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bat-do di scienee e lettere, 18 (1898), fasc . 5 : and WilliamH. Stahl, "The Greek Heliocentric Theory and Its Abandon-ment," in Transactions of the American Philological Asso-ciation, 77 (1945), 321-332 .

WILLIAM H . STAHL

ARISTOTLE (b. Stagira in Chalcidice, 384 B.C. ; d.Chalcis, 322 B.C .), the most influential ancient exponentof the methodology and division of sciences; contributedto physics, physical astronomy, meteorology, psy-chology, biology. The following article is in four parts :Method, Physics, and Cosmology ; Natural Historyand Zoology ; Anatomy and Physiology : Traditionand Influence .

Method, Physics, and Cosmology .Aristotle's father served as personal physician

to Amyntas II of Macedon, grandfather of Alexanderthe Great . Aristotle's interest in biology and in theuse of dissection is sometimes traced to his father'sprofession, but any suggestion of a rigorous familytraining in medicine can be discounted . Both parentsdied while Aristotle was a boy, and his knowledgeof human anatomy and physiology remained a nota-bly weak spot in his biology . In 367, about the timeof his seventeenth birthday, he came to Athens andbecame a member of Plato's Academy . Henceforthhis career falls naturally into three periods . He re-mained with the Academy for twenty years . Then,when Plato died in 347, he left the city and stayedaway for twelve years: his reason for going may havebeen professional, a dislike of philosophical tenden-cies represented in the Academy by Plato's nephewand successor, Speusippus, but more probably it waspolitical, the new anti-Macedonian mood of the city .He returned in 335 when Athens had come underMacedonian rule, and had twelve more years ofteaching and research there . This third period endedwith the death of his pupil, Alexander the Great(323), and the revival of Macedon's enemies . Aristotlewas faced with a charge of impiety and went againinto voluntary exile . A few months later he died onhis maternal estate in Chalcis .

His middle years away from Athens took him firstto a court on the far side of the Aegean whose ruler,Hermeias, became his father-in-law ; then (344) to theneighboring island Lesbos, probably at the suggestionof Theophrastus, a native of the island and hencefortha lifelong colleague : finally (342) back to Macedonas tutor of the young prince Alexander . After hisreturn to Athens he lectured chiefly in the groundsof the Lyceum, a Gymnasium already popular withsophists and teachers. The Peripatetic school, as aninstitution comparable to the Academy, was probably

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not founded until after his death . But with somedistinguished students and associates he collected anatural history museum and a library of maps andmanuscripts (including his own essays and lecturenotes), and organized a program of research whichinter alia laid the foundation for all histories of Greeknatural philosophy (see Theophrastus), mathematicsand astronomy (see Eudemus), and medicine .

Recent discussion of his intellectual developmenthas dwelt on the problem of distributing his worksbetween and within the three periods of his career .But part of the stimulus to this inquiry was thesupposed success with which Plato's dialogues hadbeen put in chronological order, and the analogy withPlato is misleading . Everything that Aristotle polishedfor public reading in Plato's fashion has been lost,save for fragments and later reports . The writings thatsurvive are a collection edited in the first century B.C .(see below, Aristotle : Tradition), allegedly from manu-scripts long mislaid : a few items are spurious (amongthe scientific works Mechanica, Problemata, Demundo, De plantis), most are working documentsproduced in the course of Aristotle's teaching andresearch ; and the notes and essays composing themhave been arranged and amended not only by theirauthor but also by his ancient editors and interpreters .Sometimes an editorial title covers a batch of writingson connected topics of which some seem to supersedeothers (thus Physics VII seems an unfinished attemptat the argument for a prime mover which is carriedout independently in Physics VIII) ; sometimes thetitle represents an open file, a text annotated withunabsorbed objections (e.g., the Topics) or with laterand even post-Aristotelian observations (e .g ., the His-toria anirnalium) . On the other hand it cannot beassumed that inconsistencies are always chronologicalpointers . In De caelo 1-II he argues for a fifth elementin addition to the traditional four (fire, air, water,earth) : unlike them, its natural motion is circular andit forms the divine and unchanging substance of theheavenly bodies . Yet in De caelo III-IV . a s in thePhysics, he discusses the elements without seemingto provide for any such fifth body, and these writingsare accordingly sometimes thought to be earlier. Buton another view of his methods (see below, ondialectic) it becomes more intelligible that he shouldtry different and even discrepant approaches to atopic at the same time .

Such considerations do not make it impossible toreconstruct something of the course of his scientificthinking from the extant writings, together with whatis known of his life . For instance it is sometimes saidthat his distinction between "essence" and "accident,"or between defining and nondefining characteristics,

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must be rooted in the biological studies in which itplays an integral part . But the distinction is exploredat greatest length in the Topics, a handbook of dia-lectical debate which dates substantially from hisearlier years in the Academy, whereas the inquiriesembodied in his biological works seem to come chieflyfrom his years abroad, since they refer relatively oftento the Asiatic coast and Lesbos and seldom tosouthern Greece . So this piece of conceptual appa-ratus was not produced by the work in biology . Onthe contrary, it was modified by that work : whenAristotle tries to reduce the definition of a species toone distinguishing mark (e .g ., Metaphysics VII 12,VIII 6) he is a dialectician, facing a problem whoseancestry includes Plato's theory of Forms, but whenhe rejects such definitions in favor of a cluster ofdifferentiae (De partibus animalium 1 2-3) he writesas a working biologist, armed with a set of questionsabout breathing and sleeping, movement and nourish-ment, birth and death .

The starting point in tracing his scientific progressmust therefore be his years in the Academy . Indeedwithout this starting point it is not possible to under-stand either his pronouncements on scientific theoryor, what is more important, the gap between histheory and his practice .The Mathematical Model. The Academy that

Aristotle joined in 367 was distinguished from otherAthenian schools by two interests : mathematics (in-cluding astronomy and harmonic theory, to the extentthat these could be made mathematically respect-able), and dialectic, the Socratic examination of theassumptions made in reasoning including the as-sumptions of mathematicians and cosmologists .Briefly, Plato regarded the first kind of studies asmerely preparatory and ancillary to the second ; Aris-totle, in the account of scientific and philosophicalmethod that probably dates from his Academic years,reversed the priorities (Posterior Analytics I ; Topics I1-2) . It was the mathematics he encountered that im-pressed him as providing the model for any well-or-ganized science. The work on axiomatization whichwas to culminate in Euclid's Elements was already faradvanced, and for Aristotle the pattern of a science isan axiomatic system in which theorems are validlyderived from basic principles, some proprietary to thescience ("hypotheses" and "definitions," the secondcorresponding to Euclid's "definitions"), others havingan application in more than one system ("axioms,"corresponding to Euclid's "common notions") . Theproof-theory which was characteristic of Greek mathe-matics (as against that of Babylon or Egypt) haddeveloped in the attempt to show why various mathe-matical formulae worked in practice . Aristotle pitches

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on this as the chief aim of any science : it must notmerely record but explain, and in explaining it must,so far as the special field of inquiry allows, generalize .Thus mathematical proof becomes Aristotle's firstparadigm of scientific explanation ; by contrast, thedialectic that Plato ranked higher the logical butfree-ranging analysis of the beliefs and usage of "themany and the wise"-is allowed only to help insettling those basic principles of a science that cannot,without regress or circularity, be proved within thescience itself. At any rate, this was the theory .

Aristotle duly adapts and enlarges the mathe-matical model to provide for the physical sciences .Mathematics, he holds, is itself a science (or rathera family of sciences) about the physical world, andnot about a Platonic world of transcendent objects ;but it abstracts from those characteristics of the worldthat are the special concern of physics-movementand change, and therewith time and location . So thenature and behavior of physical things will call formore sorts of explanation than mathematics recog-nizes. Faced with a man, or a tree, or a flame, onecan ask what it is made of, its "matter" ; what is itsessential character or "form" ; what external or in-ternal agency produced it ; and what the "end" orpurpose of it is . The questions make good sense whenapplied to an artifact such as a statue, and Aristotleoften introduces them by this analogy ; but he holdsthat they can be extended to every kind of thinginvolved in regular natural change . The explanationsthey produce can be embodied in the formal proofsor even the basic definitions of a science (thus a lunareclipse can be not merely accounted for, but defined,as the loss of light due to the interposition of theearth, and a biological species can be partly definedin terms of the purpose of some of its organs) . Again,the regularities studied by physics may be unlikethose of mathematics in an important respect : initiallythe Posterior Analytics depicts a science as derivingnecessary conclusions from necessary premises, truein all cases (I ii and iv), but later (I xxx) the scienceis allowed to deal in generalizations that are true inmost cases but not necessarily in all . Aristotle isadapting his model to make room for "a horse hasfour legs" as well as for "2 X 2 = 4." How he regardsthe exceptions to such generalizations is not altogetherclear. In his discussions of "luck" and "chance" inPhysics II, and of "accident" elsewhere, he seems tohold that a lucky or chance or accidental event canalways, under some description, be subsumed undera generalization expressing some regularity . His intro-duction to the Meteorologica is sometimes cited toshow that in his view sublunary happenings areinherently irregular ; but he probably means that,

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while the laws of sublunary physics are commonly(though not always) framed to allow of exceptions,these exceptions are not themselves inexplicable . Thematter is complicated by his failure to maintain asharp distinction between laws that provide a neces-sary (and even uniquely necessary), and those thatprovide a sufficient, condition of the situation to beexplained .

But in two respects the influence of mathematicson Aristotle's theory of science is radical and unmod-ified . First, the drive to axiomatize mathematics andits branches was in fact a drive for autonomy : thepremises of the science were to determine what ques-tions fell within the mathematician's competence and,no less important, what did not . This consequenceAristotle accepts for every field of knowledge : asection of Posterior Analytics I xii is given up to theproblem, what questions can be properly put to thepractitioner of such-and-such a science ; and in I vii,trading on the rule "one science to one genus," hedenounces arguments that poach outside their ownfield-which try, for instance, to deduce geometricalconclusions from arithmetical premises . He recognizesarithmetical proofs in harmonics and geometricalproofs in mechanics, but treats them as exceptions .The same impulse leads him to map all systematicknowledge into its departments-theoretical, prac-tical, and productive-and to divide the first intometaphysics (or, as he once calls it, "theology"),mathematics, and physics, these in turn being markedout in subdivisions .

This picture of the autonomous deductive systemhas had a large influence on the interpreters ofAristotle's scientific work ; yet it plays a small partin his inquiries, just because it is not a model forinquiry at all but for subsequent exposition . This isthe second major respect in which it reflects mathe-matical procedure . In nearly all the surviving produc-tions of Greek mathematics, traces of the workshophave been deliberately removed : proofs are found fortheorems that were certainly first reached by otherroutes. So Aristotle's theoretical picture of a scienceshows it in its shop window (or what he often callsits "didactic") form ; but for the most part his inquiriesare not at this stage of the business . This is a pieceof good fortune for students of the subject, who havealways lamented that no comparable record survivesof presystematic research in mathematics proper(Archimedes' public letter to Eratosthenes-theEphodos, or "Method"-is hardly such a record) . Asit is, Aristotle's model comes nearest to realizationin the systematic astronomy of De caelo I-II (cf., e .g .,I iii, "from what has been said, partly as premisesand partly as things proved from these, it

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follows . . ."), and in the proof of a prime mover inPhysics VIII . But these constructions are built on thepresystematic analyses of Physics I-VI, analyses thatare expressly undertaken to provide physics with itsbasic assumptions (cf. I i) and to define its basicconcepts, change and time and location, infinity andcontinuity (Ill i) . Ex hypothesi the latter discussions,which from Aristotle's pupils Eudemus and Stratoonward have given the chief stimulus to physicistsand philosophers of science, cannot be internal to thescience whose premises they seek to establish . Theirmethods and data need not and do not fit the theo-retical straitjacket, and in fact they rely heavily onthe dialectic that theoretically has no place in thefinished science .

Dialectic and "Phenomena." Conventionally Aris-totle has been contrasted with Plato as the com-mitted empiricist, anxious to "save the phenomena"by basing his theories on observation of the physicalworld. First the phenomena, then the theory to ex-plain them : this Baconian formula he recommendsnot only for physics (and specifically for astronomyand biology) but for ethics and generally for all artsand sciences. But "phenomena," like many of his keyterms, is a word with different uses in different con-texts. In biology and meteorology the phenomena arecommonly observations made by himself or takenfrom other sources (fishermen, travelers, etc .), andsimilar observations are evidently presupposed bythat part of his astronomy that relies on the schemesof concentric celestial spheres proposed by Eudoxusand Callippus . But in the Physics when he expoundsthe principles of the subject, and in many of thearguments in the De caelo and De generatione etcorruptione by which he settles the nature and in-teraction of the elements, and turns Eudoxus' elegantabstractions into a cumbrous physical (and theo-logical) construction, the data on which he draws aremostly of another kind. The phenomena he nowwants to save-or to give logical reasons (rather thanempirical evidence) for scrapping-are the commonconvictions and common linguistic usage of his con-temporaries, supplemented by the views of otherthinkers . They are what he always represents as thematerials of dialectic .Thus when Aristotle tries to harden the idea of

location for use in science (Physics IV 1-5) he setsout from our settled practice of locating a thing bygiving its physical surroundings, and in particularfrom established ways of talking about one thingtaking another's place . It is to save these that he treatsany location as a container, and defines the place ofX as the innermost static boundary of the bodysurrounding X . His definition turns out to be circular :

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moreover it carries the consequence that, since a pointcannot lie within a boundary, it cannot strictly have(or be used to mark) a location . Yet we shall see laterthat his theories commit him to denying this .

Again, when he defines time as that aspect ofchange that enables it to be counted (Physics IV10-14), what he wants to save and explain are thecommon ways of telling the time . This point, that heis neither inventing a new vocabulary nor assigningnew theory-based uses to current words, must beborne in mind when one encounters such expressionsas "force" and "average velocity" in versions of hisdynamics. The word sometimes translated "force"(dunamis) is the common word for the "power" or"ability" of one thing to affect or be affected byanother-to move or be moved, but also to heat orto soften or to be heated, and so forth . Aristotle makesit clear that this notion is what he is discussing inthree celebrated passages (Physics VII 5, VIII 10, Decaelo I 7) where later critics have discerned laws ofproportionality connecting the force applied, theweight moved, and the time required for the forceto move the weight a given distance . (Two of the textsdo not mention weight at all .) A second term, ischus,sometimes rendered "force" in these contexts, is thecommon word for "strength," and it is this familiarnotion that Aristotle is exploiting in the so-called lawsof forced motion set out in Physics VII 5 and pre-supposed in VIII 10 : he is relying on what a nontech-nical audience would at once grant him concerningthe comparative strengths of packhorses or (his ex-ample) gangs of shiphaulers . He says : let A be thestrength required to move a weight B over a distanceD in time T; then (1) A will move 1/2 B over 2D inT; (2) A will move 1/2 B over D in 1/2 T; (3) 1/2 Awill move 1/2 B over D in T; and (4) A will move Bover 1/2 D in 1/2 T; but (5) it does not follow thatA will move some multiple of B over a proportion-ate fraction of D in T or indeed in any time, sinceit does not follow that A will be sufficient to movethat multiple of B at all. The conjunction of (4) withthe initial assumption shows that Aristotle takes thespeed of motion in this case to be uniform ; so com-mentators have naturally thought of A as a forcewhose continued application to B is just sufficient toovercome the opposing forces of gravity, friction, andthe medium. In such circumstances propositions (3)and (4) will yield results equivalent to those of New-tonian dynamics . But then the circumstances describedin (1) and (2) should yield not just the doubling of auniform velocity which Aristotle supposes, but ac-celeration up to some appropriate terminal velocity .Others have proposed to treat A as prefiguring thelater idea not of force but of work, or else power, if

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these are defined in terms of the displacement ofweight and not of force ; and this has the advantageof leaving Aristotle discussing the case that is centralto his dynamics the carrying out of some finite taskin a finite time without importing the notion ofaction at an instant which, for reasons we shall see,he rejects . But Aristotle also assumes that, for a giventype of agent, A is multiplied in direct ratio to thesize or quantity of the agent; and to apply this tothe work done would be, once more, to overlook thedifference between conditions of uniform motion andof acceleration . The fact is that Aristotle is appealingto conventional ways of comparing the strength ofhaulers and beasts of burden, and for his purposesthe acceleration periods involved with these arenegligible . What matters is that we measure strengthby the ability to perform certain finite tasks beforefatigue sets in ; hence, when Aristotle adduces theseproportionalities in the Physics, he does so with a viewto showing that the strength required for keeping thesky turning for all time would be immeasurable . Sincesuch celestial revolutions do not in his view have toovercome any such resistance as that of gravity ora medium we are not entitled to read these notionsinto the formulae quoted . What then is the basis forthese proportionalities? He does not quote empiricalevidence in their support, and in their generalizedform he could not do so ; in the Physics and againin the De caelo he insists that they can be extendedto cover "heating and any effect of one body onanother," but the Greeks had no thermometer norindeed any device (apart from the measurement ofstrings in harmonics) for translating qualitative differ-ences into quantitative measurements . Nor on theother hand does he present them as technical defini-tions of the concepts they introduce . He simply com-ments in the Physics that the rules of proportionrequire them to be true (and it may be noticed thathe does not frame any of them as a function of morethan two variables: the proportion is always a simplerelation between two of the terms, the others remain-ing constant) . He depends on this appeal, togetherwith conventional ways of comparing strengths, togive him the steps he needs toward his conclusionabout the strength of a prime mover : it is no partof the dialectic of his argument to coin hypothesesthat require elaborate discussion in their own right .

It is part of the history of dynamics that, fromAristotle's immediate successors onward, theseformulae were taken out of context, debated andrefined, and finally jettisoned for an incomparablymore exact and powerful set of concepts which owedlittle to dialectic in Aristotle's sense . That he did notintend his proportionalities for such close scrutiny

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becomes even clearer when we turn to his so-calledlaws of natural motion . Aristotle's universe is finite,spherical, and geocentric : outside it there can be nobody nor even, therefore, any location or vacuum ortime (De caelo 1 9) ; within it there can be no vacuum(Physics IV 6-9) . Natural motion is the unimpededmovement of its elements : centripetal or "downward"in the case of earth (whose place is at the center) andof water (whose place is next to earth), centrifugalor "upward" in the case of fire and (next below fire)air. These are the sublunary elements, capable ofchanging into each other (De generatione et corrup-tione 11) and possessed of "heaviness" or "lightness"according as their natural motion is down or up .Above them all is the element whose existenceAristotle can prove only by a priori argument : ether,the substance of the spheres that carry the heavenlybodies . The natural motions of the first four elementsare rectilinear and terminate, unless they are blocked,in the part of the universe that is the element's naturalplace; the motion of the fifth is circular and cannotbe blocked, and it never leaves its natural place . Thesemotions of free fall, free ascent, and free revolutionare Aristotle's paradigms of regular movement,against which other motions can be seen as departuresdue to special agency or to the presence of more thanone element in the moving body . On several occasionshe sketches some proportional connection betweenthe variables that occur in his analysis of such naturalmotions; generally he confines himself to rectilinear(i .e ., sublunary) movement, as, for example, in P/nrsicsIV 8, the text that provoked a celebrated exchangebetween Simplicio and Salviati in Galileo's Dialoghi.There he writes : "We see a given weight or bodymoving faster than another for two reasons : eitherbecause of a difference in the medium traversed (e .g.,water as against earth, water as against air), or, otherthings being equal, because of the greater weight orlightness of the moving body ." Later he specifies thatthe proviso "other things being equal" is meant tocover identity of shape. Under the first heading, thatof differences in the medium, he remarks that themotion of the medium must be taken into accountas well as its density relative to others ; but he iscontent to assume a static medium and propound,as always, a simple proportion in which the movingobject's velocity varies inversely with the density ofthe medium . Two comments are relevant . First, in thisas in almost all comparable contexts, the "laws ofnatural motion" are dispensable from the argument .Here Aristotle uses his proportionality to rebut thepossibility of motion in a vacuum : such motion wouldencounter a medium of nil density and hence wouldhave infinite velocity, which is impossible . But this

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is only one of several independent arguments for thesame conclusion in the context . Next, the argumentdiscounts acceleration (Aristotle does not consider thepossibility of a body's speed in a vacuum remainingfinite but increasing without limit, let alone that ofits increasing to some finite terminal speed) ; yet heoften insists that for the sublunary elements naturalmotion is always acceleration . (For this reason amongothers it is irrelevant to read his proportionalities ofnatural motion as an unwitting anticipation ofStokes's law .) But it was left to his successors duringthe next thousand years to quarrel over the way inwhich the ratios he formulated could be used toaccount for the steady acceleration he required insuch natural motion ; and where in the passage quotedhe writes "we see," it was left to some namelessancient scientist to make the experiment recorded byPhiloponus and later by Galileo, of dropping differentweights from the same height and noting that whatwe see does not answer to Aristotle's claim about theirspeed of descent. It was, to repeat, no part of thedialectic of his argument to give these proportionali-ties the rigor of scientific laws or present them as therecord of exact observation .

On the other hand the existence of the naturalmotions themselves is basic to his cosmology . Platohad held that left to themselves, i .e ., without divinegovernance, the four elements (he did not recognizea fifth) would move randomly in any direction :Aristotle denies this on behalf of the inherent regu-larity of the physical world . He makes the naturalmotions his "first hypotheses" in the De caelo andapplies them over and again to the discussion of otherproblems. (The contrast between his carelessness overthe proportionalities and the importance he attachesto the movements is sometimes read as showing thathe wants to "eliminate mathematics from physics" :but more on this later .)

This leads to a more general point which must beborne in mind in understanding his way of establish-ing physical theory . When he appeals to commonviews and usage in such contexts he is applying afavorite maxim, that in the search for explanationswe must start from what is familiar or intelligible tous. (Once the science is set up, the deductions willproceed from principles "intelligible in themselves .")The same maxim governs his standard way of intro-ducing concepts by extrapolating from some famil-iar, unpuzzling situation . Consider his distinction of"matter" and "form" in Physics I . He argues that anychange implies a passage between two contrary attri-butes-from one to the other, or somewhere on aspectrum between the two-and that there must bea third thing to make this passage, a substrate which

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changes but survives the change . The situations towhich he appeals are those from which this triadicanalysis can be, so to speak, directly read off : a lightobject turning dark, an unmusical man becomingmusical. But then the analysis is extended to casesprogressively less amenable : he moves, via the detun-ing of an instrument and the shaping of a statue, tothe birth of plants and animals and generally to thesort of situation that had exercised earlier thinkers-the emergence of a new individual, the apparentcoming of something from nothing . (Not the emer-gence of a new type : Aristotle does not believe thatnew types emerge in nature, although he accepts theappearance of sports within or between existing types .In Physics II 8 he rejects a theory of evolution forputting the random occurrence of new types on thesame footing with the reproduction of existing species,arguing that a theory that is not based on such regu-larities is not scientific physics .) Ex nihilo nihil fit; andeven the emergence of a new individual must involvea substrate, "matter," which passes between twocontrary conditions, the "privation" and the "form ."But one effect of Aristotle's extrapolation is to forcea major conflict between his theories and most con-temporary and subsequent physics . In his view, thequestion "What are the essential attributes ofmatter?" must go unanswered . There is no generalanswer, for the distinction between form and matterreappears on many levels : what serves as matter toa higher form may itself be analyzed into form andmatter, as a brick which is material for a house canitself be analyzed into a shape and the clay on whichthe shape is imposed. More important, there is noanswer even when the analysis reaches the basicelements-earth, air, fire, and water . For these canbe transformed into each other, and since no changecan be intelligibly pictured as a mere succession ofdiscrete objects these too must be transformations ofsome residual subject, but one that now ex hypothesihas no permanent qualitative or quantitative deter-minations in its own right . Thus Aristotle rejects alltheories that explain physical change by the rear-rangement of some basic stuff or stuffs endowed withfixed characteristics . Atomism in particular he rebutsat length, arguing that movement in a vacuum isimpossible (we have seen one argument for this) andthat the concept of an extended indivisible body ismathematically indefensible . But although matter isnot required to identify itself by any permanentfirst-order characteristics, it does have importantsecond-order properties . Physics studies the regulari-ties in change, and for a given sort of thing at a givenlevel it is the matter that determines what kinds ofchange are open to it . In some respects the idea has

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more in common with the field theory that appearsembryonically in the Stoics than with the crudeatomism maintained by the Epicureans, but its chiefinfluence was on metaphysics (especially Neo-platonism) rather than on scientific theory . By con-trast, the correlative concept of form, the universalelement in things that allows them to be known andclassified and defined, remained powerful in science .Aristotle took it from Plato, but by way of a radicaland very early critique of Plato's Ideas ; for Aristotlethe formal element is inseparable from the thingsclassified, whereas Plato had promoted it to inde-pendent existence in a transcendent world contem-plated by disembodied souls . For Aristotle the phys-ical world is all ; its members with their qualities andquantities and interrelations are the paradigms ofreality and there are no disembodied souls .

The device of extrapolating from the familiar isevident again in his account of another of his fourtypes of "cause," or explanation, viz . the "final,"or teleological . In Physics II 8 he mentions somecentral examples of purposive activity-housebuild-ing, doctoring, writing and then by stages moveson to discerning comparable purposiveness in thebehavior of spiders and ants, the growth of rootsand leaves, the arrangement of the teeth . Again theprocess is one of weakening or discarding some ofthe conditions inherent in the original situations : theidea of purposiveness sheds its connection with thoseof having a skill and thinking out steps to an end(although Aristotle hopes to have it both ways, byrepresenting natural sports and monsters as mistakes) .The resultant "immanent teleology" moved his fol-lower Theophrastus to protest at its thinness andfacility, but its effectiveness as a heuristic device,particularly in biology, is beyond dispute .

It is worth noting that this tendency of Aristotle'sto set out from some familiar situation, or rather fromthe most familiar and unpuzzling ways of describingsuch a situation, is something more than the generalinclination of scientists to depend on "explanatoryparadigms." Such paradigms in later science (e .g .,classical mechanics) have commonly been limitingcases not encountered in common observation ordiscourse ; Aristotle's choice of the familiar is a matterof dialectical method, presystematic by contrast withthe finished science, but subject to rules of discussionwhich he was the first to codify . This, and not (aswe shall see) any attempt to extrude mathematicsfrom physics, is what separates his extant work in thefield from the most characteristic achievements of thelast four centuries . It had large consequences fordynamics. In replying to Zeno's paradox of the flyingarrow he concedes Zeno's claim that nothing can be

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said to be moving at an instant, and insists only thatit cannot be said to be stationary either . What preoc-cupies him is the requirement, embedded in commondiscourse, that any movement must take a certaintime to cover a certain distance (and, as a corollary,that any stability must take a certain time but coverno distance) ; so he discounts even those hints thatcommon discourse might have afforded of the deriva-tive idea of motion, and therefore of velocity, at aninstant . He has of course no such notion of a mathe-matical limit as the analysis of such cases requires,but in any event this notion came later than therecognition of the cases . It is illuminating to contrastthe treatment of motion in the Mechanica, a workwhich used to carry Aristotle's name but which mustbe at least a generation later . There (Mechanica 1)circular motion is resolved into two components, onetangential and one centripetal (contrast Aristotle'srefusal to assimilate circular and rectilinear move-ments, notably in Physics VII 4). And the remarkablesuggestion is made that the proportion between thesecomponents need not be maintained for any time atall, since otherwise the motion would be in a straightline. Earlier the idea had been introduced of a pointhaving motion and velocity, an idea that we shall findAristotle using although his dialectical analysis ofmovement and location disallows it ; here that ideais supplemented by the concept of a point having agiven motion or complex of motions at an instant andnot for any period, however small . The Mechanicais generally agreed to be a constructive developmentof hints and suggestions in Aristotle's writings ; butthe methods and purposes evident in his own discus-sions of motion inhibit him from such novel construc-tions in dynamics .

It is quite another thing to say, as is often said,that Aristotle wants to debar physics from any sub-stantial use of the abstract proofs and constructionsavailable to him in contemporary mathematics . It isa common fallacy that, whereas Plato had tried tomake physics mathematical and quantitative, Aris-totle aimed at keeping it qualitative .

Mathematics and Physics. Plato had tried to con-struct the physical world of two-dimensional andapparently weightless triangles. When Aristotleargues against this in the De caelo (III 7) he observes :"The principles of perceptible things must be percepti-ble, of eternal things eternal, of perishable thingsperishable : in sum, the principles must be homo-geneous with the subject-matter." These words, takentogether with his prescriptions for the autonomy ofsciences in the Analytics, are often quoted to showthat any use of mathematical constructions in hisphysics must be adventitious or presystematic, dis-

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pensable from the science proper. The province ofphysics is the class of natural bodies regarded ashaving weight (or "lightness," in the case of air andfire), heat, and color and an innate tendency to movein a certain way . But these are properties that mathe-matics expressly excludes from its purview (Meta-physics K 3) .

In fact, however, the division of sciences is not soabsolute . When Aristotle contrasts mathematics andphysics in Physics II he remarks that astronomy,which is one of the "more physical of the mathe-matical sciences," must be part of physics, since itwould be absurd to debar the physicist from discuss-ing the geometrical properties of the heavenly bod-ies. The distinction is that the physicist must, as themathematician does not, treat these properties as theattributes of physical bodies that they are ; i .e ., hemust be prepared to explain the application of hismodel. Given this tie-line a good deal of mathe-matical abstraction is evidently permissible . Aristotleholds that only extended bodies can strictly be saidto have a location (i .e ., to lie within a static perimeter)or to move, but he is often prepared to discount theextension of bodies . Thus in Physics IV 11, where heshows an isomorphic correspondence between con-tinua representing time, motion, and the path tra-versed by the moving body, he correlates the movingobject with points in time and space and for thispurpose calls it "a point-or stone, or any such thing ."In Physics V 4, he similarly argues from the motionof an unextended object, although it is to be noticedthat he does not here or anywhere ease the transitionfrom moving bodies to moving points by importingthe idea of a center of gravity, which was to play solarge a part in Archimedes' Equilibrium of Planes . Inhis meteorology, explaining the shape of halos andrainbows, he treats the luminary as a point sourceof light . In the biological works he often recurs tothe question of the number of points at which a giventype of animal moves ; these "points" are in fact themajor joints, but in De motu animalium I he makesit clear that he has a geometrical model in mind andis careful to explain what supplementary assumptionsare necessary to adapting this model to the actualsituation it illustrates . In the cosmology of the Decaelo he similarly makes use of unextended loci, incontrast to his formal account of any location as aperimeter enclosing a volume . Like Archimedes acentury later, he represents the center of the universeas a point when he proves that the surface of wateris spherical, and again when he argues that earthmoves so as to make its own (geometrical) centerultimately coincide with that of the universe . Hisattempt in De caelo IV 3 to interpret this in terms

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of perimeter locations is correct by his own principles,but confused .This readiness to import abstract mathematical

arguments and constructions into his account of thephysical world is one side of the coin whose otherface is his insistence that any mathematics must bedirectly applicable to the world . Thus, after arguing(partly on dialectical grounds, partly from his hypoth-esis of natural movements and natural places) thatthe universe must be finite in size, he adds that thisdoes not put the mathematicians out of business, sincethey do not need or use the notion of a line infinitein extension: what they require is only the possibilityof producing a line n in any required ratio with agiven line m, and however large the ratio n/m it canalways be physically exemplified for a suitable inter-pretation of m . The explanation holds good for suchlemmata as that applied in Eudoxus' method ofexhaustion, but not of some proportionalities hehimself adduces earlier in the same context or in Decaelo I . (These proportionalities are indeed used in,but they are not the subject of, reductio ad absurdumarguments. In the De caelo Aristotle even assumesthat an infinite rotating body would contain a pointat an infinite distance from its center and conse-quently moving at infinite speed .) The same concernto make mathematics applicable to the physical worldwithout postulating an actual infinite is evident in histreatment of the sequence of natural numbers . Theinfinity characteristic of the sequence, and generallyof any countable series whose members can be corre-lated with the series of numbers, consists just in thepossibility of specifying a successor to any memberof the sequence : "the infinite is that of which, as itis counted or measured off, it is always possible totake some part outside that already taken ." This istrue not only of the number series but of the partsproduced by dividing any magnitude in a constantratio; and since all physical bodies are in principleso divisible, the number series is assured of a physicalapplication without requiring the existence at anytime of an actually infinite set of objects : all that isrequired is the possibility of following any divisionwith a subdivision .

This positivistic approach is often evident inAristotle's work (e .g ., in his analysis of the locationof A as the inner static boundary of the body sur-rounding A), and it is closely connected with hismethod of building explanations on the familiar case .But here too Aristotle moves beyond the familiar casewhen he argues that infinite divisibility is characteris-tic of bodies below the level of observation . Hisdefense and exploration of such divisibility, as adefining characteristic of bodies and times and mo-

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tions, is found in Physics VI, a book often salutedas his most original contribution to the analysis ofthe continuum. Yet it is worth noticing that in thisbook as in its two predecessors Aristotle's problemsand the ideas he applies to their solution are overand again taken, with improvements, from the secondpart of Plato's Parmenides. The discussion is in thattradition of logical debate which Aristotle, like Plato,called "dialectic," and its problems are not those ofaccommodating theories to experimentally establishedfacts (or vice versa) but logical puzzles generatedby common discourse and conviction . (But thenAristotle thinks of common discourse and convic-tion as a repository of human experience .) So theargument illustrates Aristotle's anti-Platonic thesisthat mathematics-represented again in this case bysimple proportion theory-has standing as a scienceonly to the extent that it can be directly applied tothe description of physical phenomena . But the argu-ment is no more framed as an advance in the mathe-matical theory itself than as a contribution to theobservational data of physics .

Probably the best-known instance of an essentiallymathematical construction incorporated into Aris-totle's physics is the astronomical theory due toEudoxus and improved by Callippus . In this theorythe apparent motion of the "fixed stars" is representedby the rotation of one sphere about its diameter, whilethose of the sun, moon, and the five known planetsare represented each by a different nest of concentricspheres . In such a nest the first sphere carries rounda second whose poles are located on the first but withan axis inclined to that of the first ; this second,rotating in turn about its poles, carries a third simi-larly connected to it, and so on in some cases to afourth or (in Callippus' version) a fifth, the apparentmotion of the heavenly body being the resultantmotion of a point on the equator of the last sphere .To this set of abstract models, itself one of the fiveor six major advances in science, Aristotle makesadditions of which the most important is the attemptto unify the separate nests of spheres into one con-nected physical system . To this end he intercalatesreagent spheres designed to insulate the movementof each celestial body from the complex of motionspropelling the body next above it . The only motionleft uncanceled in this downward transmission is therotation of the star sphere . It is generally agreed thatAristotle in Metaphysics XII 8 miscalculates the result-ing number of agent and reagent spheres : he con-cludes that we need either fifty-five or forty-seven,the difference apparently representing one disagree-ment between the theories of Eudoxus and Callippus,but on the latest computation (that of Hanson) the

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figures should be sixty-six and forty-nine . The mistakehad no effect on the progress of astronomy : withina century astronomers had turned to a theory involv-ing epicycles, and Aristotle's physical structure ofconcentric nonoverlapping spheres was superseded .On the other hand his basic picture of the geocen-tric universe and its elements, once freed from thespecial constructions he borrowed and adaptedfrom Eudoxus, retained its authority and can beseen again in the introductory chapters of Ptolemy'sSyntaxis.

Conclusion . These arguments and theories in whatcame to be called the exact sciences are drawn prin-cipally from the Posterior Analytics, Topics, Physics,De caelo and De generatione, works that are generallyaccepted as early and of which the first four at leastprobably date substantially from Aristotle's years inthe Academy or soon after . The influence of theAcademy is strong on them . They are marked by alarge respect for mathematics and particularly for thetechniques and effects of axiomatizing that subject,but they do not pretend to any mathematical dis-coveries, and in this they are close in spirit to Plato'swritings . Even the preoccupation with physicalchange, its varieties and regularities and causes, andthe use of dialectic in analyzing these, is a positionto which Plato had been approaching in his lateryears. Aristotle the meticulous empiricist, amassingbiological data or compiling the constitutions of 158Greek states, is not yet in evidence . In these worksthe analyses neither start from nor are closely con-trolled by fresh inspections of the physical world . Noris he liable to think his analyses endangered by suchinspections : if his account of motion shows that any"forced" or "unnatural" movement requires an agentof motion in constant touch with the moving body,the movement of a projectile can be explained byinventing a set of unseen agents to fill the gap-suc-cessive stages of the medium itself, supposed to becapable of transmitting movement even after theinitial agency has ceased acting . In all the illustrativeexamples cited in these works there is nothing com-parable to even the half-controlled experiments inatomistic physics and harmonics of the followingcenturies. His main concerns were the methodologyof the sciences, which he was the first to separateadequately on grounds of field and method ; and themeticulous derivation of the technical equipment ofthese sciences from the common language and as-sumptions of men about the world they live in . Hisinfluence on science stemmed from an incomparablecleverness and sensitiveness to counterarguments,rather than from any breakthrough comparable tothose of Eudoxus or Archimedes .

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BIBLIOGRAPHY

Aristotle is still quoted by reference to the page, column,and line of Vols . I, II of I . Bekker's Berlin Academy edition(1831-1870, recently repr.) . The later texts published in theOxford Classical Texts and in the Bude and Loeb seriesare generally reliable for the works quoted . The standardOxford translation of the complete works with selectedfragments occupies 12 volumes (1909-1952) . The ancientcommentaries are still among the best (Commentaria inAristotelem Graeca, Berlin, 1882-1909) . Of recent editionswith commentaries pride of place goes to those by SirDavid Ross of the Metaphysics (2nd ed., 1953), Physics(1936), Analytics (1949), Parva naturalia (1955) . and Deanima (1961) . Others are T. Waitz, Organon (1844-1846) :H . H . Joachim, De generatione et corrupiione (1922) .Important modern works are W. Jaeger, Aristotle (2nd

English ed., Oxford, 1948) ; W. D. Ross, Aristotle (4th ed .,London, 1945) . On the mathematics and physics, T. L .Heath, Mathematics in Aristotle (Oxford, 1949); P. Duhem,Le systeme du monde, I (Paris, 1913): H . Carteron, Lanotion de force dans le systeme d'Aristote (Paris, 1924) ;A. Mansion, Introduction a la physique aristotelicienne (2nded ., Louvain-Paris, 1945) ; F. Solmsen, Aristotle's Systemof the Physical World (Ithaca, N .Y ., 1960) ; W. Wieland,Die aristotelische Physik (Gottingen, 1962) ; 1. During,Aristoteles (Heidelberg, 1966) .

On the so-called laws of motion in Aristotle, 1 . Drabkin,American Journal of Philology, 59 (1938), pp. 60-84 .

G. E . L . OWEN

ARISTOTLE: Natural History and Zoology .It is not clear when Aristotle wrote his zoology, or

how much of his natural history was his own work .This is unfortunate, for it might help us to interprethis philosophy if we knew whether he began theoriz-ing in biology before or after his main philosophicalformulations, and how many zoological specimens hehimself collected and identified . Some believe thathe began in youth, and that his theory of potentialitywas directed originally at the problem of growth .Others (especially Jaeger) hold that his interest infactual research came late in life and that he turnedto biology after founding the Lyceum . Most probably,however, it was in middle life, in the years 344-342B.C ., when he was living on Lesbos with Theo-phrastus ; many of his data are reported from placesin that area. This would imply that he wrote thezoology with his philosophical framework alreadyestablished, and on the whole the internal evidenceof the treatises bears this out. It follows that in orderto understand his zoological theory, we must keep hisphilosophy in mind . Yet it may also be true that inthinking out his philosophy, he was conscious ofbiological problems in a general way .

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