Hume’s Hume’s TreatiseTreatise, Book 1, Book 1

Peter MillicanPeter Millican

Hertford College, OxfordHertford College, Oxford

3. Abstract ideas,3. Abstract ideas,

Space and TimeSpace and Time

3(a)3(a)

Hume’s theory Hume’s theory of general (or of general (or

abstract) ideasabstract) ideas

33

Empiricism and NominalismEmpiricism and Nominalism

An empiricist account of the origin of ideas An empiricist account of the origin of ideas will naturally reject any non-sensory, purely will naturally reject any non-sensory, purely intellectual grasp of abstract essences.intellectual grasp of abstract essences.

Sensory experience is of particular things, Sensory experience is of particular things, hence empiricists tend towards hence empiricists tend towards nominalismnominalism, , that “all things that exist are only particulars” that “all things that exist are only particulars” (Locke, (Locke, EssayEssay III iii 6, cf. III iii 6, cf. TreatiseTreatise 1.1.7.6). 1.1.7.6).

How, then, do “How, then, do “general Words come to be general Words come to be mademade”? Locke says they “become general, ”? Locke says they “become general, by being made the signs of general by being made the signs of general IdeasIdeas”.”.

44

Locke on General IdeasLocke on General Ideas

““IdeasIdeas become general, by separating from become general, by separating from them the cirumstances of Time, and Place, them the cirumstances of Time, and Place, and any other and any other IdeasIdeas, that may determine , that may determine them to this or that particular Existence. By them to this or that particular Existence. By this way of abstraction they are made this way of abstraction they are made capable of representing more Individuals capable of representing more Individuals than one; each of which, having in it a than one; each of which, having in it a conformity to that abstract conformity to that abstract IdeaIdea, is (as we , is (as we call it) of that sort.” (Essay III iii 6)call it) of that sort.” (Essay III iii 6)

55

Locke’s General Idea of a PersonLocke’s General Idea of a Person

““the the IdeasIdeas of the Persons Children converse with … of the Persons Children converse with … are like the Persons themselves, only particular. … are like the Persons themselves, only particular. … The Names they first give to them, are confined to The Names they first give to them, are confined to these Individuals … these Individuals … NurseNurse and and MammaMamma (etc.)… (etc.)… Afterwards, … [they] observe, that there are a great Afterwards, … [they] observe, that there are a great many other Things in the World, that … resemble many other Things in the World, that … resemble their Father and Mother … they frame an their Father and Mother … they frame an IdeaIdea, which , which they find those many Particulars do partake in; and to they find those many Particulars do partake in; and to that they give … the name that they give … the name ManMan … Wherein they … Wherein they make nothing new, but only leave out of the complex make nothing new, but only leave out of the complex IdeaIdea they had of they had of PeterPeter and and JamesJames, , MaryMary and and JaneJane, , that which is peculiar to each, and retain only what is that which is peculiar to each, and retain only what is common to them all.” (Essay III iii 7)common to them all.” (Essay III iii 7)

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The Notorious TriangleThe Notorious Triangle

““For abstract For abstract IdeasIdeas are not so obvious or are not so obvious or easie to Children, or the yet unexercised easie to Children, or the yet unexercised Mind, as particular ones. … For example, Mind, as particular ones. … For example, Does it not require some pains and skill to Does it not require some pains and skill to form the form the general Ideageneral Idea of a of a TriangleTriangle, (which is , (which is yet none of the most abstract, yet none of the most abstract, comprehensive, and difficult,) for it must be comprehensive, and difficult,) for it must be neither Oblique, nor Rectangle, neither neither Oblique, nor Rectangle, neither Equilateral, Equicrural, nor Scalenon; but all Equilateral, Equicrural, nor Scalenon; but all and none of these at once. In effect, it is and none of these at once. In effect, it is something imperfect, that cannot exist …” something imperfect, that cannot exist …” (Essay IV vii 9)(Essay IV vii 9)

77

Berkeley’s AttackBerkeley’s Attack

““If any man has the faculty of framing in his mind If any man has the faculty of framing in his mind such an idea of a triangle as is here described, it is in such an idea of a triangle as is here described, it is in vain to pretend to dispute him out of it, nor would I go vain to pretend to dispute him out of it, nor would I go about it. All I desire is, that the reader would fully and about it. All I desire is, that the reader would fully and certainly inform himself whether he has such an idea certainly inform himself whether he has such an idea or no. … What more easy than for any one to look a or no. … What more easy than for any one to look a little into his own thoughts, and there try whether he little into his own thoughts, and there try whether he has, or can attain to have, an idea that shall has, or can attain to have, an idea that shall correspond with the description that is here given of correspond with the description that is here given of the general idea of a triangle, which is, the general idea of a triangle, which is, neither neither oblique, nor rectangle, equilateral, equicrural, nor oblique, nor rectangle, equilateral, equicrural, nor scalenon, but all and none of these at once?scalenon, but all and none of these at once?” ” ((PrinciplesPrinciples, Introduction 13), Introduction 13)

88

Berkeley’s Rival AccountBerkeley’s Rival Account

““a word becomes general by being made the sign, not a word becomes general by being made the sign, not of an abstract general idea but, of several particular of an abstract general idea but, of several particular ideas, any one of which it indifferently suggests to the ideas, any one of which it indifferently suggests to the mind. For example, when it is said mind. For example, when it is said the change of the change of motion is proportional to the impressed forcemotion is proportional to the impressed force …; these …; these propositions are to be understood of motion … in propositions are to be understood of motion … in general, and nevertheless it will not follow that they general, and nevertheless it will not follow that they suggest to my thoughts an idea of motion without a suggest to my thoughts an idea of motion without a body moved, or any determinate direction and velocity, body moved, or any determinate direction and velocity, … It is only implied that whatever motion I consider, … It is only implied that whatever motion I consider, whether it be swift or slow, perpendicular, horizontal, or whether it be swift or slow, perpendicular, horizontal, or oblique, or in whatever object, the axiom concerning it oblique, or in whatever object, the axiom concerning it holds equally true.holds equally true.” (” (PrinciplesPrinciples, Introduction 11), Introduction 11)

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““though the idea I have in view whilst I make the though the idea I have in view whilst I make the demonstration, be, for instance, that of an isosceles demonstration, be, for instance, that of an isosceles rectangular triangle, whose sides are of a determinate rectangular triangle, whose sides are of a determinate length, I may nevertheless be certain it extends to all length, I may nevertheless be certain it extends to all other rectilinear triangles, of what sort or bigness other rectilinear triangles, of what sort or bigness soever. And that, because neither the right angle, nor soever. And that, because neither the right angle, nor the equality, nor determinate length of the sides, are at the equality, nor determinate length of the sides, are at all concerned in the demonstration.” all concerned in the demonstration.” ( (PrinciplesPrinciples, , Introduction 16)Introduction 16)

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Is Berkeley Fair to Locke?Is Berkeley Fair to Locke?

Berkeley interprets Locke as believing in Berkeley interprets Locke as believing in special, intrinsically general, abstract ideas special, intrinsically general, abstract ideas (like indeterminate images). But Locke says:(like indeterminate images). But Locke says:

““IdeasIdeas are general, when they are set up, as the are general, when they are set up, as the Representatives of many particular Things: but Representatives of many particular Things: but universality belongs not to things themselves, universality belongs not to things themselves, which are all of them particular in their Existence, which are all of them particular in their Existence, even those … even those … IdeasIdeas, which in their signification, , which in their signification, are general. … For the signification they have, is are general. … For the signification they have, is nothing but a relation, that by the mind of Man is nothing but a relation, that by the mind of Man is added to them.” (added to them.” (EssayEssay III iii 11) III iii 11)

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Treatise Treatise 1.1.7: “Of abstract ideas”1.1.7: “Of abstract ideas”

Hume credits Berkeley with “one of the … Hume credits Berkeley with “one of the … most valuable discoveries that has been made most valuable discoveries that has been made … in the Republic of Letters:”… in the Republic of Letters:”

““that all general ideas are nothing but that all general ideas are nothing but particular ones, annex’d to a certain term, particular ones, annex’d to a certain term, which gives them a more extensive which gives them a more extensive signification, and makes them recal upon signification, and makes them recal upon occasion other individuals, which are similar occasion other individuals, which are similar to them.” (to them.” (T T 1.1.7.1)1.1.7.1)

Hume puts more emphasis on the associated Hume puts more emphasis on the associated “certain term” than Berkeley did.“certain term” than Berkeley did.

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General Ideas and CustomGeneral Ideas and Custom

““When we have found a resemblance among several When we have found a resemblance among several objects … we apply the same name to all of them … objects … we apply the same name to all of them … After we have acquir’d a custom of this kind, the After we have acquir’d a custom of this kind, the hearing of that name revives the idea of one of these hearing of that name revives the idea of one of these objects, and makes the imagination conceive it with objects, and makes the imagination conceive it with all its particular circumstances and proportions. But all its particular circumstances and proportions. But as the same word is suppos’d to have been frequently as the same word is suppos’d to have been frequently apply’d to other individuals … the word not being able apply’d to other individuals … the word not being able to revive the idea of all these individuals, only … to revive the idea of all these individuals, only … revives that custom, which we have acquir’d by revives that custom, which we have acquir’d by surveying them. They are not really … present to the surveying them. They are not really … present to the mind, but only in power … we … keep ourselves in a mind, but only in power … we … keep ourselves in a readiness to survey any of them” (readiness to survey any of them” (TT 1.1.7.7) 1.1.7.7)

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The Revival SetThe Revival Set

“… “… after the mind has produc’d an individual idea, after the mind has produc’d an individual idea, upon which we reason, the attendant custom, upon which we reason, the attendant custom, reviv’d by the general or abstract term, readily reviv’d by the general or abstract term, readily suggests any other individual, if by chance we form suggests any other individual, if by chance we form any reasoning, that agrees not with it.” (any reasoning, that agrees not with it.” (TT 1.1.7.8) 1.1.7.8)

““some ideas are particular in their nature, but some ideas are particular in their nature, but general in their representationgeneral in their representation. A particular idea . A particular idea becomes general by being annex’d to a general becomes general by being annex’d to a general term … which from a customary conjunction has a term … which from a customary conjunction has a relation to many other particular ideas, and readily relation to many other particular ideas, and readily recals them in the imagination.” (recals them in the imagination.” (TT 1.1.7.10) 1.1.7.10)

– Garrett calls this Garrett calls this the revival setthe revival set of associated ideas. of associated ideas.

1414

Refuting Abstract General IdeasRefuting Abstract General Ideas

Hume sets out to argue (against Locke)Hume sets out to argue (against Locke)““that the mind cannot form any notion of quantity that the mind cannot form any notion of quantity or quality without forming a precise notion of the or quality without forming a precise notion of the degrees of eachdegrees of each” (” (TT 1.1.7.3) 1.1.7.3)

He does so using three considerations:He does so using three considerations:– The Separability Principle (The Separability Principle (TT 1.1.7.3) 1.1.7.3)

– The Copy Principle: any sensory impression The Copy Principle: any sensory impression must have determinate qualities (must have determinate qualities (TT 1.1.7.4-5) 1.1.7.4-5)

– The Conceivability Principle: no indeterminate The Conceivability Principle: no indeterminate object is possible in fact or thought (object is possible in fact or thought (TT 1.1.7.6). 1.1.7.6).

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The Separability Principle (SP)The Separability Principle (SP)

Hume’s statement of the Separability Principle Hume’s statement of the Separability Principle seems to allude back to hisseems to allude back to his “second principle, “second principle, of of the liberty of the imagination to transpose and the liberty of the imagination to transpose and change its ideaschange its ideas (from (from TT 1.1.3.4): 1.1.3.4):

““We have observ’d, that whatever objects are We have observ’d, that whatever objects are different are distinguishable, and that whatever different are distinguishable, and that whatever objects are distinguishable are separable by the objects are distinguishable are separable by the thought and imagination. And … these propositions thought and imagination. And … these propositions are equally true in the are equally true in the inverseinverse, and that whatever , and that whatever objects are separable are also distinguishable, and objects are separable are also distinguishable, and that whatever objects are distinguishable are also that whatever objects are distinguishable are also different.” (T 1.1.7.3)different.” (T 1.1.7.3)

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The Argument for theThe Argument for theSeparability PrincipleSeparability Principle

Hume’s argument for the Separability Hume’s argument for the Separability Principle is extremely cursoryPrinciple is extremely cursory::

““For how is it possible we can separate what For how is it possible we can separate what is not distinguishable, or distinguish what is is not distinguishable, or distinguish what is not different?” (T 1.1.7.3)not different?” (T 1.1.7.3)

This makes the SP look trivially true, but This makes the SP look trivially true, but in fact it seems to conceal potentially in fact it seems to conceal potentially debatable assumptions about ideas, as debatable assumptions about ideas, as sensory atoms that can be moved sensory atoms that can be moved around like pixels in a computer image.around like pixels in a computer image.

1717

Separability and AbstractionSeparability and Abstraction

SP implies that thinking of an abstract line SP implies that thinking of an abstract line without a specific length is impossible:without a specific length is impossible:

“’“’tis evident at first sight, that the precise length of tis evident at first sight, that the precise length of a line is not different nor distinguishable from the a line is not different nor distinguishable from the line itself, nor the precise degree of any quality line itself, nor the precise degree of any quality from the quality” (from the quality” (TT 1.1.7.3 ). 1.1.7.3 ).

But if this is right, how is it that we can But if this is right, how is it that we can apparently distinguish “between figure and apparently distinguish “between figure and the body figur’d; motion and the body the body figur’d; motion and the body mov’d” (mov’d” (TT 1.1.7.17)? 1.1.7.17)?

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The Distinction of ReasonThe Distinction of Reason

Hume appeals to his theory of general Hume appeals to his theory of general ideas: in a single object, we can see “many ideas: in a single object, we can see “many different resemblances and relations …”different resemblances and relations …”

““Thus when a globe of white marble is presented, we Thus when a globe of white marble is presented, we receive only the impression of a white colour dispos’d receive only the impression of a white colour dispos’d in a certain form. … But observing afterwards a in a certain form. … But observing afterwards a globe of black marble and a cube of white, … we find globe of black marble and a cube of white, … we find two separate resemblances, in what formerly seem’d, two separate resemblances, in what formerly seem’d, and really is, perfectly inseparable. … we … distin-and really is, perfectly inseparable. … we … distin-guish the figure from the colour by a guish the figure from the colour by a distinction of distinction of reasonreason … view[ing] them in different aspects, … view[ing] them in different aspects, according to the resemblances …” (according to the resemblances …” (TT 1.1.7.18) 1.1.7.18)

3(b)3(b)

Space and TimeSpace and Time

2020

TreatiseTreatise Book 1 Part 2 Book 1 Part 2

Treatise 1.2 is often ignored in the Hume Treatise 1.2 is often ignored in the Hume literature, and considered very dubious.literature, and considered very dubious.

In it he applies his theory of ideas to draw In it he applies his theory of ideas to draw ambitious conclusions about the nature of ambitious conclusions about the nature of our ideas of space and time, and hence our ideas of space and time, and hence the nature of space and time themselves.the nature of space and time themselves.

He starts by arguing that neither our ideas, He starts by arguing that neither our ideas, nor – consequently – space and time nor – consequently – space and time themselves, can be infinitely divisible.themselves, can be infinitely divisible.

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TreatiseTreatise 1.2.1: “Of the infinite divisibility 1.2.1: “Of the infinite divisibility of our ideas of space and time”of our ideas of space and time”

It is “evident from the plainest observation” “that It is “evident from the plainest observation” “that the capacity of the mind is limited, and can never the capacity of the mind is limited, and can never attain a full and adequate conception of infinity”.attain a full and adequate conception of infinity”.

Hence “the Hence “the ideaidea, which we form of any finite , which we form of any finite quantity, is not infinitely divisible” (quantity, is not infinitely divisible” (TT 1.2.1.2). 1.2.1.2).

If we divide our ideas in imagination, we must If we divide our ideas in imagination, we must eventually reach “a eventually reach “a minimumminimum” (” (TT 1.2.1.3). 1.2.1.3).

The same goes for sensory impressions, as The same goes for sensory impressions, as illustrated by the experiment in which we view an illustrated by the experiment in which we view an ink spot then gradually retreat from it until the ink spot then gradually retreat from it until the point point just beforejust before it becomes invisible. ( it becomes invisible. (T T 1.2.1.4)1.2.1.4)

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An Interesting SpeculationAn Interesting Speculation

Rolf George Rolf George (in (in Hume StudiesHume Studies, 2006) , 2006) suggests that Hume’s confidence in the suggests that Hume’s confidence in the Separability Principle might well have been Separability Principle might well have been shaken by Jurin’s shaken by Jurin’s Essay Upon Distinct and Essay Upon Distinct and Indistinct VisionIndistinct Vision (1738). (1738).

If we retreat until the red dot just disappears, If we retreat until the red dot just disappears, the (thinner) red line will still be visible. So the (thinner) red line will still be visible. So our visual field does not in fact appear to be our visual field does not in fact appear to be made up of a grid of “pixels”.made up of a grid of “pixels”.

SP does not feature in the SP does not feature in the EnquiryEnquiry of 1748, of 1748, where Hume also seems far less committed where Hume also seems far less committed to the simple/complex distinction.to the simple/complex distinction.

2323

Conceiving of Tiny ThingsConceiving of Tiny Things

Because our minimal perceptions are Because our minimal perceptions are atomic (without any parts),atomic (without any parts),

““Nothing can be more minute, than some ideas, Nothing can be more minute, than some ideas, which we form in the fancy; and images, which which we form in the fancy; and images, which appear to the senses; since these are ideas appear to the senses; since these are ideas and images perfectly simple and indivisible. and images perfectly simple and indivisible. The only defect of our senses is, that they give The only defect of our senses is, that they give us disproportion’d images of things, and us disproportion’d images of things, and represent as minute and uncompounded what represent as minute and uncompounded what is really great and compos’d of a vast number is really great and compos’d of a vast number of parts.” (of parts.” (TT 1.2.1.5 ) 1.2.1.5 )

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““This however is certain, that we can form ideas, This however is certain, that we can form ideas, which shall be no greater than the smallest atom of which shall be no greater than the smallest atom of the animal spirits of an insect a thousand times the animal spirits of an insect a thousand times less than a mite: And we ought rather to conclude, less than a mite: And we ought rather to conclude, that the difficulty lies in enlarging our conceptions that the difficulty lies in enlarging our conceptions so much as to form a just notion of aso much as to form a just notion of a

Hooke, Hooke, MicrographiaMicrographia, , 16651665

mite, or even of an mite, or even of an insect a thousand times insect a thousand times less than a mite. For in less than a mite. For in order to form a just order to form a just notion of these animals, notion of these animals, we must have a distinct we must have a distinct idea representing every idea representing every part of them …”part of them …”((TT 1.2.1.5 ) 1.2.1.5 )

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TreatiseTreatise 1.2.2: “Of the infinite 1.2.2: “Of the infinitedivisibility of space and time”divisibility of space and time”

TreatiseTreatise 1.2.2 starts with a bold statement: 1.2.2 starts with a bold statement:““Wherever ideas are adequate representations of Wherever ideas are adequate representations of objects, the relations, contradictions and agreements objects, the relations, contradictions and agreements of the ideas are all applicable to the objects; … But of the ideas are all applicable to the objects; … But our ideas are adequate representations of the most our ideas are adequate representations of the most minute parts of extension; and thro’ whatever minute parts of extension; and thro’ whatever divisions and sub-divisions we may suppose these divisions and sub-divisions we may suppose these parts to be arriv’d at, they can never become infereior parts to be arriv’d at, they can never become infereior to some ideas, which we form. The plain to some ideas, which we form. The plain consequence is, that whatever consequence is, that whatever appearsappears impossible impossible and contradictory upon the comparison of these and contradictory upon the comparison of these ideas, must be ideas, must be reallyreally impossible and contradictory, impossible and contradictory, without any farther excuse or evasion.” (without any farther excuse or evasion.” (TT 1.2.2.1) 1.2.2.1)

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From Inconceivability to ImpossibilityFrom Inconceivability to Impossibility

Hume appears to be arguing here from the Hume appears to be arguing here from the inconceivabilityinconceivability of certain relations of ideas to of certain relations of ideas to the the impossibilityimpossibility of things in the world (this is the of things in the world (this is the converseconverse of the Conceivability Principle). of the Conceivability Principle).

In general this seems dubious: why should our In general this seems dubious: why should our powers of conception (with our limited stock of powers of conception (with our limited stock of ideas derived from experience etc.) reach to ideas derived from experience etc.) reach to everything that’s possible in nature?everything that’s possible in nature?

But Hume restricts use of this Inconceivability But Hume restricts use of this Inconceivability Principle to where “our ideas are adequate”.Principle to where “our ideas are adequate”.

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The Adequacy of Our IdeasThe Adequacy of Our Ideas

Since Hume thinks “our ideas are adequate Since Hume thinks “our ideas are adequate representations of the most minute parts of representations of the most minute parts of extension”, he argues that the impossibility of extension”, he argues that the impossibility of infinite division of our ideas implies the infinite division of our ideas implies the impossibility of infinite division of space:impossibility of infinite division of space:

““I first take the least idea I can form of a part of I first take the least idea I can form of a part of extension, and being certain that there is extension, and being certain that there is nothing more minute than this idea, I conclude, nothing more minute than this idea, I conclude, that whatever I discover by its means must be that whatever I discover by its means must be a real quality of extension. I then repeat this a real quality of extension. I then repeat this idea once, twice, thrice, idea once, twice, thrice, &c.&c. …” ( …” (TT 1.2.2.2) 1.2.2.2)

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The Impossibility of Infinite DivisibilityThe Impossibility of Infinite Divisibility

Although each of our minimal ideas is Although each of our minimal ideas is indivisible and therefore not indivisible and therefore not extendedextended, when , when we place them adjacent to each other we get we place them adjacent to each other we get an extended pattern.an extended pattern.

Repeating this Repeating this in infinitumin infinitum would produce an would produce an infinite extension, so it follows that no finite infinite extension, so it follows that no finite extension can accommodate an infinite extension can accommodate an infinite number of such minima:number of such minima:

““the idea of an infinite number of parts is … the the idea of an infinite number of parts is … the same idea with that of an infinite extension”.same idea with that of an infinite extension”.

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A Mathematical ObjectionA Mathematical Objection

Mathematically, Hume’s argument seems Mathematically, Hume’s argument seems dubious. Imagine dividing an extension in two dubious. Imagine dividing an extension in two and taking the first half, then dividing that in two and taking the first half, then dividing that in two and again taking the first half, and so on …and again taking the first half, and so on …

It seems that one could potentially go on forever, It seems that one could potentially go on forever, yielding an infinite number of yielding an infinite number of proportionalproportional (rather (rather than than aliquotaliquot i.e. equal-sized) parts. In a footnote i.e. equal-sized) parts. In a footnote to to TT 1.2.2.2, Hume calls this objection “frivolous”, 1.2.2.2, Hume calls this objection “frivolous”, insisting that even proportional parts “cannot be insisting that even proportional parts “cannot be inferior to those minute parts we conceive”.inferior to those minute parts we conceive”.

3030

Rebutting the MathematiciansRebutting the Mathematicians

Later in the section, Hume appeals to the Later in the section, Hume appeals to the Conceivability Principle to rebut the Conceivability Principle to rebut the arguments of mathematicians in favour of arguments of mathematicians in favour of infinite divisibility:infinite divisibility:

““Here then is an idea of extension, which Here then is an idea of extension, which consists of parts or inferior ideas, that are consists of parts or inferior ideas, that are perfectly indivisible: Consequently this idea perfectly indivisible: Consequently this idea implies no contradiction: Consequently ’tis implies no contradiction: Consequently ’tis possible for extension really to exist possible for extension really to exist conformable to it …” (conformable to it …” (TT 1.2.2.9) 1.2.2.9)

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The Actual Parts MetaphysicThe Actual Parts Metaphysic

Hume’s argument seems to beg the Hume’s argument seems to beg the question, because if space is infinitely question, because if space is infinitely divisible, then our minimal ideas of it divisible, then our minimal ideas of it (which are indivisible) are (which are indivisible) are notnot adequate. adequate.

Tom Holden (2004) suggests that Hume is Tom Holden (2004) suggests that Hume is presupposing an “actual parts” presupposing an “actual parts” metaphysic, whereby anything that is metaphysic, whereby anything that is divisible must divisible must in advancein advance consist of the consist of the actual parts into which it is divided.actual parts into which it is divided.

3232

Fundamental PartsFundamental Parts

Holden’s suggestion is supported by Holden’s suggestion is supported by Hume’s appeal to an argument by Nicholas Hume’s appeal to an argument by Nicholas de Malezieu:de Malezieu:“’“’Tis evident, that existence in itself belongs only Tis evident, that existence in itself belongs only

to unity, and is never applicable to number, but to unity, and is never applicable to number, but on account of the unites, of which the number on account of the unites, of which the number is compos’d. … ’Tis therefore utterly absurd to is compos’d. … ’Tis therefore utterly absurd to suppose any number to exist, and yet deny the suppose any number to exist, and yet deny the existence of unites; and as extension is always existence of unites; and as extension is always a number …” (a number …” (TT 1.2.2.3) 1.2.2.3)

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The Experienced ManifoldThe Experienced Manifold

Don Baxter (2009) provides an alternative Don Baxter (2009) provides an alternative suggestion, that Hume’s (somewhat Kantian) suggestion, that Hume’s (somewhat Kantian) aim “was to find out about objects aim “was to find out about objects as they as they appear to usappear to us by examination of the ideas we by examination of the ideas we use to represent them” (p. 117).use to represent them” (p. 117).

On this account, Hume’s ambition goes no On this account, Hume’s ambition goes no further than “knowing perfectly the manner in further than “knowing perfectly the manner in which objects affect my senses, and their which objects affect my senses, and their connexions with each other, connexions with each other, as far as as far as experience informs me of them” experience informs me of them” ((TT 1.2.5.26) 1.2.5.26)

3434

Space and TimeSpace and Time

““All this reasoning takes place with regard All this reasoning takes place with regard to time”, and besides, it is of the essence to time”, and besides, it is of the essence of temporal moments to be successive of temporal moments to be successive (rather than co-existent). ((rather than co-existent). (TT 1.2.2.4) 1.2.2.4)

““The infinite divisibility of space implies The infinite divisibility of space implies that of time, as is evident from the nature that of time, as is evident from the nature of motion. If the latter, therefore, be of motion. If the latter, therefore, be impossible, the former must be equally impossible, the former must be equally so.” (so.” (TT 1.2.2.5) 1.2.2.5)

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Extension as a “Manner of Appearance”Extension as a “Manner of Appearance”

The Copy Principle should reveal the nature The Copy Principle should reveal the nature of our idea of extension (of our idea of extension (TT 1.2.3.1), but we 1.2.3.1), but we don’t seem to have any distinct don’t seem to have any distinct impressionimpression from which it could be derived.from which it could be derived.

The idea of extension is The idea of extension is abstractabstract (in Hume’s (in Hume’s sense of a revival set linked to a general sense of a revival set linked to a general term) and derived from the resemblance in term) and derived from the resemblance in the “manner of appearance” of our spatially the “manner of appearance” of our spatially disposed impressions, whether of coloured disposed impressions, whether of coloured points or impressions of touch (points or impressions of touch (TT 1.2.3.5). 1.2.3.5).

3636

Time and Perceivable SuccessionTime and Perceivable Succession

““The idea of time [is] deriv’d from the succession of The idea of time [is] deriv’d from the succession of our perceptions … ideas as well as impressions … our perceptions … ideas as well as impressions … of reflection as well as of sensation, … [it is] an of reflection as well as of sensation, … [it is] an abstract idea, which comprehends a still greater abstract idea, which comprehends a still greater variety than that of space, and yet is represented in variety than that of space, and yet is represented in the fancy by some particular individual idea of a the fancy by some particular individual idea of a determinate quantity and quality.” (determinate quantity and quality.” (TT 1.2.3.6) 1.2.3.6)

So the idea of duration “must be deriv’d from a So the idea of duration “must be deriv’d from a succession of [perceivably] changeable objects”succession of [perceivably] changeable objects”((TT 1.2.3.8), and – since it is not separable from such 1.2.3.8), and – since it is not separable from such a succession (a succession (TT 1.2.3.10) – cannot properly be 1.2.3.10) – cannot properly be applied to anything unchangeable (applied to anything unchangeable (T T 1.2.3.11).1.2.3.11).

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Spatial AtomsSpatial Atoms

““The idea of space is convey’d to the mind by … the The idea of space is convey’d to the mind by … the sight and touch … That compound impression, sight and touch … That compound impression, which represents extension, consists of several which represents extension, consists of several lesser impressions, that are indivisible to the eye or lesser impressions, that are indivisible to the eye or feeling, and may be call’d impressions of atoms or feeling, and may be call’d impressions of atoms or corpuscules endow’d with colour and solidity. … corpuscules endow’d with colour and solidity. … There is nothing but the idea of their colour or There is nothing but the idea of their colour or tangibility, which can render them conceivable by tangibility, which can render them conceivable by the mind.” (the mind.” (TT 1.2.3.15) 1.2.3.15)

““We have therefore no idea of space or extension, We have therefore no idea of space or extension, but when we regard it as an object either of our sight but when we regard it as an object either of our sight or feeling.” (or feeling.” (TT 1.2.3.16) 1.2.3.16)

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Geometry, and the VacuumGeometry, and the Vacuum

TT 1.2.4.17-32 argues that geometrical ideas, 1.2.4.17-32 argues that geometrical ideas, deriving from visual and tangible appearances, deriving from visual and tangible appearances, cannot achieve a precision beyond the limits of cannot achieve a precision beyond the limits of possible perception. So we cannot conclude, for possible perception. So we cannot conclude, for example, that the diagonal of an isosceles right example, that the diagonal of an isosceles right triangle will be triangle will be exactlyexactly 22 times the other sides. times the other sides.

““If … If … the idea of space or extension is nothing the idea of space or extension is nothing by the idea of visible or tangible points by the idea of visible or tangible points distributed in a certain order distributed in a certain order ; it follows, that we ; it follows, that we can form no idea of a vacuum, or space, where can form no idea of a vacuum, or space, where there is nothing visible or tangible.” (there is nothing visible or tangible.” (TT 1.2.5.1) 1.2.5.1)

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Humean “Fictions”Humean “Fictions”We imagine we have an exact standard of We imagine we have an exact standard of equality, applicable even to a supposed infinitely equality, applicable even to a supposed infinitely divisible space, but that imaginary standard is a divisible space, but that imaginary standard is a “fiction” which arises from the tendency of our “fiction” which arises from the tendency of our imagination to over-extrapolate (imagination to over-extrapolate (TT 1.2.4.24). 1.2.4.24).

The “idea” of a vacuum is a fiction, whose origin The “idea” of a vacuum is a fiction, whose origin Hume traces to natural tendencies to confuse of Hume traces to natural tendencies to confuse of ideas and use words without ideas (ideas and use words without ideas (TT 1.2.5.19- 1.2.5.19-23). Likewise duration as applied to unchanging 23). Likewise duration as applied to unchanging objects, which cannot be a genuine impression-objects, which cannot be a genuine impression-copied idea (copied idea (TT 1.2.5.28-9, cf. 1.2.3.11). 1.2.5.28-9, cf. 1.2.3.11).

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Is Hume Denying a Vacuum?Is Hume Denying a Vacuum?At At TT 1.2.5.25-6, Hume addresses the objection 1.2.5.25-6, Hume addresses the objection that he discusses “only the manner in which that he discusses “only the manner in which objects affect the senses, without endeavouring objects affect the senses, without endeavouring to account for their real nature and operations”.to account for their real nature and operations”.

““I answer this objection, by pleading guilty, and by I answer this objection, by pleading guilty, and by confessing that my intention never was to penetrate confessing that my intention never was to penetrate into the nature of bodies, or explain the secret causes into the nature of bodies, or explain the secret causes of their operations. … I am afraid, that such an of their operations. … I am afraid, that such an enterprize is beyond the reach of human enterprize is beyond the reach of human understanding, and that we can never pretend to understanding, and that we can never pretend to know body otherwise than by those external know body otherwise than by those external properties, which discover themselves to the senses.”properties, which discover themselves to the senses.”

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Our Idea of ExistenceOur Idea of Existence

The final section of Part 2 applies similar The final section of Part 2 applies similar considerations to our idea of existence:considerations to our idea of existence:

““The idea of existence … is the very same with The idea of existence … is the very same with the idea of what we conceive to be existent. To the idea of what we conceive to be existent. To reflect on any thing simply, and to reflect on it reflect on any thing simply, and to reflect on it as existent, are nothing different” (as existent, are nothing different” (TT 1.2.6.4) 1.2.6.4)

The Copy Principle also implies that we The Copy Principle also implies that we cannot think of external objects as anything cannot think of external objects as anything ““specificallyspecifically different from our perceptions” different from our perceptions” ((TT 1.2.6.7-9) – this is important in 1.2.6.7-9) – this is important in TT 1.4.2. 1.4.2.

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Afterword on Space and TimeAfterword on Space and Time

In January 1772, Hume wrote to his printer, In January 1772, Hume wrote to his printer, William Strahan:William Strahan:

“… “… about seventeen Years ago … I intended to print four about seventeen Years ago … I intended to print four Dissertations, the natural History of Religion, on the Passions, on Dissertations, the natural History of Religion, on the Passions, on Tragedy, and on the metaphisical Principles of Geometry. … but Tragedy, and on the metaphisical Principles of Geometry. … but before the last was printed, I happend to meet with Lord Stanhope before the last was printed, I happend to meet with Lord Stanhope who was in this Country, and he convincd me, that either there who was in this Country, and he convincd me, that either there was some Defect in the Argument or in its perspicuity; I forget was some Defect in the Argument or in its perspicuity; I forget which; and I wrote to Mr Millar, that I woud not print that Essay; … which; and I wrote to Mr Millar, that I woud not print that Essay; … I wrote a new Essay on the Standard of Taste …”I wrote a new Essay on the Standard of Taste …”

Lord Philip Stanhope was a notable mathematician, and Lord Philip Stanhope was a notable mathematician, and Hume was friendly (perhaps related) with his wife. Space Hume was friendly (perhaps related) with his wife. Space and time feature very little in Hume’s later works, playing and time feature very little in Hume’s later works, playing only a minor role in the first only a minor role in the first EnquiryEnquiry, Section 12 Part 2., Section 12 Part 2.