here by compulsion) andnot *here it is its nature to be.

9ven if it is true as true can be that the *hole is not moved 3for*hat is fi6ed by itself and is in itself must be immovable4) yet *emust e6plain *hy it is not its nature to be moved. It is not enough'ust to ma+e this statement and then decamp. Anything else might bein a state of rest) but there is no reason *hy it should not be itsnature to be moved. The earth is not carried along) and *ould notbe carried along if it *ere infinite) provided it is held togetherby the centre. But it *ould not be because there *as no other regionin *hich it could be carried along that it *ould remain at the centre)but because this is its nature. et in this case also *e may say thatit fi6es itself. If then in the case of the earth) supposed to beinfinite) it is at rest) not because it is infinite) but because ithas *eight and *hat is heavy rests at the centre and the earth isat the centre) similarly the infinite also *ould rest in itself) notbecause it is infinite and fi6es itself) but o*ing to some othercause.

Another difficulty emerges at the same time. Any part of the infinitebody ought to remain at rest. Hust as the infinite remains at restin itself because it fi6es itself) so too any part of it you may ta+e*ill remain in itself. The appropriate places of the *hole and ofthe part are ali+e) e.g. of the *hole earth and of a clod theappropriateplace is the lo*er region of fire as a *hole and of a spar+) theupper region. If) therefore) to be in itself is the place of theinfinite)that also *ill be appropriate to the part. Therefore it *ill remainin itself.

In general) the vie* that there is an infinite body is plainlyincompatible*ith the doctrine that there is necessarily a proper place for each+ind of body) if every sensible body has either *eight or lightness)



and if a body has a natural locomotion to*ards the centre if it isheavy) and up*ards if it is light. This *ould need to be true of theinfinite also. But neither character can belong to it: it cannot beeither as a *hole) nor can it be half the one and half the other.,or ho* should you divide it7 or ho* can the infinite have the onepart up and the other do*n) or an e6tremity and a centre7

,urther) every sensible body is in place) and the +inds or differencesof place are up0do*n) before0behind) right0left and thesedistinctionshold not only in relation to us and by arbitrary agreement) but alsoin the *hole itself. But in the infinite body they cannot e6ist. Ingeneral) if it is impossible that there should be an infinite place)and if every body is in place) there cannot be an infinite body.

Surely *hat is in a special place is in place) and *hat is in placeis in a special place. Hust) then) as the infinite cannot be (uantity0that*ould imply that it has a particular (uantity) e)g) t*o or threecubits(uantity 'ust means these0so a thing s being in place means that itis some*here) and that is either up or do*n or in some other of thesi6 differences of position: but each of these is a limit.

It is plain from these arguments that there is no body *hich isactuallyinfinite.

Part

But on the other hand to suppose that the infinite does not e6istin any *ay leads obviously to many impossible conse(uences: there*ill be a beginning and an end of time) a magnitude *ill not bedivisibleinto magnitudes) number *ill not be infinite. If) then) in vie* ofthe above considerations) neither alternative seems possible) anarbitermust be called in and clearly there is a sense in *hich the infinitee6ists and another in *hich it does not.

&e must +eep in mind that the *ord is means either *hat potentiallyis or *hat fully is. ,urther) a thing is infinite either by additionor by division.

-o*) as *e have seen) magnitude is not actually infinite. But bydivisionit is infinite. 3There is no difficulty in refuting the theory ofindivisible lines.4 The alternative then remains that the infinitehas a potential e6istence.

But the phrase potential e6istence is ambiguous. &hen *e spea+ ofthe potential e6istence of a statue *e mean that there *ill be anactual statue. It is not so *ith the infinite. There *ill not be anactual infinite. The *ord is has many senses) and *e say that theinfinite is in the sense in *hich *e say it is day or it is thegames ) because one thing after another is al*ays coming intoe6istence.,or of these things too the distinction bet*een potential and actuale6istence holds. &e say that there are $lympic games) both in thesense that they may occur and that they are actually occurring.



The infinite e6hibits itself in different *ays0in time) in thegenerationsof man) and in the division of magnitudes. ,or generally the infinitehas this mode of e6istence: one thing is al*ays being ta+en afteranother) and each thing that is ta+en is al*ays finite) but al*aysdifferent. Again) being has more than one sense) so that *e must

not regard the infinite as a this ) such as a man or a horse) butmust suppose it to e6ist in the sense in *hich *e spea+ of the dayor the games as e6isting things *hose being has not come to them li+ethat of a substance) but consists in a process of coming to be orpassing a*ay definite if you li+e at each stage) yet al*aysdifferent.

But *hen this ta+es place in spatial magnitudes) *hat is ta+enperists)*hile in the succession of time and of men it ta+es place by thepassinga*ay of these in such a *ay that the source of supply never givesout.

In a *ay the infinite by addition is the same thing as the infiniteby division. In a finite magnitude) the infinite by addition comesabout in a *ay inverse to that of the other. ,or in proportion as*e see division going on) in the same proportion *e see addition beingmade to *hat is already mar+ed off. ,or if *e ta+e a determinate partof a finite magnitude and add another part determined by the sameratio 3not ta+ing in the same amount of the original *hole4) and soon) *e shall not traverse the given magnitude. But if *e increasethe ratio of the part) so as al*ays to ta+e in the same amount) *eshall traverse the magnitude) for every finite magnitude is e6haustedby means of any determinate (uantity ho*ever small.

The infinite) then) e6ists in no other *ay) but in this *ay it doese6ist) potentially and by reduction. It e6ists fully in the sensein *hich *e say it is day or it is the games and potentiallyas matter e6ists) not independently as *hat is finite does.

By addition then) also) there is potentially an infinite) namely)*hat *e have described as being in a sense the same as the infinitein respect of division. ,or it *ill al*ays be possible to ta+esomethingah e6tra. et the sum of the parts ta+en *ill not e6ceed everydeterminatemagnitude) 'ust as in the direction of division every determinatemagnitude is surpassed in smallness and there *ill be a smaller part.

But in respect of addition there cannot be an infinite *hich evenpotentially e6ceeds every assignable magnitude) unless it has theattribute of being actually infinite) as the physicists hold to betrue of the body *hich is outside the *orld) *hose essential natureis air or something of the +ind. But if there cannot be in this *aya sensible body *hich is infinite in the full sense) evidently therecan no more be a body *hich is potentially infinite in respect ofaddition) e6cept as the inverse of the infinite by division) as *ehave said. It is for this reason that Plato also made the infinitest*o in number) because it is supposed to be possible to e6ceed alllimits and to proceed ad infinitum in the direction both of increaseand of reduction. et though he ma+es the infinites t*o) he does notuse them. ,or in the numbers the infinite in the direction ofreductionis not present) as the monad is the smallest nor is the infinite



in the direction of increase) for the parts number only up to thedecad.

The infinite turns out to be the contrary of *hat it is said to be.It is not *hat has nothing outside it that is infinite) but *hatal*ays

has something outside it. This is indicated by the fact that ringsalso that have no be8el are described as endless ) because it isal*ays possible to ta+e a part *hich is outside a given part. Thedescription depends on a certain similarity) but it is not true inthe full sense of the *ord. This condition alone is not sufficient:it is necessary also that the ne6t part *hich is ta+en should neverbe the same. In the circle) the latter condition is not satisfied:it is only the ad'acent part from *hich the ne* part is different.

$ur definition then is as follo*s:A (uantity is infinite if it is such that *e can al*ays ta+e a partoutside *hat has been already ta+en. $n the other hand) *hat hasnothingoutside it is complete and *hole. ,or thus *e define the *hole0thatfrom *hich nothing is *anting) as a *hole man or a *hole bo6. &hatis true of each particular is true of the *hole as such0the *holeis that of *hich nothing is outside. $n the other hand that from *hichsomething is absent and outside) ho*ever small that may be) is not

all . &hole and complete are either (uite identical or closelya+in. -othing is complete 3teleion4 *hich has no end 3telos4 andthe end is a limit.

!ence Parmenides must be thought to have spo+en better than 1elissus.The latter says that the *hole is infinite) but the former describesit as limited) e(ually balanced from the middle . ,or to connectthe infinite *ith the all and the *hole is not li+e 'oining t*o piecesof string for it is from this they get the dignity they ascribe tothe infinite0its containing all things and holding the all in itself0fromits having a certain similarity to the *hole. It is in fact the matterof the completeness *hich belongs to si8e) and *hat is potentiallya *hole) though not in the full sense. It is divisible both in thedirection of reduction and of the inverse addition. It is a *holeand limited not) ho*ever) in virtue of its o*n nature) but in virtueof *hat is other than it. It does not contain) but) in so far as itis infinite) is contained. Conse(uently) also) it is un+no*able) (uainfinite for the matter has no form. 3!ence it is plain that theinfinite stands in the relation of part rather than of *hole. ,orthe matter is part of the *hole) as the bron8e is of the bron8estatue.4If it contains in the case of sensible things) in the case ofintelligiblethings the great and the small ought to contain them. But it is absurdand impossible to suppose that the un+no*able and indeterminate shouldcontain and determine.

Part

It is reasonable that there should not be held to be an infinite inrespect of addition such as to surpass every magnitude) but that thereshould be thought to be such an infinite in the direction of division.,or the matter and the infinite are contained inside *hat containsthem) *hile it is the form *hich contains. It is natural too tosupposethat in number there is a limit in the direction of the minimum) and



that in the other direction every assigned number is surpassed. Inmagnitude) on the contrary) every assigned magnitude is surpassedin the direction of smallness) *hile in the other direction thereis no infinite magnitude. The reason is that *hat is one isindivisible*hatever it may be) e.g. a man is one man) not many. -umber on the

other hand is a plurality of ones and a certain (uantity of them.!ence number must stop at the indivisible: for t*o and three aremerely derivative terms) and so *ith each of the other numbers. Butin the direction of largeness it is al*ays possible to thin+ of alarger number: for the number of times a magnitude can be bisectedis infinite. !ence this infinite is potential) never actual: thenumberof parts that can be ta+en al*ays surpasses any assigned number. Butthis number is not separable from the process of bisection) and itsinfinity is not a permanent actuality but consists in a process ofcoming to be) li+e time and the number of time.

&ith magnitudes the contrary holds. &hat is continuous is dividedad infinitum) but there is no infinite in the direction of increase.,or the si8e *hich it can potentially be) it can also actually be.!ence since no sensible magnitude is infinite) it is impossible toe6ceed every assigned magnitude for if it *ere possible there *ouldbe something bigger than the heavens.

The infinite is not the same in magnitude and movement and time) inthe sense of a single nature) but its secondary sense depends on itsprimary sense) i.e. movement is called infinite in virtue of themagnitudecovered by the movement 3or alteration or gro*th4) and time becauseof the movement. 3I use these terms for the moment. ater I shalle6plain *hat each of them means) and also *hy every magnitude isdivisibleinto magnitudes.4

$ur account does not rob the mathematicians of their science) bydisprovingthe actual e6istence of the infinite in the direction of increase)in the sense of the untraversable. In point of fact they do not needthe infinite and do not use it. They postulate only that the finitestraight line may be produced as far as they *ish. It is possibleto have divided in the same ratio as the largest (uantity anothermagnitude of any si8e you li+e. !ence) for the purposes of proof)it *ill ma+e no difference to them to have such an infinite instead)*hile its e6istence *ill be in the sphere of real magnitudes.

In the fourfold scheme of causes) it is plain that the infinite isa cause in the sense of matter) and that its essence is privation)the sub'ect as such being *hat is continuous and sensible. All theother thin+ers) too) evidently treat the infinite as matter0that is*hy it is inconsistent in them to ma+e it *hat contains) and not *hatis contained.

Part D

It remains to dispose of the arguments *hich are supposed to supportthe vie* that the infinite e6ists not only potentially but as aseparatething. Some have no cogency others can be met by fresh ob'ectionsthat are valid.



3%4 In order that coming to be should not fail) it is not necessarythat there should be a sensible body *hich is actually infinite. Thepassing a*ay of one thing may be the coming to be of another) theAll being limited.

324 There is a difference bet*een touching and being limited. The

former is relative to something and is the touching of something 3foreverything that touches touches something4) and further is anattributeof some one of the things *hich are limited. $n the other hand) *hatis limited is not limited in relation to anything. Again) contactis not necessarily possible bet*een any t*o things ta+en at random.

3;4 To rely on mere thin+ing is absurd) for then the e6cess or defectis not in the thing but in the thought. $ne might thin+ that one ofus is bigger than he is and magnify him ad infinitum. But it doesnot follo* that he is bigger than the si8e *e are) 'ust because someone thin+s he is) but only because he is the si8e he is. The thoughtis an accident.

3a4 Time indeed and movement are infinite) and also thin+ing) in thesense that each part that is ta+en passes in succession out ofe6istence.

3b4 1agnitude is not infinite either in the *ay of reduction or ofmagnification in thought.

This concludes my account of the *ay in *hich the infinite e6ists)and of the *ay in *hich it does not e6ist) and of *hat it is.

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B$$" I

Part %

The physicist must have a +no*ledge of Place) too) as *ell as ofthe infinite0namely) *hether there is such a thing or not) and themanner of its e6istence and *hat it is0both because all suppose thatthings *hich e6ist are some*here 3the non0e6istent is no*here00*hereis the goat0stag or the sphin674) and because motion in its mostgeneral and primary sense is change of place) *hich *e call

locomotion .

The (uestion) *hat is place7 presents many difficulties. Ane6aminationof all the relevant facts seems to lead to divergent conclusions.1oreover) *e have inherited nothing from previous thin+ers) *hetherin the *ay of a statement of difficulties or of a solution.

The e6istence of place is held to be obvious from the fact of mutualreplacement. &here *ater no* is) there in turn) *hen the *ater hasgone out as from a vessel) air is present. &hen therefore anotherbody occupies this same place) the place is thought to be differentfrom all the bodies *hich come to be in it and replace one another.&hat no* contains air formerly contained *ater) so that clearly theplace or space into *hich and out of *hich they passed *as somethingdifferent from both.

,urther) the typical locomotions of the elementary natural bodies0namely)



fire) earth) and the li+e0sho* not only that place is something) butalso that it e6erts a certain influence. 9ach is carried to its o*nplace) if it is not hindered) the one up) the other do*n. -o* theseare regions or +inds of place0up and do*n and the rest of the si6directions. -or do such distinctions 3up and do*n and right and left)Fc.4 hold only in relation to us. To us they are not al*ays the same

but change *ith the direction in *hich *e are turned: that is *hythe same thing may be both right and left) up and do*n) before andbehind. But in nature each is distinct) ta+en apart by itself. Itis not every chance direction *hich is up ) but *here fire and *hatis light are carried similarly) too) do*n is not any chancedirectionbut *here *hat has *eight and *hat is made of earth are carried0theimplication being that these places do not differ merely in relativeposition) but also as possessing distinct potencies. This is madeplain also by the ob'ects studied by mathematics. Though they haveno real place) they nevertheless) in respect of their positionrelativelyto us) have a right and left as attributes ascribed to them only inconse(uence of their relative position) not having by nature thesevarious characteristics. Again) the theory that the void e6istsinvolvesthe e6istence of place: for one *ould define void as place bereftof body.

These considerations then *ould lead us to suppose that place issomethingdistinct from bodies) and that every sensible body is in place. !esiodtoo might be held to have given a correct account of it *hen he madechaos first. At least he says:

,irst of all things came chaos to being) then broad0breasted earth)implying that things need to have space first) because he thought)*ith most people) that everything is some*here and in place. If thisis its nature) the potency of place must be a marvellous thing) andta+e precedence of all other things. ,or that *ithout *hich nothingelse can e6ist) *hile it can e6ist *ithout the others) must needsbe first for place does not pass out of e6istence *hen the thingsin it are annihilated.

True) but even if *e suppose its e6istence settled) the (uestion ofits nature presents difficulty0*hether it is some sort of bul+ ofbody or some entity other than that) for *e must first determine itsgenus.

3%4 -o* it has three dimensions) length) breadth) depth) thedimensionsby *hich all body also is bounded. But the place cannot be body forif it *ere there *ould be t*o bodies in the same place.

324 ,urther) if body has a place and space) clearly so too havesurfaceand the other limits of body for the same statement *ill apply tothem: *here the bounding planes of the *ater *ere) there in turn *illbe those of the air. But *hen *e come to a point *e cannot ma+e adistinction bet*een it and its place. !ence if the place of a pointis not different from the point) no more *ill that of any of theothersbe different) and place *ill not be something different from eachof them.



3;4 &hat in the *orld then are *e to suppose place to be7 If it hasthe sort of nature described) it cannot be an element or composedof elements) *hether these be corporeal or incorporeal: for *hileit has si8e) it has not body. But the elements of sensible bodiesare bodies) *hile nothing that has si8e results from a combinationof intelligible elements.

3>4 Also *e may as+: of *hat in things is space the cause7 -one ofthe four modes of causation can be ascribed to it. It is neither inthe sense of the matter of e6istents 3for nothing is composed of it4)nor as the form and definition of things) nor as end) nor does itmove e6istents.

3?4 ,urther) too) if it is itself an e6istent) *here *ill it be7Jeno sdifficulty demands an e6planation: for if everything that e6ists hasa place) place too *ill have a place) and so on ad infinitum.

3 4 Again) 'ust as every body is in place) so) too) every place hasa body in it. &hat then shall *e say about gro*ing things7 It follo*sfrom these premisses that their place must gro* *ith them) if theirplace is neither less nor greater than they are.

By as+ing these (uestions) then) *e must raise the *hole problem aboutplace0not only as to *hat it is) but even *hether there is such athing.

Part 2

&e may distinguish generally bet*een predicating B of A because it3A4 is itself) and because it is something else and particularlybet*een place *hich is common and in *hich all bodies are) and thespecial place occupied primarily by each. I mean) for instance) thatyou are no* in the heavens because you are in the air and it is inthe heavens and you are in the air because you are on the earthand similarly on the earth because you are in this place *hichcontainsno more than you.

-o* if place is *hat primarily contains each body) it *ould be alimit)so that the place *ould be the form or shape of each body by *hichthe magnitude or the matter of the magnitude is defined: for thisis the limit of each body.

If) then) *e loo+ at the (uestion in this *ay the place of a thingis its form. But) if *e regard the place as the e6tension of themagnitude)it is the matter. ,or this is different from the magnitude: it is*hat is contained and defined by the form) as by a bounding plane.1atter or the indeterminate is of this nature *hen the boundary andattributes of a sphere are ta+en a*ay) nothing but the matter is left.

This is *hy Plato in the Timaeus says that matter and space are thesame for the participant and space are identical. 3It is true)indeed) that the account he gives there of the participant isdifferentfrom *hat he says in his so0called un*ritten teaching . -evertheless)he did identify place and space.4 I mention Plato because) *hile allhold place to be something) he alone tried to say *hat it is.



In vie* of these facts *e should naturally e6pect to find difficultyin determining *hat place is) if indeed it is one of these t*o things)matter or form. They demand a very close scrutiny) especially as itis not easy to recogni8e them apart.

But it is at any rate not difficult to see that place cannot be either

of them. The form and the matter are not separate from the thing)*hereas the place can be separated. As *e pointed out) *here air *as)*ater in turn comes to be) the one replacing the other and similarly*ith other bodies. !ence the place of a thing is neither a part nora state of it) but is separable from it. ,or place is supposed tobe something li+e a vessel0the vessel being a transportable place.But the vessel is no part of the thing.

In so far then as it is separable from the thing) it is not the form:(ua containing) it is different from the matter.

Also it is held that *hat is any*here is both itself something andthat there is a different thing outside it. 3Plato of course) if *emay digress) ought to tell us *hy the form and the numbers are notin place) if *hat participates is place0*hether *hat participatesis the #reat and the Small or the matter) as he called it in *ritingin the Timaeus.4

,urther) ho* could a body be carried to its o*n place) if place *asthe matter or the form7 It is impossible that *hat has no referenceto motion or the distinction of up and do*n can be place. So placemust be loo+ed for among things *hich have these characteristics.

If the place is in the thing 3it must be if it is either shape ormatter4 place *ill have a place: for both the form and theindeterminateundergo change and motion along *ith the thing) and are not al*aysin the same place) but are *here the thing is. !ence the place *illhave a place.

,urther) *hen *ater is produced from air) the place has beendestroyed)for the resulting body is not in the same place. &hat sort ofdestructionthen is that7

This concludes my statement of the reasons *hy space must besomething)and again of the difficulties that may be raised about its essentialnature.

Part ;

The ne6t step *e must ta+e is to see in ho* many senses one thingis said to be in another.

3%4 As the finger is in the hand and generally the part in the*hole.

324 As the *hole is in the parts: for there is no *hole over andabove the parts.

3;4 As man is in animal and generally species in genus.

3>4 As the genus is in the species and generally the part of the



specific form in the definition of the specific form.

3?4 As health is in the hot and the cold and generally the formin the matter.

3 4 As the affairs of #reece centre in the +ing) and generally

eventscentre in their primary motive agent.

3 4 As the e6istence of a thing centres in its good and generallyin its end) i.e. in that for the sa+e of *hich it e6ists.

3D4 In the strictest sense of all) as a thing is in a vessel) andgenerally in place.

$ne might raise the (uestion *hether a thing can be in itself) or*hether nothing can be in itself0everything being either no*here orin something else.

The (uestion is ambiguous *e may mean the thing (ua itself or (uasomething else.

&hen there are parts of a *hole0the one that in *hich a thing is)the other the thing *hich is in it0the *hole *ill be described asbeing in itself. ,or a thing is described in terms of its parts) as*ell as in terms of the thing as a *hole) e.g. a man is said to be*hite because the visible surface of him is *hite) or to be scientificbecause his thin+ing faculty has been trained. The 'ar then *ill notbe in itself and the *ine *ill not be in itself. But the 'ar of *ine*ill: for the contents and the container are both parts of the same*hole.

In this sense then) but not primarily) a thing can be in itself)namely)as *hite is in body 3for the visible surface is in body4) andscienceis in the mind.

It is from these) *hich are parts 3in the sense at least of beingin the man4) that the man is called *hite) Fc. But the 'ar and the

*ine in separation are not parts of a *hole) though together theyare. So *hen there are parts) a thing *ill be in itself) as *hiteis in man because it is in body) and in body because it resides inthe visible surface. &e cannot go further and say that it is insurfacein virtue of something other than itself. 3 et it is not in itself:though these are in a *ay the same thing)4 they differ in essence)each having a special nature and capacity) surface and *hite .

Thus if *e loo+ at the matter inductively *e do not find anythingto be in itself in any of the senses that have been distinguishedand it can be seen by argument that it is impossible. ,or each oft*o things *ill have to be both) e.g. the 'ar *ill have to be bothvessel and *ine) and the *ine both *ine and 'ar) if it is possiblefor a thing to be in itself so that) ho*ever true it might be thatthey *ere in each other) the 'ar *ill receive the *ine in virtue notof its being *ine but of the *ine s being *ine) and the *ine *illbe in the 'ar in virtue not of its being a 'ar but of the 'ar s beinga 'ar. -o* that they are different in respect of their essence isevident for that in *hich something is and that *hich is in it*ould be differently defined.



-or is it possible for a thing to be in itself even incidentally:for t*o things *ould at the same time in the same thing. The 'ar *ouldbe in itself0if a thing *hose nature it is to receive can be initselfand that *hich it receives) namely 3if *ine4 *ine) *ill be in it.

$bviously then a thing cannot be in itself primarily.Jeno s problem0that if Place is something it must be in something0isnot difficult to solve. There is nothing to prevent the first placefrom being in something else0not indeed in that as in place) butas health is in the hot as a positive determination of it or asthe hot is in body as an affection. So *e escape the infiniteregress.

Another thing is plain: since the vessel is no part of *hat is init 3*hat contains in the strict sense is different from *hat iscontained4)place could not be either the matter or the form of the thingcontained)but must different0for the latter) both the matter and the shape)are parts of *hat is contained.

This then may serve as a critical statement of the difficultiesinvolved.

Part >

&hat then after all is place7 The ans*er to this (uestion may beelucidatedas follo*s.

et us ta+e for granted about it the various characteristics *hichare supposed correctly to belong to it essentially. &e assume then0

3%4 Place is *hat contains that of *hich it is the place.

324 Place is no part of the thing.3;4 The immediate place of a thing is neither less nor greater thanthe thing.

3>4 Place can be left behind by the thing and is separable. Inaddition:

3?4 All place admits of the distinction of up and do*n) and each ofthe bodies is naturally carried to its appropriate place and reststhere) and this ma+es the place either up or do*n.

!aving laid these foundations) *e must complete the theory. &e oughtto try to ma+e our investigation such as *ill render an account ofplace) and *ill not only solve the difficulties connected *ith it)but *ill also sho* that the attributes supposed to belong to it doreally belong to it) and further *ill ma+e clear the cause of thetrouble and of the difficulties about it. Such is the mostsatisfactory+ind of e6position.

,irst then *e must understand that place *ould not have been thoughtof) if there had not been a special +ind of motion) namely that *ithrespect to place. It is chiefly for this reason that *e suppose theheaven also to be in place) because it is in constant movement. $f



this +ind of change there are t*o species0locomotion on the one handand) on the other) increase and diminution. ,or these too involvevariation of place: *hat *as then in this place has no* in turnchangedto *hat is larger or smaller.

Again) *hen *e say a thing is moved ) the predicate either 3%4belongsto it actually) in virtue of its o*n nature) or 324 in virtue ofsomethingcon'oined *ith it. In the latter case it may be either 3a4 something*hich by its o*n nature is capable of being moved) e.g. the partsof the body or the nail in the ship) or 3b4 something *hich is notin itself capable of being moved) but is al*ays moved through itscon'unction *ith something else) as *hiteness or science . Thesehave changed their place only because the sub'ects to *hich theybelongdo so.

&e say that a thing is in the *orld) in the sense of in place) becauseit is in the air) and the air is in the *orld and *hen *e say itis in the air) *e do not mean it is in every part of the air) butthat it is in the air because of the outer surface of the air *hichsurrounds it for if all the air *ere its place) the place of a thing*ould not be e(ual to the thing0*hich it is supposed to be) and *hichthe primary place in *hich a thing is actually is.

&hen *hat surrounds) then) is not separate from the thing) but isin continuity *ith it) the thing is said to be in *hat surrounds it)not in the sense of in place) but as a part in a *hole. But *hen thething is separate and in contact) it is immediately in the innersurface of the surrounding body) and this surface is neither a partof *hat is in it nor yet greater than its e6tension) but e(ual toit for the e6tremities of things *hich touch are coincident.

,urther) if one body is in continuity *ith another) it is not movedin that but *ith that. $n the other hand it is moved in that if itis separate. It ma+es no difference *hether *hat contains is movedor not.

Again) *hen it is not separate it is described as a part in a *hole)as the pupil in the eye or the hand in the body: *hen it is separate)as the *ater in the cas+ or the *ine in the 'ar. ,or the hand is moved*ith the body and the *ater in the cas+.

It *ill no* be plain from these considerations *hat place is. Thereare 'ust four things of *hich place must be one0the shape) or thematter) or some sort of e6tension bet*een the bounding surfaces ofthe containing body) or this boundary itself if it contains noe6tensionover and above the bul+ of the body *hich comes to be in it.

Three of these it obviously cannot be:3%4 The shape is supposed to be place because it surrounds) for thee6tremities of *hat contains and of *hat is contained are coincident.Both the shape and the place) it is true) are boundaries. But notof the same thing: the form is the boundary of the thing) the placeis the boundary of the body *hich contains it.

324 The e6tension bet*een the e6tremities is thought to be something)because *hat is contained and separate may often be changed *hile



the container remains the same 3as *ater may be poured from a vessel40theassumption being that the e6tension is something over and above thebody displaced. But there is no such e6tension. $ne of the bodies*hich change places and are naturally capable of being in contact*ith the container falls in *hichever it may chance to be.

If there *ere an e6tension *hich *ere such as to e6ist independentlyand be permanent) there *ould be an infinity of places in the samething. ,or *hen the *ater and the air change places) all the portionsof the t*o together *ill play the same part in the *hole *hich *aspreviously played by all the *ater in the vessel at the same timethe place too *ill be undergoing change so that there *ill be anotherplace *hich is the place of the place) and many places *ill becoincident.There is not a different place of the part) in *hich it is moved)*hen the *hole vessel changes its place: it is al*ays the same: forit is in the 3pro6imate4 place *here they are that the air and the*ater 3or the parts of the *ater4 succeed each other) not in thatplace in *hich they come to be) *hich is part of the place *hich isthe place of the *hole *orld.

3;4 The matter) too) might seem to be place) at least if *e considerit in *hat is at rest and is thus separate but in continuity. ,or'ust as in change of (uality there is something *hich *as formerlyblac+ and is no* *hite) or formerly soft and no* hard0this is 'ust*hy *e say that the matter e6ists0so place) because it presents asimilar phenomenon) is thought to e6ist0only in the one case *e sayso because *hat *as air is no* *ater) in the other because *here airformerly *as there a is no* *ater. But the matter) as *e said before)is neither separable from the thing nor contains it) *hereas placehas both characteristics.

&ell) then) if place is none of the three0neither the form nor thematter nor an e6tension *hich is al*ays there) different from) andover and above) the e6tension of the thing *hich is displaced0placenecessarily is the one of the four *hich is left) namely) the boundaryof the containing body at *hich it is in contact *ith the containedbody. 3By the contained body is meant *hat can be moved by *ay oflocomotion.4

Place is thought to be something important and hard to grasp) bothbecause the matter and the shape present themselves along *ith it)and because the displacement of the body that is moved ta+es placein a stationary container) for it seems possible that there shouldbe an interval *hich is other than the bodies *hich are moved. Theair) too) *hich is thought to be incorporeal) contributes somethingto the belief: it is not only the boundaries of the vessel *hich seemto be place) but also *hat is bet*een them) regarded as empty. Hust)in fact) as the vessel is transportable place) so place is a non0portablevessel. So *hen *hat is *ithin a thing *hich is moved) is moved andchanges its place) as a boat on a river) *hat contains plays the partof a vessel rather than that of place. Place on the other hand israther *hat is motionless: so it is rather the *hole river that isplace) because as a *hole it is motionless.

!ence *e conclude that the innermost motionless boundary of *hatcontainsis place.



This e6plains *hy the middle of the heaven and the surface *hich facesus of the rotating system are held to be up and do*n in the strictand fullest sense for all men: for the one is al*ays at rest) *hilethe inner side of the rotating body remains al*ays coincident *ithitself. !ence since the light is *hat is naturally carried up) andthe heavy *hat is carried do*n) the boundary *hich contains in the

direction of the middle of the universe) and the middle itself) aredo*n) and that *hich contains in the direction of the outermost partof the universe) and the outermost part itself) are up.

,or this reason) too) place is thought to be a +ind of surface) andas it *ere a vessel) i.e. a container of the thing.

,urther) place is coincident *ith the thing) for boundaries arecoincident*ith the bounded.

Part ?

If then a body has another body outside it and containing it) it isin place) and if not) not. That is *hy) even if there *ere to be *ater*hich had not a container) the parts of it) on the one hand) *illbe moved 3for one part is contained in another4) *hile) on the otherhand) the *hole *ill be moved in one sense) but not in another. ,oras a *hole it does not simultaneously change its place) though it*ill be moved in a circle: for this place is the place of its parts.3Some things are moved) not up and do*n) but in a circle others upand do*n) such things namely as admit of condensation andrarefaction.4

As *as e6plained) some things are potentially in place) othersactually.So) *hen you have a homogeneous substance *hich is continuous) theparts are potentially in place: *hen the parts are separated) butin contact) li+e a heap) they are actually in place.

Again) 3%4 some things are per se in place) namely every body *hichis movable either by *ay of locomotion or by *ay of increase is perse some*here) but the heaven) as has been said) is not any*here asa *hole) nor in any place) if at least) as *e must suppose) no bodycontains it. $n the line on *hich it is moved) its parts have place:for each is contiguous the ne6t.

But 324 other things are in place indirectly) through somethingcon'oined*ith them) as the soul and the heaven. The latter is) in a *ay) inplace) for all its parts are: for on the orb one part containsanother.That is *hy the upper part is moved in a circle) *hile the All isnot any*here. ,or *hat is some*here is itself something) and theremust be alongside it some other thing *herein it is and *hich containsit. But alongside the All or the &hole there is nothing outside theAll) and for this reason all things are in the heaven for the heaven)*e may say) is the All. et their place is not the same as the heaven.It is part of it) the innermost part of it) *hich is in contact *iththe movable body and for this reason the earth is in *ater) and thisin the air) and the air in the aether) and the aether in heaven) but*e cannot go on and say that the heaven is in anything else.

It is clear) too) from these considerations that all the problems*hich *ere raised about place *ill be solved *hen it is e6plained



in this *ay:

3%4 There is no necessity that the place should gro* *ith the bodyin it)

324 -or that a point should have a place)

3;4 -or that t*o bodies should be in the same place)3>4 -or that place should be a corporeal interval: for *hat is bet*eenthe boundaries of the place is any body *hich may chance to be there)not an interval in body.

,urther) 3?4 place is also some*here) not in the sense of being ina place) but as the limit is in the limited for not everything thatis is in place) but only movable body.

Also 3 4 it is reasonable that each +ind of body should be carriedto its o*n place. ,or a body *hich is ne6t in the series and incontact3not by compulsion4 is a+in) and bodies *hich are united do not affecteach other) *hile those *hich are in contact interact on each other.

-or 3 4 is it *ithout reason that each should remain naturally inits proper place. ,or this part has the same relation to its place)as a separable part to its *hole) as *hen one moves a part of *ateror air: so) too) air is related to *ater) for the one is li+e matter)the other form0*ater is the matter of air) air as it *ere theactualityof *ater) for *ater is potentially air) *hile air is potentially*ater)though in another *ay.

These distinctions *ill be dra*n more carefully later. $n the presentoccasion it *as necessary to refer to them: *hat has no* been statedobscurely *ill then be made more clear. If the matter and thefulfilmentare the same thing 3for *ater is both) the one potentially) the othercompletely4) *ater *ill be related to air in a *ay as part to *hole.That is *hy these have contact: it is organic union *hen both becomeactually one.

This concludes my account of place0both of its e6istence and of itsnature.

Part

The investigation of similar (uestions about the void) also) mustbe held to belong to the physicist0namely *hether it e6ists or not)and ho* it e6ists or *hat it is0'ust as about place. The vie*s ta+enof it involve arguments both for and against) in much the same sortof *ay. ,or those *ho hold that the void e6ists regard it as a sortof place or vessel *hich is supposed to be full *hen it holds thebul+ *hich it is capable of containing) void *hen it is deprivedof that0as if void and full and place denoted the same thing)though the essence of the three is different.

&e must begin the in(uiry by putting do*n the account given by those*ho say that it e6ists) then the account of those *ho say that itdoes not e6ist) and third the current vie* on these (uestions.

Those *ho try to sho* that the void does not e6ist do not disprove



*hat people really mean by it) but only their erroneous *ay ofspea+ingthis is true of Ana6agoras and of those *ho refute the e6istence ofthe void in this *ay. They merely give an ingenious demonstrationthat air is something00by straining *ine0s+ins and sho*ing theresistance

of the air) and by cutting it off in clepsydras. But people reallymean that there is an empty interval in *hich there is no sensiblebody. They hold that everything *hich is in body is body and say that*hat has nothing in it at all is void 3so *hat is full of air isvoid4.It is not then the e6istence of air that needs to be proved) but thenon0e6istence of an interval) different from the bodies) eitherseparableor actual0an interval *hich divides the *hole body so as to brea+its continuity) as 5emocritus and eucippus hold) and many otherphysicists0oreven perhaps as something *hich is outside the *hole body) *hichremainscontinuous.

These people) then) have not reached even the threshold of theproblem)but rather those *ho say that the void e6ists.

3%4 They argue) for one thing) that change in place 3i.e. locomotionand increase4 *ould not be. ,or it is maintained that motion *ouldseem not to e6ist) if there *ere no void) since *hat is full cannotcontain anything more. If it could) and there *ere t*o bodies in thesame place) it *ould also be true that any number of bodies couldbe together for it is impossible to dra* a line of division beyond*hich the statement *ould become untrue. If this *ere possible) it*ould follo* also that the smallest body *ould contain the greatestfor many a little ma+es a mic+le : thus if many e(ual bodies canbe together) so also can many une(ual bodies.

1elissus) indeed) infers from these considerations that the All isimmovable for if it *ere moved there must) he says) be void) butvoid is not among the things that e6ist.

This argument) then) is one *ay in *hich they sho* that there is avoid.

324 They reason from the fact that some things are observed tocontractand be compressed) as people say that a cas+ *ill hold the *ine *hichformerly filled it) along *ith the s+ins into *hich the *ine has beendecanted) *hich implies that the compressed body contracts into thevoids present in it.

Again 3;4 increase) too) is thought to ta+e al*ays by means of void)for nutriment is body) and it is impossible for t*o bodies to betogether.A proof of this they find also in *hat happens to ashes) *hich absorbas much *ater as the empty vessel.

The Pythagoreans) too) 3>4 held that void e6ists and that it entersthe heaven itself) *hich as it *ere inhales it) from the infiniteair. ,urther it is the void *hich distinguishes the natures of things)as if it *ere li+e *hat separates and distinguishes the terms of a



series. This holds primarily in the numbers) for the voiddistinguishestheir nature.

These) then) and so many) are the main grounds on *hich people haveargued for and against the e6istence of the void.

Part

As a step to*ards settling *hich vie* is true) *e must determine themeaning of the name.

The void is thought to be place *ith nothing in it. The reason forthis is that people ta+e *hat e6ists to be body) and hold that *hileevery body is in place) void is place in *hich there is no body) sothat *here there is no body) there must be void.

9very body) again) they suppose to be tangible and of this natureis *hatever has *eight or lightness.

!ence) by a syllogism) *hat has nothing heavy or light in it) is void.

This result) then) as I have said) is reached by syllogism. It *ouldbe absurd to suppose that the point is void for the void must beplace *hich has in it an interval in tangible body.

But at all events *e observe then that in one *ay the void isdescribedas *hat is not full of body perceptible to touch and *hat hasheavinessand lightness is perceptible to touch. So *e *ould raise the (uestion:*hat *ould they say of an interval that has colour or sound0is itvoid or not7 Clearly they *ould reply that if it could receive *hatis tangible it *as void) and if not) not.

In another *ay void is that in *hich there is no this or corporealsubstance. So some say that the void is the matter of the body 3theyidentify the place) too) *ith this4) and in this they spea+incorrectlyfor the matter is not separable from the things) but they arein(uiringabout the void as about something separable.

Since *e have determined the nature of place) and void must) if ite6ists) be place deprived of body) and *e have stated both in *hatsense place e6ists and in *hat sense it does not) it is plain thaton this sho*ing void does not e6ist) either unseparated or separatedthe void is meant to be) not body but rather an interval in body.This is *hy the void is thought to be something) vi8. because placeis) and for the same reasons. ,or the fact of motion in respect ofplace comes to the aid both of those *ho maintain that place issomethingover and above the bodies that come to occupy it) and of those *homaintain that the void is something. They state that the void is thecondition of movement in the sense of that in *hich movement ta+esplace and this *ould be the +ind of thing that some say place is.

But there is no necessity for there being a void if there is movement.It is not in the least needed as a condition of movement in general)for a reason *hich) incidentally) escaped 1elissus vi8. that thefull can suffer (ualitative change.



But not even movement in respect of place involves a void for bodiesmay simultaneously ma+e room for one another) though there is nointervalseparate and apart from the bodies that are in movement. And thisis plain even in the rotation of continuous things) as in that of

li(uids.

And things can also be compressed not into a void but because theys(uee8e out *hat is contained in them 3as) for instance) *hen *ateris compressed the air *ithin it is s(uee8ed out4 and things canincreasein si8e not only by the entrance of something but also by (ualitativechange e.g. if *ater *ere to be transformed into air.

In general) both the argument about increase of si8e and that about*ater poured on to the ashes get in their o*n *ay. ,or either notany and every part of the body is increased) or bodies may beincreasedother*ise than by the addition of body) or there may be t*o bodiesin the same place 3in *hich case they are claiming to solve a (uitegeneral difficulty) but are not proving the e6istence of void4) orthe *hole body must be void) if it is increased in every part andis increased by means of void. The same argument applies to the ashes.

It is evident) then) that it is easy to refute the arguments by *hichthey prove the e6istence of the void.

Part D

et us e6plain again that there is no void e6isting separately) assome maintain. If each of the simple bodies has a natural locomotion)e.g. fire up*ard and earth do*n*ard and to*ards the middle of theuniverse) it is clear that it cannot be the void that is the conditionof locomotion. &hat) then) *ill the void be the condition of7 It isthought to be the condition of movement in respect of place) and itis not the condition of this.

Again) if void is a sort of place deprived of body) *hen there isa void *here *ill a body placed in it move to7 It certainly cannotmove into the *hole of the void. The same argument applies as againstthose *ho thin+ that place is something separate) into *hich thingsare carried vi8. ho* *ill *hat is placed in it move) or rest7 1uchthe same argument *ill apply to the void as to the up and do*nin place) as is natural enough since those *ho maintain the e6istenceof the void ma+e it a place.

And in *hat *ay *ill things be present either in place0or in the void7,or the e6pected result does not ta+e place *hen a body is placedas a *hole in a place conceived of as separate and permanent fora part of it) unless it be placed apart) *ill not be in a place butin the *hole. ,urther) if separate place does not e6ist) neither *illvoid.

If people say that the void must e6ist) as being necessary if thereis to be movement) *hat rather turns out to be the case) if one thematter) is the opposite) that not a single thing can be moved if thereis a void for as *ith those *ho for a li+e reason say the earth isat rest) so) too) in the void things must be at rest for there isno place to *hich things can move more or less than to another sincethe void in so far as it is void admits no difference.



The second reason is this: all movement is either compulsory oraccordingto nature) and if there is compulsory movement there must also benatural 3for compulsory movement is contrary to nature) and movementcontrary to nature is posterior to that according to nature) so that

if each of the natural bodies has not a natural movement) none ofthe other movements can e6ist4 but ho* can there be natural movementif there is no difference throughout the void or the infinite7 ,orin so far as it is infinite) there *ill be no up or do*n or middle)and in so far as it is a void) up differs no *hit from do*n for asthere is no difference in *hat is nothing) there is none in the void3for the void seems to be a non0e6istent and a privation of being4)but natural locomotion seems to be differentiated) so that the thingsthat e6ist by nature must be differentiated. 9ither) then) nothinghas a natural locomotion) or else there is no void.

,urther) in point of fact things that are thro*n move though that*hich gave them their impulse is not touching them) either by reasonof mutual replacement) as some maintain) or because the air that hasbeen pushed pushes them *ith a movement (uic+er than the naturallocomotionof the pro'ectile *here*ith it moves to its proper place. But in avoid none of these things can ta+e place) nor can anything be movedsave as that *hich is carried is moved.

,urther) no one could say *hy a thing once set in motion should stopany*here for *hy should it stop here rather than here7 So that athing *ill either be at rest or must be moved ad infinitum) unlesssomething more po*erful get in its *ay.

,urther) things are no* thought to move into the void because ityieldsbut in a void this (uality is present e(ually every*here) so thatthings should move in all directions.

,urther) the truth of *hat *e assert is plain from the follo*ingconsiderations.&e see the same *eight or body moving faster than another for t*oreasons) either because there is a difference in *hat it movesthrough)as bet*een *ater) air) and earth) or because) other things beinge(ual)the moving body differs from the other o*ing to e6cess of *eight orof lightness.

-o* the medium causes a difference because it impedes the movingthing)most of all if it is moving in the opposite direction) but in asecondarydegree even if it is at rest and especially a medium that is noteasily divided) i.e. a medium that is some*hat dense. A) then) *illmove through B in time #) and through 5) *hich is thinner) in time9 3if the length of B is egual to 54) in proportion to the densityof the hindering body. ,or let B be *ater and 5 air then by so muchas air is thinner and more incorporeal than *ater) A *ill move through5 faster than through B. et the speed have the same ratio to thespeed) then) that air has to *ater. Then if air is t*ice as thin)the body *ill traverse B in t*ice the time that it does 5) and thetime # *ill be t*ice the time 9. And al*ays) by so much as the mediumis more incorporeal and less resistant and more easily divided) the



faster *ill be the movement.

-o* there is no ratio in *hich the void is e6ceeded by body) as thereis no ratio of K to a number. ,or if > e6ceeds ; by %) and 2 by morethan %) and % by still more than it e6ceeds 2) still there is no ratioby *hich it e6ceeds K for that *hich e6ceeds must be divisible into

the e6cess L that *hich is e6ceeded) so that *ill be *hat it e6ceedsK by L K. ,or this reason) too) a line does not e6ceed a point unlessit is composed of pointsM Similarly the void can bear no ratio tothe full) and therefore neither can movement through the one tomovementthrough the other) but if a thing moves through the thic+est mediumsuch and such a distance in such and such a time) it moves throughthe void *ith a speed beyond any ratio. ,or let J be void) e(ual inmagnitude to B and to 5. Then if A is to traverse and move throughit in a certain time) !) a time less than 9) ho*ever) the void *illbear this ratio to the full. But in a time e(ual to !) A *ill traversethe part $ of A. And it *ill surely also traverse in that time anysubstance J *hich e6ceeds air in thic+ness in the ratio *hich thetime 9 bears to the time !. ,or if the body J be as much thinner than5 as 9 e6ceeds !) A) if it moves through J) *ill traverse it in atime inverse to the speed of the movement) i.e. in a time e(ual to!. If) then) there is no body in J) A *ill traverse J still more(uic+ly.But *e supposed that its traverse of J *hen J *as void occupied thetime !. So that it *ill traverse J in an e(ual time *hether J be fullor void. But this is impossible. It is plain) then) that if thereis a time in *hich it *ill move through any part of the void) thisimpossible result *ill follo*: it *ill be found to traverse a certaindistance) *hether this be full or void) in an e(ual time for there*ill be some body *hich is in the same ratio to the other body asthe time is to the time.

To sum the matter up) the cause of this result is obvious) vi8. thatbet*een any t*o movements there is a ratio 3for they occupy time)and there is a ratio bet*een any t*o times) so long as both arefinite4)but there is no ratio of void to full.

These are the conse(uences that result from a difference in the mediathe follo*ing depend upon an e6cess of one moving body over another.&e see that bodies *hich have a greater impulse either of *eight orof lightness) if they are ali+e in other respects) move faster overan e(ual space) and in the ratio *hich their magnitudes bear to eachother. Therefore they *ill also move through the void *ith this ratioof speed. But that is impossible for *hy should one move faster73In moving through plena it must be so for the greater divides themfaster by its force. ,or a moving thing cleaves the medium eitherby its shape) or by the impulse *hich the body that is carried alongor is pro'ected possesses.4 Therefore all *ill possess e(ual velocity.But this is impossible.

It is evident from *hat has been said) then) that) if there is a void)a result follo*s *hich is the very opposite of the reason for *hichthose *ho believe in a void set it up. They thin+ that if movementin respect of place is to e6ist) the void cannot e6ist) separatedall by itself but this is the same as to say that place is a separatecavity and this has already been stated to be impossible.

But even if *e consider it on its o*n merits the so0called vacuum*ill be found to be really vacuous. ,or as) if one puts a cube in



*ater) an amount of *ater e(ual to the cube *ill be displaced sotoo in air but the effect is imperceptible to sense. And indeedal*aysin the case of any body that can be displaced) must) if it is notcompressed) be displaced in the direction in *hich it is its natureto be displaced0al*ays either do*n) if its locomotion is do*n*ards

as in the case of earth) or up) if it is fire) or in both directions0*hateverbe the nature of the inserted body. -o* in the void this isimpossiblefor it is not body the void must have penetrated the cube to adistancee(ual to that *hich this portion of void formerly occupied in thevoid) 'ust as if the *ater or air had not been displaced by the *oodencube) but had penetrated right through it.

But the cube also has a magnitude e(ual to that occupied by the voida magnitude *hich) if it is also hot or cold) or heavy or light) isnone the less different in essence from all its attributes) even ifit is not separable from them I mean the volume of the *ooden cube.So that even if it *ere separated from everything else and *ereneitherheavy nor light) it *ill occupy an e(ual amount of void) and fillthe same place) as the part of place or of the void e(ual to itself.!o* then *ill the body of the cube differ from the void or place thatis e(ual to it7 And if there can be t*o such things) *hy cannot therebe any number coinciding7

This) then) is one absurd and impossible implication of the theory.It is also evident that the cube *ill have this same volume even ifit is displaced) *hich is an attribute possessed by all other bodiesalso. Therefore if this differs in no respect from its place) *hyneed *e assume a place for bodies over and above the volume of each)if their volume be conceived of as free from attributes7 Itcontributesnothing to the situation if there is an e(ual interval attached toit as *ell. <,urther it ought to be clear by the study of movingthings*hat sort of thing void is. But in fact it is found no*here in the*orld. ,or air is something) though it does not seem to be so0nor)for that matter) *ould *ater) if fishes *ere made of iron for thediscrimination of the tangible is by touch.=

It is clear) then) from these considerations that there is no separatevoid.

Part E

There are some *ho thin+ that the e6istence of rarity and densitysho*s that there is a void. If rarity and density do not e6ist) theysay) neither can things contract and be compressed. But if this *erenot to ta+e place) either there *ould be no movement at all) or theuniverse *ould bulge) as Guthus said) or air and *ater must al*ayschange into e(ual amounts 3e.g. if air has been made out of a cupfulof *ater) at the same time out of an e(ual amount of air a cupfulof *ater must have been made4) or void must necessarily e6ist forcompression and e6pansion cannot ta+e place other*ise.

-o*) if they mean by the rare that *hich has many voids e6istingseparately)it is plain that if void cannot e6ist separate any more than a place



can e6ist *ith an e6tension all to itself) neither can the rare e6istin this sense. But if they mean that there is void) not separatelye6istent) but still present in the rare) this is less impossible)yet) first) the void turns out not to be a condition of all movement)but only of movement up*ards 3for the rare is light) *hich is thereason *hy they say fire is rare4 second) the void turns out to be

a condition of movement not as that in *hich it ta+es place) but inthat the void carries things up as s+ins by being carried upthemselvescarry up *hat is continuous *ith them. et ho* can void have a localmovement or a place7 ,or thus that into *hich void moves is till thenvoid of a void.

Again) ho* *ill they e6plain) in the case of *hat is heavy) itsmovementdo*n*ards7 And it is plain that if the rarer and more void a thingis the (uic+er it *ill move up*ards) if it *ere completely void it*ould move *ith a ma6imum speedM But perhaps even this is impossible)that it should move at all the same reason *hich sho*ed that in thevoid all things are incapable of moving sho*s that the void cannotmove) vi8. the fact that the speeds are incomparable.

Since *e deny that a void e6ists) but for the rest the problem hasbeen truly stated) that either there *ill be no movement) if thereis not to be condensation and rarefaction) or the universe *ill bulge)or a transformation of *ater into air *ill al*ays be balanced by ane(ual transformation of air into *ater 3for it is clear that the airproduced from *ater is bul+ier than the *ater4: it is necessarytherefore)if compression does not e6ist) either that the ne6t portion *ill bepushed out*ards and ma+e the outermost part bulge) or that some*hereelse there must be an e(ual amount of *ater produced out of air) sothat the entire bul+ of the *hole may be e(ual) or that nothing moves.,or *hen anything is displaced this *ill al*ays happen) unless itcomes round in a circle but locomotion is not al*ays circular) butsometimes in a straight line.

These then are the reasons for *hich they might say that there isa void our statement is based on the assumption that there is asinglematter for contraries) hot and cold and the other naturalcontrarieties)and that *hat e6ists actually is produced from a potential e6istent)and that matter is not separable from the contraries but its beingis different) and that a single matter may serve for colour and heatand cold.

The same matter also serves for both a large and a small body. Thisis evident for *hen air is produced from *ater) the same matter hasbecome something different) not by ac(uiring an addition to it) buthas become actually *hat it *as potentially) and) again) *ater isproduced from air in the same *ay) the change being sometimes fromsmallness to greatness) and sometimes from greatness to smallness.Similarly) therefore) if air *hich is large in e6tent comes to havea smaller volume) or becomes greater from being smaller) it is thematter *hich is potentially both that comes to be each of the t*o.

,or as the same matter becomes hot from being cold) and cold frombeing hot) because it *as potentially both) so too from hot it canbecome more hot) though nothing in the matter has become hot that*as not hot *hen the thing *as less hot 'ust as) if the arc or curve



of a greater circle becomes that of a smaller) *hether it remainsthe same or becomes a different curve) conve6ity has not come to e6istin anything that *as not conve6 but straight 3for differences ofdegreedo not depend on an intermission of the (uality4 nor can *e get anyportion of a flame) in *hich both heat and *hiteness are not present.

So too) then) is the earlier heat related to the later. So that thegreatness and smallness) also) of the sensible volume are e6tended)not by the matter s ac(uiring anything ne*) but because the matteris potentially matter for both states so that the same thing is denseand rare) and the t*o (ualities have one matter.

The dense is heavy) and the rare is light. <Again) as the arc of acircle *hen contracted into a smaller space does not ac(uire a ne*part *hich is conve6) but *hat *as there has been contracted andas any part of fire that one ta+es *ill be hot so) too) it is alla (uestion of contraction and e6pansion of the same matter.= Thereare t*o types in each case) both in the dense and in the rare forboth the heavy and the hard are thought to be dense) and contrari*iseboth the light and the soft are rare and *eight and hardness failto coincide in the case of lead and iron.

,rom *hat has been said it is evident) then) that void does not e6isteither separate 3either absolutely separate or as a separate elementin the rare4 or potentially) unless one is *illing to call theconditionof movement void) *hatever it may be. At that rate the matter of theheavy and the light) (ua matter of them) *ould be the void for thedense and the rare are productive of locomotion in virtue of thiscontrariety) and in virtue of their hardness and softness productiveof passivity and impassivity) i.e. not of locomotion but rather of(ualitative change.

So much) then) for the discussion of the void) and of the sense in*hich it e6ists and the sense in *hich it does not e6ist.

Part %K

-e6t for discussion after the sub'ects mentioned is Time. The bestplan *ill be to begin by *or+ing out the difficulties connected *ithit) ma+ing use of the current arguments. ,irst) does it belong tothe class of things that e6ist or to that of things that do not e6ist7Then secondly) *hat is its nature7 To start) then: the follo*ingconsiderations*ould ma+e one suspect that it either does not e6ist at all or barely)and in an obscure *ay. $ne part of it has been and is not) *hile theother is going to be and is not yet. et time0both infinite time andany time you li+e to ta+e0is made up of these. $ne *ould naturallysuppose that *hat is made up of things *hich do not e6ist could haveno share in reality.

,urther) if a divisible thing is to e6ist) it is necessary that) *henit e6ists) all or some of its parts must e6ist. But of time some partshave been) *hile others have to be) and no part of it is though itis divisible. ,or *hat is no* is not a part: a part is a measureof the *hole) *hich must be made up of parts. Time) on the other hand)is not held to be made up of no*s .

Again) the no* *hich seems to bound the past and the future0doesit al*ays remain one and the same or is it al*ays other and other7It is hard to say.



3%4 If it is al*ays different and different) and if none of the partsin time *hich are other and other are simultaneous 3unless the onecontains and the other is contained) as the shorter time is by thelonger4) and if the no* *hich is not) but formerly *as) must haveceased0to0be at some time) the no*s too cannot be simultaneous *ith

one another) but the prior no* must al*ays have ceased0to0be. Butthe prior no* cannot have ceased0to0be in itself 3since it thene6isted4 yet it cannot have ceased0to0be in another no* . ,or *emay lay it do*n that one no* cannot be ne6t to another) any morethan point to point. If then it did not cease0to0be in the ne6t no*but in another) it *ould e6ist simultaneously *ith the innumerable

no*s bet*een the t*o0*hich is impossible.

es) but 324 neither is it possible for the no* to remain al*aysthe same. -o determinate divisible thing has a single termination)*hether it is continuously e6tended in one or in more than onedimension:but the no* is a termination) and it is possible to cut off adeterminatetime. ,urther) if coincidence in time 3i.e. being neither prior norposterior4 means to be in one and the same Nno*N ) then) if both*hat is before and *hat is after are in this same no* ) things *hichhappened ten thousand years ago *ould be simultaneous *ith *hat hashappened to0day) and nothing *ould be before or after anything else.

This may serve as a statement of the difficulties about the attributesof time.

As to *hat time is or *hat is its nature) the traditional accountsgive us as little light as the preliminary problems *hich *e have*or+ed through.

Some assert that it is 3%4 the movement of the *hole) others thatit is 324 the sphere itself.

3%4 et part) too) of the revolution is a time) but it certainly isnot a revolution: for *hat is ta+en is part of a revolution) not arevolution. Besides) if there *ere more heavens than one) the movementof any of them e(ually *ould be time) so that there *ould be manytimes at the same time.

324 Those *ho said that time is the sphere of the *hole thought so)no doubt) on the ground that all things are in time and all thingsare in the sphere of the *hole. The vie* is too naive for it to be*orth *hile to consider the impossibilities implied in it.

But as time is most usually supposed to be 3;4 motion and a +ind ofchange) *e must consider this vie*.

-o* 3a4 the change or movement of each thing is only in the thing*hich changes or *here the thing itself *hich moves or changes maychance to be. But time is present e(ually every*here and *ith allthings.

Again) 3b4 change is al*ays faster or slo*er) *hereas time is not:for fast and slo* are defined by time0 fast is *hat moves muchin a short time) slo* *hat moves little in a long time but timeis not defined by time) by being either a certain amount or a certain+ind of it.



Clearly then it is not movement. 3&e need not distinguish at presentbet*een movement and change .4

Part %%

But neither does time e6ist *ithout change for *hen the state of

our o*n minds does not change at all) or *e have not noticed itschanging)*e do not reali8e that time has elapsed) any more than those *ho arefabled to sleep among the heroes in Sardinia do *hen they area*a+enedfor they connect the earlier no* *ith the later and ma+e them one)cutting out the interval because of their failure to notice it. So)'ust as) if the no* *ere not different but one and the same) there*ould not have been time) so too *hen its difference escapes ournoticethe interval does not seem to be time. If) then) the non0reali8ationof the e6istence of time happens to us *hen *e do not distinguishany change) but the soul seems to stay in one indivisible state) and*hen *e perceive and distinguish *e say time has elapsed) evidentlytime is not independent of movement and change. It is evident) then)that time is neither movement nor independent of movement.

&e must ta+e this as our starting0point and try to discover0since*e *ish to +no* *hat time is0*hat e6actly it has to do *ith movement.

-o* *e perceive movement and time together: for even *hen it is dar+and *e are not being affected through the body) if any movement ta+esplace in the mind *e at once suppose that some time also has elapsedand not only that but also) *hen some time is thought to have passed)some movement also along *ith it seems to have ta+en place. !encetime is either movement or something that belongs to movement. Sincethen it is not movement) it must be the other.

But *hat is moved is moved from something to something) and allmagnitudeis continuous. Therefore the movement goes *ith the magnitude. Becausethe magnitude is continuous) the movement too must be continuous)and if the movement) then the time for the time that has passed isal*ays thought to be in proportion to the movement.

The distinction of before and after holds primarily) then) inplace and there in virtue of relative position. Since then beforeand after hold in magnitude) they must hold also in movement) thesecorresponding to those. But also in time the distinction of beforeand after must hold) for time and movement al*ays correspond *itheach other. The before and after in motion is identical insubstratum*ith motion yet differs from it in definition) and is not identical*ith motion.

But *e apprehend time only *hen *e have mar+ed motion) mar+ing itby before and after and it is only *hen *e have perceived

beforeand after in motion that *e say that time has elapsed. -o* *e mar+them by 'udging that A and B are different) and that some third thingis intermediate to them. &hen *e thin+ of the e6tremes as differentfrom the middle and the mind pronounces that the no*s are t*o) onebefore and one after) it is then that *e say that there is time) andthis that *e say is time. ,or *hat is bounded by the no* is thoughtto be time0*e may assume this.



&hen) therefore) *e perceive the no* one) and neither as beforeand after in a motion nor as an identity but in relation to a beforeand an after ) no time is thought to have elapsed) because therehas been no motion either. $n the other hand) *hen *e do perceivea before and an after ) then *e say that there is time. ,or time

is 'ust this0number of motion in respect of before and after .

!ence time is not movement) but only movement in so far as it admitsof enumeration. A proof of this: *e discriminate the more or the lessby number) but more or less movement by time. Time then is a +indof number. 3-umber) *e must note) is used in t*o senses0both of *hatis counted or the countable and also of that *ith *hich *e count.Time obviously is *hat is counted) not that *ith *hich *e count: thereare different +inds of thing.4 Hust as motion is a perpetualsuccession)so also is time. But every simultaneous time is self0identical forthe no* as a sub'ect is an identity) but it accepts differentattributes.The no* measures time) in so far as time involves the before andafter .

The no* in one sense is the same) in another it is not the same.In so far as it is in succession) it is different 3*hich is 'ust *hatits being *as supposed to mean4) but its substratum is an identity:for motion) as *as said) goes *ith magnitude) and time) as *emaintain)*ith motion. Similarly) then) there corresponds to the point the body*hich is carried along) and by *hich *e are a*are of the motion andof the before and after involved in it. This is an identicalsubstratum3*hether a point or a stone or something else of the +ind4) but ithas different attributes as the sophists assume that Coriscus beingin the yceum is a different thing from Coriscus being in the mar+et0place.And the body *hich is carried along is different) in so far as itis at one time here and at another there. But the no* correspondsto the body that is carried along) as time corresponds to the motion.,or it is by means of the body that is carried along that *e becomea*are of the before and after the motion) and if *e regard theseas countable *e get the no* . !ence in these also the no* assubstratumremains the same 3for it is *hat is before and after in movement4)but *hat is predicated of it is different for it is in so far asthe before and after is numerable that *e get the no* . This is*hat is most +no*able: for) similarly) motion is +no*n because ofthat *hich is moved) locomotion because of that *hich is carried.*hat is carried is a real thing) the movement is not. Thus *hat iscalled no* in one sense is al*ays the same in another it is notthe same: for this is true also of *hat is carried.

Clearly) too) if there *ere no time) there *ould be no no* ) andvice versa. 'ust as the moving body and its locomotion involve eachother mutually) so too do the number of the moving body and the numberof its locomotion. ,or the number of the locomotion is time) *hilethe no* corresponds to the moving body) and is li+e the unit ofnumber.

Time) then) also is both made continuous by the no* and dividedat it. ,or here too there is a correspondence *ith the locomotionand the moving body. ,or the motion or locomotion is made one by the



thing *hich is moved) because it is one0not because it is one in itso*n nature 3for there might be pauses in the movement of such athing40butbecause it is one in definition: for this determines the movementas before and after . !ere) too there is a correspondence *iththe point for the point also both connects and terminates the length0

itis the beginning of one and the end of another. But *hen you ta+eit in this *ay) using the one point as t*o) a pause is necessary)if the same point is to be the beginning and the end. The no* onthe other hand) since the body carried is moving) is al*ays different.

!ence time is not number in the sense in *hich there is number ofthe same point because it is beginning and end) but rather as thee6tremities of a line form a number) and not as the parts of the linedo so) both for the reason given 3for *e can use the middle pointas t*o) so that on that analogy time might stand still4) and furtherbecause obviously the no* is no part of time nor the section anypart of the movement) any more than the points are parts of the line0forit is t*o lines that are parts of one line.

In so far then as the no* is a boundary) it is not time) but anattribute of it in so far as it numbers) it is number for boundariesbelong only to that *hich they bound) but number 3e.g. ten4 is thenumber of these horses) and belongs also else*here.

It is clear) then) that time is number of movement in respect ofthe before and after ) and is continuous since it is an attributeof *hat is continuous.

Part %2

The smallest number) in the strict sense of the *ord number ) ist*o. But of number as concrete) sometimes there is a minimum)sometimesnot: e.g. of a line ) the smallest in respect of multiplicity ist*o 3or) if you li+e) one4) but in respect of si8e there is nominimumfor every line is divided ad infinitum. !ence it is so *ith time.In respect of number the minimum is one 3or t*o4 in point of e6tentthere is no minimum.

It is clear) too) that time is not described as fast or slo*) butas many or fe* and as long or short. ,or as continuous it is longor short and as a number many or fe*) but it is not fast or slo*0anymore than any number *ith *hich *e number is fast or slo*.

,urther) there is the same time every*here at once) but not the sametime before and after) for *hile the present change is one) the change*hich has happened and that *hich *ill happen are different. Timeis not number *ith *hich *e count) but the number of things *hichare counted) and this according as it occurs before or after is al*aysdifferent) for the no*s are different. And the number of a hundredhorses and a hundred men is the same) but the things numbered aredifferent0the horses from the men. ,urther) as a movement can be oneand the same again and again) so too can time) e.g. a year or a springor an autumn.

-ot only do *e measure the movement by the time) but also the timeby the movement) because they define each other. The time mar+s the



movement) since it is its number) and the movement the time. &edescribethe time as much or little) measuring it by the movement) 'ust as*e +no* the number by *hat is numbered) e.g. the number of the horsesby one horse as the unit. ,or *e +no* ho* many horses there are bythe use of the number and again by using the one horse as unit *e

+no* the number of the horses itself. So it is *ith the time and themovement for *e measure the movement by the time and vice versa.It is natural that this should happen for the movement goes *iththe distance and the time *ith the movement) because they are (uantaand continuous and divisible. The movement has these attributesbecausethe distance is of this nature) and the time has them because of themovement. And *e measure both the distance by the movement and themovement by the distance for *e say that the road is long) if the'ourney is long) and that this is long) if the road is long0the time)too) if the movement) and the movement) if the time.

Time is a measure of motion and of being moved) and it measures themotion by determining a motion *hich *ill measure e6actly the *holemotion) as the cubit does the length by determining an amount *hich*ill measure out the *hole. ,urther to be in time means formovement)that both it and its essence are measured by time 3for simultaneouslyit measures both the movement and its essence) and this is *hat beingin time means for it) that its essence should be measured4.

Clearly then to be in time has the same meaning for other thingsalso) namely) that their being should be measured by time. To bein time is one of t*o things: 3%4 to e6ist *hen time e6ists) 324as *e say of some things that they are in number . The latter meanseither *hat is a part or mode of number0in general) something *hichbelongs to number0or that things have a number.

-o*) since time is number) the no* and the before and the li+eare in time) 'ust as unit and odd and even are in number) i.e.in the sense that the one set belongs to number) the other to time.But things are in time as they are in number. If this is so) theyare contained by time as things in place are contained by place.

Plainly) too) to be in time does not mean to co0e6ist *ith time) anymore than to be in motion or in place means to co0e6ist *ith motionor place. ,or if to be in something is to mean this) then all things*ill be in anything) and the heaven *ill be in a grain for *hen thegrain is) then also is the heaven. But this is a merely incidentalcon'unction) *hereas the other is necessarily involved: that *hichis in time necessarily involves that there is time *hen it is) andthat *hich is in motion that there is motion *hen it is.

Since *hat is in time is so in the same sense as *hat is in numberis so) a time greater than everything in time can be found. So itis necessary that all the things in time should be contained by time)'ust li+e other things also *hich are in anything ) e.g. the things

in place by place.

A thing) then) *ill be affected by time) 'ust as *e are accustomedto say that time *astes things a*ay) and that all things gro* oldthrough time) and that there is oblivion o*ing to the lapse of time)but *e do not say the same of getting to +no* or of becoming youngor fair. ,or time is by its nature the cause rather of decay) sinceit is the number of change) and change removes *hat is.



!ence) plainly) things *hich are al*ays are not) as such) in time)for they are not contained time) nor is their being measured by time.A proof of this is that none of them is affected by time) *hichindicatesthat they are not in time.

Since time is the measure of motion) it *ill be the measure of resttoo0indirectly. ,or all rest is in time. ,or it does not follo* that*hat is in time is moved) though *hat is in motion is necessarilymoved. ,or time is not motion) but number of motion : and *hat isat rest) also) can be in the number of motion. -ot everything thatis not in motion can be said to be at rest 0but only that *hich canbe moved) though it actually is not moved) as *as said above.

To be in number means that there is a number of the thing) and thatits being is measured by the number in *hich it is. !ence if a thingis in time it *ill be measured by time. But time *ill measure *hatis moved and *hat is at rest) the one (ua moved) the other (ua atrest for it *ill measure their motion and rest respectively.

!ence *hat is moved *ill not be measurable by the time simply in sofar as it has (uantity) but in so far as its motion has (uantity.Thus none of the things *hich are neither moved nor at rest are intime: for to be in time is to be measured by time ) *hile timeis the measure of motion and rest.

Plainly) then) neither *ill everything that does not e6ist be in time)i.e. those non0e6istent things that cannot e6ist) as the diagonalcannot be commensurate *ith the side.

#enerally) if time is directly the measure of motion and indirectlyof other things) it is clear that a thing *hose e6istence is measuredby it *ill have its e6istence in rest or motion. Those thingstherefore*hich are sub'ect to perishing and becoming0generally) those *hichat one time e6ist) at another do not0are necessarily in time: forthere is a greater time *hich *ill e6tend both beyond their e6istenceand beyond the time *hich measures their e6istence. $f things *hichdo not e6ist but are contained by time some *ere) e.g. !omer once*as) some *ill be) e.g. a future event this depends on the directionin *hich time contains them if on both) they have both modes ofe6istence.As to such things as it does not contain in any *ay) they neither*ere nor are nor *ill be. These are those none6istents *hose oppositesal*ays are) as the incommensurability of the diagonal al*ays is0andthis *ill not be in time. -or *ill the commensurability) thereforehence this eternally is not) because it is contrary to *hat eternallyis. A thing *hose contrary is not eternal can be and not be) and itis of such things that there is coming to be and passing a*ay.

Part %;

The no* is the lin+ of time) as has been said 3for it connects pastand future time4) and it is a limit of time 3for it is the beginningof the one and the end of the other4. But this is not obvious as itis *ith the point) *hich is fi6ed. It divides potentially) and inso far as it is dividing the no* is al*ays different) but in sofar as it connects it is al*ays the same) as it is *ith mathematicallines. ,or the intellect it is not al*ays one and the same point)since it is other and other *hen one divides the line but in so far



as it is one) it is the same in every respect.

So the no* also is in one *ay a potential dividing of time) inanotherthe termination of both parts) and their unity. And the dividing andthe uniting are the same thing and in the same reference) but in

essencethey are not the same.

So one +ind of no* is described in this *ay: another is *hen thetime is near this +ind of no* . !e *ill come no* because he *illcome to0day he has come no* because he came to0day. But the thingsin the Iliad have not happened no* ) nor is the flood no* 0not thatthe time from no* to them is not continuous) but because they arenot near.

At some time means a time determined in relation to the first ofthe t*o types of no* ) e.g. at some time Troy *as ta+en) and atsome time there *ill be a flood for it must be determined *ithreferenceto the no* . There *ill thus be a determinate time from this no*to that) and there *as such in reference to the past event. But ifthere be no time *hich is not sometime ) every time *ill bedetermined.

&ill time then fail7 Surely not) if motion al*ays e6ists. Is timethen al*ays different or does the same time recur7 Clearly time is)in the same *ay as motion is. ,or if one and the same motion sometimesrecurs) it *ill be one and the same time) and if not) not.

Since the no* is an end and a beginning of time) not of the sametime ho*ever) but the end of that *hich is past and the beginningof that *hich is to come) it follo*s that) as the circle has itsconve6ityand its concavity) in a sense) in the same thing) so time is al*aysat a beginning and at an end. And for this reason it seems to beal*aysdifferent for the no* is not the beginning and the end of the samething if it *ere) it *ould be at the same time and in the samerespectt*o opposites. And time *ill not fail for it is al*ays at abeginning.

Presently or 'ust refers to the part of future time *hich is nearthe indivisible present no* 3 &hen do you *al+7 Presently ) becausethe time in *hich he is going to do so is near4) and to the part ofpast time *hich is not far from the no* 3 &hen do you *al+7 Ihave 'ust been *al+ing 4. But to say that Troy has 'ust been ta+en0*edo not say that) because it is too far from the no* . ately ) too)refers to the part of past time *hich is near the present no* . &hendid you go7 ately ) if the time is near the e6isting no*. ongago refers to the distant past.

Suddenly refers to *hat has departed from its former condition ina time imperceptible because of its smallness but it is the natureof all change to alter things from their former condition. In timeall things come into being and pass a*ay for *hich reason some calledit the *isest of all things) but the Pythagorean Paron called it themost stupid) because in it *e also forget and his *as the truer vie*.It is clear then that it must be in itself) as *e said before) thecondition of destruction rather than of coming into being 3for change)



in itself) ma+es things depart from their former condition4) and onlyincidentally of coming into being) and of being. A sufficient evidenceof this is that nothing comes into being *ithout itself moving someho*and acting) but a thing can be destroyed even if it does not moveat all. And this is *hat) as a rule) *e chiefly mean by a thing sbeing destroyed by time. Still) time does not *or+ even this change

even this sort of change ta+es place incidentally in time.

&e have stated) then) that time e6ists and *hat it is) and in ho*many senses *e spea+ of the no* ) and *hat at some time ) lately )

presently or 'ust ) long ago ) and suddenly mean.

Part %>

These distinctions having been dra*n) it is evident that every changeand everything that moves is in time for the distinction of fasterand slo*er e6ists in reference to all change) since it is found inevery instance. In the phrase moving faster I refer to that *hichchanges before another into the condition in (uestion) *hen it movesover the same interval and *ith a regular movement e.g. in the caseof locomotion) if both things move along the circumference of acircle)or both along a straight line and similarly in all other cases. But*hat is before is in time for *e say before and after *ithreferenceto the distance from the no* ) and the no* is the boundary of thepast and the future so that since no*s are in time) the beforeand the after *ill be in time too for in that in *hich the no*is) the distance from the no* *ill also be. But before is usedcontrari*ise *ith reference to past and to future time for in thepast *e call before *hat is farther from the no* ) and after*hat is nearer) but in the future *e call the nearer before andthe farther after . So that since the before is in time) and everymovement involves a before ) evidently every change and everymovementis in time.

It is also *orth considering ho* time can be related to the souland *hy time is thought to be in everything) both in earth and insea and in heaven. Is because it is an attribute) or state) ormovement3since it is the number of movement4 and all these things are movable3for they are all in place4) and time and movement are together) bothin respect of potentiality and in respect of actuality7

&hether if soul did not e6ist time *ould e6ist or not) is a (uestionthat may fairly be as+ed for if there cannot be some one to countthere cannot be anything that can be counted) so that evidently therecannot be number for number is either *hat has been) or *hat canbe) counted. But if nothing but soul) or in soul reason) is (ualifiedto count) there *ould not be time unless there *ere soul) but onlythat of *hich time is an attribute) i.e. if movement can e6ist *ithoutsoul) and the before and after are attributes of movement) and timeis these (ua numerable.

$ne might also raise the (uestion *hat sort of movement time is thenumber of. 1ust *e not say of any +ind 7 ,or things both come intobeing in time and pass a*ay) and gro*) and are altered in time) andare moved locally thus it is of each movement (ua movement that timeis the number. And so it is simply the number of continuous movement)not of any particular +ind of it.



But other things as *ell may have been moved no*) and there *ouldbe a number of each of the t*o movements. Is there another time) then)and *ill there be t*o e(ual times at once7 Surely not. ,or a timethat is both e(ual and simultaneous is one and the same time) andeven those that are not simultaneous are one in +ind for if there

*ere dogs) and horses) and seven of each) it *ould be the same number.So) too) movements that have simultaneous limits have the same time)yet the one may in fact be fast and the other not) and one may belocomotion and the other alteration still the time of the t*o changesis the same if their number also is e(ual and simultaneous and forthis reason) *hile the movements are different and separate) the timeis every*here the same) because the number of e(ual and simultaneousmovements is every*here one and the same.

-o* there is such a thing as locomotion) and in locomotion there isincluded circular movement) and everything is measured by some onething homogeneous *ith it) units by a unit) horses by a horse) andsimilarly times by some definite time) and) as *e said) time ismeasuredby motion as *ell as motion by time 3this being so because by a motiondefinite in time the (uantity both of the motion and of the time ismeasured4: if) then) *hat is first is the measure of everythinghomogeneous*ith it) regular circular motion is above all else the measure)becausethe number of this is the best +no*n. -o* neither alteration norincreasenor coming into being can be regular) but locomotion can be. Thisalso is *hy time is thought to be the movement of the sphere) vi8.because the other movements are measured by this) and time by thismovement.

This also e6plains the common saying that human affairs form a circle)and that there is a circle in all other things that have a naturalmovement and coming into being and passing a*ay. This is because allother things are discriminated by time) and end and begin as thoughconforming to a cycle for even time itself is thought to be a circle.And this opinion again is held because time is the measure of this+ind of locomotion and is itself measured by such. So that to saythat the things that come into being form a circle is to say thatthere is a circle of time and this is to say that it is measuredby the circular movement for apart from the measure nothing elseto be measured is observed the *hole is 'ust a plurality of measures.

It is said rightly) too) that the number of the sheep and of the dogsis the same number if the t*o numbers are e(ual) but not the samedecad or the same ten 'ust as the e(uilateral and the scalene arenot the same triangle) yet they are the same figure) because theyare both triangles. ,or things are called the same so0and0so if theydo not differ by a differentia of that thing) but not if they doe.g. triangle differs from triangle by a differentia of triangle)therefore they are different triangles but they do not differ bya differentia of figure) but are in one and the same division of it.,or a figure of the one +ind is a circle and a figure of another +indof triangle) and a triangle of one +ind is e(uilateral and a triangleof another +ind scalene. They are the same figure) then) that)triangle)but not the same triangle. Therefore the number of t*o groups also0isthe same number 3for their number does not differ by a differentiaof number4) but it is not the same decad for the things of *hich



it is asserted differ one group are dogs) and the other horses.

&e have no* discussed time0both time itself and the mattersappropriateto the consideration of it.

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Part %

9verything *hich changes does so in one of three senses. It may change3%4 accidentally) as for instance *hen *e say that something musical*al+s) that *hich *al+s being something in *hich aptitude for musicis an accident. Again 324 a thing is said *ithout (ualification tochange because something belonging to it changes) i.e. in statements*hich refer to part of the thing in (uestion: thus the body isrestoredto health because the eye or the chest) that is to say a part of the*hole body) is restored to health. And above all there is 3;4 thecase of a thing *hich is in motion neither accidentally nor in respectof something else belonging to it) but in virtue of being itselfdirectlyin motion. !ere *e have a thing *hich is essentially movable: andthat *hich is so is a different thing according to the particularvariety of motion: for instance it may be a thing capable ofalteration:and *ithin the sphere of alteration it is again a different thingaccording as it is capable of being restored to health or capableof being heated. And there are the same distinctions in the case ofthe mover: 3%4 one thing causes motion accidentally) 324 anotherpartially3because something belonging to it causes motion4) 3;4 another ofitself directly) as) for instance) the physician heals) the handstri+es.&e have) then) the follo*ing factors: 3a4 on the one hand that *hichdirectly causes motion) and 3b4 on the other hand that *hich is inmotion: further) *e have 3c4 that in *hich motion ta+es place) namelytime) and 3distinct from these three) d4 that from *hich and 3e4that to *hich it proceeds: for every motion proceeds from somethingand to something) that *hich is directly in motion being distinctfrom that to *hich it is in motion and that from *hich it is inmotion:for instance) *e may ta+e the three things *ood ) hot ) and cold )of *hich the first is that *hich is in motion) the second is thatto *hich the motion proceeds) and the third is that from *hich itproceeds. This being so) it is clear that the motion is in the *ood)not in its form: for the motion is neither caused nor e6periencedby the form or the place or the (uantity. So *e are left *ith a mover)a moved) and a goal of motion. I do not include the starting0pointof motion: for it is the goal rather than the starting0point of motionthat gives its name to a particular process of change. Thus

perishingis change to not0being) though it is also true that that that *hichperishes changes from being: and becoming is change to being) thoughit is also change from not0being.

-o* a definition of motion has been given above) from *hich it *illbe seen that every goal of motion) *hether it be a form) an affection)or a place) is immovable) as) for instance) +no*ledge and heat. !ere)



ho*ever) a difficulty may be raised. Affections) it may be said) aremotions) and *hiteness is an affection: thus there may be change toa motion. To this *e may reply that it is not *hiteness but *hiteningthat is a motion. !ere also the same distinctions are to be observed:a goal of motion may be so accidentally) or partially and *ithreference

to something other than itself) or directly and *ith no referenceto anything else: for instance) a thing *hich is becoming *hitechangesaccidentally to an ob'ect of thought) the colour being onlyaccidentallythe ob'ect of thought it changes to colour) because *hite is a partof colour) or to 9urope) because Athens is a part of 9urope but itchanges essentially to *hite colour. It is no* clear in *hat sensea thing is in motion essentially) accidentally) or in respect ofsomethingother than itself) and in *hat sense the phrase itself directlyis used in the case both of the mover and of the moved: and it isalso clear that the motion is not in the form but in that *hich isin motion) that is to say the movable in activity . -o* accidentalchange *e may leave out of account: for it is to be found ineverything)at any time) and in any respect. Change *hich is not accidental onthe other hand is not to be found in everything) but only incontraries)in things intermediate contraries) and in contradictories) as maybe proved by induction. An intermediate may be a starting0point ofchange) since for the purposes of the change it serves as contraryto either of t*o contraries: for the intermediate is in a sense thee6tremes. !ence *e spea+ of the intermediate as in a sense a contraryrelatively to the e6tremes and of either e6treme as a contraryrelativelyto the intermediate: for instance) the central note is lo* relatively0tothe highest and high relatively to the lo*est) and grey is lightrelativelyto blac+ and dar+ relatively to *hite.

And since every change is from something to something0as the *orditself 3metabole4 indicates) implying something after 3meta4somethingelse) that is to say something earlier and something later0that *hichchanges must change in one of four *ays: from sub'ect to sub'ect)from sub'ect to nonsub'ect) from non0sub'ect to sub'ect) or from non0sub'ectto non0sub'ect) *here by sub'ect I mean *hat is affirmativelye6pressed.So it follo*s necessarily from *hat has been said above that thereare only three +inds of change) that from sub'ect to sub'ect) thatfrom sub'ect to non0sub'ect) and that from non0sub'ect to sub'ect:for the fourth conceivable +ind) that from non0sub'ect to nonsub'ect)is not change) as in that case there is no opposition either ofcontrariesor of contradictories.

-o* change from non0sub'ect to sub'ect) the relation being that ofcontradiction) is coming to be 0 un(ualified coming to be *hen thechange ta+es place in an un(ualified *ay) particular coming to be*hen the change is change in a particular character: for instance)a change from not0*hite to *hite is a coming to be of the particularthing) *hite) *hile change from un(ualified not0being to being is



coming to be in an un(ualified *ay) in respect of *hich *e say thata thing comes to be *ithout (ualification) not that it comes tobe some particular thing. Change from sub'ect to non0sub'ect is

perishing 0 un(ualifiedperishing *hen the change is from being to not0being) particularperishing *hen the change is to the opposite negation) the

distinctionbeing the same as that made in the case of coming to be.

-o* the e6pression not0being is used in several senses: and therecan be motion neither of that *hich is not in respect of theaffirmationor negation of a predicate) nor of that *hich is not in the sensethat it only potentially is ) that is to say the opposite of that*hich actually is in an un(ualified sense: for although that *hichis not0*hite or not0good may nevertheless he in motionaccidentally3for e6ample that *hich is not0*hite might be a man4) yet that *hichis *ithout (ualification not0so0and0so cannot in any sense be inmotion: therefore it is impossible for that *hich is not to be inmotion. This being so) it follo*s that becoming cannot be a motion:for it is that *hich is not that becomes . ,or ho*ever true itmay be that it accidentally becomes ) it is nevertheless correctto say that it is that *hich is not that in an un(ualified sense

becomes . And similarly it is impossible for that *hich is notto be at rest.

There are these difficulties) then) in the *ay of the assumption thatthat *hich is not can be in motion: and it may be further ob'ectedthat) *hereas everything *hich is in motion is in space) that *hich

is not is not in space: for then it *ould be some*here.

So) too) perishing is not a motion: for a motion has for itscontraryeither another motion or rest) *hereas perishing is the contraryof becoming .

Since) then) every motion is a +ind of change) and there are onlythe three +inds of change mentioned above) and since of these threethose *hich ta+e the form of becoming and perishing ) that is tosay those *hich imply a relation of contradiction) are not motions:it necessarily follo*s that only change from sub'ect to sub'ect ismotion. And every such sub'ect is either a contrary or an intermediate3for a privation may be allo*ed to ran+ as a contrary4 and can beaffirmatively e6pressed) as na+ed) toothless) or blac+. If) then)the categories are severally distinguished as Being) Ouality) Place)Time) elation) Ouantity) and Activity or Passivity) it necessarilyfollo*s that there are three +inds of motion0(ualitative)(uantitative)and local.

Part 2

In respect of Substance there is no motion) because Substance hasno contrary among things that are. -or is there motion in respectof elation: for it may happen that *hen one correlative changes)the other) although this does not itself change) is no longerapplicable)so that in these cases the motion is accidental. -or is there motionin respect of Agent and Patient0in fact there can never be motion



of mover and moved) because there cannot be motion of motion orbecomingof becoming or in general change of change.

,or in the first place there are t*o senses in *hich motion of motionis conceivable. 3%4 The motion of *hich there is motion might be

conceivedas sub'ect e.g. a man is in motion because he changes from fair todar+. Can it be that in this sense motion gro*s hot or cold) orchangesplace) or increases or decreases7 Impossible: for change is not asub'ect. $r 324 can there be motion of motion in the sense that someother sub'ect changes from a change to another mode of being) as e.g.a man changes from falling ill to getting *ell7 9ven this is possibleonly in an accidental sense. ,or) *hatever the sub'ect may be)movementis change from one form to another. 3And the same holds good ofbecomingand perishing) e6cept that in these processes *e have a change toa particular +ind of opposite) *hile the other) motion) is a changeto a different +ind.4 So) if there is to be motion of motion) that*hich is changing from health to sic+ness must simultaneously bechangingfrom this very change to another. It is clear) then) that by the timethat it has become sic+) it must also have changed to *hatever maybe the other change concerned 3for that it should be at rest) thoughlogically possible) is e6cluded by the theory4. 1oreover this othercan never be any casual change) but must be a change from somethingdefinite to some other definite thing. So in this case it must bethe opposite change) vi8. convalescence. It is only accidentally thatthere can be change of change) e.g. there is a change from rememberingto forgetting only because the sub'ect of this change changes at onetime to +no*ledge) at another to ignorance.

In the second place) if there is to be change of change and becomingof becoming) *e shall have an infinite regress. Thus if one of aseriesof changes is to be a change of change) the preceding change mustalso be so: e.g. if simple becoming *as ever in process of becoming)then that *hich *as becoming simple becoming *as also in process ofbecoming) so that *e should not yet have arrived at *hat *as inprocessof simple becoming but only at *hat *as already in process of becomingin process of becoming. And this again *as sometime in process ofbecoming) so that even then *e should not have arrived at *hat *asin process of simple becoming. And since in an infinite series thereis no first term) here there *ill be no first stage and thereforeno follo*ing stage either. $n this hypothesis) then) nothing canbecomeor be moved or change.

Thirdly) if a thing is capable of any particular motion) it is alsocapable of the corresponding contrary motion or the correspondingcoming to rest) and a thing that is capable of becoming is alsocapableof perishing: conse(uently) if there be becoming of becoming) that*hich is in process of becoming is in process of perishing at thevery moment *hen it has reached the stage of becoming: since it cannotbe in process of perishing *hen it is 'ust beginning to become orafter it has ceased to become: for that *hich is in process ofperishing



and a thing s possessing a (uality in a greater or in a lesser degreemeans the presence or absence in it of more or less of the opposite(uality. It is no* clear) then) that there are only these three +indsof motion.

The term immovable *e apply in the first place to that *hich is

absolutely incapable of being moved 3'ust as *e correspondingly applythe term invisible to sound4 in the second place to that *hich ismoved *ith difficulty after a long time or *hose movement is slo*at the start0in fact) *hat *e describe as hard to move and in thethird place to that *hich is naturally designed for and capable ofmotion) but is not in motion *hen) *here) and as it naturally *ouldbe so. This last is the only +ind of immovable thing of *hich I usethe term being at rest : for rest is contrary to motion) so thatrest *ill be negation of motion in that *hich is capable of admittingmotion.

The foregoing remar+s are sufficient to e6plain the essential natureof motion and rest) the number of +inds of change) and the differentvarieties of motion.

Part ;

et us no* proceed to define the terms together and apart ) incontact ) bet*een ) in succession ) contiguous ) and continuous )and to sho* in *hat circumstances each of these terms is naturallyapplicable.

Things are said to be together in place *hen they are in one place3in the strictest sense of the *ord place 4 and to be apart *henthey are in different places.

Things are said to be in contact *hen their e6tremities are together.

That *hich a changing thing) if it changes continuously in a naturalmanner) naturally reaches before it reaches that to *hich it changeslast) is bet*een. Thus bet*een implies the presence of at leastthree things: for in a process of change it is the contrary that is

last : and a thing is moved continuously if it leaves no gap or onlythe smallest possible gap in the material0not in the time 3for a gapin the time does not prevent things having a bet*een ) *hile) onthe other hand) there is nothing to prevent the highest note soundingimmediately after the lo*est4 but in the material in *hich the motionta+es place. This is manifestly true not only in local changes butin every other +ind as *ell. 3-o* every change implies a pair ofopposites)and opposites may be either contraries or contradictories since thencontradiction admits of no mean term) it is obvious that bet*eenmust imply a pair of contraries4 That is locally contrary *hich ismost distant in a straight line: for the shortest line is definitelylimited) and that *hich is definitely limited constitutes a measure.

A thing is in succession *hen it is after the beginning in positionor in form or in some other respect in *hich it is definitely soregarded)and *hen further there is nothing of the same +ind as itself bet*eenit and that to *hich it is in succession) e.g. a line or lines ifit is a line) a unit or units if it is a unit) a house if it is ahouse 3there is nothing to prevent something of a different +ind beingbet*een4. ,or that *hich is in succession is in succession to aparticular



thing) and is something posterior: for one is not in successionto t*o) nor is the first day of the month to be second: in each casethe latter is in succession to the former.

A thing that is in succession and touches is contiguous . Thecontinuous

is a subdivision of the contiguous: things are called continuous *henthe touching limits of each become one and the same and are) as the*ord implies) contained in each other: continuity is impossible ifthese e6tremities are t*o. This definition ma+es it plain thatcontinuitybelongs to things that naturally in virtue of their mutual contactform a unity. And in *hatever *ay that *hich holds them together isone) so too *ill the *hole be one) e.g. by a rivet or glue or contactor organic union.

It is obvious that of these terms in succession is first in orderof analysis: for that *hich touches is necessarily in succession)but not everything that is in succession touches: and so successionis a property of things prior in definition) e.g. numbers) *hilecontactis not. And if there is continuity there is necessarily contact) butif there is contact) that alone does not imply continuity: for thee6tremities of things may be together *ithout necessarily beingone: but they cannot be one *ithout being necessarily together. Sonatural 'unction is last in coming to be: for the e6tremities mustnecessarily come into contact if they are to be naturally 'oined:but things that are in contact are not all naturally 'oined) *hilethere is no contact clearly there is no natural 'unction either.!ence)if as some say point and unit have an independent e6istence oftheir o*n) it is impossible for the t*o to be identical: for pointscan touch *hile units can only be in succession. 1oreover) there canal*ays be something bet*een points 3for all lines are intermediatebet*een points4) *hereas it is not necessary that there shouldpossiblybe anything bet*een units: for there can be nothing bet*een thenumbersone and t*o.

&e have no* defined *hat is meant by together and apart )contact )bet*een and in succession ) contiguous and continuous : and

*e have sho*n in *hat circumstances each of these terms is applicable.

Part >

There are many senses in *hich motion is said to be one : for *euse the term one in many senses.

1otion is one generically according to the different categories to*hich it may be assigned: thus any locomotion is one generically *ithany other locomotion) *hereas alteration is different genericallyfrom locomotion.

1otion is one specifically *hen besides being one generically it alsota+es place in a species incapable of subdivision: e.g. colour hasspecific differences: therefore blac+ening and *hitening differspecificallybut at all events every *hitening *ill be specifically the same *ith



every other *hitening and every blac+ening *ith every otherblac+ening.But *hite is not further subdivided by specific differences: henceany *hitening is specifically one *ith any other *hitening. &hereit happens that the genus is at the same time a species) it is clearthat the motion *ill then in a sense be one specifically though not

in an un(ualified sense: learning is an e6ample of this) +no*ledgebeing on the one hand a species of apprehension and on the other handa genus including the various +no*ledges. A difficulty) ho*ever) maybe raised as to *hether a motion is specifically one *hen the samething changes from the same to the same) e.g. *hen one point changesagain and again from a particular place to a particular place: ifthis motion is specifically one) circular motion *ill be the sameas rectilinear motion) and rolling the same as *al+ing. But is notthis difficulty removed by the principle already laid do*n that ifthat in *hich the motion ta+es place is specifically different 3asin the present instance the circular path is specifically differentfrom the straight4 the motion itself is also different7 &e havee6plained)then) *hat is meant by saying that motion is one generically or onespecifically.

1otion is one in an un(ualified sense *hen it is one essentially ornumerically: and the follo*ing distinctions *ill ma+e clear *hat this+ind of motion is. There are three classes of things in conne6ion*ith *hich *e spea+ of motion) the that *hich ) the that in *hich )and the that during *hich . I mean that there must he something thatis in motion) e.g. a man or gold) and it must be in motion insomething)e.g. a place or an affection) and during something) for all motionta+es place during a time. $f these three it is the thing in *hichthe motion ta+es place that ma+es it one generically or specifically)it is the thing moved that ma+es the motion one in sub'ect) and itis the time that ma+es it consecutive: but it is the three togetherthat ma+e it one *ithout (ualification: to effect this) that in *hichthe motion ta+es place 3the species4 must be one and incapable ofsubdivision) that during *hich it ta+es place 3the time4 must be oneand unintermittent) and that *hich is in motion must be one0not inan accidental sense 3i.e. it must be one as the *hite that blac+ensis one or Coriscus *ho *al+s is one) not in the accidental sense in*hich Coriscus and *hite may be one4) nor merely in virtue ofcommunityof nature 3for there might be a case of t*o men being restored tohealth at the same time in the same *ay) e.g. from inflammation ofthe eye) yet this motion is not really one) but only specificallyone4.

Suppose) ho*ever) that Socrates undergoes an alteration specificallythe same but at one time and again at another: in this case if itis possible for that *hich ceased to be again to come into being andremain numerically the same) then this motion too *ill be one:other*iseit *ill be the same but not one. And a+in to this difficulty thereis another vi8. is health one7 and generally are the states andaffectionsin bodies severally one in essence although 3as is clear4 the thingsthat contain them are obviously in motion and in flu67 Thus if aperson shealth at daybrea+ and at the present moment is one and the same)*hy should not this health be numerically one *ith that *hich herecovers



after an interval7 The same argument applies in each case. There is)ho*ever) *e may ans*er) this difference: that if the states are t*othen it follo*s simply from this fact that the activities must alsoin point of number be t*o 3for only that *hich is numerically onecan give rise to an activity that is numerically one4) but if thestate is one) this is not in itself enough to ma+e us regard the

activityalso as one: for *hen a man ceases *al+ing) the *al+ing no longeris) but it *ill again be if he begins to *al+ again. But) be thisas it may) if in the above instance the health is one and the same)then it must be possible for that *hich is one and the same to cometo be and to cease to be many times. !o*ever) these difficulties lieoutside our present in(uiry.

Since every motion is continuous) a motion that is one in anun(ualifiedsense must 3since every motion is divisible4 be continuous) and acontinuous motion must be one. There *ill not be continuity bet*eenany motion and any other indiscriminately any more than there isbet*eenany t*o things chosen at random in any other sphere: there can becontinuity only *hen the e6tremities of the t*o things are one. -o*some things have no e6tremities at all: and the e6tremities of othersdiffer specifically although *e give them the same name of end :ho* should e.g. the end of a line and the end of *al+ing touchor come to be one7 1otions that are not the same either specificallyor generically may) it is true) be consecutive 3e.g. a man may runand then at once fall ill of a fever4) and again) in the torch0race*e have consecutive but not continuous locomotion: for according toour definition there can be continuity only *hen the ends of the t*othings are one. !ence motions may be consecutive or successive invirtue of the time being continuous) but there can be continuity onlyin virtue of the motions themselves being continuous) that is *henthe end of each is one *ith the end of the other. 1otion) therefore)that is in an un(ualified sense continuous and one must bespecificallythe same) of one thing) and in one time. @nity is re(uired in respectof time in order that there may be no interval of immobility) for*here there is intermission of motion there must be rest) and a motionthat includes intervals of rest *ill be not one but many) so thata motion that is interrupted by stationariness is not one orcontinuous)and it is so interrupted if there is an interval of time. And thoughof a motion that is not specifically one 3even if the time isunintermittent4the time is one) the motion is specifically different) and so cannotreally be one) for motion that is one must be specifically one) thoughmotion that is specifically one is not necessarily one in anun(ualifiedsense. &e have no* e6plained *hat *e mean *hen *e call a motion one*ithout (ualification.

,urther) a motion is also said to be one generically) specifically)or essentially *hen it is complete) 'ust as in other casescompletenessand *holeness are characteristics of *hat is one: and sometimes amotion even if incomplete is said to be one) provided only that itis continuous.

And besides the cases already mentioned there is another in *hicha motion is said to be one) vi8. *hen it is regular: for in a sense



a motion that is irregular is not regarded as one) that titlebelongingrather to that *hich is regular) as a straight line is regular) theirregular being as such divisible. But the difference *ould seem tobe one of degree. In every +ind of motion *e may have regularity orirregularity: thus there may be regular alteration) and locomotion

in a regular path) e.g. in a circle or on a straight line) and itis the same *ith regard to increase and decrease. The difference thatma+es a motion irregular is sometimes to be found in its path: thusa motion cannot be regular if its path is an irregular magnitude)e.g. a bro+en line) a spiral) or any other magnitude that is not suchthat any part of it ta+en at random fits on to any other that maybe chosen. Sometimes it is found neither in the place nor in the timenor in the goal but in the manner of the motion: for in some casesthe motion is differentiated by (uic+ness and slo*ness: thus if itsvelocity is uniform a motion is regular) if not it is irregular. So(uic+ness and slo*ness are not species of motion nor do theyconstitutespecific differences of motion) because this distinction occurs inconne6ion *ith all the distinct species of motion. The same is trueof heaviness and lightness *hen they refer to the same thing: e.g.they do not specifically distinguish earth from itself or fire fromitself. Irregular motion) therefore) *hile in virtue of beingcontinuousit is one) is so in a lesser degree) as is the case *ith locomotionin a bro+en line: and a lesser degree of something al*ays means anadmi6ture of its contrary. And since every motion that is one canbe both regular and irregular) motions that are consecutive but notspecifically the same cannot be one and continuous: for ho* shoulda motion composed of alteration and locomotion be regular7 If a motionis to be regular its parts ought to fit one another.

Part ?

&e have further to determine *hat motions are contrary to each other)and to determine similarly ho* it is *ith rest. And *e have firstto decide *hether contrary motions are motions respectively from andto the same thing) e.g. a motion from health and a motion to health3*here the opposition) it *ould seem) is of the same +ind as thatbet*een coming to be and ceasing to be4 or motions respectively fromcontraries) e.g. a motion from health and a motion from disease ormotions respectively to contraries) e.g. a motion to health and amotion to disease or motions respectively from a contrary and tothe opposite contrary) e.g. a motion from health and a motion todiseaseor motions respectively from a contrary to the opposite contrary andfrom the latter to the former) e.g. a motion from health to diseaseand a motion from disease to health: for motions must be contraryto one another in one or more of these *ays) as there is no other*ay in *hich they can be opposed.

-o* motions respectively from a contrary and to the opposite contrary)e.g. a motion from health and a motion to disease) are not contrarymotions: for they are one and the same. 3 et their essence is notthe same) 'ust as changing from health is different from changingto disease.4 -or are motion respectively from a contrary and fromthe opposite contrary contrary motions) for a motion from a contraryis at the same time a motion to a contrary or to an intermediate 3ofthis) ho*ever) *e shall spea+ later4) but changing to a contraryrather



than changing from a contrary *ould seem to be the cause of thecontrarietyof motions) the latter being the loss) the former the gain) ofcontrariness.1oreover) each several motion ta+es its name rather from the goalthan from the starting0point of change) e.g. motion to health *e call

convalescence) motion to disease sic+ening. Thus *e are left *ithmotions respectively to contraries) and motions respectively tocontrariesfrom the opposite contraries. -o* it *ould seem that motions tocontrariesare at the same time motions from contraries 3though their essencemay not be the same to health is distinct) I mean) from fromdisease )and from health from to disease 4.

Since then change differs from motion 3motion being change from aparticular sub'ect to a particular sub'ect4) it follo*s that contrarymotions are motions respectively from a contrary to the oppositecontraryand from the latter to the former) e.g. a motion from health todiseaseand a motion from disease to health. 1oreover) the consideration ofparticular e6amples *ill also sho* *hat +inds of processes aregenerallyrecogni8ed as contrary: thus falling ill is regarded as contrary torecovering one s health) these processes having contrary goals) andbeing taught as contrary to being led into error by another) it beingpossible to ac(uire error) li+e +no*ledge) either by one s o*n agencyor by that of another. Similarly *e have up*ard locomotion anddo*n*ardlocomotion) *hich are contrary length*ise) locomotion to the rightand locomotion to the left) *hich are contrary breadth*ise) andfor*ardlocomotion and bac+*ard locomotion) *hich too are contraries. $n theother hand) a process simply to a contrary) e.g. that denoted by thee6pression becoming *hite ) *here no starting0point is specified)is a change but not a motion. And in all cases of a thing that hasno contrary *e have as contraries change from and change to the samething. Thus coming to be is contrary to ceasing to be) and losingto gaining. But these are changes and not motions. And *herever apair of contraries admit of an intermediate) motions to thatintermediatemust be held to be in a sense motions to one or other of thecontraries:for the intermediate serves as a contrary for the purposes of themotion) in *hichever direction the change may be) e.g. grey in amotionfrom grey to *hite ta+es the place of blac+ as starting0point) ina motion from *hite to grey it ta+es the place of blac+ as goal) andin a motion from blac+ to grey it ta+es the place of *hite as goal:for the middle is opposed in a sense to either of the e6tremes) ashas been said above. Thus *e see that t*o motions are contrary toeach other only *hen one is a motion from a contrary to the oppositecontrary and the other is a motion from the latter to the former.

Part

But since a motion appears to have contrary to it not only anothermotion but also a state of rest) *e must determine ho* this is so.A motion has for its contrary in the strict sense of the term another



motion) but it also has for an opposite a state of rest 3for restis the privation of motion and the privation of anything may be calledits contrary4) and motion of one +ind has for its opposite rest ofthat +ind) e.g. local motion has local rest. This statement) ho*ever)needs further (ualification: there remains the (uestion) is theopposite

of remaining at a particular place motion from or motion to thatplace7It is surely clear that since there are t*o sub'ects bet*een *hichmotion ta+es place) motion from one of these 3A4 to its contrary 3B4has for its opposite remaining in A *hile the reverse motion has forits opposite remaining in B. At the same time these t*o are alsocontraryto each other: for it *ould be absurd to suppose that there arecontrarymotions and not opposite states of rest. States of rest in contrariesare opposed. To ta+e an e6ample) a state of rest in health is 3%4contrary to a state of rest in disease) and 324 the motion to *hichit is contrary is that from health to disease. ,or 324 it *ould beabsurd that its contrary motion should be that from disease to health)since motion to that in *hich a thing is at rest is rather a comingto rest) the coming to rest being found to come into beingsimultaneously*ith the motion and one of these t*o motions it must be. And 3%4rest in *hiteness is of course not contrary to rest in health.

$f all things that have no contraries there are opposite changes 3vi8.change from the thing and change to the thing) e.g. change from beingand change to being4) but no motion. So) too) of such things thereis no remaining though there is absence of change. Should there bea particular sub'ect) absence of change in its being *ill be contraryto absence of change in its not0being. And here a difficulty may beraised: if not0being is not a particular something) *hat is it) itmay be as+ed) that is contrary to absence of change in a thing sbeing7and is this absence of change a state of rest7 If it is) then eitherit is not true that every state of rest is contrary to a motion orelse coming to be and ceasing to be are motion. It is clear then that)since *e e6clude these from among motions) *e must not say that thisabsence of change is a state of rest: *e must say that it is similarto a state of rest and call it absence of change. And it *ill havefor its contrary either nothing or absence of change in the thing snot0being) or the ceasing to be of the thing: for such ceasing tobe is change from it and the thing s coming to be is change to it.

Again) a further difficulty may be raised. !o* is it) it may be as+ed)that *hereas in local change both remaining and moving may be naturalor unnatural) in the other changes this is not so7 e.g. alterationis not no* natural and no* unnatural) for convalescence is no morenatural or unnatural than falling ill) *hitening no more natural orunnatural than blac+ening so) too) *ith increase and decrease: theseare not contrary to each other in the sense that either of them isnatural *hile the other is unnatural) nor is one increase contraryto another in this sense and the same account may be given ofbecomingand perishing: it is not true that becoming is natural and perishingunnatural 3for gro*ing old is natural4) nor do *e observe one becomingto be natural and another unnatural. &e ans*er that if *hat happensunder violence is unnatural) then violent perishing is unnatural andas such contrary to natural perishing. Are there then also somebecomings



that are violent and not the result of natural necessity) and aretherefore contrary to natural becomings) and violent increases anddecreases) e.g. the rapid gro*th to maturity of profligates and therapid ripening of seeds even *hen not pac+ed close in the earth7 Andho* is it *ith alterations7 Surely 'ust the same: *e may say thatsome alterations are violent *hile others are natural) e.g. patients

alter naturally or unnaturally according as they thro* off feverson the critical days or not. But) it may be ob'ected) then *e shallhave perishings contrary to one another) not to becoming. Certainly:and *hy should not this in a sense be so7 Thus it is so if oneperishingis pleasant and another painful: and so one perishing *ill be contraryto another not in an un(ualified sense) but in so far as one has this(uality and the other that.

-o* motions and states of rest universally e6hibit contrariety inthe manner described above) e.g. up*ard motion and rest above arerespectively contrary to do*n*ard motion and rest belo*) these beinginstances of local contrariety and up*ard locomotion belongsnaturallyto fire and do*n*ard to earth) i.e. the locomotions of the t*o arecontrary to each other. And again) fire moves up naturally and do*nunnaturally: and its natural motion is certainly contrary to itsunnaturalmotion. Similarly *ith remaining: remaining above is contrary tomotionfrom above do*n*ards) and to earth this remaining comes unnaturally)this motion naturally. So the unnatural remaining of a thing iscontraryto its natural motion) 'ust as *e find a similar contrariety in themotion of the same thing: one of its motions) the up*ard or thedo*n*ard)*ill be natural) the other unnatural.

!ere) ho*ever) the (uestion arises) has every state of rest that isnot permanent a becoming) and is this becoming a coming to astandstill7If so) there must be a becoming of that *hich is at rest unnaturally)e.g. of earth at rest above: and therefore this earth during the timethat it *as being carried violently up*ard *as coming to a standstill.But *hereas the velocity of that *hich comes to a standstill seemsal*ays to increase) the velocity of that *hich is carried violentlyseems al*ays to decrease: so it *ill he in a state of rest *ithouthaving become so. 1oreover coming to a standstill is generallyrecogni8edto be identical or at least concomitant *ith the locomotion of a thingto its proper place.

There is also another difficulty involved in the vie* that remainingin a particular place is contrary to motion from that place. ,or *hena thing is moving from or discarding something) it still appears tohave that *hich is being discarded) so that if a state of rest isitself contrary to the motion from the state of rest to its contrary)the contraries rest and motion *ill be simultaneously predicable ofthe same thing. 1ay *e not say) ho*ever) that in so far as the thingis still stationary it is in a state of rest in a (ualified sense7,or) in fact) *henever a thing is in motion) part of it is at thestarting0point *hile part is at the goal to *hich it is changing:and conse(uently a motion finds its true contrary rather in anothermotion than in a state of rest.



&ith regard to motion and rest) then) *e have no* e6plained in *hatsense each of them is one and under *hat conditions they e6hibitcontrariety.

<&ith regard to coming to a standstill the (uestion may be raised*hether there is an opposite state of rest to unnatural as *ell as

to natural motions. It *ould be absurd if this *ere not the case:for a thing may remain still merely under violence: thus *e shallhave a thing being in a non0permanent state of rest *ithout havingbecome so. But it is clear that it must be the case: for 'ust as thereis unnatural motion) so) too) a thing may be in an unnatural stateof rest. ,urther) some things have a natural and an unnatural motion)e.g. fire has a natural up*ard motion and an unnatural do*n*ardmotion:is it) then) this unnatural do*n*ard motion or is it the naturaldo*n*ardmotion of earth that is contrary to the natural up*ard motion7 Surelyit is clear that both are contrary to it though not in the same sense:the natural motion of earth is contrary inasmuch as the motion offire is also natural) *hereas the up*ard motion of fire as beingnaturalis contrary to the do*n*ard motion of fire as being unnatural. Thesame is true of the corresponding cases of remaining. But there *ouldseem to be a sense in *hich a state of rest and a motion areopposites.=

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B$$" I

Part %

-o* if the terms continuous ) in contact ) and in successionare understood as defined above things being continuous if theire6tremities are one) in contact if their e6tremities are together)and in succession if there is nothing of their o*n +ind intermediatebet*een them0nothing that is continuous can be composed ofindivisibles :e.g. a line cannot be composed of points) the line being continuousand the point indivisible. ,or the e6tremities of t*o points canneitherbe one 3since of an indivisible there can be no e6tremity as distinctfrom some other part4 nor together 3since that *hich has no partscan have no e6tremity) the e6tremity and the thing of *hich it isthe e6tremity being distinct4.

1oreover) if that *hich is continuous is composed of points) thesepoints must be either continuous or in contact *ith one another: andthe same reasoning applies in the case of all indivisibles. -o* forthe reason given above they cannot be continuous: and one thing canbe in contact *ith another only if *hole is in contact *ith *holeor part *ith part or part *ith *hole. But since indivisibles haveno parts) they must be in contact *ith one another as *hole *ith*hole.And if they are in contact *ith one another as *hole *ith *hole) they*ill not be continuous: for that *hich is continuous has distinctparts: and these parts into *hich it is divisible are different inthis *ay) i.e. spatially separate.

-or) again) can a point be in succession to a point or a moment toa moment in such a *ay that length can be composed of points or time



of moments: for things are in succession if there is nothing of theiro*n +ind intermediate bet*een them) *hereas that *hich is intermediatebet*een points is al*ays a line and that *hich is intermediate bet*eenmoments is al*ays a period of time.

Again) if length and time could thus be composed of indivisibles)

they could be divided into indivisibles) since each is divisible intothe parts of *hich it is composed. But) as *e sa*) no continuous thingis divisible into things *ithout parts. -or can there be anythingof any other +ind intermediate bet*een the parts or bet*een themoments:for if there could be any such thing it is clear that it must beeitherindivisible or divisible) and if it is divisible) it must be divisibleeither into indivisibles or into divisibles that are infinitelydivisible)in *hich case it is continuous.

1oreover) it is plain that everything continuous is divisible intodivisibles that are infinitely divisible: for if it *ere divisibleinto indivisibles) *e should have an indivisible in contact *ith anindivisible) since the e6tremities of things that are continuous *ithone another are one and are in contact.

The same reasoning applies e(ually to magnitude) to time) and tomotion:either all of these are composed of indivisibles and are divisibleinto indivisibles) or none. This may be made clear as follo*s. Ifa magnitude is composed of indivisibles) the motion over thatmagnitudemust be composed of corresponding indivisible motions: e.g. if themagnitude AB# is composed of the indivisibles A) B) #) eachcorrespondingpart of the motion 59J of $ over AB# is indivisible. Therefore) since*here there is motion there must be something that is in motion) and*here there is something in motion there must be motion) thereforethe being0moved *ill also be composed of indivisibles. So $ traversedA *hen its motion *as 5) B *hen its motion *as 9) and # similarly*hen its motion *as J. -o* a thing that is in motion from one placeto another cannot at the moment *hen it *as in motion both be inmotionand at the same time have completed its motion at the place to *hichit *as in motion: e.g. if a man is *al+ing to Thebes) he cannot be*al+ing to Thebes and at the same time have completed his *al+ toThebes: and) as *e sa*) $ traverses a the partless section A in virtueof the presence of the motion 5. Conse(uently) if $ actually passedthrough A after being in process of passing through) the motion mustbe divisible: for at the time *hen $ *as passing through) it neither*as at rest nor had completed its passage but *as in an intermediatestate: *hile if it is passing through and has completed its passageat the same moment) then that *hich is *al+ing *ill at the moment*hen it is *al+ing have completed its *al+ and *ill be in the placeto *hich it is *al+ing that is to say) it *ill have completed itsmotion at the place to *hich it is in motion. And if a thing is inmotion over the *hole "bg and its motion is the three 5) 9) and J)and if it is not in motion at all over the partless section A buthas completed its motion over it) then the motion *ill consist notof motions but of starts) and *ill ta+e place by a thing s havingcompleted a motion *ithout being in motion: for on this assumptionit has completed its passage through A *ithout passing through it.So it *ill be possible for a thing to have completed a *al+ *ithout



ever *al+ing: for on this assumption it has completed a *al+ overa particular distance *ithout *al+ing over that distance. Since) then)everything must be either at rest or in motion) and $ is thereforeat rest in each of the sections A) B) and #) it follo*s that a thingcan be continuously at rest and at the same time in motion: for) as*e sa*) $ is in motion over the *hole AB# and at rest in any part

3and conse(uently in the *hole4 of it. 1oreover) if the indivisiblescomposing 59J are motions) it *ould be possible for a thing in spiteof the presence in it of motion to be not in motion but at rest) *hileif they are not motions) it *ould be possible for motion to becomposedof something other than motions.

And if length and motion are thus indivisible) it is neither morenor less necessary that time also be similarly indivisible) that isto say be composed of indivisible moments: for if the *hole distanceis divisible and an e(ual velocity *ill cause a thing to pass throughless of it in less time) the time must also be divisible) andconversely)if the time in *hich a thing is carried over the section A isdivisible)this section A must also be divisible.

Part 2

And since every magnitude is divisible into magnitudes0for *e havesho*n that it is impossible for anything continuous to be composedof indivisible parts) and every magnitude is continuous0it necessarilyfollo*s that the (uic+er of t*o things traverses a greater magnitudein an e(ual time) an e(ual magnitude in less time) and a greatermagnitudein less time) in conformity *ith the definition sometimes given of

the (uic+er . Suppose that A is (uic+er than B. -o* since of t*othings that *hich changes sooner is (uic+er) in the time J!) in *hichA has changed from # to 5) B *ill not yet have arrived at 5 but *illbe short of it: so that in an e(ual time the (uic+er *ill pass overa greater magnitude. 1ore than this) it *ill pass over a greatermagnitudein less time: for in the time in *hich A has arrived at 5) B beingthe slo*er has arrived) let us say) at 9. Then since A has occupiedthe *hole time J! in arriving at 5) *ill have arrived at $ in lesstime than this) say J". -o* the magnitude #$ that A has passed overis greater than the magnitude #9) and the time J" is less than the*hole time J!: so that the (uic+er *ill pass over a greater magnitudein less time. And from this it is also clear that the (uic+er *illpass over an e(ual magnitude in less time than the slo*er. ,or sinceit passes over the greater magnitude in less time than the slo*er)and 3regarded by itself4 passes over 1 the greater in more time than

G the lesser) the time P h in *hich it passes over 1 *ill be morethan the time PS) *hich it passes over G: so that) the time P h beingless than the time PCh in *hich the slo*er passes over G) the timePS *ill also be less than the time PG: for it is less than the timeP h) and that *hich is less than something else that is less thana thing is also itself less than that thing. !ence it follo*s thatthe (uic+er *ill traverse an e(ual magnitude in less time than theslo*er. Again) since the motion of anything must al*ays occupy eitheran e(ual time or less or more time in comparison *ith that of anotherthing) and since) *hereas a thing is slo*er if its motion occupiesmore time and of e(ual velocity if its motion occupies an e(ual time)the (uic+er is neither of e(ual velocity nor slo*er) it follo*s thatthe motion of the (uic+er can occupy neither an e(ual time nor more



time. It can only be) then) that it occupies less time) and thus *eget the necessary conse(uence that the (uic+er *ill pass over an e(ualmagnitude 3as *ell as a greater4 in less time than the slo*er.

And since every motion is in time and a motion may occupy any time)and the motion of everything that is in motion may be either (uic+er

or slo*er) both (uic+er motion and slo*er motion may occupy any time:and this being so) it necessarily follo*s that time also iscontinuous.By continuous I mean that *hich is divisible into divisibles thatare infinitely divisible: and if *e ta+e this as the definition ofcontinuous) it follo*s necessarily that time is continuous. ,or sinceit has been sho*n that the (uic+er *ill pass over an e(ual magnitudein less time than the slo*er) suppose that A is (uic+er and B slo*er)and that the slo*er has traversed the magnitude #5 in the time J!.-o* it is clear that the (uic+er *ill traverse the same magnitudein less time than this: let us say in the time J$. Again) since the(uic+er has passed over the *hole 5 in the time J$) the slo*er *illin the same time pass over #") say) *hich is less than #5. And sinceB) the slo*er) has passed over #" in the time J$) the (uic+er *illpass over it in less time: so that the time J$ *ill again be divided.And if this is divided the magnitude #" *ill also be divided 'ustas #5 *as: and again) if the magnitude is divided) the time *ill alsobe divided. And *e can carry on this process for ever) ta+ing theslo*er after the (uic+er and the (uic+er after the slo*er alternately)and using *hat has been demonstrated at each stage as a ne* pointof departure: for the (uic+er *ill divide the time and the slo*er*ill divide the length. If) then) this alternation al*ays holds good)and at every turn involves a division) it is evident that all timemust be continuous. And at the same time it is clear that allmagnitudeis also continuous for the divisions of *hich time and magnituderespectively are susceptible are the same and e(ual.

1oreover) the current popular arguments ma+e it plain that) if timeis continuous) magnitude is continuous also) inasmuch as a thing assesover half a given magnitude in half the time ta+en to cover the *hole:in fact *ithout (ualification it passes over a less magnitude in lesstime for the divisions of time and of magnitude *ill be the same.And if either is infinite) so is the other) and the one is so in thesame *ay as the other i.e. if time is infinite in respect of itse6tremities) length is also infinite in respect of its e6tremities:if time is infinite in respect of divisibility) length is alsoinfinitein respect of divisibility: and if time is infinite in both respects)magnitude is also infinite in both respects.

!ence Jeno s argument ma+es a false assumption in asserting that itis impossible for a thing to pass over or severally to come in contact*ith infinite things in a finite time. ,or there are t*o senses in*hich length and time and generally anything continuous are called

infinite : they are called so either in respect of divisibility orin respect of their e6tremities. So *hile a thing in a finite timecannot come in contact *ith things (uantitatively infinite) it cancome in contact *ith things infinite in respect of divisibility: forin this sense the time itself is also infinite: and so *e find thatthe time occupied by the passage over the infinite is not a finitebut an infinite time) and the contact *ith the infinites is made bymeans of moments not finite but infinite in number.

The passage over the infinite) then) cannot occupy a finite time)



and the passage over the finite cannot occupy an infinite time: ifthe time is infinite the magnitude must be infinite also) and if themagnitude is infinite) so also is the time. This may be sho*n asfollo*s.

et AB be a finite magnitude) and let us suppose that it is traversedin infinite time #) and let a finite period #5 of the time be ta+en.

-o* in this period the thing in motion *ill pass over a certainsegmentof the magnitude: let B9 be the segment that it has thus passed over.3This *ill be either an e6act measure of AB or less or greater thanan e6act measure: it ma+es no difference *hich it is.4 Then) sincea magnitude e(ual to B9 *ill al*ays be passed over in an e(ual time)and B9 measures the *hole magnitude) the *hole time occupied inpassingover AB *ill be finite: for it *ill be divisible into periods e(ualin number to the segments into *hich the magnitude is divisible.1oreover)if it is the case that infinite time is not occupied in passing overevery magnitude) but it is possible to ass over some magnitude) sayB9) in a finite time) and if this B9 measures the *hole of *hich itis a part) and if an e(ual magnitude is passed over in an e(ual time)then it follo*s that the time li+e the magnitude is finite. Thatinfinitetime *ill not be occupied in passing over B9 is evident if the timebe ta+en as limited in one direction: for as the part *ill be passedover in less time than the *hole) the time occupied in traversingthis part must be finite) the limit in one direction being given.The same reasoning *ill also sho* the falsity of the assumption thatinfinite length can be traversed in a finite time. It is evident)then) from *hat has been said that neither a line nor a surface norin fact anything continuous can be indivisible.

This conclusion follo*s not only from the present argument but fromthe consideration that the opposite assumption implies thedivisibilityof the indivisible. ,or since the distinction of (uic+er and slo*ermay apply to motions occupying any period of time and in an e(ualtime the (uic+er passes over a greater length) it may happen thatit *ill pass over a length t*ice) or one and a half times) as greatas that passed over by the slo*er: for their respective velocitiesmay stand to one another in this proportion. Suppose) then) that the(uic+er has in the same time been carried over a length one and ahalf times as great as that traversed by the slo*er) and that therespective magnitudes are divided) that of the (uic+er) the magnitudeAB#5) into three indivisibles) and that of the slo*er into the t*oindivisibles 9J) J!. Then the time may also be divided into threeindivisibles) for an e(ual magnitude *ill be passed over in an e(ualtime. Suppose then that it is thus divided into " ) m) 1-. Again)since in the same time the slo*er has been carried over 98) J!) thetime may also be similarly divided into t*o. Thus the indivisible*ill be divisible) and that *hich has no parts *ill be passed overnot in an indivisible but in a greater time. It is evident) therefore)that nothing continuous is *ithout parts.

Part ;

The present also is necessarily indivisible0the present) that is)not in the sense in *hich the *ord is applied to one thing in virtueof another) but in its proper and primary sense in *hich sense itis inherent in all time. ,or the present is something that is ane6tremity



of the past 3no part of the future being on this side of it4 and alsoof the future 3no part of the past being on the other side of it4:it is) as *e have said) a limit of both. And if it is once sho*n thatit is essentially of this character and one and the same) it *illat once be evident also that it is indivisible.

-o* the present that is the e6tremity of both times must be one andthe same: for if each e6tremity *ere different) the one could notbe in succession to the other) because nothing continuous can becomposedof things having no parts: and if the one is apart from the other)there *ill be time intermediate bet*een them) because everythingcontinuousis such that there is something intermediate bet*een its limits anddescribed by the same name as itself. But if the intermediate thingis time) it *ill be divisible: for all time has been sho*n to bedivisible.Thus on this assumption the present is divisible. But if the presentis divisible) there *ill be part of the past in the future and partof the future in the past: for past time *ill be mar+ed off fromfuturetime at the actual point of division. Also the present *ill be apresentnot in the proper sense but in virtue of something else: for thedivision*hich yields it *ill not be a division proper. ,urthermore) there*ill be a part of the present that is past and a part that is future)and it *ill not al*ays be the same part that is past or future: infact one and the same present *ill not be simultaneous: for the timemay be divided at many points. If) therefore) the present cannotpossiblyhave these characteristics) it follo*s that it must be the samepresentthat belongs to each of the t*o times. But if this is so it is evidentthat the present is also indivisible: for if it is divisible it *illbe involved in the same implications as before. It is clear) then)from *hat has been said that time contains something indivisible)and this is *hat *e call a present.

&e *ill no* sho* that nothing can be in motion in a present. ,or ifthis is possible) there can be both (uic+er and slo*er motion in thepresent. Suppose then that in the present - the (uic+er has traversedthe distance AB. That being so) the slo*er *ill in the same presenttraverse a distance less than AB) say A#. But since the slo*er *illhave occupied the *hole present in traversing A#) the (uic+er *illoccupy less than this in traversing it. Thus *e shall have a divisionof the present) *hereas *e found it to be indivisible. It isimpossible)therefore) for anything to be in motion in a present.

-or can anything be at rest in a present: for) as *e *ere saying)only can be at rest *hich is naturally designed to be in motion butis not in motion *hen) *here) or as it *ould naturally be so: since)therefore) nothing is naturally designed to be in motion in a present)it is clear that nothing can be at rest in a present either.

1oreover) inasmuch as it is the same present that belongs to boththe times) and it is possible for a thing to be in motion throughoutone time and to be at rest throughout the other) and that *hich isin motion or at rest for the *hole of a time *ill be in motion orat rest as the case may be in any part of it in *hich it is naturally



designed to be in motion or at rest: this being so) the assumptionthat there can be motion or rest in a present *ill carry *ith it theimplication that the same thing can at the same time be at rest andin motion: for both the times have the same e6tremity) vi8. thepresent.

Again) *hen *e say that a thing is at rest) *e imply that itsconditionin *hole and in part is at the time of spea+ing uniform *ith *hatit *as previously: but the present contains no previously :conse(uently)there can be no rest in it.

It follo*s then that the motion of that *hich is in motion and therest of that *hich is at rest must occupy time.

Part >

,urther) everything that changes must be divisible. ,or since everychange is from something to something) and *hen a thing is at thegoal of its change it is no longer changing) and *hen both it itselfand all its parts are at the starting0point of its change it is notchanging 3for that *hich is in *hole and in part in an unvaryingconditionis not in a state of change4 it follo*s) therefore) that part ofthat *hich is changing must be at the starting0point and part at thegoal: for as a *hole it cannot be in both or in neither. 3!ere by

goal of change I mean that *hich comes first in the process ofchange:e.g. in a process of change from *hite the goal in (uestion *ill begrey) not blac+: for it is not necessary that that that *hich ischangingshould be at either of the e6tremes.4 It is evident) therefore) thateverything that changes must be divisible.

-o* motion is divisible in t*o senses. In the first place it isdivisiblein virtue of the time that it occupies. In the second place it isdivisible according to the motions of the several parts of that *hichis in motion: e.g. if the *hole A# is in motion) there *ill be amotionof AB and a motion of B#. That being so) let 59 be the motion of thepart AB and 9J the motion of the part B#. Then the *hole 58 must bethe motion of A#: for 5J must constitute the motion of A# inasmuchas 59 and 9J severally constitute the motions of each of its parts.But the motion of a thing can never be constituted by the motion ofsomething else: conse(uently the *hole motion is the motion of the*hole magnitude.

Again) since every motion is a motion of something) and the *holemotion 5J is not the motion of either of the parts 3for each of theparts 59) 9J is the motion of one of the parts AB) B#4 or of anythingelse 3for) the *hole motion being the motion of a *hole) the partsof the motion are the motions of the parts of that *hole: and theparts of 5J are the motions of AB) B# and of nothing else: for) as*e sa*) a motion that is one cannot be the motion of more things thanone4: since this is so) the *hole motion *ill be the motion of themagnitude AB#.

Again) if there is a motion of the *hole other than 5J) say the theof each of the arts may be subtracted from it: and these motions *ill



be e(ual to 59) 9J respectively: for the motion of that *hich is onemust be one. So if the *hole motion $I may be divided into the motionsof the parts) $I *ill be e(ual to 5J: if on the other hand there isany remainder) say "I) this *ill be a motion of nothing: for it canbe the motion neither of the *hole nor of the parts 3as the motionof that *hich is one must be one4 nor of anything else: for a motion

that is continuous must be the motion of things that are continuous.And the same result follo*s if the division of $I reveals a surpluson the side of the motions of the parts. Conse(uently) if this isimpossible) the *hole motion must be the same as and e(ual to 5J.

This then is *hat is meant by the division of motion according tothe motions of the parts: and it must be applicable to everythingthat is divisible into parts.

1otion is also susceptible of another +ind of division) that accordingto time. ,or since all motion is in time and all time is divisible)and in less time the motion is less) it follo*s that every motionmust be divisible according to time. And since everything that isin motion is in motion in a certain sphere and for a certain timeand has a motion belonging to it) it follo*s that the time) themotion)the being0in0motion) the thing that is in motion) and the sphere ofthe motion must all be susceptible of the same divisions 3thoughspheresof motion are not all divisible in a li+e manner: thus (uantity isessentially) (uality accidentally divisible4. ,or suppose that A isthe time occupied by the motion B. Then if all the time has beenoccupiedby the *hole motion) it *ill ta+e less of the motion to occupy halfthe time) less again to occupy a further subdivision of the time)and so on to infinity. Again) the time *ill be divisible similarlyto the motion: for if the *hole motion occupies all the time halfthe motion *ill occupy half the time) and less of the motion again*ill occupy less of the time.

In the same *ay the being0in0motion *ill also be divisible. ,or let# be the *hole being0in0motion. Then the being0in0motion thatcorrespondsto half the motion *ill be less than the *hole being0in0motion) that*hich corresponds to a (uarter of the motion *ill be less again) andso on to infinity. 1oreover by setting out successively the being0in0motioncorresponding to each of the t*o motions 5# 3say4 and #9) *e may arguethat the *hole being0in0motion *ill correspond to the *hole motion3for if it *ere some other being0in0motion that corresponded to the*hole motion) there *ould be more than one being0in motioncorrespondingto the same motion4) the argument being the same as that *hereby *esho*ed that the motion of a thing is divisible into the motions ofthe parts of the thing: for if *e ta+e separately the being0in motioncorresponding to each of the t*o motions) *e shall see that the *holebeing0in motion is continuous.

The same reasoning *ill sho* the divisibility of the length) and infact of everything that forms a sphere of change 3though some of theseare only accidentally divisible because that *hich changes is so4:for the division of one term *ill involve the division of all. So)too) in the matter of their being finite or infinite) they *ill allali+e be either the one or the other. And *e no* see that in most



cases the fact that all the terms are divisible or infinite is adirectconse(uence of the fact that the thing that changes is divisible orinfinite: for the attributes divisible and infinite belong inthe first instance to the thing that changes. That divisibility doesso *e have already sho*n: that infinity does so *ill be made clear

in *hat follo*s7

Part ?

Since everything that changes changes from something to something)that *hich has changed must at the moment *hen it has first changedbe in that to *hich it has changed. ,or that *hich changes retiresfrom or leaves that from *hich it changes: and leaving) if notidentical*ith changing) is at any rate a conse(uence of it. And if leavingis a conse(uence of changing) having left is a conse(uence of havingchanged: for there is a li+e relation bet*een the t*o in each case.

$ne +ind of change) then) being change in a relation of contradiction)*here a thing has changed from not0being to being it has left not0being.Therefore it *ill be in being: for everything must either be or notbe. It is evident) then) that in contradictory change that *hich haschanged must be in that to *hich it has changed. And if this is truein this +ind of change) it *ill be true in all other +inds as *ell:for in this matter *hat holds good in the case of one *ill hold goodli+e*ise in the case of the rest.

1oreover) if *e ta+e each +ind of change separately) the truth ofour conclusion *ill be e(ually evident) on the ground that that that*hich has changed must be some*here or in something. ,or) since ithas left that from *hich it has changed and must be some*here) itmust be either in that to *hich it has changed or in something else.If) then) that *hich has changed to B is in something other than B)say #) it must again be changing from # to B: for it cannot be assumedthat there is no interval bet*een # and B) since change is continuous.Thus *e have the result that the thing that has changed) at the moment*hen it has changed) is changing to that to *hich it has changed)*hich is impossible: that *hich has changed) therefore) must be inthat to *hich it has changed. So it is evident li+e*ise that thatthat *hich has come to be) at the moment *hen it has come to be) *illbe) and that *hich has ceased to be *ill not0be: for *hat *e havesaid applies universally to every +ind of change) and its truth ismost obvious in the case of contradictory change. It is clear) then)that that *hich has changed) at the moment *hen it has first changed)is in that to *hich it has changed.

&e *ill no* sho* that the primary *hen in *hich that *hich haschangedeffected the completion of its change must be indivisible) *here by

primary I mean possessing the characteristics in (uestion of itselfand not in virtue of the possession of them by something elsebelongingto it. ,or let A# be divisible) and let it be divided at B. If thenthe completion of change has been effected in AB or again in B#) A#cannot be the primary thing in *hich the completion of change hasbeen effected. If) on the other hand) it has been changing in bothAB and B# 3for it must either have changed or be changing in eachof them4) it must have been changing in the *hole A#: but ourassumption



*as that A# contains only the completion of the change. It is e(uallyimpossible to suppose that one part of A# contains the process andthe other the completion of the change: for then *e shall havesomethingprior to *hat is primary. So that in *hich the completion of changehas been effected must be indivisible. It is also evident) therefore)

that that that in *hich that *hich has ceased to be has ceased tobe and that in *hich that *hich has come to be has come to be areindivisible.

But there are t*o senses of the e6pression the primary *hen in *hichsomething has changed . $n the one hand it may mean the primary *hencontaining the completion of the process of change0 the moment *henit is correct to say it has changed : on the other hand it may meanthe primary *hen containing the beginning of the process of change.-o* the primary *hen that has reference to the end of the change issomething really e6istent: for a change may really be completed) andthere is such a thing as an end of change) *hich *e have in fact sho*nto be indivisible because it is a limit. But that *hich has referenceto the beginning is not e6istent at all: for there is no such thingas a beginning of a process of change) and the time occupied by thechange does not contain any primary *hen in *hich the change began.,or suppose that A5 is such a primary *hen. Then it cannot beindivisible:for) if it *ere) the moment immediately preceding the change and themoment in *hich the change begins *ould be consecutive 3and momentscannot be consecutive4. Again) if the changing thing is at rest inthe *hole preceding time #A 3for *e may suppose that it is at rest4)it is at rest in A also: so if A5 is *ithout parts) it *illsimultaneouslybe at rest and have changed: for it is at rest in A and has changedin 5. Since then A5 is not *ithout parts) it must be divisible) andthe changing thing must have changed in every part of it 3for if ithas changed in neither of the t*o parts into *hich A5 is divided)it has not changed in the *hole either: if) on the other hand) itis in process of change in both parts) it is li+e*ise in process ofchange in the *hole: and if) again) it has changed in one of the t*oparts) the *hole is not the primary *hen in *hich it has changed:it must therefore have changed in every part4. It is evident) then)that *ith reference to the beginning of change there is no primary*hen in *hich change has been effected: for the divisions areinfinite.

So) too) of that *hich has changed there is no primary part that haschanged. ,or suppose that of A9 the primary part that has changedis A8 3everything that changes having been sho*n to be divisible4:and let $I be the time in *hich 5J has changed. If) then) in the *holetime 5J has changed) in half the time there *ill be a part that haschanged) less than and therefore prior to 5J: and again there *illbe another part prior to this) and yet another) and so on to infinity.Thus of that *hich changes there cannot be any primary part that haschanged. It is evident) then) from *hat has been said) that neitherof that *hich changes nor of the time in *hich it changes is thereany primary part.

&ith regard) ho*ever) to the actual sub'ect of change0that is to saythat in respect of *hich a thing changes0there is a difference tobe observed. ,or in a process of change *e may distinguish threeterms0that*hich changes) that in *hich it changes) and the actual sub'ect ofchange) e.g. the man) the time) and the fair comple6ion. $f these



the man and the time are divisible: but *ith the fair comple6ion itis other*ise 3though they are all divisible accidentally) for thatin *hich the fair comple6ion or any other (uality is an accident isdivisible4. ,or of actual sub'ects of change it *ill be seen thatthose *hich are classed as essentially) not accidentally) divisiblehave no primary part. Ta+e the case of magnitudes: let AB be a

magnitude)and suppose that it has moved from B to a primary *here #. Thenif B# is ta+en to be indivisible) t*o things *ithout parts *ill haveto be contiguous 3*hich is impossible4: if on the other hand it ista+en to be divisible) there *ill be something prior to # to *hichthe magnitude has changed) and something else again prior to that)and so on to infinity) because the process of division may becontinued*ithout end. Thus there can be no primary *here to *hich a thinghas changed. And if *e ta+e the case of (uantitative change) *e shallget a li+e result) for here too the change is in something continuous.It is evident) then) that only in (ualitative motion can there beanything essentially indivisible.

Part

-o* everything that changes changes time) and that in t*o senses:for the time in *hich a thing is said to change may be the primarytime) or on the other hand it may have an e6tended reference) as e.g.*hen *e say that a thing changes in a particular year because itchangesin a particular day. That being so) that *hich changes must bechangingin any part of the primary time in *hich it changes. This is clearfrom our definition of primary ) in *hich the *ord is said to e6press'ust this: it may also) ho*ever) be made evident by the follo*ingargument. et Ch h be the primary time in *hich that *hich is inmotionis in motion: and 3as all time is divisible4 let it be divided at". -o* in the time Ch" it either is in motion or is not in motion)and the same is li+e*ise true of the time " h. Then if it is in motionin neither of the t*o parts) it *ill be at rest in the *hole: forit is impossible that it should be in motion in a time in no partof *hich it is in motion. If on the other hand it is in motion inonly one of the t*o parts of the time) Ch h cannot be the primarytime in *hich it is in motion: for its motion *ill have referenceto a time other than Ch h. It must) then) have been in motion in anypart of Ch h.

And no* that this has been proved) it is evident that everything thatis in motion must have been in motion before. ,or if that *hich isin motion has traversed the distance " in the primary time Ch h)in half the time a thing that is in motion *ith e(ual velocity andbegan its motion at the same time *ill have traversed half thedistance.But if this second thing *hose velocity is e(ual has traversed acertaindistance in a certain time) the original thing that is in motion musthave traversed the same distance in the same time. !ence that *hichis in motion must have been in motion before.

Again) if by ta+ing the e6treme moment of the time0for it is themomentthat defines the time) and time is that *hich is intermediate bet*eenmoments0*e are enabled to say that motion has ta+en place in the *hole



time Ch h or in fact in any period of it) motion may li+e*ise be saidto have ta+en place in every other such period. But half the timefinds an e6treme in the point of division. Therefore motion *ill haveta+en place in half the time and in fact in any part of it: for assoon as any division is made there is al*ays a time defined bymoments.

If) then) all time is divisible) and that *hich is intermediatebet*eenmoments is time) everything that is changing must have completed aninfinite number of changes.

Again) since a thing that changes continuously and has not perishedor ceased from its change must either be changing or have changedin any part of the time of its change) and since it cannot be changingin a moment) it follo*s that it must have changed at every momentin the time: conse(uently) since the moments are infinite in number)everything that is changing must have completed an infinite numberof changes.

And not only must that *hich is changing have changed) but that *hichhas changed must also previously have been changing) since everythingthat has changed from something to something has changed in a periodof time. ,or suppose that a thing has changed from A to B in a moment.-o* the moment in *hich it has changed cannot be the same as thatin *hich it is at A 3since in that case it *ould be in A and B atonce4: for *e have sho*n above that that that *hich has changed) *henit has changed) is not in that from *hich it has changed. If) on theother hand) it is a different moment) there *ill be a period of timeintermediate bet*een the t*o: for) as *e sa*) moments are notconsecutive.Since) then) it has changed in a period of time) and all time isdivisible)in half the time it *ill have completed another change) in a (uarteranother) and so on to infinity: conse(uently *hen it has changed)it must have previously been changing.

1oreover) the truth of *hat has been said is more evident in the caseof magnitude) because the magnitude over *hich *hat is changingchangesis continuous. ,or suppose that a thing has changed from # to 5. Thenif #5 is indivisible) t*o things *ithout parts *ill be consecutive.But since this is impossible) that *hich is intermediate bet*een themmust be a magnitude and divisible into an infinite number of segments:conse(uently) before the change is completed) the thing changes tothose segments. 9verything that has changed) therefore) mustpreviouslyhave been changing: for the same proof also holds good of change *ithrespect to *hat is not continuous) changes) that is to say) bet*eencontraries and bet*een contradictories. In such cases *e have onlyto ta+e the time in *hich a thing has changed and again apply thesame reasoning. So that *hich has changed must have been changingand that *hich is changing must have changed) and a process of changeis preceded by a completion of change and a completion by a process:and *e can never ta+e any stage and say that it is absolutely thefirst. The reason of this is that no t*o things *ithout parts canbe contiguous) and therefore in change the process of division isinfinite) 'ust as lines may be infinitely divided so that one partis continually increasing and the other continually decreasing.

So it is evident also that that that *hich has become must previouslyhave been in process of becoming) and that *hich is in process of



becoming must previously have become) everything 3that is4 that isdivisible and continuous: though it is not al*ays the actual thingthat is in process of becoming of *hich this is true: sometimes itis something else) that is to say) some part of the thing in (uestion)e.g. the foundation0stone of a house. So) too) in the case of that*hich is perishing and that *hich has perished: for that *hich becomes

and that *hich perishes must contain an element of infiniteness asan immediate conse(uence of the fact that they are continuous things:and so a thing cannot be in process of becoming *ithout having becomeor have become *ithout having been in process of becoming. So) too)in the case of perishing and having perished: perishing must beprecededby having perished) and having perished must be preceded by perishing.It is evident) then) that that *hich has become must previously havebeen in process of becoming) and that *hich is in process of becomingmust previously have become: for all magnitudes and all periods oftime are infinitely divisible.

Conse(uently no absolutely first stage of change can be representedby any particular part of space or time *hich the changing thing mayoccupy.

Part

-o* since the motion of everything that is in motion occupies a periodof time) and a greater magnitude is traversed in a longer time) itis impossible that a thing should undergo a finite motion in aninfinitetime) if this is understood to mean not that the same motion or apart of it is continually repeated) but that the *hole infinite timeis occupied by the *hole finite motion. In all cases *here a thingis in motion *ith uniform velocity it is clear that the finitemagnitudeis traversed in a finite time. ,or if *e ta+e a part of the motion*hich shall be a measure of the *hole) the *hole motion is completedin as many e(ual periods of the time as there are parts of the motion.Conse(uently) since these parts are finite) both in si8e individuallyand in number collectively) the *hole time must also be finite: forit *ill be a multiple of the portion) e(ual to the time occupied incompleting the aforesaid part multiplied by the number of the parts.

But it ma+es no difference even if the velocity is not uniform. ,orlet us suppose that the line AB represents a finite stretch over *hicha thing has been moved in the given time) and let #5 be the infinitetime. -o* if one part of the stretch must have been traversed beforeanother part 3this is clear) that in the earlier and in the laterpart of the time a different part of the stretch has been traversed:for as the time lengthens a different part of the motion *ill al*aysbe completed in it) *hether the thing in motion changes *ith uniformvelocity or not: and *hether the rate of motion increases ordiminishesor remains stationary this is none the less so4) let us then ta+eA9 a part of the *hole stretch of motion AB *hich shall be a measureof AB. -o* this part of the motion occupies a certain period of theinfinite time: it cannot itself occupy an infinite time) for *e areassuming that that is occupied by the *hole AB. And if again I ta+eanother part e(ual to A9) that also must occupy a finite time inconse(uenceof the same assumption. And if I go on ta+ing parts in this *ay) onthe one hand there is no part *hich *ill be a measure of the infinitetime 3for the infinite cannot be composed of finite parts *hether



e(ual or une(ual) because there must be some unity *hich *ill be ameasure of things finite in multitude or in magnitude) *hich) *hetherthey are e(ual or une(ual) are none the less limited in magnitude4*hile on the other hand the finite stretch of motion AB is a certainmultiple of A9: conse(uently the motion AB must be accomplished ina finite time. 1oreover it is the same *ith coming to rest as *ith

motion. And so it is impossible for one and the same thing to beinfinitelyin process of becoming or of perishing. The reasoning he *ill provethat in a finite time there cannot be an infinite e6tent of motionor of coming to rest) *hether the motion is regular or irregular.,or if *e ta+e a part *hich shall be a measure of the *hole time)in this part a certain fraction) not the *hole) of the magnitude *illbe traversed) because *e assume that the traversing of the *holeoccupiesall the time. Again) in another e(ual part of the time another partof the magnitude *ill be traversed: and similarly in each part ofthe time that *e ta+e) *hether e(ual or une(ual to the part originallyta+en. It ma+es no difference *hether the parts are e(ual or not)if only each is finite: for it is clear that *hile the time ise6haustedby the subtraction of its parts) the infinite magnitude *ill not bethus e6hausted) since the process of subtraction is finite both inrespect of the (uantity subtracted and of the number of times asubtractionis made. Conse(uently the infinite magnitude *ill not be traversedin finite time: and it ma+es no difference *hether the magnitude isinfinite in only one direction or in both: for the same reasoning*ill hold good.

This having been proved) it is evident that neither can a finitemagnitudetraverse an infinite magnitude in a finite time) the reason beingthe same as that given above: in part of the time it *ill traversea finite magnitude and in each several part li+e*ise) so that in the*hole time it *ill traverse a finite magnitude.

And since a finite magnitude *ill not traverse an infinite in a finitetime) it is clear that neither *ill an infinite traverse a finitein a finite time. ,or if the infinite could traverse the finite) thefinite could traverse the infinite for it ma+es no difference *hichof the t*o is the thing in motion either case involves the traversingof the infinite by the finite. ,or *hen the infinite magnitude A isin motion a part of it) say #5) *ill occupy the finite and thenanother)and then another) and so on to infinity. Thus the t*o results *illcoincide: the infinite *ill have completed a motion over the finiteand the finite *ill have traversed the infinite: for it *ould seemto be impossible for the motion of the infinite over the finite tooccur in any *ay other than by the finite traversing the infiniteeither by locomotion over it or by measuring it. Therefore) sincethis is impossible) the infinite cannot traverse the finite.

-or again *ill the infinite traverse the infinite in a finite time.$ther*ise it *ould also traverse the finite) for the infinite includesthe finite. &e can further prove this in the same *ay by ta+ing thetime as our starting0point.

Since) then) it is established that in a finite time neither *illthe finite traverse the infinite) nor the infinite the finite) northe infinite the infinite) it is evident also that in a finite time



there cannot be infinite motion: for *hat difference does it ma+e*hether *e ta+e the motion or the magnitude to be infinite7 If eitherof the t*o is infinite) the other must be so li+e*ise: for alllocomotionis in space.

Part D

Since everything to *hich motion or rest is natural is in motion orat rest in the natural time) place) and manner) that *hich is comingto a stand) *hen it is coming to a stand) must be in motion: for ifit is not in motion it must be at rest: but that *hich is at restcannot be coming to rest. ,rom this it evidently follo*s that comingto a stand must occupy a period of time: for the motion of that *hichis in motion occupies a period of time) and that *hich is coming toa stand has been sho*n to be in motion: conse(uently coming to a standmust occupy a period of time.

Again) since the terms (uic+er and slo*er are used only of that*hich occupies a period of time) and the process of coming to a standmay be (uic+er or slo*er) the same conclusion follo*s.

And that *hich is coming to a stand must be coming to a stand in anypart of the primary time in *hich it is coming to a stand. ,or ifit is coming to a stand in neither of t*o parts into *hich the timemay be divided) it cannot be coming to a stand in the *hole time)*ith the result that that that *hich is coming to a stand *ill notbe coming to a stand. If on the other hand it is coming to a standin only one of the t*o parts of the time) the *hole cannot be theprimary time in *hich it is coming to a stand: for it is coming toa stand in the *hole time not primarily but in virtue of somethingdistinct from itself) the argument being the same as that *hich *eused above about things in motion.

And 'ust as there is no primary time in *hich that *hich is in motionis in motion) so too there is no primary time in *hich that *hichis coming to a stand is coming to a stand) there being no primarystage either of being in motion or of coming to a stand. ,or let ABbe the primary time in *hich a thing is coming to a stand. -o* ABcannot be *ithout parts: for there cannot be motion in that *hichis *ithout parts) because the moving thing *ould necessarily havebeen already moved for part of the time of its movement: and that*hich is coming to a stand has been sho*n to be in motion. But sinceAb is therefore divisible) the thing is coming to a stand in everyone of the parts of AB: for *e have sho*n above that it is comingto a stand in every one of the parts in *hich it is primarily comingto a stand. Since then) that in *hich primarily a thing is comingto a stand must be a period of time and not something indivisible)and since all time is infinitely divisible) there cannot be anythingin *hich primarily it is coming to a stand.

-or again can there be a primary time at *hich the being at rest ofthat *hich is at rest occurred: for it cannot have occurred in that*hich has no parts) because there cannot be motion in that *hich isindivisible) and that in *hich rest ta+es place is the same as thatin *hich motion ta+es place: for *e defined a state of rest to bethe state of a thing to *hich motion is natural but *hich is not inmotion *hen 3that is to say in that in *hich4 motion *ould be naturalto it. Again) our use of the phrase being at rest also implies thatthe previous state of a thing is still unaltered) not one point only



but t*o at least being thus needed to determine its presence:conse(uentlythat in *hich a thing is at rest cannot be *ithout parts. Since) thenit is divisible) it must be a period of time) and the thing must beat rest in every one of its parts) as may be sho*n by the same methodas that used above in similar demonstrations.

So there can be no primary part of the time: and the reason is thatrest and motion are al*ays in a period of time) and a period of timehas no primary part any more than a magnitude or in fact anythingcontinuous: for everything continuous is divisible into an infinitenumber of parts.

And since everything that is in motion is in motion in a period oftime and changes from something to something) *hen its motion iscomprised*ithin a particular period of time essentially0that is to say *henit fills the *hole and not merely a part of the time in (uestion0itis impossible that in that time that *hich is in motion should beover against some particular thing primarily. ,or if a thing0itselfand each of its parts0occupies the same space for a definite periodof time) it is at rest: for it is in 'ust these circumstances that*e use the term being at rest 0*hen at one moment after another itcan be said *ith truth that a thing) itself and its parts) occupiesthe same space. So if this is being at rest it is impossible for that*hich is changing to be as a *hole) at the time *hen it is primarilychanging) over against any particular thing 3for the *hole periodof time is divisible4) so that in one part of it after another it*ill be true to say that the thing) itself and its parts) occupiesthe same space. If this is not so and the aforesaid proposition istrue only at a single moment) then the thing *ill be over againsta particular thing not for any period of time but only at a momentthat limits the time. It is true that at any moment it is al*ays overagainst something stationary: but it is not at rest: for at a momentit is not possible for anything to be either in motion or at rest.So *hile it is true to say that that *hich is in motion is at a momentnot in motion and is opposite some particular thing) it cannot ina period of time be over against that *hich is at rest: for that *ouldinvolve the conclusion that that *hich is in locomotion is at rest.

Part E

Jeno s reasoning) ho*ever) is fallacious) *hen he says that ifeverything*hen it occupies an e(ual space is at rest) and if that *hich is inlocomotion is al*ays occupying such a space at any moment) the flyingarro* is therefore motionless. This is false) for time is not composedof indivisible moments any more than any other magnitude is composedof indivisibles.

Jeno s arguments about motion) *hich cause so much dis(uietude tothose *ho try to solve the problems that they present) are four innumber. The first asserts the non0e6istence of motion on the groundthat that *hich is in locomotion must arrive at the half0*ay stagebefore it arrives at the goal. This *e have discussed above.

The second is the so0called Achilles ) and it amounts to this) thatin a race the (uic+est runner can never overta+e the slo*est) sincethe pursuer must first reach the point *hence the pursued started)so that the slo*er must al*ays hold a lead. This argument is the samein principle as that *hich depends on bisection) though it differs



from it in that the spaces *ith *hich *e successively have to dealare not divided into halves. The result of the argument is that theslo*er is not overta+en: but it proceeds along the same lines as thebisection0argument 3for in both a division of the space in a certain*ay leads to the result that the goal is not reached) though the

Achilles

goes further in that it affirms that even the (uic+est runner inlegendarytradition must fail in his pursuit of the slo*est4) so that thesolutionmust be the same. And the a6iom that that *hich holds a lead is neveroverta+en is false: it is not overta+en) it is true) *hile it holdsa lead: but it is overta+en nevertheless if it is granted that ittraverses the finite distance prescribed. These then are t*o of hisarguments.

The third is that already given above) to the effect that the flyingarro* is at rest) *hich result follo*s from the assumption that timeis composed of moments: if this assumption is not granted) theconclusion*ill not follo*.

The fourth argument is that concerning the t*o ro*s of bodies) eachro* being composed of an e(ual number of bodies of e(ual si8e) passingeach other on a race0course as they proceed *ith e(ual velocity inopposite directions) the one ro* originally occupying the spacebet*eenthe goal and the middle point of the course and the other that bet*eenthe middle point and the starting0post. This) he thin+s) involvesthe conclusion that half a given time is e(ual to double that time.The fallacy of the reasoning lies in the assumption that a bodyoccupiesan e(ual time in passing *ith e(ual velocity a body that is in motionand a body of e(ual si8e that is at rest *hich is false. ,or instance3so runs the argument4) let A) A...be the stationary bodies of e(ualsi8e) B) B...the bodies) e(ual in number and in si8e to A)A...)originallyoccupying the half of the course from the starting0post to the middleof the A s) and #) #...those originally occupying the other half fromthe goal to the middle of the A s) e(ual in number) si8e) and velocityto B) B....Then three conse(uences follo*:

,irst) as the B s and the # s pass one another) the first B reachesthe last # at the same moment as the first # reaches the last B.Secondlyat this moment the first # has passed all the A s) *hereas the firstB has passed only half the A s) and has conse(uently occupied onlyhalf the time occupied by the first #) since each of the t*o occupiesan e(ual time in passing each A. Thirdly) at the same moment all theB s have passed all the # s: for the first # and the first B *illsimultaneously reach the opposite ends of the course) since 3so saysJeno4 the time occupied by the first # in passing each of the B sis e(ual to that occupied by it in passing each of the A s) becausean e(ual time is occupied by both the first B and the first # inpassingall the A s. This is the argument) but it presupposed the aforesaidfallacious assumption.

-or in reference to contradictory change shall *e find anythingunans*erablein the argument that if a thing is changing from not0*hite) say) to



*hite) and is in neither condition) then it *ill be neither *hitenor not0*hite: for the fact that it is not *holly in either condition*ill not preclude us from calling it *hite or not0*hite. &e call athing *hite or not0*hite not necessarily because it is be one or theother) but cause most of its parts or the most essential parts ofit are so: not being in a certain condition is different from not

being *holly in that condition. So) too) in the case of being andnot0being and all other conditions *hich stand in a contradictoryrelation: *hile the changing thing must of necessity be in one ofthe t*o opposites) it is never *holly in either.

Again) in the case of circles and spheres and everything *hose motionis confined *ithin the space that it occupies) it is not true to saythe motion can be nothing but rest) on the ground that such thingsin motion) themselves and their parts) *ill occupy the same positionfor a period of time) and that therefore they *ill be at once at restand in motion. ,or in the first place the parts do not occupy thesame position for any period of time: and in the second place the*hole also is al*ays changing to a different position: for if *e ta+ethe orbit as described from a point A on a circumference) it *illnot be the same as the orbit as described from B or # or any otherpoint on the same circumference e6cept in an accidental sense) thesense that is to say in *hich a musical man is the same as a man.Thus one orbit is al*ays changing into another) and the thing *illnever be at rest. And it is the same *ith the sphere and everythingelse *hose motion is confined *ithin the space that it occupies.

Part %K

$ur ne6t point is that that *hich is *ithout parts cannot be in motione6cept accidentally: i.e. it can be in motion only in so far as thebody or the magnitude is in motion and the partless is in motion byinclusion therein) 'ust as that *hich is in a boat may be in motionin conse(uence of the locomotion of the boat) or a part may be inmotion in virtue of the motion of the *hole. 3It must be remembered)ho*ever) that by that *hich is *ithout parts I mean that *hich is(uantitatively indivisible 3and that the case of the motion of a partis not e6actly parallel4: for parts have motions belonging essentiallyand severally to themselves distinct from the motion of the *hole.The distinction may be seen most clearly in the case of a revolvingsphere) in *hich the velocities of the parts near the centre and ofthose on the surface are different from one another and from thatof the *hole this implies that there is not one motion but many4.As *e have said) then) that *hich is *ithout parts can be in motionin the sense in *hich a man sitting in a boat is in motion *hen theboat is travelling) but it cannot be in motion of itself. ,or supposethat it is changing from AB to B#0either from one magnitude toanother)or from one form to another) or from some state to its contradictory0andlet 5 be the primary time in *hich it undergoes the change. Then inthe time in *hich it is changing it must be either in AB or in B#or partly in one and partly in the other: for this) as *e sa*) istrue of everything that is changing. -o* it cannot be partly in eachof the t*o: for then it *ould be divisible into parts. -or again canit be in B#: for then it *ill have completed the change) *hereas theassumption is that the change is in process. It remains) then) thatin the time in *hich it is changing) it is in Ab. That being so) it*ill be at rest: for) as *e sa*) to be in the same condition for aperiod of time is to be at rest. So it is not possible for that *hichhas no parts to be in motion or to change in any *ay: for only one



condition could have made it possible for it to have motion) vi8.that time should be composed of moments) in *hich case at any momentit *ould have completed a motion or a change) so that it *ould neverbe in motion) but *ould al*ays have been in motion. But this *e havealready sho*n above to be impossible: time is not composed of moments)'ust as a line is not composed of points) and motion is not composed

of starts: for this theory simply ma+es motion consist of indivisiblesin e6actly the same *ay as time is made to consist of moments or alength of points.

Again) it may be sho*n in the follo*ing *ay that there can be nomotionof a point or of any other indivisible. That *hich is in motion cannever traverse a space greater than itself *ithout first traversinga space e(ual to or less than itself. That being so) it is evidentthat the point also must first traverse a space e(ual to or less thanitself. But since it is indivisible) there can be no space less thanitself for it to traverse first: so it *ill have to traverse adistancee(ual to itself. Thus the line *ill be composed of points) for thepoint) as it continually traverses a distance e(ual to itself) *illbe a measure of the *hole line. But since this is impossible) it isli+e*ise impossible for the indivisible to be in motion.

Again) since motion is al*ays in a period of time and never in amoment)and all time is divisible) for everything that is in motion theremust be a time less than that in *hich it traverses a distance asgreat as itself. ,or that in *hich it is in motion *ill be a time)because all motion is in a period of time and all time has been sho*nabove to be divisible. Therefore) if a point is in motion) there mustbe a time less than that in *hich it has itself traversed anydistance.But this is impossible) for in less time it must traverse lessdistance)and thus the indivisible *ill be divisible into something less thanitself) 'ust as the time is so divisible: the fact being that theonly condition under *hich that *hich is *ithout parts and indivisiblecould be in motion *ould have been the possibility of the infinitelysmall being in motion in a moment: for in the t*o (uestions0that ofmotion in a moment and that of motion of something indivisible0thesame principle is involved.

$ur ne6t point is that no process of change is infinite: for everychange) *hether bet*een contradictories or bet*een contraries) isa change from something to something. Thus in contradictory changesthe positive or the negative) as the case may be) is the limit) e.g.being is the limit of coming to be and not0being is the limit ofceasingto be: and in contrary changes the particular contraries are thelimits)since these are the e6treme points of any such process of change)and conse(uently of every process of alteration: for alteration isal*ays dependent upon some contraries. Similarly contraries are thee6treme points of processes of increase and decrease: the limit ofincrease is to be found in the complete magnitude proper to thepeculiarnature of the thing that is increasing) *hile the limit of decreaseis the complete loss of such magnitude. ocomotion) it is true) *ecannot sho* to be finite in this *ay) since it is not al*ays bet*eencontraries. But since that *hich cannot be cut 3in the sense that



it is inconceivable that it should be cut) the term cannot beingused in several senses40since it is inconceivable that that *hichin this sense cannot be cut should be in process of being cut) andgenerally that that *hich cannot come to be should be in process ofcoming to be) it follo*s that it is inconceivable that that *hichcannot complete a change should be in process of changing to that

to *hich it cannot complete a change. If) then) it is to be assumedthat that *hich is in locomotion is in process of changing) it mustbe capable of completing the change. Conse(uently its motion is notinfinite) and it *ill not be in locomotion over an infinite distance)for it cannot traverse such a distance.

It is evident) then) that a process of change cannot be infinite inthe sense that it is not defined by limits. But it remains to beconsidered*hether it is possible in the sense that one and the same processof change may be infinite in respect of the time *hich it occupies.If it is not one process) it *ould seem that there is nothing topreventits being infinite in this sense e.g. if a process of locomotionbe succeeded by a process of alteration and that by a process ofincreaseand that again by a process of coming to be: in this *ay there maybe motion for ever so far as the time is concerned) but it *ill notbe one motion) because all these motions do not compose one. If itis to be one process) no motion can be infinite in respect of thetime that it occupies) *ith the single e6ception of rotatorylocomotion.

0000000000000000000000000000000000000000000000000000000000000000000000

B$$" II

Part %

9verything that is in motion must be moved by something. ,or if ithas not the source of its motion in itself it is evident that it ismoved by something other than itself) for there must be somethingelse that moves it. If on the other hand it has the source of itsmotion in itself) let AB be ta+en to represent that *hich is in motionessentially of itself and not in virtue of the fact that somethingbelonging to it is in motion. -o* in the first place to assume thatAb) because it is in motion as a *hole and is not moved by anythinge6ternal to itself) is therefore moved by itself0this is 'ust as if)supposing that " is moving 1 and is also itself in motion) *e *ereto deny that "1 is moved by anything on the ground that it is notevident *hich is the part that is moving it and *hich the part thatis moved. In the second place that *hich is in motion *ithout beingmoved by anything does not necessarily cease from its motion becausesomething else is at rest) but a thing must be moved by somethingif the fact of something else having ceased from its motion causesit to be at rest. Thus) if this is accepted) everything that is inmotion must be moved by something. ,or AB) *hich has been ta+en torepresent that *hich is in motion) must be divisible since everythingthat is in motion is divisible. et it be divided) then) at #. -o*if #B is not in motion) then AB *ill not be in motion: for if it is)it is clear that A# *ould be in motion *hile B# is at rest) and thusAB cannot be in motion essentially and primarily. But e6 hypothesiAB is in motion essentially and primarily. Therefore if #B is notin motion AB *ill be at rest. But *e have agreed that that *hich isat rest if something else is not in motion must be moved by something.



Conse(uently) everything that is in motion must be moved by something:for that *hich is in motion *ill al*ays be divisible) and if a partof it is not in motion the *hole must be at rest.

Since everything that is in motion must be moved by something) letus ta+e the case in *hich a thing is in locomotion and is moved by

something that is itself in motion) and that again is moved bysomethingelse that is in motion) and that by something else) and so oncontinually:then the series cannot go on to infinity) but there must be some firstmovent. ,or let us suppose that this is not so and ta+e the seriesto be infinite. et A then be moved by B) B by #) # by 5) and so on)each member of the series being moved by that *hich comes ne6t toit. Then since e6 hypothesi the movent *hile causing motion is alsoitself in motion) and the motion of the moved and the motion of themovent must proceed simultaneously 3for the movent is causing motionand the moved is being moved simultaneously4 it is evident that therespective motions of A) B) #) and each of the other moved moventsare simultaneous. et us ta+e the motion of each separately and let9 be the motion of A) J of B) and ! and $ respectively the motionsof # and 5: for though they are all moved severally one by another)yet *e may still ta+e the motion of each as numerically one) sinceevery motion is from something to something and is not infinite inrespect of its e6treme points. By a motion that is numerically oneI mean a motion that proceeds from something numerically one and thesame to something numerically one and the same in a period of timenumerically one and the same: for a motion may be the samegenerically)specifically) or numerically: it is generically the same if it belongsto the same category) e.g. substance or (uality: it is specificallythe same if it proceeds from something specifically the same tosomethingspecifically the same) e.g. from *hite to blac+ or from good to bad)*hich is not of a +ind specifically distinct: it is numerically thesame if it proceeds from something numerically one to somethingnumericallyone in the same period of time) e.g. from a particular *hite to aparticular blac+) or from a particular place to a particular place)in a particular period of time: for if the period of time *ere notone and the same) the motion *ould no longer be numerically one thoughit *ould still be specifically one.

&e have dealt *ith this (uestion above. -o* let us further ta+e thetime in *hich A has completed its motion) and let it be representedby ". Then since the motion of A is finite the time *ill also befinite.But since the movents and the things moved are infinite) the motion9J!$) i.e. the motion that is composed of all the individual motions)must be infinite. ,or the motions of A) B) and the others may bee(ual)or the motions of the others may be greater: but assuming *hat isconceivable) *e find that *hether they are e(ual or some are greater)in both cases the *hole motion is infinite. And since the motion ofA and that of each of the others are simultaneous) the *hole motionmust occupy the same time as the motion of A: but the time occupiedby the motion of A is finite: conse(uently the motion *ill be infinitein a finite time) *hich is impossible.

It might be thought that *hat *e set out to prove has thus been sho*n)but our argument so far does not prove it) because it does not yet



prove that anything impossible results from the contrary supposition:for in a finite time there may be an infinite motion) though not ofone thing) but of many: and in the case that *e are considering thisis so: for each thing accomplishes its o*n motion) and there is noimpossibility in many things being in motion simultaneously. But if3as *e see to be universally the case4 that *hich primarily is moved

locally and corporeally must be either in contact *ith or continuous*ith that *hich moves it) the things moved and the movents must becontinuous or in contact *ith one another) so that together they allform a single unity: *hether this unity is finite or infinite ma+esno difference to our present argument for in any case since thethingsin motion are infinite in number the *hole motion *ill be infinite)if) as is theoretically possible) each motion is either e(ual to orgreater than that *hich follo*s it in the series: for *e shall ta+eas actual that *hich is theoretically possible. If) then) A) B) #)5 form an infinite magnitude that passes through the motion 9J!$ inthe finite time ") this involves the conclusion that an infinitemotionis passed through in a finite time: and *hether the magnitude in(uestionis finite or infinite this is in either case impossible. Thereforethe series must come to an end) and there must be a first movent anda first moved: for the fact that this impossibility results only fromthe assumption of a particular case is immaterial) since the caseassumed is theoretically possible) and the assumption of atheoreticallypossible case ought not to give rise to any impossible result.

Part 2

That *hich is the first movement of a thing0in the sense that itsuppliesnot that for the sa+e of *hich but the source of the motion0isal*aystogether *ith that *hich is moved by it by together I mean thatthere is nothing intermediate bet*een them4. This is universally true*herever one thing is moved by another. And since there are three+inds of motion) local) (ualitative) and (uantitative) there mustalso be three +inds of movent) that *hich causes locomotion) that*hich causes alteration) and that *hich causes increase or decrease.

et us begin *ith locomotion) for this is the primary motion.9verythingthat is in locomotion is moved either by itself or by something else.In the case of things that are moved by themselves it is evident thatthe moved and the movent are together: for they contain *ithinthemselvestheir first movent) so that there is nothing in bet*een. The motionof things that are moved by something else must proceed in one offour *ays: for there are four +inds of locomotion caused by somethingother than that *hich is in motion) vi8. pulling) pushing) carrying)and t*irling. All forms of locomotion are reducible to these. Thuspushing on is a form of pushing in *hich that *hich is causing motiona*ay from itself follo*s up that *hich it pushes and continues topush it: pushing off occurs *hen the movent does not follo* up thething that it has moved: thro*ing *hen the movent causes a motiona*ay from itself more violent than the natural locomotion of the thingmoved) *hich continues its course so long as it is controlled by themotion imparted to it. Again) pushing apart and pushing together are



forms respectively of pushing off and pulling: pushing apart ispushingoff) *hich may be a motion either a*ay from the pusher or a*ay fromsomething else) *hile pushing together is pulling) *hich may be amotion to*ards something else as *ell as the puller. &e may similarlyclassify all the varieties of these last t*o) e.g. pac+ing and

combing:the former is a form of pushing together) the latter a form of pushingapart. The same is true of the other processes of combination andseparation 3they *ill all be found to be forms of pushing apart orof pushing together4) e6cept such as are involved in the processesof becoming and perishing. 3At same time it is evident that thereis no other +ind of motion but combination and separation: for theymay all be apportioned to one or other of those already mentioned.4Again) inhaling is a form of pulling) e6haling a form of pushing:and the same is true of spitting and of all other motions that proceedthrough the body) *hether secretive or assimilative) the assimilativebeing forms of pulling) the secretive of pushing off. All other +indsof locomotion must be similarly reduced) for they all fall under oneor other of our four heads. And again) of these four) carrying andt*irling are to pulling and pushing. ,or carrying al*ays follo*s oneof the other three methods) for that *hich is carried is in motionaccidentally) because it is in or upon something that is in motion)and that *hich carries it is in doing so being either pulled or pushedor t*irled thus carrying belongs to all the other three +inds ofmotion in common. And t*irling is a compound of pulling and pushing)for that *hich is t*irling a thing must be pulling one part of thething and pushing another part) since it impels one part a*ay fromitself and another part to*ards itself. If) therefore) it can be sho*nthat that *hich is pushing and that *hich is pushing and pulling aread'acent respectively to that *hich is being pushed and that *hichis being pulled) it *ill be evident that in all locomotion there isnothing intermediate bet*een moved and movent. But the former factis clear even from the definitions of pushing and pulling) for pushingis motion to something else from oneself or from something else) andpulling is motion from something else to oneself or to something else)*hen the motion of that *hich is pulling is (uic+er than the motionthat *ould separate from one another the t*o things that arecontinuous:for it is this that causes one thing to be pulled on along *ith theother. 3It might indeed be thought that there is a form of pullingthat arises in another *ay: that *ood) e.g. pulls fire in a mannerdifferent from that described above. But it ma+es no difference*hetherthat *hich pulls is in motion or is stationary *hen it is pulling:in the latter case it pulls to the place *here it is) *hile in theformer it pulls to the place *here it *as.4 -o* it is impossible tomove anything either from oneself to something else or something elseto oneself *ithout being in contact *ith it: it is evident) therefore)that in all locomotion there is nothing intermediate bet*een movedand movent.

-or again is there anything intermediate bet*een that *hich undergoesand that *hich causes alteration: this can be proved by induction:for in every case *e find that the respective e6tremities of that*hich causes and that *hich undergoes alteration are ad'acent. ,orour assumption is that things that are undergoing alteration arealteredin virtue of their being affected in respect of their so0calledaffective(ualities) since that *hich is of a certain (uality is altered in



so far as it is sensible) and the characteristics in *hich bodiesdiffer from one another are sensible characteristics: for every bodydiffers from another in possessing a greater or lesser number ofsensiblecharacteristics or in possessing the same sensible characteristicsin a greater or lesser degree. But the alteration of that *hich

undergoesalteration is also caused by the above0mentioned characteristics)*hich are affections of some particular underlying (uality. Thus *esay that a thing is altered by becoming hot or s*eet or thic+ or dryor *hite: and *e ma+e these assertions ali+e of *hat is inanimateand of *hat is animate) and further) *here animate things are in(uestion)*e ma+e them both of the parts that have no po*er of sense0perceptionand of the senses themselves. ,or in a *ay even the senses undergoalteration) since the active sense is a motion through the body inthe course of *hich the sense is affected in a certain *ay. &e see)then) that the animate is capable of every +ind of alteration of *hichthe inanimate is capable: but the inanimate is not capable of every+ind of alteration of *hich the animate is capable) since it is notcapable of alteration in respect of the senses: moreover the inanimateis unconscious of being affected by alteration) *hereas the animateis conscious of it) though there is nothing to prevent the animatealso being unconscious of it *hen the process of the alteration doesnot concern the senses. Since) then) the alteration of that *hichundergoes alteration is caused by sensible things) in every case ofsuch alteration it is evident that the respective e6tremities of that*hich causes and that *hich undergoes alteration are ad'acent. Thusthe air is continuous *ith that *hich causes the alteration) and thebody that undergoes alteration is continuous *ith the air. Again)the colour is continuous *ith the light and the light *ith the sight.And the same is true of hearing and smelling: for the primary moventin respect to the moved is the air. Similarly) in the case of tasting)the flavour is ad'acent to the sense of taste. And it is 'ust thesame in the case of things that are inanimate and incapable of sense0perception.Thus there can be nothing intermediate bet*een that *hich undergoesand that *hich causes alteration.

-or) again) can there be anything intermediate bet*een that *hichsuffers and that *hich causes increase: for the part of the latterthat starts the increase does so by becoming attached in such a *ayto the former that the *hole becomes one. Again) the decrease of that*hich suffers decrease is caused by a part of the thing becomingdetached.So that *hich causes increase and that *hich causes decrease mustbe continuous *ith that *hich suffers increase and that *hich suffersdecrease respectively: and if t*o things are continuous *ith oneanotherthere can be nothing intermediate bet*een them.

It is evident) therefore) that bet*een the e6tremities of the movedand the movent that are respectively first and last in reference tothe moved there is nothing intermediate.

Part ;

9verything) *e say) that undergoes alteration is altered by sensiblecauses) and there is alteration only in things that are said to beessentially affected by sensible things. The truth of this is to beseen from the follo*ing considerations. $f all other things it *ould



be most natural to suppose that there is alteration in figures andshapes) and in ac(uired states and in the processes of ac(uiring andlosing these: but as a matter of fact in neither of these t*o classesof things is there alteration.

In the first place) *hen a particular formation of a thing is

completed)*e do not call it by the name of its material: e.g. *e do not callthe statue bron8e or the pyramid *a6 or the bed *ood ) but *euse a derived e6pression and call them of bron8e ) *a6en ) and

*oodenrespectively. But *hen a thing has been affected and altered in any*ay *e still call it by the original name: thus *e spea+ of the bron8eor the *a6 being dry or fluid or hard or hot.

And not only so: *e also spea+ of the particular fluid or hotsubstanceas being bron8e) giving the material the same name as that *hich *euse to describe the affection.

Since) therefore) having regard to the figure or shape of a thing*e no longer call that *hich has become of a certain figure by thename of the material that e6hibits the figure) *hereas having regardto a thing s affections or alterations *e still call it by the nameof its material) it is evident that becomings of the former +indcannotbe alterations.

1oreover it *ould seem absurd even to spea+ in this *ay) to spea+)that is to say) of a man or house or anything else that has come intoe6istence as having been altered. Though it may be true that everysuch becoming is necessarily the result of something s being altered)the result) e.g. of the material s being condensed or rarefied orheated or cooled) nevertheless it is not the things that are cominginto e6istence that are altered) and their becoming is not analteration.

Again) ac(uired states) *hether of the body or of the soul) are notalterations. ,or some are e6cellences and others are defects) andneither e6cellence nor defect is an alteration: e6cellence is aperfection3for *hen anything ac(uires its proper e6cellence *e call it perfect)since it is then if ever that *e have a thing in its natural state:e.g. *e have a perfect circle *hen *e have one as good as possible4)*hile defect is a perishing of or departure from this condition. Soas *hen spea+ing of a house *e do not call its arrival at perfectionan alteration 3for it *ould be absurd to suppose that the coping orthe tiling is an alteration or that in receiving its coping or itstiling a house is altered and not perfected4) the same also holdsgood in the case of e6cellences and defects and of the persons orthings that possess or ac(uire them: for e6cellences are perfectionsof a thing s nature and defects are departures from it: conse(uentlythey are not alterations.

,urther) *e say that all e6cellences depend upon particular relations.Thus bodily e6cellences such as health and a good state of body *eregard as consisting in a blending of hot and cold elements *ithinthe body in due proportion) in relation either to one another or tothe surrounding atmosphere: and in li+e manner *e regard beauty)strength)and all the other bodily e6cellences and defects. 9ach of them e6ists



in virtue of a particular relation and puts that *hich possesses itin a good or bad condition *ith regard to its proper affections) *hereby proper affections I mean those influences that from the naturalconstitution of a thing tend to promote or destroy its e6istence.Since then) relatives are neither themselves alterations nor thesub'ects

of alteration or of becoming or in fact of any change *hatever) itis evident that neither states nor the processes of losing andac(uiringstates are alterations) though it may be true that their becomingor perishing is necessarily) li+e the becoming or perishing of aspecificcharacter or form) the result of the alteration of certain otherthings)e.g. hot and cold or dry and *et elements or the elements) *hateverthey may be) on *hich the states primarily depend. ,or each severalbodily defect or e6cellence involves a relation *ith those thingsfrom *hich the possessor of the defect or e6cellence is naturallysub'ect to alteration: thus e6cellence disposes its possessor to beunaffected by these influences or to be affected by those of themthat ought to be admitted) *hile defect disposes its possessor tobe affected by them or to be unaffected by those of them that oughtto be admitted.

And the case is similar in regard to the states of the soul) all of*hich 3li+e those of body4 e6ist in virtue of particular relations)the e6cellences being perfections of nature and the defects departuresfrom it: moreover) e6cellence puts its possessor in good condition)*hile defect puts its possessor in a bad condition) to meet his properaffections. Conse(uently these cannot any more than the bodily statesbe alterations) nor can the processes of losing and ac(uiring thembe so) though their becoming is necessarily the result of analterationof the sensitive part of the soul) and this is altered by sensibleob'ects: for all moral e6cellence is concerned *ith bodily pleasuresand pains) *hich again depend either upon acting or upon rememberingor upon anticipating. -o* those that depend upon action are determinedby sense0perception) i.e. they are stimulated by something sensible:and those that depend upon memory or anticipation are li+e*ise tobe traced to sense0perception) for in these cases pleasure is felteither in remembering *hat one has e6perienced or in anticipating*hat one is going to e6perience. Thus all pleasure of this +ind mustbe produced by sensible things: and since the presence in any oneof moral defect or e6cellence involves the presence in him of pleasureor pain 3*ith *hich moral e6cellence and defect are al*ays concerned4)and these pleasures and pains are alterations of the sensitive part)it is evident that the loss and ac(uisition of these states no lessthan the loss and ac(uisition of the states of the body must be theresult of the alteration of something else. Conse(uently) though theirbecoming is accompanied by an alteration) they are not themselvesalterations.

Again) the states of the intellectual part of the soul are notalterations)nor is there any becoming of them. In the first place it is much moretrue of the possession of +no*ledge that it depends upon a particularrelation. And further) it is evident that there is no becoming ofthese states. ,or that *hich is potentially possessed of +no*ledgebecomes actually possessed of it not by being set in motion at allitself but by reason of the presence of something else: i.e. it is*hen it meets *ith the particular ob'ect that it +no*s in a manner



the particular through its +no*ledge of the universal. 3Again) thereis no becoming of the actual use and activity of these states) unlessit is thought that there is a becoming of vision and touching andthat the activity in (uestion is similar to these.4 And the originalac(uisition of +no*ledge is not a becoming or an alteration: for theterms +no*ing and understanding imply that the intellect has

reacheda state of rest and come to a standstill) and there is no becomingthat leads to a state of rest) since) as *e have said above) changeat all can have a becoming. 1oreover) 'ust as to say) *hen any onehas passed from a state of into6ication or sleep or disease to thecontrary state) that he has become possessed of +no*ledge again isincorrect in spite of the fact that he *as previously incapable ofusing his +no*ledge) so) too) *hen any one originally ac(uires thestate) it is incorrect to say that he becomes possessed of +no*ledge:for the possession of understanding and +no*ledge is produced by thesoul s settling do*n out of the restlessness natural to it. !ence)too) in learning and in forming 'udgements on matters relating totheir sense0perceptions children are inferior to adults o*ing to thegreat amount of restlessness and motion in their souls. -ature itselfcauses the soul to settle do*n and come to a state of rest for theperformance of some of its functions) *hile for the performance ofothers other things do so: but in either case the result is broughtabout through the alteration of something in the body) as *e see inthe case of the use and activity of the intellect arising from a man sbecoming sober or being a*a+ened. It is evident) then) from theprecedingargument that alteration and being altered occur in sensible thingsand in the sensitive part of the soul) and) e6cept accidentally) innothing else.

Part >

A difficulty may be raised as to *hether every motion is commensurable*ith every other or not. -o* if they are all commensurable and ift*o things to have the same velocity must accomplish an e(ual motionin an e(ual time) then *e may have a circumference e(ual to a straightline) or) of course) the one may be greater or less than the other.,urther) if one thing alters and another accomplishes a locomotionin an e(ual time) *e may have an alteration and a locomotion e(ualto one another: thus an affection *ill be e(ual to a length) *hichis impossible. But is it not only *hen an e(ual motion is accomplishedby t*o things in an e(ual time that the velocities of the t*o aree(ual7 -o* an affection cannot be e(ual to a length. Therefore therecannot be an alteration e(ual to or less than a locomotion: andconse(uentlyit is not the case that every motion is commensurable *ith everyother.

But ho* *ill our conclusion *or+ out in the case of the circle andthe straight line7 It *ould be absurd to suppose that the motion ofone in a circle and of another in a straight line cannot be similar)but that the one must inevitably move more (uic+ly or more slo*lythan the other) 'ust as if the course of one *ere do*nhill and ofthe other uphill. 1oreover it does not as a matter of fact ma+e anydifference to the argument to say that the one motion must inevitablybe (uic+er or slo*er than the other: for then the circumference canbe greater or less than the straight line and if so it is possiblefor the t*o to be e(ual. ,or if in the time A the (uic+er 3B4 passesover the distance B and the slo*er 3#4 passes over the distance # )B *ill be greater than # : for this is *hat *e too+ (uic+er to



mean: and so (uic+er motion also implies that one thing traversesan e(ual distance in less time than another: conse(uently there *illbe a part of A in *hich B *ill pass over a part of the circle e(ualto # ) *hile # *ill occupy the *hole of A in passing over # . -onethe less) if the t*o motions are commensurable) *e are confronted*ith the conse(uence stated above) vi8. that there may be a straight

line e(ual to a circle. But these are not commensurable: and so thecorresponding motions are not commensurable either.

But may *e say that things are al*ays commensurable if the same termsare applied to them *ithout e(uivocation7 e.g. a pen) a *ine) andthe highest note in a scale are not commensurable: *e cannot say*hetherany one of them is sharper than any other: and *hy is this7 they areincommensurable because it is only e(uivocally that the same term

sharp is applied to them: *hereas the highest note in a scale iscommensurable *ith the leading0note) because the term sharp hasthe same meaning as applied to both. Can it be) then) that the term

(uic+ has not the same meaning as applied to straight motion andto circular motion respectively7 If so) far less *ill it have thesame meaning as applied to alteration and to locomotion.

$r shall *e in the first place deny that things are al*ayscommensurableif the same terms are applied to them *ithout e(uivocation7 ,or theterm much has the same meaning *hether applied to *ater or to air)yet *ater and air are not commensurable in respect of it: or) if thisillustration is not considered satisfactory) double at any rate*ould seem to have the same meaning as applied to each 3denoting ineach case the proportion of t*o to one4) yet *ater and air are notcommensurable in respect of it. But here again may *e not ta+e upthe same position and say that the term much is e(uivocal7 In factthere are some terms of *hich even the definitions are e(uivocale.g. if much *ere defined as so much and more ) so much *ouldmean something different in different cases: e(ual is similarlye(uivocal and one again is perhaps inevitably an e(uivocal termand if one is e(uivocal) so is t*o . $ther*ise *hy is it that somethings are commensurable *hile others are not) if the nature of theattribute in the t*o cases is really one and the same7

Can it be that the incommensurability of t*o things in respect ofany attribute is due to a difference in that *hich is primarilycapableof carrying the attribute7 Thus horse and dog are so commensurablethat *e may say *hich is the *hiter) since that *hich primarilycontainsthe *hiteness is the same in both) vi8. the surface: and similarlythey are commensurable in respect of si8e. But *ater and speech arenot commensurable in respect of clearness) since that *hich primarilycontains the attribute is different in the t*o cases. It *ould seem)ho*ever that *e must re'ect this solution) since clearly *e couldthus ma+e all e(uivocal attributes univocal and say merely that thatcontains each of them is different in different cases: thus

e(uality )s*eetness ) and *hiteness *ill severally al*ays be the same) though

that *hich contains them is different in different cases. 1oreover)it is not any casual thing that is capable of carrying any attribute:each single attribute can be carried primarily only by one singlething.



1ust *e then say that) if t*o things are to be commensurable inrespectof any attribute) not only must the attribute in (uestion beapplicableto both *ithout e(uivocation) but there must also be no specificdifferences

either in the attribute itself or in that *hich contains theattribute0thatthese) I mean) must not be divisible in the *ay in *hich colour isdivided into +inds7 Thus in this respect one thing *ill not becommensurable*ith another) i.e. *e cannot say that one is more coloured than theother *here only colour in general and not any particular colour ismeant but they are commensurable in respect of *hiteness.

Similarly in the case of motion: t*o things are of the same velocityif they occupy an e(ual time in accomplishing a certain e(ual amountof motion. Suppose) then) that in a certain time an alteration isundergone by one half of a body s length and a locomotion isaccomplishedthe other half: can be say that in this case the alteration is e(ualto the locomotion and of the same velocity7 That *ould be absurd)and the reason is that there are different species of motion. Andif in conse(uence of this *e must say that t*o things are of e(ualvelocity if they accomplish locomotion over an e(ual distance in ane(ual time) *e have to admit the e(uality of a straight line and acircumference. &hat) then) is the reason of this7 Is it thatlocomotionis a genus or that line is a genus7 3&e may leave the time out ofaccount) since that is one and the same.4 If the lines arespecificallydifferent) the locomotions also differ specifically from one another:for locomotion is specifically differentiated according to thespecificdifferentiation of that over *hich it ta+es place. 3It is alsosimilarlydifferentiated) it *ould seem) accordingly as the instrument of thelocomotion is different: thus if feet are the instrument) it is*al+ing)if *ings it is flying but perhaps *e should rather say that thisis not so) and that in this case the differences in the locomotionare merely differences of posture in that *hich is in motion.4 &emay say) therefore) that things are of e(ual velocity in an e(ualtime they traverse the same magnitude: and *hen I call it the sameI mean that it contains no specific difference and therefore nodifferencein the motion that ta+es place over it. So *e have no* to considerho* motion is differentiated: and this discussion serves to sho* thatthe genus is not a unity but contains a plurality latent in it anddistinct from it) and that in the case of e(uivocal terms sometimesthe different senses in *hich they are used are far removed from oneanother) *hile sometimes there is a certain li+eness bet*een them)and sometimes again they are nearly related either generically oranalogically) *ith the result that they seem not to be e(uivocalthoughthey really are.

&hen) then) is there a difference of species7 Is an attributespecificallydifferent if the sub'ect is different *hile the attribute is the same)or must the attribute itself be different as *ell7 And ho* are *e



to define the limits of a species7 &hat *ill enable us to decide thatparticular instances of *hiteness or s*eetness are the same ordifferent7Is it enough that it appears different in one sub'ect from *hatappearsin another7 $r must there be no sameness at all7 And further) *here

alteration is in (uestion) ho* is one alteration to be of e(ualvelocity*ith another7 $ne person may be cured (uic+ly and another slo*ly)and cures may also be simultaneous: so that) recovery of health beingan alteration) *e have here alterations of e(ual velocity) since eachalteration occupies an e(ual time. But *hat alteration7 &e cannothere spea+ of an e(ual alteration: *hat corresponds in the categoryof (uality to e(uality in the category of (uantity is li+eness .!o*ever) let us say that there is e(ual velocity *here the same changeis accomplished in an e(ual time. Are *e) then) to find thecommensurabilityin the sub'ect of the affection or in the affection itself7 In thecase that *e have 'ust been considering it is the fact that healthis one and the same that enables us to arrive at the conclusion thatthe one alteration is neither more nor less than the other) but thatboth are ali+e. If on the other hand the affection is different inthe t*o cases) e.g. *hen the alterations ta+e the form of becoming*hite and becoming healthy respectively) here there is no samenessor e(uality or li+eness inasmuch as the difference in the affectionsat once ma+es the alterations specifically different) and there isno unity of alteration any more than there *ould be unity oflocomotionunder li+e conditions. So *e must find out ho* many species thereare of alteration and of locomotion respectively. -o* if the thingsthat are in motion0that is to say) the things to *hich the motionsbelong essentially and not accidentally0differ specifically) thentheir respective motions *ill also differ specifically: if on theother hand they differ generically or numerically) the motions also*ill differ generically or numerically as the case may be. But therestill remains the (uestion *hether) supposing that t*o alterationsare of e(ual velocity) *e ought to loo+ for this e(uality in thesameness3or li+eness4 of the affections) or in the things altered) to seee.g. *hether a certain (uantity of each has become *hite. $r ought*e not rather to loo+ for it in both7 That is to say) the alterationsare the same or different according as the affections are the sameor different) *hile they are e(ual or une(ual according as the thingsaltered are e(ual or une(ual.

And no* *e must consider the same (uestion in the case of becomingand perishing: ho* is one becoming of e(ual velocity *ith another7They are of e(ual velocity if in an e(ual time there are producedt*o things that are the same and specifically inseparable) e.g. t*omen 3not merely generically inseparable as e.g. t*o animals4.Similarlyone is (uic+er than the other if in an e(ual time the product isdifferentin the t*o cases. I state it thus because *e have no pair of termsthat *ill convey this difference in the *ay in *hich unli+enessis conveyed. If *e adopt the theory that it is number that constitutesbeing) *e may indeed spea+ of a greater number and a lesser number*ithin the same species) but there is no common term that *ill includeboth relations) nor are there terms to e6press each of them separatelyin the same *ay as *e indicate a higher degree or preponderance ofan affection by more ) of a (uantity by greater.



Part ?

-o* since *herever there is a movent) its motion al*ays acts uponsomething) is al*ays in something) and al*ays e6tends to something3by is al*ays in something I mean that it occupies a time: and by

e6tends to something I mean that it involves the traversing of acertain amount of distance: for at any moment *hen a thing is causingmotion) it also has caused motion) so that there must al*ays be acertain amount of distance that has been traversed and a certainamountof time that has been occupied4. then) A the movement have moved Ba distance # in a time 5) then in the same time the same force A *illmove %/2B t*ice the distance #) and in %/25 it *ill move %/2B the*hole distance for #: thus the rules of proportion *ill be observed.Again if a given force move a given *eight a certain distance in acertain time and half the distance in half the time) half the motivepo*er *ill move half the *eight the same distance in the same time.

et 9 represent half the motive po*er A and J half the *eight B: thenthe ratio bet*een the motive po*er and the *eight in the one caseis similar and proportionate to the ratio in the other) so that eachforce *ill cause the same distance to be traversed in the same time.But if 9 move J a distance # in a time 5) it does not necessarilyfollo* that 9 can move t*ice J half the distance # in the same time.If) then) A move B a distance # in a time 5) it does not follo* that9) being half of A) *ill in the time 5 or in any fraction of it causeB to traverse a part of # the ratio bet*een *hich and the *hole of# is proportionate to that bet*een A and 9 3*hatever fraction of A9may be4: in fact it might *ell be that it *ill cause no motion atall for it does not follo* that) if a given motive po*er causes acertain amount of motion) half that po*er *ill cause motion eitherof any particular amount or in any length of time: other*ise one manmight move a ship) since both the motive po*er of the ship0haulersand the distance that they all cause the ship to traverse aredivisibleinto as many parts as there are men. !ence Jeno s reasoning is false*hen he argues that there is no part of the millet that does not ma+ea sound: for there is no reason *hy any such part should not in anylength of time fail to move the air that the *hole bushel moves infalling. In fact it does not of itself move even such a (uantity ofthe air as it *ould move if this part *ere by itself: for no parteven e6ists other*ise than potentially.

If on the other hand *e have t*o forces each of *hich separately movesone of t*o *eights a given distance in a given time) then the forcesin combination *ill move the combined *eights an e(ual distance inan e(ual time: for in this case the rules of proportion apply.

Then does this hold good of alteration and of increase also7 Surelyit does) for in any given case *e have a definite thing that causeincrease and a definite thing that suffers increase) and the onecausesand the other suffers a certain amount of increase in a certain amountof time. Similarly *e have a definite thing that causes alterationand a definite thing that undergoes alteration) and a certain amount)or rather degree) of alteration is completed in a certain amount oftime: thus in t*ice as much time t*ice as much alteration *ill becompleted and conversely t*ice as much alteration *ill occupy t*iceas much time: and the alteration of half of its ob'ect *ill occupyhalf as much time and in half as much time half of the ob'ect *illbe altered: or again) in the same amount of time it *ill be altered



t*ice as much.

$n the other hand if that *hich causes alteration or increase causesa certain amount of increase or alteration respectively in a certainamount of time) it does not necessarily follo* that half the force*ill occupy t*ice the time in altering or increasing the ob'ect) or

that in t*ice the time the alteration or increase *ill be completedby it: it may happen that there *ill be no alteration or increaseat all) the case being the same as *ith the *eight.

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B$$" III

Part %

It remains to consider the follo*ing (uestion. &as there ever abecomingof motion before *hich it had no being) and is it perishing againso as to leave nothing in motion7 $r are *e to say that it never hadany becoming and is not perishing) but al*ays *as and al*ays *illbe7 Is it in fact an immortal never0failing property of things thatare) a sort of life as it *ere to all naturally constituted things7

-o* the e6istence of motion is asserted by all *ho have anything tosay about nature) because they all concern themselves *ith theconstructionof the *orld and study the (uestion of becoming and perishing) *hichprocesses could not come about *ithout the e6istence of motion. Butthose *ho say that there is an infinite number of *orlds) some of*hich are in process of becoming *hile others are in process ofperishing)assert that there is al*ays motion 3for these processes of becomingand perishing of the *orlds necessarily involve motion4) *hereas those*ho hold that there is only one *orld) *hether everlasting or not)ma+e corresponding assumptions in regard to motion. If then it ispossible that at any time nothing should be in motion) this must comeabout in one of t*o *ays: either in the manner described byAna6agoras)*ho says that all things *ere together and at rest for an infiniteperiod of time) and that then 1ind introduced motion and separatedthem or in the manner described by 9mpedocles) according to *homthe universe is alternately in motion and at rest0in motion) *hen

ove is ma+ing the one out of many) or Strife is ma+ing many out ofone) and at rest in the intermediate periods of time0his account beingas follo*s:

Since $ne hath learned to spring from 1anifold) And $ne dis'oinedma+es manifold arise) Thus they Become) nor stable is their life:But since their motion must alternate be) Thus have they ever estupon their round : for *e must suppose that he means by this thatthey alternate from the one motion to the other. &e must consider)then) ho* this matter stands) for the discovery of the truth aboutit is of importance) not only for the study of nature) but also forthe investigation of the ,irst Principle.

et us ta+e our start from *hat *e have already laid do*n in ourcourseon Physics. 1otion) *e say) is the fulfilment of the movable in sofar as it is movable. 9ach +ind of motion) therefore) necessarilyinvolves the presence of the things that are capable of that motion.



In fact) even apart from the definition of motion) every one *ouldadmit that in each +ind of motion it is that *hich is capable of thatmotion that is in motion: thus it is that *hich is capable ofalterationthat is altered) and that *hich is capable of local change that isin locomotion: and so there must be something capable of being burned

before there can be a process of being burned) and something capableof burning before there can be a process of burning. 1oreover) thesethings also must either have a beginning before *hich they had nobeing) or they must be eternal. -o* if there *as a becoming of everymovable thing) it follo*s that before the motion in (uestion anotherchange or motion must have ta+en place in *hich that *hich *as capableof being moved or of causing motion had its becoming. To suppose)on the other hand) that these things *ere in being throughout allprevious time *ithout there being any motion appears unreasonableon a moment s thought) and still more unreasonable) *e shall find)on further consideration. ,or if *e are to say that) *hile there areon the one hand things that are movable) and on the other hand thingsthat are motive) there is a time *hen there is a first movent anda first moved) and another time *hen there is no such thing but onlysomething that is at rest) then this thing that is at rest mustpreviouslyhave been in process of change: for there must have been some causeof its rest) rest being the privation of motion. Therefore) beforethis first change there *ill be a previous change. ,or some thingscause motion in only one *ay) *hile others can produce either of t*ocontrary motions: thus fire causes heating but not cooling) *hereasit *ould seem that +no*ledge may be directed to t*o contrary ends*hile remaining one and the same. 9ven in the former class) ho*ever)there seems to be something similar) for a cold thing in a sensecausesheating by turning a*ay and retiring) 'ust as one possessed of+no*ledgevoluntarily ma+es an error *hen he uses his +no*ledge in the reverse*ay. But at any rate all things that are capable respectively ofaffectingand being affected) or of causing motion and being moved) are capableof it not under all conditions) but only *hen they are in a particularcondition and approach one another: so it is on the approach of onething to another that the one causes motion and the other is moved)and *hen they are present under such conditions as rendered the onemotive and the other movable. So if the motion *as not al*ays inprocess)it is clear that they must have been in a condition not such as torender them capable respectively of being moved and of causing motion)and one or other of them must have been in process of change: forin *hat is relative this is a necessary conse(uence: e.g. if one thingis double another *hen before it *as not so) one or other of them)if not both) must have been in process of change. It follo*s then)that there *ill be a process of change previous to the first.

3,urther) ho* can there be any before and after *ithout thee6istenceof time7 $r ho* can there be any time *ithout the e6istence of motion7If) then) time is the number of motion or itself a +ind of motion)it follo*s that) if there is al*ays time) motion must also be eternal.But so far as time is concerned *e see that all *ith one e6ceptionare in agreement in saying that it is uncreated: in fact) it is 'ustthis that enables 5emocritus to sho* that all things cannot have hada becoming: for time) he says) is uncreated. Plato alone asserts thecreation of time) saying that it had a becoming together *ith the



universe) the universe according to him having had a becoming. -o*since time cannot e6ist and is unthin+able apart from the moment)and the moment a +ind of middle0point) uniting as it does in itselfboth a beginning and an end) a beginning of future time and an endof past time) it follo*s that there must al*ays be time: for thee6tremity

of the last period of time that *e ta+e must be found in some moment)since time contains no point of contact for us e6cept the moment.Therefore) since the moment is both a beginning and an end) theremust al*ays be time on both sides of it. But if this is true of time)it is evident that it must also be true of motion) time being a +indof affection of motion.4

The same reasoning *ill also serve to sho* the imperishability ofmotion: 'ust as a becoming of motion *ould involve) as *e sa*) thee6istence of a process of change previous to the first) in the same*ay a perishing of motion *ould involve the e6istence of a processof change subse(uent to the last: for *hen a thing ceases to be moved)it does not therefore at the same time cease to be movable0e.g. thecessation of the process of being burned does not involve thecessationof the capacity of being burned) since a thing may be capable of beingburned *ithout being in process of being burned0nor) *hen a thingceases to be movent) does it therefore at the same time cease to abe motive. Again) the destructive agent *ill have to be destroyed)after *hat it destroys has been destroyed) and then that *hich hasthe capacity of destroying it *ill have to be destroyed after*ards)3so that there *ill be a process of change subse(uent to the last)4for being destroyed also is a +ind of change. If) then) vie* *hich*e are critici8ing involves these impossible conse(uences) it is clearthat motion is eternal and cannot have e6isted at one time and notat another: in fact such a vie* can hardly be described as anythlingelse than fantastic.

And much the same may be said of the vie* that such is the ordinanceof nature and that this must be regarded as a principle) as *ouldseem to be the vie* of 9mpedocles *hen he says that the constitutionof the *orld is of necessity such that ove and Strife alternatelypredominate and cause motion) *hile in the intermediate period oftime there is a state of rest. Probably also those *ho li+e li+eAna6agoras)assert a single principle 3of motion4 *ould hold this vie*. But that*hich is produced or directed by nature can never be anythingdisorderly:for nature is every*here the cause of order. 1oreover) there is noratio in the relation of the infinite to the infinite) *hereas orderal*ays means ratio. But if *e say that there is first a state of restfor an infinite time) and then motion is started at some moment) andthat the fact that it is this rather than a previous moment is ofno importance) and involves no order) then *e can no longer say thatit is nature s *or+: for if anything is of a certain characternaturally)it either is so invariably and is not sometimes of this and sometimesof another character 3e.g. fire) *hich travels up*ards naturally)does not sometimes do so and sometimes not4 or there is a ratio inthe variation. It *ould be better) therefore) to say *ith 9mpedoclesand any one else *ho may have maintained such a theory as his thatthe universe is alternately at rest and in motion: for in a systemof this +ind *e have at once a certain order. But even here the holderof the theory ought not only to assert the fact: he ought to e6plainthe cause of it: i.e. he should not ma+e any mere assumption or lay



do*n any gratuitous a6iom) but should employ either inductive ordemonstrativereasoning. The ove and Strife postulated by 9mpedocles are not inthemselves causes of the fact in (uestion) nor is it of the essenceof either that it should be so) the essential function of the formerbeing to unite) of the latter to separate. If he is to go on to

e6plainthis alternate predominance) he should adduce cases *here such a stateof things e6ists) as he points to the fact that among man+ind *e havesomething that unites men) namely ove) *hile on the other handenemiesavoid one another: thus from the observed fact that this occurs incertain cases comes the assumption that it occurs also in theuniverse.Then) again) some argument is needed to e6plain *hy the predominanceof each of the t*o forces lasts for an e(ual period of time. But itis a *rong assumption to suppose universally that *e have an ade(uatefirst principle in virtue of the fact that something al*ays is soor al*ays happens so. Thus 5emocritus reduces the causes that e6plainnature to the fact that things happened in the past in the same *ayas they happen no*: but he does not thin+ fit to see+ for a firstprinciple to e6plain this al*ays : so) *hile his theory is rightin so far as it is applied to certain individual cases) he is *rongin ma+ing it of universal application. Thus) a triangle al*ays hasits angles e(ual to t*o right angles) but there is nevertheless anulterior cause of the eternity of this truth) *hereas first principlesare eternal and have no ulterior cause. et this conclude *hat *ehave to say in support of our contention that there never *as a time*hen there *as not motion) and never *ill be a time *hen there *illnot be motion.

Part 2

The arguments that may be advanced against this position are notdifficultto dispose of. The chief considerations that might be thought toindicatethat motion may e6ist though at one time it had not e6isted at allare the follo*ing:

,irst) it may be said that no process of change is eternal: for thenature of all change is such that it proceeds from something tosomething)so that every process of change must be bounded by the contrariesthat mar+ its course) and no motion can go on to infinity.

Secondly) *e see that a thing that neither is in motion nor containsany motion *ithin itself can be set in motion e.g. inanimate thingsthat are 3*hether the *hole or some part is in (uestion4 not in motionbut at rest) are at some moment set in motion: *hereas) if motioncannot have a becoming before *hich it had no being) these thingsought to be either al*ays or never in motion.

Thirdly) the fact is evident above all in the case of animate beings:for it sometimes happens that there is no motion in us and *e are(uite still) and that nevertheless *e are then at some moment setin motion) that is to say it sometimes happens that *e produce abeginningof motion in ourselves spontaneously *ithout anything having set usin motion from *ithout. &e see nothing li+e this in the case ofinanimate



things) *hich are al*ays set in motion by something else from *ithout:the animal) on the other hand) *e say) moves itself: therefore) ifan animal is ever in a state of absolute rest) *e have a motionlessthing in *hich motion can be produced from the thing itself) and notfrom *ithout. -o* if this can occur in an animal) *hy should not thesame be true also of the universe as a *hole7 If it can occur in a

small *orld it could also occur in a great one: and if it can occurin the *orld) it could also occur in the infinite that is) if theinfinite could as a *hole possibly be in motion or at rest.

$f these ob'ections) then) the first0mentioned motion to oppositesis not al*ays the same and numerically one a correct statement infact) this may be said to be a necessary conclusion) provided thatit is possible for the motion of that *hich is one and the same tobe not al*ays one and the same. 3I mean that e.g. *e may (uestion*hether the note given by a single string is one and the same) oris different each time the string is struc+) although the string isin the same condition and is moved in the same *ay.4 But still)ho*everthis may be) there is nothing to prevent there being a motion thatis the same in virtue of being continuous and eternal: *e shall havesomething to say later that *ill ma+e this point clearer.

As regards the second ob'ection) no absurdity is involved in the factthat something not in motion may be set in motion) that *hich causedthe motion from *ithout being at one time present) and at anotherabsent. -evertheless) ho* this can be so remains matter for in(uiryho* it comes about) I mean) that the same motive force at one timecauses a thing to be in motion) and at another does not do so: forthe difficulty raised by our ob'ector really amounts to this0*hy isit that some things are not al*ays at rest) and the rest al*ays inmotion7

The third ob'ection may be thought to present more difficulty thanthe others) namely) that *hich alleges that motion arises in thingsin *hich it did not e6ist before) and adduces in proof the case ofanimate things: thus an animal is first at rest and after*ards *al+s)not having been set in motion apparently by anything from *ithout.This) ho*ever) is false: for *e observe that there is al*ays somepart of the animal s organism in motion) and the cause of the motionof this part is not the animal itself) but) it may be) itsenvironment.1oreover) *e say that the animal itself originates not all of itsmotions but its locomotion. So it may *ell be the case0or rather *emay perhaps say that it must necessarily be the case0that many motionsare produced in the body by its environment) and some of these setin motion the intellect or the appetite) and this again then setsthe *hole animal in motion: this is *hat happens *hen animals areasleep: though there is then no perceptive motion in them) there issome motion that causes them to *a+e up again. But *e *ill leave thispoint also to be elucidated at a later stage in our discussion.

Part ;

$ur en(uiry *ill resolve itself at the outset into a considerationof the above0mentioned problem0*hat can be the reason *hy some thingsin the *orld at one time are in motion and at another are at restagain7 -o* one of three things must be true: either all things areal*ays at rest) or all things are al*ays in motion) or some thingsare in motion and others at rest: and in this last case again eitherthe things that are in motion are al*ays in motion and the things



that are at rest are al*ays at rest) or they are all constituted soas to be capable ali+e of motion and of rest or there is yet a thirdpossibility remaining0it may be that some things in the *orld areal*ays motionless) others al*ays in motion) *hile others again admitof both conditions. This last is the account of the matter that *emust give: for herein lies the solution of all the difficulties raised

and the conclusion of the investigation upon *hich *e are engaged.

To maintain that all things are at rest) and to disregard sense0perceptionin an attempt to sho* the theory to be reasonable) *ould be aninstanceof intellectual *ea+ness: it *ould call in (uestion a *hole system)not a particular detail: moreover) it *ould be an attac+ not onlyon the physicist but on almost all sciences and all received opinions)since motion plays a part in all of them. ,urther) 'ust as inargumentsabout mathematics ob'ections that involve first principles do notaffect the mathematician0and the other sciences are in similar case0so)too) ob'ections involving the point that *e have 'ust raised do notaffect the physicist: for it is a fundamental assumption *ith himthat motion is ultimately referable to nature herself.

The assertion that all things are in motion *e may fairly regard ase(ually false) though it is less subversive of physical science: forthough in our course on physics it *as laid do*n that rest no lessthan motion is ultimately referable to nature herself) neverthelessmotion is the characteristic fact of nature: moreover) the vie* isactually held by some that not merely some things but all things inthe *orld are in motion and al*ays in motion) though *e cannotapprehendthe fact by sense0perception. Although the supporters of this theorydo not state clearly *hat +ind of motion they mean) or *hether theymean all +inds) it is no hard matter to reply to them: thus *e maypoint out that there cannot be a continuous process either of increaseor of decrease: that *hich comes bet*een the t*o has to be included.The theory resembles that about the stone being *orn a*ay by the dropof *ater or split by plants gro*ing out of it: if so much has beene6truded or removed by the drop) it does not follo* that half theamount has previously been e6truded or removed in half the time: thecase of the hauled ship is e6actly comparable: here *e have so manydrops setting so much in motion) but a part of them *ill not set asmuch in motion in any period of time. The amount removed is) it istrue) divisible into a number of parts) but no one of these *as setin motion separately: they *ere all set in motion together. It isevident) then) that from the fact that the decrease is divisible intoan infinite number of parts it does not follo* that some part mustal*ays be passing a*ay: it all passes a*ay at a particular moment.Similarly) too) in the case of any alteration *hatever if that *hichsuffers alteration is infinitely divisible it does not follo* fromthis that the same is true of the alteration itself) *hich oftenoccursall at once) as in free8ing. Again) *hen any one has fallen ill) theremust follo* a period of time in *hich his restoration to health isin the future: the process of change cannot ta+e place in an instant:yet the change cannot be a change to anything else but health. Theassertion. therefore) that alteration is continuous is an e6travagantcalling into (uestion of the obvious: for alteration is a change fromone contrary to another. 1oreover) *e notice that a stone becomesneither harder nor softer. Again) in the matter of locomotion) it



*ould be a strange thing if a stone could be falling or resting onthe ground *ithout our being able to perceive the fact. ,urther) itis a la* of nature that earth and all other bodies should remain intheir proper places and be moved from them only by violence: fromthe fact then that some of them are in their proper places it follo*sthat in respect of place also all things cannot be in motion. These

and other similar arguments) then) should convince us that it isimpossibleeither that all things are al*ays in motion or that all things areal*ays at rest.

-or again can it be that some things are al*ays at rest) others al*aysin motion) and nothing sometimes at rest and sometimes in motion.This theory must be pronounced impossible on the same grounds as thosepreviously mentioned: vi8. that *e see the above0mentioned changesoccurring in the case of the same things. &e may further point outthat the defender of this position is fighting against the obvious)for on this theory there can be no such thing as increase: nor canthere be any such thing as compulsory motion) if it is impossiblethat a thing can be at rest before being set in motion unnaturally.This theory) then) does a*ay *ith becoming and perishing. 1oreover)motion) it *ould seem) is generally thought to be a sort of becomingand perishing) for that to *hich a thing changes comes to be) oroccupancyof it comes to be) and that from *hich a thing changes ceases to be)or there ceases to be occupancy of it. It is clear) therefore) thatthere are cases of occasional motion and occasional rest.

&e have no* to ta+e the assertion that all things are sometimes atrest and sometimes in motion and to confront it *ith the argumentspreviously advanced. &e must ta+e our start as before from thepossibilitiesthat *e distinguished 'ust above. 9ither all things are at rest) orall things are in motion) or some things are at rest and others inmotion. And if some things are at rest and others in motion) thenit must be that either all things are sometimes at rest and sometimesin motion) or some things are al*ays at rest and the remainder al*aysin motion) or some of the things are al*ays at rest and others al*aysin motion *hile others again are sometimes at rest and sometimes inmotion. -o* *e have said before that it is impossible that all thingsshould be at rest: nevertheless *e may no* repeat that assertion.&e may point out that) even if it is really the case) as certainpersonsassert) that the e6istent is infinite and motionless) it certainlydoes not appear to be so if *e follo* sense0perception: many thingsthat e6ist appear to be in motion. -o* if there is such a thing asfalse opinion or opinion at all) there is also motion and similarlyif there is such a thing as imagination) or if it is the case thatanything seems to be different at different times: for imaginationand opinion are thought to be motions of a +ind. But to investigatethis (uestion at all0to see+ a reasoned 'ustification of a belief*ith regard to *hich *e are too *ell off to re(uire reasoned'ustification0impliesbad 'udgement of *hat is better and *hat is *orse) *hat commendsitselfto belief and *hat does not) *hat is ultimate and *hat is not. Itis li+e*ise impossible that all things should be in motion or thatsome things should be al*ays in motion and the remainder al*ays atrest. &e have sufficient ground for re'ecting all these theories inthe single fact that *e see some things that are sometimes in motionand sometimes at rest. It is evident) therefore) that it is no less



impossible that some things should be al*ays in motion and theremainderal*ays at rest than that all things should be at rest or that allthings should be in motion continuously. It remains) then) to consider*hether all things are so constituted as to be capable both of beingin motion and of being at rest) or *hether) *hile some things are

so constituted) some are al*ays at rest and some are al*ays in motion:for it is this last vie* that *e have to sho* to be true.

Part >

-o* of things that cause motion or suffer motion) to some the motionis accidental) to others essential: thus it is accidental to *hatmerely belongs to or contains as a part a thing that causes motionor suffers motion) essential to a thing that causes motion or suffersmotion not merely by belonging to such a thing or containing it asa part.

$f things to *hich the motion is essential some derive their motionfrom themselves) others from something else: and in some cases theirmotion is natural) in others violent and unnatural. Thus in thingsthat derive their motion from themselves) e.g. all animals) the motionis natural 3for *hen an animal is in motion its motion is derivedfrom itself4: and *henever the source of the motion of a thing isin the thing itself *e say that the motion of that thing is natural.Therefore the animal as a *hole moves itself naturally: but the bodyof the animal may be in motion unnaturally as *ell as naturally: itdepends upon the +ind of motion that it may chance to be sufferingand the +ind of element of *hich it is composed. And the motion ofthings that derive their motion from something else is in some casesnatural) in other unnatural: e.g. up*ard motion of earthy things anddo*n*ard motion of fire are unnatural. 1oreover the parts of animalsare often in motion in an unnatural *ay) their positions and thecharacterof the motion being abnormal. The fact that a thing that is in motionderives its motion from something is most evident in things that arein motion unnaturally) because in such cases it is clear that themotion is derived from something other than the thing itself. -e6tto things that are in motion unnaturally those *hose motion *hilenatural is derived from themselves0e.g. animals0ma+e this fact clear:for here the uncertainty is not as to *hether the motion is derivedfrom something but as to ho* *e ought to distinguish in the thingbet*een the movent and the moved. It *ould seem that in animals) 'ustas in ships and things not naturally organi8ed) that *hich causesmotion is separate from that *hich suffers motion) and that it isonly in this sense that the animal as a *hole causes its o*n motion.

The greatest difficulty) ho*ever) is presented by the remaining caseof those that *e last distinguished. &here things derive their motionfrom something else *e distinguished the cases in *hich the motionis unnatural: *e are left *ith those that are to be contrasted *iththe others by reason of the fact that the motion is natural. It isin these cases that difficulty *ould be e6perienced in deciding *hencethe motion is derived) e.g. in the case of light and heavy things.&hen these things are in motion to positions the reverse of thosethey *ould properly occupy) their motion is violent: *hen they arein motion to their proper positions0the light thing up and the heavything do*n0their motion is natural but in this latter case it isno longer evident) as it is *hen the motion is unnatural) *hence theirmotion is derived. It is impossible to say that their motion isderived



from themselves: this is a characteristic of life and peculiar toliving things. ,urther) if it *ere) it *ould have been in their po*erto stop themselves 3I mean that if e.g. a thing can cause itself to*al+ it can also cause itself not to *al+4) and so) since on thissupposition fire itself possesses the po*er of up*ard locomotion)it is clear that it should also possess the po*er of do*n*ard

locomotion.1oreover if things move themselves) it *ould be unreasonable tosupposethat in only one +ind of motion is their motion derived fromthemselves.Again) ho* can anything of continuous and naturally connectedsubstancemove itself7 In so far as a thing is one and continuous not merelyin virtue of contact) it is impassive: it is only in so far as a thingis divided that one part of it is by nature active and anotherpassive.Therefore none of the things that *e are no* considering movethemselves3for they are of naturally connected substance4) nor does anythingelse that is continuous: in each case the movent must be separatefrom the moved) as *e see to be the case *ith inanimate things *henan animate thing moves them. It is the fact that these things alsoal*ays derive their motion from something: *hat it is *ould becomeevident if *e *ere to distinguish the different +inds of cause.

The above0mentioned distinctions can also be made in the case ofthingsthat cause motion: some of them are capable of causing motionunnaturally3e.g. the lever is not naturally capable of moving the *eight4) othersnaturally 3e.g. *hat is actually hot is naturally capable of moving*hat is potentially hot4: and similarly in the case of all otherthingsof this +ind.

In the same *ay) too) *hat is potentially of a certain (uality orof a certain (uantity in a certain place is naturally movable *henit contains the corresponding principle in itself and not accidentally3for the same thing may be both of a certain (uality and of a certain(uantity) but the one is an accidental) not an essential propertyof the other4. So *hen fire or earth is moved by something the motionis violent *hen it is unnatural) and natural *hen it brings toactualitythe proper activities that they potentially possess. But the factthat the term potentially is used in more than one sense is thereason *hy it is not evident *hence such motions as the up*ard motionof fire and the do*n*ard motion of earth are derived. $ne *ho islearninga science potentially +no*s it in a different sense from one *ho *hilealready possessing the +no*ledge is not actually e6ercising it.&herever*e have something capable of acting and something capable of beingcorrespondingly acted on) in the event of any such pair being incontact*hat is potential becomes at times actual: e.g. the learner becomesfrom one potential something another potential something: for one*ho possesses +no*ledge of a science but is not actually e6ercisingit +no*s the science potentially in a sense) though not in the samesense as he +ne* it potentially before he learnt it. And *hen he isin this condition) if something does not prevent him) he actively



e6ercises his +no*ledge: other*ise he *ould be in the contradictorystate of not +no*ing. In regard to natural bodies also the case issimilar. Thus *hat is cold is potentially hot: then a change ta+esplace and it is fire) and it burns) unless something prevents andhinders it. So) too) *ith heavy and light: light is generated fromheavy) e.g. air from *ater 3for *ater is the first thing that is

potentiallylight4) and air is actually light) and *ill at once reali8e its properactivity as such unless something prevents it. The activity oflightnessconsists in the light thing being in a certain situation) namely highup: *hen it is in the contrary situation) it is being prevented fromrising. The case is similar also in regard to (uantity and (uality.But) be it noted) this is the (uestion *e are trying to ans*er0ho*can *e account for the motion of light things and heavy things totheir proper situations7 The reason for it is that they have a naturaltendency respectively to*ards a certain position: and this constitutesthe essence of lightness and heaviness) the former being determinedby an up*ard) the latter by a do*n*ard) tendency. As *e have said)a thing may be potentially light or heavy in more senses than one.Thus not only *hen a thing is *ater is it in a sense potentiallylight)but *hen it has become air it may be still potentially light: forit may be that through some hindrance it does not occupy an upperposition) *hereas) if *hat hinders it is removed) it reali8es itsactivity and continues to rise higher. The process *hereby *hat isof a certain (uality changes to a condition of active e6istence issimilar: thus the e6ercise of +no*ledge follo*s at once upon thepossessionof it unless something prevents it. So) too) *hat is of a certain(uantity e6tends itself over a certain space unless something preventsit. The thing in a sense is and in a sense is not moved by one *homoves *hat is obstructing and preventing its motion 3e.g. one *hopulls a*ay a pillar from under a roof or one *ho removes a stone froma *ines+in in the *ater is the accidental cause of motion4: and inthe same *ay the real cause of the motion of a ball rebounding froma *all is not the *all but the thro*er. So it is clear that in allthese cases the thing does not move itself) but it contains *ithinitself the source of motion0not of moving something or of causingmotion) but of suffering it.

If then the motion of all things that are in motion is either naturalor unnatural and violent) and all things *hose motion is violent andunnatural are moved by something) and something other than themselves)and again all things *hose motion is natural are moved by something0boththose that are moved by themselves and those that are not moved bythemselves 3e.g. light things and heavy things) *hich are moved eitherby that *hich brought the thing into e6istence as such and made itlight and heavy) or by that *hich released *hat *as hindering andpreventing it4 then all things that are in motion must be moved bysomething.

Part ?

-o* this may come about in either of t*o *ays. 9ither the movent isnot itself responsible for the motion) *hich is to be referred tosomething else *hich moves the movent) or the movent is itselfresponsiblefor the motion. ,urther) in the latter case) either the moventimmediately



precedes the last thing in the series) or there may be one or moreintermediate lin+s: e.g. the stic+ moves the stone and is moved bythe hand) *hich again is moved by the man: in the man) ho*ever) *ehave reached a movent that is not so in virtue of being moved bysomethingelse. -o* *e say that the thing is moved both by the last and by the

first movent in the series) but more strictly by the first) sincethe first movent moves the last) *hereas the last does not move thefirst) and the first *ill move the thing *ithout the last) but thelast *ill not move it *ithout the first: e.g. the stic+ *ill not moveanything unless it is itself moved by the man. If then everythingthat is in motion must be moved by something) and the movent musteither itself be moved by something else or not) and in the formercase there must be some first movent that is not itself moved byanythingelse) *hile in the case of the immediate movent being of this +indthere is no need of an intermediate movent that is also moved 3forit is impossible that there should be an infinite series of movents)each of *hich is itself moved by something else) since in an infiniteseries there is no first term40if then everything that is in motionis moved by something) and the first movent is moved but not byanythingelse) it much be moved by itself.

This same argument may also be stated in another *ay as follo*s. 9verymovent moves something and moves it *ith something) either *ith itselfor *ith something else: e.g. a man moves a thing either himself or*ith a stic+) and a thing is +noc+ed do*n either by the *ind itselfor by a stone propelled by the *ind. But it is impossible for that*ith *hich a thing is moved to move it *ithout being moved by that*hich imparts motion by its o*n agency: on the other hand) if a thingimparts motion by its o*n agency) it is not necessary that thereshouldbe anything else *ith *hich it imparts motion) *hereas if there isa different thing *ith *hich it imparts motion) there must besomethingthat imparts motion not *ith something else but *ith itself) or elsethere *ill be an infinite series. If) then) anything is a movent *hilebeing itself moved) the series must stop some*here and not beinfinite.Thus) if the stic+ moves something in virtue of being moved by thehand) the hand moves the stic+: and if something else moves *ith thehand) the hand also is moved by something different from itself. So*hen motion by means of an instrument is at each stage caused bysomethingdifferent from the instrument) this must al*ays be preceded bysomethingelse *hich imparts motion *ith itself. Therefore) if this last moventis in motion and there is nothing else that moves it) it must moveitself. So this reasoning also sho*s that *hen a thing is moved) ifit is not moved immediately by something that moves itself) the seriesbrings us at some time or other to a movent of this +ind.

And if *e consider the matter in yet a third *a y *e shall get thissame result as follo*s. If everything that is in motion is moved bysomething that is in motion) ether this being in motion is anaccidentalattribute of the movents in (uestion) so that each of them movessomething*hile being itself in motion) but not al*ays because it is itselfin motion) or it is not accidental but an essential attribute. et



us consider the former alternative. If then it is an accidentalattribute)it is not necessary that that is in motion should be in motion: andif this is so it is clear that there may be a time *hen nothing thate6ists is in motion) since the accidental is not necessary butcontingent.

-o* if *e assume the e6istence of a possibility) any conclusion that*e thereby reach *ill not be an impossibility though it may becontraryto fact. But the none6istence of motion is an impossibility: for *ehave sho*n above that there must al*ays be motion.

1oreover) the conclusion to *hich *e have been led is a reasonableone. ,or there must be three things0the moved) the movent) and theinstrument of motion. -o* the moved must be in motion) but it neednot move anything else: the instrument of motion must both movesomethingelse and be itself in motion 3for it changes together *ith the moved)*ith *hich it is in contact and continuous) as is clear in the caseof things that move other things locally) in *hich case the t*o thingsmust up to a certain point be in contact4: and the movent0that isto say) that *hich causes motion in such a manner that it is notmerelythe instrument of motion0must be unmoved. -o* *e have visuale6perienceof the last term in this series) namely that *hich has the capacityof being in motion) but does not contain a motive principle) and alsoof that *hich is in motion but is moved by itself and not by anythingelse: it is reasonable) therefore) not to say necessary) to supposethe e6istence of the third term also) that *hich causes motion butis itself unmoved. So) too) Ana6agoras is right *hen he says that1ind is impassive and unmi6ed) since he ma+es it the principle ofmotion: for it could cause motion in this sense only by being itselfunmoved) and have supreme control only by being unmi6ed.

&e *ill no* ta+e the second alternative. If the movement is notaccidentallybut necessarily in motion0so that) if it *ere not in motion) it *ouldnot move anything0then the movent) in so far as it is in motion) mustbe in motion in one of t*o *ays: it is moved either as that is *hichis moved *ith the same +ind of motion) or *ith a different +ind0eitherthat *hich is heating) I mean) is itself in process of becoming hot)that *hich is ma+ing healthy in process of becoming healthy) and that*hich is causing locomotion in process of locomotion) or else that*hich is ma+ing healthy is) let us say) in process of locomotion)and that *hich is causing locomotion in process of) say) increase.But it is evident that this is impossible. ,or if *e adopt the firstassumption *e have to ma+e it apply *ithin each of the very lo*estspecies into *hich motion can be divided: e.g. *e must say that ifsome one is teaching some lesson in geometry) he is also in processof being taught that same lesson in geometry) and that if he isthro*inghe is in process of being thro*n in 'ust the same manner. $r if *ere'ect this assumption *e must say that one +ind of motion is derivedfrom another e.g. that that *hich is causing locomotion is in processof increase) that *hich is causing this increase is in process ofbeing altered by something else) and that *hich is causing thisalterationis in process of suffering some different +ind of motion. But theseries must stop some*here) since the +inds of motion are limitedand if *e say that the process is reversible) and that that *hich



is causing alteration is in process of locomotion) *e do no more thanif *e had said at the outset that that *hich is causing locomotionis in process of locomotion) and that one *ho is teaching is inprocessof being taught: for it is clear that everything that is moved ismoved by the movent that is further bac+ in the series as *ell as

by that *hich immediately moves it: in fact the earlier movent isthat *hich more strictly moves it. But this is of course impossible:for it involves the conse(uence that one *ho is teaching is in processof learning *hat he is teaching) *hereas teaching necessarily impliespossessing +no*ledge) and learning not possessing it. Still moreunreasonableis the conse(uence involved that) since everything that is moved ismoved by something that is itself moved by something else) everythingthat has a capacity for causing motion has as such a correspondingcapacity for being moved: i.e. it *ill have a capacity for being movedin the sense in *hich one might say that everything that has acapacityfor ma+ing healthy) and e6ercises that capacity) has as such acapacityfor being made healthy) and that *hich has a capacity for buildinghas as such a capacity for being built. It *ill have the capacityfor being thus moved either immediately or through one or more lin+s3as it *ill if) *hile everything that has a capacity for causingmotionhas as such a capacity for being moved by something else) the motionthat it has the capacity for suffering is not that *ith *hich itaffects*hat is ne6t to it) but a motion of a different +ind e.g. that *hichhas a capacity for ma+ing healthy might as such have a capacity forlearn. the series) ho*ever) could be traced bac+) as *e said before)until at some time or other *e arrived at the same +ind of motion4.-o* the first alternative is impossible) and the second is fantastic:it is absurd that that *hich has a capacity for causing alterationshould as such necessarily have a capacity) let us say) for increase.It is not necessary) therefore) that that *hich is moved should al*aysbe moved by something else that is itself moved by something else:so there *ill be an end to the series. Conse(uently the first thingthat is in motion *ill derive its motion either from something thatis at rest or from itself. But if there *ere any need to consider*hich of the t*o) that *hich moves itself or that *hich is moved bysomething else) is the cause and principle of motion) every one *oulddecide the former: for that *hich is itself independently a causeis al*ays prior as a cause to that *hich is so only in virtue of beingitself dependent upon something else that ma+es it so.

&e must therefore ma+e a fresh start and consider the (uestion ifa thing moves itself) in *hat sense and in *hat manner does it doso7 -o* everything that is in motion must be infinitely divisible)for it has been sho*n already in our general course on Physics) thateverything that is essentially in motion is continuous. -o* it isimpossible that that *hich moves itself should in its entirety moveitself: for then) *hile being specifically one and indivisible) it*ould as a &hole both undergo and cause the same locomotion oralteration:thus it *ould at the same time be both teaching and being taught 3thesame thing4) or both restoring to and being restored to the samehealth.1oreover) *e have established the fact that it is the movable thatis moved and this is potentially) not actually) in motion) but thepotential is in process to actuality) and motion is an incomplete



actuality of the movable. The movent on the other hand is alreadyin activity: e.g. it is that *hich is hot that produces heat: in fact)that *hich produces the form is al*ays something that possesses it.Conse(uently 3if a thing can move itself as a *hole4) the same thingin respect of the same thing may be at the same time both hot andnot hot. So) too) in every other case *here the movent must be

describedby the same name in the same sense as the moved. Therefore *hen athing moves itself it is one part of it that is the movent and anotherpart that is moved. But it is not self0moving in the sense that eachof the t*o parts is moved by the other part: the follo*ingconsiderationsma+e this evident. In the first place) if each of the t*o parts isto move the other) there *ill be no first movent. If a thing is movedby a series of movents) that *hich is earlier in the series is morethe cause of its being moved than that *hich comes ne6t) and *illbe more truly the movent: for *e found that there are t*o +inds ofmovent) that *hich is itself moved by something else and that *hichderives its motion from itself: and that *hich is further from thething that is moved is nearer to the principle of motion than that*hich is intermediate. In the second place) there is no necessityfor the movent part to be moved by anything but itself: so it canonly be accidentally that the other part moves it in return. I ta+ethen the possible case of its not moving it: then there *ill be apart that is moved and a part that is an unmoved movent. In the thirdplace) there is no necessity for the movent to be moved in return:on the contrary the necessity that there should al*ays be motion ma+esit necessary that there should be some movent that is either unmovedor moved by itself. In the fourth place *e should then have a thingundergoing the same motion that it is causing0that *hich is producingheat) therefore) being heated. But as a matter of fact that *hichprimarily moves itself cannot contain either a single part that movesitself or a number of parts each of *hich moves itself. ,or) if the*hole is moved by itself) it must be moved either by some part ofitself or as a *hole by itself as a *hole. If) then) it is moved invirtue of some part of it being moved by that part itself) it is thispart that *ill be the primary self0movent) since) if this part isseparated from the *hole) the part *ill still move itself) but the*hole *ill do so no longer. If on the other hand the *hole is movedby itself as a *hole) it must be accidentally that the parts movethemselves: and therefore) their self0motion not being necessary)*e may ta+e the case of their not being moved by themselves. Thereforein the *hole of the thing *e may distinguish that *hich imparts motion*ithout itself being moved and that *hich is moved: for only in this*ay is it possible for a thing to be self0moved. ,urther) if the *holemoves itself *e may distinguish in it that *hich imparts the motionand that *hich is moved: so *hile *e say that AB is moved by itself)*e may also say that it is moved by A. And since that *hich impartsmotion may be either a thing that is moved by something else or athing that is unmoved) and that *hich is moved may be either a thingthat imparts motion to something else or a thing that does not) that*hich moves itself must be composed of something that is unmoved butimparts motion and also of something that is moved but does notnecessarilyimpart motion but may or may not do so. Thus let A be something thatimparts motion but is unmoved) B something that is moved by A andmoves #) # something that is moved by B but moves nothing 3grantedthat *e eventually arrive at # *e may ta+e it that there is only oneintermediate term) though there may be more4. Then the *hole AB# movesitself. But if I ta+e a*ay #) AB *ill move itself) A imparting motionand B being moved) *hereas # *ill not move itself or in fact be moved



at all. -or again *ill B# move itself apart from A: for B impartsmotion only through being moved by something else) not through beingmoved by any part of itself. So only AB moves itself. That *hich movesitself) therefore) must comprise something that imparts motion butis unmoved and something that is moved but does not necessarily moveanything else: and each of these t*o things) or at any rate one of

them) must be in contact *ith the other. If) then) that *hich impartsmotion is a continuous substance0that *hich is moved must of coursebe so0it is clear that it is not through some part of the *hole beingof such a nature as to be capable of moving itself that the *holemoves itself: it moves itself as a *hole) both being moved andimpartingmotion through containing a part that imparts motion and a part thatis moved. It does not impart motion as a *hole nor is it moved asa *hole: it is A alone that imparts motion and B alone that is moved.It is not true) further) that # is moved by A) *hich is impossible.

!ere a difficulty arises: if something is ta+en a*ay from A 3supposingthat that *hich imparts motion but is unmoved is a continuoussubstance4)or from B the part that is moved) *ill the remainder of A continueto impart motion or the remainder of B continue to be moved7 If so)it *ill not be AB primarily that is moved by itself) since) *hensomethingis ta+en a*ay from AB) the remainder of AB *ill still continue tomove itself. Perhaps *e may state the case thus: there is nothingto prevent each of the t*o parts) or at any rate one of them) that*hich is moved) being divisible though actually undivided) so thatif it is divided it *ill not continue in the possession of the samecapacity: and so there is nothing to prevent self0motion residingprimarily in things that are potentially divisible.

,rom *hat has been said) then) it is evident that that *hich primarilyimparts motion is unmoved: for) *hether the series is closed at onceby that *hich is in motion but moved by something else deriving itsmotion directly from the first unmoved) or *hether the motion isderivedfrom *hat is in motion but moves itself and stops its o*n motion)on both suppositions *e have the result that in all cases of thingsbeing in motion that *hich primarily imparts motion is unmoved.

Part

Since there must al*ays be motion *ithout intermission) there mustnecessarily be something) one thing or it may be a plurality) thatfirst imparts motion) and this first movent must be unmoved. -o* the(uestion *hether each of the things that are unmoved but impart motionis eternal is irrelevant to our present argument: but the follo*ingconsiderations *ill ma+e it clear that there must necessarily be somesuch thing) *hich) *hile it has the capacity of moving something else)is itself unmoved and e6empt from all change) *hich can affect itneither in an un(ualified nor in an accidental sense. et us suppose)if any one li+es) that in the case of certain things it is possiblefor them at different times to be and not to be) *ithout any processof becoming and perishing 3in fact it *ould seem to be necessary)if a thing that has not parts at one time is and at another time isnot) that any such thing should *ithout undergoing any process ofchange at one time be and at another time not be4. And let us furthersuppose it possible that some principles that are unmoved but capableof imparting motion at one time are and at another time are not. 9ven



so) this cannot be true of all such principles) since there mustclearlybe something that causes things that move themselves at one time tobe and at another not to be. ,or) since nothing that has not partscan be in motion) that *hich moves itself must as a *hole havemagnitude)

though nothing that *e have said ma+es this necessarily true of everymovent. So the fact that some things become and others perish) andthat this is so continuously) cannot be caused by any one of thosethings that) though they are unmoved) do not al*ays e6ist: nor againcan it be caused by any of those *hich move certain particular things)*hile others move other things. The eternity and continuity of theprocess cannot be caused either by any one of them singly or by thesum of them) because this causal relation must be eternal andnecessary)*hereas the sum of these movents is infinite and they do not all e6isttogether. It is clear) then) that though there may be countlessinstancesof the perishing of some principles that are unmoved but impartmotion)and though many things that move themselves perish and are succeededby others that come into being) and though one thing that is unmovedmoves one thing *hile another moves another) nevertheless there issomething that comprehends them all) and that as something apart fromeach one of them) and this it is that is the cause of the fact thatsome things are and others are not and of the continuous process ofchange: and this causes the motion of the other movents) *hile theyare the causes of the motion of other things. 1otion) then) beingeternal) the first movent) if there is but one) *ill be eternal also:if there are more than one) there *ill be a plurality of such eternalmovents. &e ought) ho*ever) to suppose that there is one rather thanmany) and a finite rather than an infinite number. &hen theconse(uencesof either assumption are the same) *e should al*ays assume that thingsare finite rather than infinite in number) since in things constitutedby nature that *hich is finite and that *hich is better ought) ifpossible) to be present rather than the reverse: and here it issufficientto assume only one movent) the first of unmoved things) *hich beingeternal *ill be the principle of motion to everything else.

The follo*ing argument also ma+es it evident that the first moventmust be something that is one and eternal. &e have sho*n that theremust al*ays be motion. That being so) motion must also be continuous)because *hat is al*ays is continuous) *hereas *hat is merely insuccessionis not continuous. But further) if motion is continuous) it is one:and it is one only if the movent and the moved that constitute itare each of them one) since in the event of a thing s being movedno* by one thing and no* by another the *hole motion *ill not becontinuousbut successive.

1oreover a conviction that there is a first unmoved something maybe reached not only from the foregoing arguments) but also byconsideringagain the principles operative in movents. -o* it is evident thatamong e6isting things there are some that are sometimes in motionand sometimes at rest. This fact has served above to ma+e it clearthat it is not true either that all things are in motion or that allthings are at rest or that some things are al*ays at rest and the



remainder al*ays in motion: on this matter proof is supplied by thingsthat fluctuate bet*een the t*o and have the capacity of beingsometimesin motion and sometimes at rest. The e6istence of things of this +indis clear to all: but *e *ish to e6plain also the nature of each ofthe other t*o +inds and sho* that there are some things that are

al*aysunmoved and some things that are al*ays in motion. In the course ofour argument directed to this end *e established the fact thateverythingthat is in motion is moved by something) and that the movent is eitherunmoved or in motion) and that) if it is in motion) it is moved eitherby itself or by something else and so on throughout the series: andso *e proceeded to the position that the first principle that directlycauses things that are in motion to be moved is that *hich movesitself)and the first principle of the *hole series is the unmoved. ,urtherit is evident from actual observation that there are things that havethe characteristic of moving themselves) e.g. the animal +ingdom andthe *hole class of living things. This being so) then) the vie* *assuggested that perhaps it may be possible for motion to come to bein a thing *ithout having been in e6istence at all before) because*e see this actually occurring in animals: they are unmoved at onetime and then again they are in motion) as it seems. &e must graspthe fact) therefore) that animals move themselves only *ith one +indof motion) and that this is not strictly originated by them. The causeof it is not derived from the animal itself: it is connected *ithother natural motions in animals) *hich they do not e6perience throughtheir o*n instrumentality) e.g. increase) decrease) and respiration:these are e6perienced by every animal *hile it is at rest and notin motion in respect of the motion set up by its o*n agency: herethe motion is caused by the atmosphere and by many things that enterinto the animal: thus in some cases the cause is nourishment: *henit is being digested animals sleep) and *hen it is being distributedthrough the system they a*a+e and move themselves) the first principleof this motion being thus originally derived from outside. Thereforeanimals are not al*ays in continuous motion by their o*n agency: itis something else that moves them) itself being in motion and changingas it comes into relation *ith each several thing that moves itself.31oreover in all these self0moving things the first movent and causeof their self0motion is itself moved by itself) though in anaccidentalsense: that is to say) the body changes its place) so that that *hichis in the body changes its place also and is a self0movent throughits e6ercise of leverage.4 !ence *e may confidently conclude thatif a thing belongs to the class of unmoved movents that are alsothemselvesmoved accidentally) it is impossible that it should cause continuousmotion. So the necessity that there should be motion continuouslyre(uires that there should be a first movent that is unmoved evenaccidentally) if) as *e have said) there is to be in the *orld ofthings an unceasing and undying motion) and the *orld is to remainpermanently self0contained and *ithin the same limits: for if thefirst principle is permanent) the universe must also be permanent)since it is continuous *ith the first principle. 3&e must distinguish)ho*ever) bet*een accidental motion of a thing by itself and suchmotionby something else) the former being confined to perishable things)*hereas the latter belongs also to certain first principles ofheavenlybodies) of all those) that is to say) that e6perience more than one



locomotion.4

And further) if there is al*ays something of this nature) a moventthat is itself unmoved and eternal) then that *hich is first movedby it must be eternal. Indeed this is clear also from theconsideration

that there *ould other*ise be no becoming and perishing and no changeof any +ind in other things) *hich re(uire something that is in motionto move them: for the motion imparted by the unmoved *ill al*ays beimparted in the same *ay and be one and the same) since the unmoveddoes not itself change in relation to that *hich is moved by it. Butthat *hich is moved by something that) though it is in motion) ismoved directly by the unmoved stands in varying relations to thethingsthat it moves) so that the motion that it causes *ill not be al*aysthe same: by reason of the fact that it occupies contrary positionsor assumes contrary forms at different times it *ill produce contrarymotions in each several thing that it moves and *ill cause it to beat one time at rest and at another time in motion.

The foregoing argument) then) has served to clear up the point about*hich *e raised a difficulty at the outset0*hy is it that insteadof all things being either in motion or at rest) or some things beingal*ays in motion and the remainder al*ays at rest) there are thingsthat are sometimes in motion and sometimes not7 The cause of thisis no* plain: it is because) *hile some things are moved by an eternalunmoved movent and are therefore al*ays in motion) other things aremoved by a movent that is in motion and changing) so that they toomust change. But the unmoved movent) as has been said) since itremainspermanently simple and unvarying and in the same state) *ill causemotion that is one and simple.

Part

This matter *ill be made clearer) ho*ever) if *e start afresh fromanother point. &e must consider *hether it is or is not possible thatthere should be a continuous motion) and) if it is possible) *hichthis motion is) and *hich is the primary motion: for it is plain thatif there must al*ays be motion) and a particular motion is primaryand continuous) then it is this motion that is imparted by the firstmovent) and so it is necessarily one and the same and continuous andprimary.

-o* of the three +inds of motion that there are0motion in respectof magnitude) motion in respect of affection) and motion in respectof place0it is this last) *hich *e call locomotion) that must beprimary.This may be sho*n as follo*s. It is impossible that there should beincrease *ithout the previous occurrence of alteration: for that *hichis increased) although in a sense it is increased by *hat is li+eitself) is in a sense increased by *hat is unli+e itself: thus itis said that contrary is nourishment to contrary: but gro*th iseffectedonly by things becoming li+e to li+e. There must be alteration) then)in that there is this change from contrary to contrary. But the factthat a thing is altered re(uires that there should be something thatalters it) something e.g. that ma+es the potentially hot into theactually hot: so it is plain that the movent does not maintain auniformrelation to it but is at one time nearer to and at another farther



from that *hich is altered: and *e cannot have this *ithoutlocomotion.If) therefore) there must al*ays be motion) there must also al*aysbe locomotion as the primary motion) and) if there is a primary asdistinguished from a secondary form of locomotion) it must be theprimary form. Again) all affections have their origin in condensation

and rarefaction: thus heavy and light) soft and hard) hot and cold)are considered to be forms of density and rarity. But condensationand rarefaction are nothing more than combination and separation)processes in accordance *ith *hich substances are said to become andperish: and in being combined and separated things must change inrespect of place. And further) *hen a thing is increased or decreasedits magnitude changes in respect of place.

Again) there is another point of vie* from *hich it *ill be clearlyseen that locomotion is primary. As in the case of other things sotoo in the case of motion the *ord primary may be used in severalsenses. A thing is said to be prior to other things *hen) if it doesnot e6ist) the others *ill not e6ist) *hereas it can e6ist *ithoutthe others: and there is also priority in time and priority inperfectionof e6istence. et us begin) then) *ith the first sense. -o* theremust be motion continuously) and there may be continuously eithercontinuous motion or successive motion) the former) ho*ever) in ahigher degree than the latter: moreover it is better that it shouldbe continuous rather than successive motion) and *e al*ays assumethe presence in nature of the better) if it be possible: since) then)continuous motion is possible 3this *ill be proved later: for thepresent let us ta+e it for granted4) and no other motion can becontinuouse6cept locomotion) locomotion must be primary. ,or there is nonecessityfor the sub'ect of locomotion to be the sub'ect either of increaseor of alteration) nor need it become or perish: on the other handthere cannot be any one of these processes *ithout the e6istence ofthe continuous motion imparted by the first movent.

Secondly) locomotion must be primary in time: for this is the onlymotion possible for things. It is true indeed that) in the case ofany individual thing that has a becoming) locomotion must be the lastof its motions: for after its becoming it first e6periences alterationand increase) and locomotion is a motion that belongs to such thingsonly *hen they are perfected. But there must previously be somethingelse that is in process of locomotion to be the cause even of thebecoming of things that become) *ithout itself being in process ofbecoming) as e.g. the begotten is preceded by *hat begot it: other*isebecoming might be thought to be the primary motion on the ground thatthe thing must first become. But though this is so in the case ofany individual thing that becomes) nevertheless before anythingbecomes)something else must be in motion) not itself becoming but being) andbefore this there must again be something else. And since becomingcannot be primary0for) if it *ere) everything that is in motion *ouldbe perishable0it is plain that no one of the motions ne6t in ordercan be prior to locomotion. By the motions ne6t in order I meanincreaseand then alteration) decrease) and perishing. All these are posteriorto becoming: conse(uently) if not even becoming is prior tolocomotion)then no one of the other processes of change is so either.



Thirdly) that *hich is in process of becoming appears universallyas something imperfect and proceeding to a first principle: and so*hat is posterior in the order of becoming is prior in the order ofnature. -o* all things that go through the process of becoming ac(uirelocomotion last. It is this that accounts for the fact that someliving

things) e.g. plants and many +inds of animals) o*ing to lac+ of there(uisite organ) are entirely *ithout motion) *hereas others ac(uireit in the course of their being perfected. Therefore) if the degreein *hich things possess locomotion corresponds to the degree in *hichthey have reali8ed their natural development) then this motion mustbe prior to all others in respect of perfection of e6istence: andnot only for this reason but also because a thing that is in motionloses its essential character less in the process of locomotion thanin any other +ind of motion: it is the only motion that does notinvolvea change of being in the sense in *hich there is a change in (uality*hen a thing is altered and a change in (uantity *hen a thing isincreasedor decreased. Above all it is plain that this motion) motion inrespectof place) is *hat is in the strictest sense produced by that *hichmoves itself but it is the self0movent that *e declare to be thefirst principle of things that are moved and impart motion and theprimary source to *hich things that are in motion are to be referred.

It is clear) then) from the foregoing arguments that locomotion isthe primary motion. &e have no* to sho* *hich +ind of locomotion isprimary. The same process of reasoning *ill also ma+e clear at thesame time the truth of the assumption *e have made both no* and ata previous stage that it is possible that there should be a motionthat is continuous and eternal. -o* it is clear from the follo*ingconsiderations that no other than locomotion can be continuous. 9veryother motion and change is from an opposite to an opposite: thus forthe processes of becoming and perishing the limits are the e6istentand the non0e6istent) for alteration the various pairs of contraryaffections) and for increase and decrease either greatness andsmallnessor perfection and imperfection of magnitude: and changes to therespectivecontraries are contrary changes. -o* a thing that is undergoing anyparticular +ind of motion) but though previously e6istent has notal*ays undergone it) must previously have been at rest so far as thatmotion is concerned. It is clear) then) that for the changing thingthe contraries *ill be states of rest. And *e have a similar resultin the case of changes that are not motions: for becoming andperishing)*hether regarded simply as such *ithout (ualification or as affectingsomething in particular) are opposites: therefore provided it isimpossiblefor a thing to undergo opposite changes at the same time) the change*ill not be continuous) but a period of time *ill intervene bet*eenthe opposite processes. The (uestion *hether these contradictorychangesare contraries or not ma+es no difference) provided only it isimpossiblefor them both to be present to the same thing at the same time: thepoint is of no importance to the argument. -or does it matter if thething need not rest in the contradictory state) or if there is nostate of rest as a contrary to the process of change: it may be truethat the non0e6istent is not at rest) and that perishing is a process



to the non0e6istent. All that matters is the intervention of a time:it is this that prevents the change from being continuous: so) too)in our previous instances the important thing *as not the relationof contrariety but the impossibility of the t*o processes beingpresentto a thing at the same time. And there is no need to be disturbed

by the fact that on this sho*ing there may be more than one contraryto the same thing) that a particular motion *ill be contrary bothto rest and to motion in the contrary direction. &e have only to graspthe fact that a particular motion is in a sense the opposite bothof a state of rest and of the contrary motion) in the same *ay asthat *hich is of e(ual or standard measure is the opposite both ofthat *hich surpasses it and of that *hich it surpasses) and that itis impossible for the opposite motions or changes to be present toa thing at the same time. ,urthermore) in the case of becoming andperishing it *ould seem to be an utterly absurd thing if as soon asanything has become it must necessarily perish and cannot continueto e6ist for any time: and) if this is true of becoming and perishing)*e have fair grounds for inferring the same to be true of the other+inds of change) since it *ould be in the natural order of thingsthat they should be uniform in this respect.

Part D

et us no* proceed to maintain that it is possible that there shouldbe an infinite motion that is single and continuous) and that thismotion is rotatory motion. The motion of everything that is in processof locomotion is either rotatory or rectilinear or a compound of thet*o: conse(uently) if one of the former t*o is not continuous) that*hich is composed of them both cannot be continuous either. -o* itis plain that if the locomotion of a thing is rectilinear and finiteit is not continuous locomotion: for the thing must turn bac+) andthat *hich turns bac+ in a straight line undergoes t*o contrarylocomotions)since) so far as motion in respect of place is concerned) up*ardmotionis the contrary of do*n*ard motion) for*ard motion of bac+*ard motion)and motion to the left of motion to the right) these being the pairsof contraries in the sphere of place. But *e have already definedsingle and continuous motion to be motion of a single thing in asingleperiod of time and operating *ithin a sphere admitting of no furtherspecific differentiation 3for *e have three things to consider) firstthat *hich is in motion) e.g. a man or a god) secondly the *henof the motion) that is to say) the time) and thirdly the sphere *ithin*hich it operates) *hich may be either place or affection or essentialform or magnitude4: and contraries are specifically not one and thesame but distinct: and *ithin the sphere of place *e have the above0mentioneddistinctions. 1oreover *e have an indication that motion from A toB is the contrary of motion from B to A in the fact that) if theyoccur at the same time) they arrest and stop each other. And the sameis true in the case of a circle: the motion from A to*ards B is thecontrary of the motion from A to*ards #: for even if they arecontinuousand there is no turning bac+ they arrest each other) becausecontrariesannihilate or obstruct one another. $n the other hand lateral motionis not the contrary of up*ard motion. But *hat sho*s most clearlythat rectilinear motion cannot be continuous is the fact that turningbac+ necessarily implies coming to a stand) not only *hen it is a



straight line that is traversed) but also in the case of locomotionin a circle 3*hich is not the same thing as rotatory locomotion: for)*hen a thing merely traverses a circle) it may either proceed on itscourse *ithout a brea+ or turn bac+ again *hen it has reached thesame point from *hich it started4. &e may assure ourselves of thenecessity of this coming to a stand not only on the strength of

observation)but also on theoretical grounds. &e may start as follo*s: *e havethree points) starting0point) middle0point) and finishing0point) of*hich the middle0point in virtue of the relations in *hich it standsseverally to the other t*o is both a starting0point and a finishing0point)and though numerically one is theoretically t*o. &e have further thedistinction bet*een the potential and the actual. So in the straightline in (uestion any one of the points lying bet*een the t*o e6tremesis potentially a middle0point: but it is not actually so unless that*hich is in motion divides the line by coming to a stand at that pointand beginning its motion again: thus the middle0point becomes botha starting0point and a goal) the starting0point of the latter partand the finishing0point of the first part of the motion. This is thecase e.g. *hen A in the course of its locomotion comes to a standat B and starts again to*ards #: but *hen its motion is continuousA cannot either have come to be or have ceased to be at the pointB: it can only have been there at the moment of passing) its passagenot being contained *ithin any period of time e6cept the *hole of*hich the particular moment is a dividing0point. To maintain thatit has come to be and ceased to be there *ill involve the conse(uencethat A in the course of its locomotion *ill al*ays be coming to astand: for it is impossible that A should simultaneously have cometo be at B and ceased to be there) so that the t*o things must havehappened at different points of time) and therefore there *ill bethe intervening period of time: conse(uently A *ill be in a stateof rest at B) and similarly at all other points) since the samereasoningholds good in every case. &hen to A) that *hich is in process oflocomotion)B) the middle0point) serves both as a finishing0point and as astarting0pointfor its motion) A must come to a stand at B) because it ma+es it t*o'ust as one might do in thought. !o*ever) the point A is the realstarting0point at *hich the moving body has ceased to be) and it isat # that it has really come to be *hen its course is finished andit comes to a stand. So this is ho* *e must meet the difficulty thatthen arises) *hich is as follo*s. Suppose the line 9 is e(ual to theline J) that A proceeds in continuous locomotion from the e6tremepoint of 9 to #) and that) at the moment *hen A is at the point B)5 is proceeding in uniform locomotion and *ith the same velocity asA from the e6tremity of J to !: then) says the argument) 5 *ill havereached ! before A has reached # for that *hich ma+es an earlier startand departure must ma+e an earlier arrival: the reason) then) forthe late arrival of A is that it has not simultaneously come to beand ceased to be at B: other*ise it *ill not arrive later: for thisto happen it *ill be necessary that it should come to a stand there.Therefore *e must not hold that there *as a moment *hen A came tobe at B and that at the same moment 5 *as in motion from the e6tremityof J: for the fact of A s having come to be at B *ill involve thefact of its also ceasing to be there) and the t*o events *ill notbe simultaneous) *hereas the truth is that A is at B at a sectionalpoint of time and does not occupy time there. In this case) therefore)*here the motion of a thing is continuous) it is impossible to usethis form of e6pression. $n the other hand in the case of a thing



that turns bac+ in its course *e must do so. ,or suppose ! in thecourse of its locomotion proceeds to 5 and then turns bac+ andproceedsdo*n*ards again: then the e6treme point 5 has served as finishing0pointand as starting0point for it) one point thus serving as t*o: therefore

! must have come to a stand there: it cannot have come to be at 5and departed from 5 simultaneously) for in that case it *ouldsimultaneouslybe there and not be there at the same moment. And here *e cannot applythe argument used to solve the difficulty stated above: *e cannotargue that ! is at 5 at a sectional point of time and has not cometo be or ceased to be there. ,or here the goal that is reached isnecessarily one that is actually) not potentially) e6istent. -o* thepoint in the middle is potential: but this one is actual) and regardedfrom belo* it is a finishing0point) *hile regarded from above it isa starting0point) so that it stands in these same t*o respectiverelationsto the t*o motions. Therefore that *hich turns bac+ in traversinga rectilinear course must in so doing come to a stand. Conse(uentlythere cannot be a continuous rectilinear motion that is eternal.

The same method should also be adopted in replying to those *ho as+)in the terms of Jeno s argument) *hether *e admit that before anydistance can be traversed half the distance must be traversed) thatthese half0distances are infinite in number) and that it is impossibleto traverse distances infinite in number0or some on the lines of thissame argument put the (uestions in another form) and *ould have usgrant that in the time during *hich a motion is in progress it shouldbe possible to rec+on a half0motion before the *hole for every half0distancethat *e get) so that *e have the result that *hen the *hole distanceis traversed *e have rec+oned an infinite number) *hich is admittedlyimpossible. -o* *hen *e first discussed the (uestion of motion *eput for*ard a solution of this difficulty turning on the fact thatthe period of time occupied in traversing the distance contains *ithinitself an infinite number of units: there is no absurdity) *e said)in supposing the traversing of infinite distances in infinite time)and the element of infinity is present in the time no less than inthe distance. But) although this solution is ade(uate as a reply tothe (uestioner 3the (uestion as+ed being *hether it is possible ina finite time to traverse or rec+on an infinite number of units4)nevertheless as an account of the fact and e6planation of its truenature it is inade(uate. ,or suppose the distance to be left out ofaccount and the (uestion as+ed to be no longer *hether it is possiblein a finite time to traverse an infinite number of distances) andsuppose that the in(uiry is made to refer to the time ta+en by itself3for the time contains an infinite number of divisions4: then thissolution *ill no longer be ade(uate) and *e must apply the truth that*e enunciated in our recent discussion) stating it in the follo*ing*ay. In the act of dividing the continuous distance into t*o halvesone point is treated as t*o) since *e ma+e it a starting0point anda finishing0point: and this same result is also produced by the actof rec+oning halves as *ell as by the act of dividing into halves.But if divisions are made in this *ay) neither the distance nor themotion *ill be continuous: for motion if it is to be continuous mustrelate to *hat is continuous: and though *hat is continuous containsan infinite number of halves) they are not actual but potentialhalves.If the halves are made actual) *e shall get not a continuous but anintermittent motion. In the case of rec+oning the halves) it is clear



that this result follo*s: for then one point must be rec+oned as t*o:it *ill be the finishing0point of the one half and the starting0pointof the other) if *e rec+on not the one continuous *hole but the t*ohalves. Therefore to the (uestion *hether it is possible to passthroughan infinite number of units either of time or of distance *e must

reply that in a sense it is and in a sense it is not. If the unitsare actual) it is not possible: if they are potential) it is possible.,or in the course of a continuous motion the traveller has traversedan infinite number of units in an accidental sense but not in anun(ualifiedsense: for though it is an accidental characteristic of the distanceto be an infinite number of half0distances) this is not its real andessential character. It is also plain that unless *e hold that thepoint of time that divides earlier from later al*ays belongs onlyto the later so far as the thing is concerned) *e shall be involvedin the conse(uence that the same thing is at the same moment e6istentand not e6istent) and that a thing is not e6istent at the moment *henit has become. It is true that the point is common to both times)the earlier as *ell as the later) and that) *hile numerically oneand the same) it is theoretically not so) being the finishing0pointof the one and the starting0point of the other: but so far as thething is concerned it belongs to the later stage of *hat happens toit. et us suppose a time AB# and a thing 5) 5 being *hite in thetime A and not0*hite in the time B. Then 5 is at the moment # *hiteand not0*hite: for if *e *ere right in saying that it is *hite duringthe *hole time A) it is true to call it *hite at any moment of A)and not0*hite in B) and # is in both A and B. &e must not allo*)therefore)that it is *hite in the *hole of A) but must say that it is so inall of it e6cept the last moment #. # belongs already to the laterperiod) and if in the *hole of A not0*hite *as in process of becomingand *hite of perishing) at # the process is complete. And so # isthe first moment at *hich it is true to call the thing *hite or not*hite respectively. $ther*ise a thing may be non0e6istent at themoment*hen it has become and e6istent at the moment *hen it has perished:or else it must be possible for a thing at the same time to be *hiteand not *hite and in fact to be e6istent and non0e6istent. ,urther)if anything that e6ists after having been previously non0e6istentmust become e6istent and does not e6ist *hen it is becoming) timecannot be divisible into time0atoms. ,or suppose that 5 *as becoming*hite in the time A and that at another time B) a time0atomconsecutive*ith the last atom of A) 5 has already become *hite and so is *hiteat that moment: then) inasmuch as in the time A it *as becoming *hiteand so *as not *hite and at the moment B it is *hite) there must havebeen a becoming bet*een A and B and therefore also a time in *hichthe becoming too+ place. $n the other hand) those *ho deny atoms oftime 3as *e do4 are not affected by this argument: according to them5 has become and so is *hite at the last point of the actual timein *hich it *as becoming *hite: and this point has no other pointconsecutive *ith or in succession to it) *hereas time0atoms areconceivedas successive. 1oreover it is clear that if 5 *as becoming *hite inthe *hole time A) the time occupied by it in having become *hite inaddition to having been in process of becoming *hite is no more thanall that it occupied in the mere process of becoming *hite.

These and such0li+e) then) are the arguments for our conclusion thatderive cogency from the fact that they have a special bearing on the



point at issue. If *e loo+ at the (uestion from the point of vie*of general theory) the same result *ould also appear to be indicatedby the follo*ing arguments. 9verything *hose motion is continuousmust) on arriving at any point in the course of its locomotion) havebeen previously also in process of locomotion to that point) if itis not forced out of its path by anything: e.g. on arriving at B a

thing must also have been in process of locomotion to B) and thatnot merely *hen it *as near to B) but from the moment of its startingon its course) since there can be) no reason for its being so at anyparticular stage rather than at an earlier one. So) too) in the caseof the other +inds of motion. -o* *e are to suppose that a thingproceedsin locomotion from A to # and that at the moment of its arrival at# the continuity of its motion is unbro+en and *ill remain so untilit has arrived bac+ at A. Then *hen it is undergoing locomotion fromA to # it is at the same time undergoing also its locomotion to Afrom #: conse(uently it is simultaneously undergoing t*o contrarymotions) since the t*o motions that follo* the same straight lineare contrary to each other. &ith this conse(uence there also follo*sanother: *e have a thing that is in process of change from a positionin *hich it has not yet been: so) inasmuch as this is impossible)the thing must come to a stand at #. Therefore the motion is not asingle motion) since motion that is interrupted by stationarinessis not single.

,urther) the follo*ing argument *ill serve better to ma+e this pointclear universally in respect of every +ind of motion. If the motionundergone by that *hich is in motion is al*ays one of those alreadyenumerated) and the state of rest that it undergoes is one of thosethat are the opposites of the motions 3for *e found that there couldbe no other besides these4) and moreover that *hich is undergoingbut does not al*ays undergo a particular motion 3by this I mean oneof the various specifically distinct motions) not some particularpart of the *hole motion4 must have been previously undergoing thestate of rest that is the opposite of the motion) the state of restbeing privation of motion then) inasmuch as the t*o motions thatfollo* the same straight line are contrary motions) and it isimpossiblefor a thing to undergo simultaneously t*o contrary motions) that *hichis undergoing locomotion from A to # cannot also simultaneously beundergoing locomotion from # to A: and since the latter locomotionis not simultaneous *ith the former but is still to be undergone)before it is undergone there must occur a state of rest at #: forthis) as *e found) is the state of rest that is the opposite of themotion from #. The foregoing argument) then) ma+es it plain that themotion in (uestion is not continuous.

$ur ne6t argument has a more special bearing than the foregoing onthe point at issue. &e *ill suppose that there has occurred insomethingsimultaneously a perishing of not0*hite and a becoming of *hite. Thenif the alteration to *hite and from *hite is a continuous processand the *hite does not remain any time) there must have occurredsimultaneouslya perishing of not0*hite) a becoming of *hite) and a becoming of not0*hite:for the time of the three *ill be the same.

Again) from the continuity of the time in *hich the motion ta+es place*e cannot infer continuity in the motion) but only successiveness:in fact) ho* could contraries) e.g. *hiteness and blac+ness) meet



in the same e6treme point7

$n the other hand) in motion on a circular line *e shall findsinglenessand continuity: for here *e are met by no impossible conse(uence:that *hich is in motion from A *ill in virtue of the same direction

of energy be simultaneously in motion to A 3since it is in motionto the point at *hich it *ill finally arrive4) and yet *ill not beundergoing t*o contrary or opposite motions: for a motion to a pointand a motion from that point are not al*ays contraries or opposites:they are contraries only if they are on the same straight line 3forthen they are contrary to one another in respect of place) as e.g.the t*o motions along the diameter of the circle) since the ends ofthis are at the greatest possible distance from one another4) andthey are opposites only if they are along the same line. Thereforein the case *e are no* considering there is nothing to prevent themotion being continuous and free from all intermission: for rotatorymotion is motion of a thing from its place to its place) *hereasrectilinearmotion is motion from its place to another place.

1oreover the progress of rotatory motion is never locali8ed *ithincertain fi6ed limits) *hereas that of rectilinear motion repeatedlyis so. -o* a motion that is al*ays shifting its ground from momentto moment can be continuous: but a motion that is repeatedly locali8ed*ithin certain fi6ed limits cannot be so) since then the same thing*ould have to undergo simultaneously t*o opposite motions. So) too)there cannot be continuous motion in a semicircle or in any otherarc of a circle) since here also the same ground must be traversedrepeatedly and t*o contrary processes of change must occur. The reasonis that in these motions the starting0point and the termination donot coincide) *hereas in motion over a circle they do coincide) andso this is the only perfect motion.

This differentiation also provides another means of sho*ing that theother +inds of motion cannot be continuous either: for in all of them*e find that there is the same ground to be traversed repeatedlythus in alteration there are the intermediate stages of the process)and in (uantitative change there are the intervening degrees ofmagnitude:and in becoming and perishing the same thing is true. It ma+es nodifference *hether *e ta+e the intermediate stages of the processto be fe* or many) or *hether *e add or subtract one: for in eithercase *e find that there is still the same ground to be traversedrepeatedly.1oreover it is plain from *hat has been said that those physicists*ho assert that all sensible things are al*ays in motion are *rong:for their motion must be one or other of the motions 'ust mentioned:in fact they mostly conceive it as alteration 3things are al*ays influ6 and decay) they say4) and they go so far as to spea+ even ofbecoming and perishing as a process of alteration. $n the other hand)our argument has enabled us to assert the fact) applying universallyto all motions) that no motion admits of continuity e6cept rotatorymotion: conse(uently neither alteration nor increase admits ofcontinuity.&e need no* say no more in support of the position that there is noprocess of change that admits of infinity or continuity e6ceptrotatorylocomotion.

Part E



It can no* be sho*n plainly that rotation is the primary locomotion.9very locomotion) as *e said before) is either rotatory or rectilinearor a compound of the t*o: and the t*o former must be prior to thelast) since they are the elements of *hich the latter consists.1oreover

rotatory locomotion is prior to rectilinear locomotion) because itis more simple and complete) *hich may be sho*n as follo*s. Thestraightline traversed in rectilinear motion cannot be infinite: for thereis no such thing as an infinite straight line and even if there *ere)it *ould not be traversed by anything in motion: for the impossibledoes not happen and it is impossible to traverse an infinite distance.$n the other hand rectilinear motion on a finite straight line isif it turns bac+ a composite motion) in fact t*o motions) *hile ifit does not turn bac+ it is incomplete and perishable: and in theorder of nature) of definition) and of time ali+e the complete isprior to the incomplete and the imperishable to the perishable. Again)a motion that admits of being eternal is prior to one that does not.-o* rotatory motion can be eternal: but no other motion) *hetherlocomotionor motion of any other +ind) can be so) since in all of them restmust occur and *ith the occurrence of rest the motion has perished.1oreover the result at *hich *e have arrived) that rotatory motionis single and continuous) and rectilinear motion is not) is areasonableone. In rectilinear motion *e have a definite starting0point)finishing0point)middle0point) *hich all have their place in it in such a *ay thatthere is a point from *hich that *hich is in motion can be said tostart and a point at *hich it can be said to finish its course 3for*hen anything is at the limits of its course) *hether at the starting0pointor at the finishing0point) it must be in a state of rest4. $n theother hand in circular motion there are no such definite points: for*hy should any one point on the line be a limit rather than any other7Any one point as much as any other is ali+e starting0point) middle0point)and finishing0point) so that *e can say of certain things both thatthey are al*ays and that they never are at a starting0point and ata finishing0point 3so that a revolving sphere) *hile it is in motion)is also in a sense at rest) for it continues to occupy the sameplace4.The reason of this is that in this case all these characteristicsbelong to the centre: that is to say) the centre is ali+e starting0point)middle0point) and finishing0point of the space traversed conse(uentlysince this point is not a point on the circular line) there is nopoint at *hich that *hich is in process of locomotion can be in astate of rest as having traversed its course) because in itslocomotionit is proceeding al*ays about a central point and not to an e6tremepoint: therefore it remains still) and the *hole is in a sense al*aysat rest as *ell as continuously in motion. $ur ne6t point gives aconvertible result: on the one hand) because rotation is the measureof motions it must be the primary motion 3for all things are measuredby *hat is primary4: on the other hand) because rotation is theprimarymotion it is the measure of all other motions. Again) rotatory motionis also the only motion that admits of being regular. In rectilinearlocomotion the motion of things in leaving the starting0point is not



uniform *ith their motion in approaching the finishing0point) sincethe velocity of a thing al*ays increases proportionately as it removesitself farther from its position of rest: on the other hand rotatorymotion is the only motion *hose course is naturally such that it hasno starting0point or finishing0point in itself but is determined fromelse*here.

As to locomotion being the primary motion) this is a truth that isattested by all *ho have ever made mention of motion in theirtheories:they all assign their first principles of motion to things that impartmotion of this +ind. Thus separation and combination are motionsin respect of place) and the motion imparted by ove and Strifeta+es these forms) the latter separating and the former combining .Ana6agoras) too) says that 1ind ) his first movent) separates .Similarly those *ho assert no cause of this +ind but say that voidaccounts for motion0they also hold that the motion of naturalsubstanceis motion in respect of place: for their motion that is accountedfor by void is locomotion) and its sphere of operation may be saidto be place. 1oreover they are of opinion that the primary substancesare not sub'ect to any of the other motions) though the things thatare compounds of these substances are so sub'ect: the processes ofincrease and decrease and alteration) they say) are effects of the

combination and separation of atoms. It is the same) too) *iththose *ho ma+e out that the becoming or perishing of a thing isaccountedfor by density or rarity : for it is by combination and

separationthat the place of these things in their systems is determined.1oreoverto these *e may add those *ho ma+e Soul the cause of motion: for theysay that things that undergo motion have as their first principle

that *hich moves itself : and *hen animals and all living thingsmove themselves) the motion is motion in respect of place. ,inallyit is to be noted that *e say that a thing is in motion in thestrictsense of the term only *hen its motion is motion in respect of place:if a thing is in process of increase or decrease or is undergoingsome alteration *hile remaining at rest in the same place) *e saythat it is in motion in some particular respect: *e do not say thatit is in motion *ithout (ualification.

$ur present position) then) is this: &e have argued that there al*ays*as motion and al*ays *ill be motion throughout all time) and *e havee6plained *hat is the first principle of this eternal motion: *e havee6plained further *hich is the primary motion and *hich is the onlymotion that can be eternal: and *e have pronounced the first moventto be unmoved.

Part %K

&e have no* to assert that the first movent must be *ithout partsand *ithout magnitude) beginning *ith the establishment of thepremisseson *hich this conclusion depends.

$ne of these premisses is that nothing finite can cause motion duringan infinite time. &e have three things) the movent) the moved) andthirdly that in *hich the motion ta+es place) namely the time: andthese are either all infinite or all finite or partly0that is to say



in the infinite magnitude) so that this force *ill be a measure ofthe finite force residing in the infinite magnitude.

It is plain) then) from the foregoing arguments that it is impossiblefor an infinite force to reside in a finite magnitude or for a finiteforce to reside in an infinite magnitude. But before proceeding to

our conclusion it *ill be *ell to discuss a difficulty that arisesin conne6ion *ith locomotion. If everything that is in motion *iththe e6ception of things that move themselves is moved by somethingelse) ho* is it that some things) e.g. things thro*n) continue tobe in motion *hen their movent is no longer in contact *ith them7If *e say that the movent in such cases moves something else at thesame time) that the thro*er e.g. also moves the air) and that thisin being moved is also a movent) then it *ould be no more possiblefor this second thing than for the original thing to be in motion*hen the original movent is not in contact *ith it or moving it: allthe things moved *ould have to be in motion simultaneously and alsoto have ceased simultaneously to be in motion *hen the original moventceases to move them) even if) li+e the magnet) it ma+es that *hichit has moved capable of being a movent. Therefore) *hile *e mustacceptthis e6planation to the e6tent of saying that the original moventgives the po*er of being a movent either to air or to *ater or tosomething else of the +ind) naturally adapted for imparting andundergoingmotion) *e must say further that this thing does not ceasesimultaneouslyto impart motion and to undergo motion: it ceases to be in motionat the moment *hen its movent ceases to move it) but it still remainsa movent) and so it causes something else consecutive *ith it to bein motion) and of this again the same may be said. The motion beginsto cease *hen the motive force produced in one member of theconsecutiveseries is at each stage less than that possessed by the precedingmember) and it finally ceases *hen one member no longer causes thene6t member to be a movent but only causes it to be in motion. Themotion of these last t*o0of the one as movent and of the other asmoved0must cease simultaneously) and *ith this the *hole motionceases.-o* the things in *hich this motion is produced are things that admitof being sometimes in motion and sometimes at rest) and the motionis not continuous but only appears so: for it is motion of thingsthat are either successive or in contact) there being not one moventbut a number of movents consecutive *ith one another: and so motionof this +ind ta+es place in air and *ater. Some say that it is mutualreplacement : but *e must recogni8e that the difficulty raised cannotbe solved other*ise than in the *ay *e have described. So far as theyare affected by mutual replacement ) all the members of the seriesare moved and impart motion simultaneously) so that their motionsalso cease simultaneously: but our present problem concerns theappearanceof continuous motion in a single thing) and therefore) since it cannotbe moved throughout its motion by the same movent) the (uestion is)*hat moves it7

esuming our main argument) *e proceed from the positions that theremust be continuous motion in the *orld of things) that this is asinglemotion) that a single motion must be a motion of a magnitude 3forthat *hich is *ithout magnitude cannot be in motion4) and that themagnitude must be a single magnitude moved by a single movent 3for



other*ise there *ill not be continuous motion but a consecutive seriesof separate motions4) and that if the movement is a single thing)it is either itself in motion or itself unmoved: if) then) it is inmotion) it *ill have to be sub'ect to the same conditions as that*hich it moves) that is to say it *ill itself be in process of changeand in being so *ill also have to be moved by something: so *e have

a series that must come to an end) and a point *ill be reached at*hich motion is imparted by something that is unmoved. Thus *e havea movent that has no need to change along *ith that *hich it movesbut *ill be able to cause motion al*ays 3for the causing of motionunder these conditions involves no effort4: and this motion aloneis regular) or at least it is so in a higher degree than any other)since the movent is never sub'ect to any change. So) too) in orderthat the motion may continue to be of the same character) the movedmust not be sub'ect to change in respect of its relation to themovent.1oreover the movent must occupy either the centre or thecircumference)since these are the first principles from *hich a sphere is derived.But the things nearest the movent are those *hose motion is (uic+est)and in this case it is the motion of the circumference that is the(uic+est: therefore the movent occupies the circumference.

There is a further difficulty in supposing it to be possible foranythingthat is in motion to cause motion continuously and not merely in the*ay in *hich it is caused by something repeatedly pushing 3in *hichcase the continuity amounts to no more than successiveness4. Sucha movent must either itself continue to push or pull or perform boththese actions) or else the action must be ta+en up by something elseand be passed on from one movent to another 3the process that *edescribedbefore as occurring in the case of things thro*n) since the air orthe *ater) being divisible) is a movent only in virtue of the factthat different parts of the air are moved one after another4: andin either case the motion cannot be a single motion) but only aconsecutiveseries of motions. The only continuous motion) then) is that *hichis caused by the unmoved movent: and this motion is continuous becausethe movent remains al*ays invariable) so that its relation to that*hich it moves remains also invariable and continuous.

-o* that these points are settled) it is clear that the first unmovedmovent cannot have any magnitude. ,or if it has magnitude) this mustbe either a finite or an infinite magnitude. -o* *e havealready provedin our course on Physics that there cannot be an infinite magnitude:and *e have no* proved that it is impossible for a finite magnitudeto have an infinite force) and also that it is impossible for a thingto be moved by a finite magnitude during an infinite time. But thefirst movent causes a motion that is eternal and does cause it duringan infinite time. It is clear) therefore) that the first movent isindivisible and is *ithout parts and *ithout magnitude.

T!9 9-5

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