2 Humes Theory of Space and Time

8/22/2019 2 Humes Theory of Space and Time

1/36

Page 1 of 36 Hume's Theory of Space and Time

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2012.

All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a

monograph in OSO for personal use (for details see http://www.oxfordscholarship.com/page/privacy-policy). Subscriber: London

School of Economics and Political Science; date: 23 January 2013

Custom and Reason in Hume: A Kantian Reading of the First Bookof the TreatiseHenry E. Allison

Print publication date: 2008Print ISBN-13: 9780199532889Published to Oxford Scholarship Online: Sep-08DOI: 10.1093/acprof:oso/9780199532889.001.0001

Hume's Theory of Space and Time

Henry E. Allison

DOI: 10.1093/acprof:oso/9780199532889.003.0003

Abstract and Keywords

This chapter analyzes Hume's conception of space and time as orders ormanners of appearing. It also discusses the deep tension between this viewand the Copy Principle, and compares it with Kant's conception of space andtime as forms of appearances. Although the best known and oft criticizedfeature of Hume's account is his claim that space and time are not infinitelydivisible, with extension being composed of an aggregate of perceptual

minima (coloured or tangible points) and time of discrete moments, it isargued that the philosophical significance of Hume's account lies in theforementioned feature, which is logically independent of the latter and yieldsa relational theory that brings his account closer to those of Leibniz and Kantthan to other empiricists.

Keywords: Copy Principle, form of appearances, manner of appearing, perceptual minima,space, time, Leibniz

Until recently, the critical reaction to Hume's account of space and time inthe Treatise has been decidedly negative. 1 Although useful discussions of

the historical context of Hume's account were provided by earlier scholars,these did little to generate philosophical interest in the views themselves. 2

Accordingly, this aspect of Hume's thought is often passed over completelyin what purport to be analyses of the central topics in his epistemology.3 Epitomizing this dismissive response is the remark of C. D. Broad that[T]here seems to me to be nothing whatever in Hume's doctrine of space
http://www.oxfordscholarship.com/page/privacy-policy


2/36






except a great deal of ingenuity wasted in recommending and defendingpalpable nonsense. 4 And by way of explanation and partial exoneration, it issometimes pointed out that this is the work of the young Hume and is largelysuperseded by the mature doctrine of the Enquiry. 5

Although there are numerous reasons for this reaction, including the inherentobscurity of Hume's account and his view of geometry as an empiricalscience, I believe that the main reason lies in Hume's focus on the archaicissue of infinite divisibility, which led him, as it did Berkeley before him, toconclude that space, which he equated with extension, is composed of nonextended points (visible or tangible minima). 6 Nevertheless, the critiqueof the doctrine of infinite divisibility and its replacement with a theory ofperceptual minima does not exhaust Hume's account of space and it playsonly a subsidiary role in his treatment of time. Rather, what turns out to be

central is Hume's account of space and time as manners or orders of theappearing, which suggests an interesting comparison with Kant's view ofspace and time as forms of appearances. Thus, while not attempting to denyor explain away the underlying problems with the doctrine of perceptualminima, I shall here focus mainly on the abovementioned and relativelyneglected aspect of Hume's account, which amounts to a kind of relationaltheory that one might tend to associate with a rationalist rather than anempiricist.

(p. 39 )The chapter is divided into four parts. The first analyzes Hume'saccount of the ideas of space and time as orders or manners of the

appearing. The second takes up the issue of the compatibility of this accountwith the Copy Principle. The third compares Hume's account of space andtime with Kant's and explores the similarities as well as the differences. Thefourth responds to the charge that Kant failed to answer Hume's argumentagainst infinite divisibility in the antithesis to the Second Antinomy.

I

Hume gives a clear statement of the overall structure of his argument, when,as a prelude to dealing with objections, he describes his twopart system

concerning space and time. The first part (which reflects the finitisticarguments ofT1.2.12) consists of a chain of reasoning from the premisethat the mind has a merely finite capacity. Hume reiterates his thesis that itfollows from this that our ideas of extension and duration must consist of afinite number of indivisible parts, from which he concludes that it is possiblefor space and time to exist conformable to this idea. And if this be possible,


3/36






Hume further claims that 'tis certain they actually do exist conformable toit; since their infinite divisibility is utterly impossible and contradictory (T1.2.4.1; SBN 39). Given this result, the second part of the system, whichHume presents as a consequence of the first, maintains that The ideas of

space and time are . . . no separate or distinct ideas, but merely those of themanner or order in which objects exist (T1.2.4.2; SBN 3940).

Although my focus shall be on the second part of this system, it will beconvenient to begin with the consideration of an objection, which Humehimself poses and is directed to the relation between its two parts. Assumingthe voice of a critic, Hume notes: It has often been maintain'd in theschools, that extension must be divisible, in infinitum, because the systemof mathematical points is absurd; and that system is absurd, because amathematical point is a nonentity, and consequently can never by its

conjunction with others form a real existence (T1.2.4.3; SBN 40).This is basically a reiteration of Bayle's thesis that the doctrine of infinitedivisibility derives its whole force from the absurdity of its assumedalternatives. Consequently, the critic whom Hume is addressing at this pointis Bayle, and the objection takes the form of a reminder that because of thedialectical nature of the argument for infinite divisibility, it is futile to drawany positive conclusions from its rejection. Instead, so the objection goes,the proper response (p. 40 ) is a total skepticism regarding the compositionof the continuum, which is just Bayle's position. 7

Hume admits that this conclusion would be unavoidable, were there nomedium betwixt the infinite divisibility of matter, and the nonentity ofmathematical points; but he rejects this conclusion by offering his ownaccount as just such a medium. Somewhat confusingly, however, hepresents his alternative as a variation on the system of mathematical points,namely, such points considered as possessing color or solidity. And, afterdismissing another possible alternative, that of physical points, as tooabsurd to need a refutation, since it assumes a real extension without parts,he concludes that the absurdity of both the extremes is a demonstration ofthe truth and reality of this medium (T1.2.4.3; SBN 40).

Hume's strategy here is noteworthy because of its contrast with his morefamiliar procedure of presenting sceptical challenges to entrenchedphilosophical views. 8 Instead of offering such a challenge, he proposes anonsceptical solution to Bayle's sceptical critique by introducing a hithertoneglected alternative. Whereas the latter had assumed that there were onlythree possible positions regarding the composition of the continuum (infinite


4/36






divisibility, mathematical, and physical points), Hume suggests a fourthoption, or at least an alternative version of the second (colored or tangiblemathematical points). 9

This is a bold move on Hume's part, inasmuch as it requires showing that hisview is both distinct from and not subject to the objections raised against theother alternatives. At least at first glance, however, it does not seem verypromising. The problem is that in order to escape the alleged absurdity ofphysical points, which, qua physical, would be divisible, Hume affirms thereality of nonextended but colored or tangible points, that is, perceptualminima. But this, in turn, opens him up to the obvious objection, alreadyinsisted upon by Bayle, that several nonentities of extension joined togetherwill never make up an extension. 10

Since he was certainly aware of the problem, it is somewhat surprising thatHume does not discuss it at any length. As the above account suggests, hisbasic position seems to be that it is adequately addressed by insisting on thecolor or tangibility of the points. Apparently, the idea is that this assures thereality of these points against the hypothesis of mathematical points withoutcompromising their indivisibility, which is lost in the system of physicalpoints. 11 Moreover, it is the reality of these points that enables a pluralityof them to constitute, by aggregation, a determinate line, area, or volume,even though each point by itself is extensionless. 12

Needless to say, this account of extension has not been well received in

the literature. In particular, it is unclear how the attribution of color ortangibility (p. 41 ) to these points makes the difference on which Humeinsists and provides the basis for an answer to the classical objection againstmathematical points. For whatever nonextensive qualities these points maypossess, as far as extension is concerned, it still seems like an attempt tomake something out of nothing. In the case of the tangible, this problemdoes not arise, but we are there confronted with the opposite problem of howsomething tangible could be extensionless.

Nevertheless, without trying to minimize these difficulties, it must be

emphasized that there is more to Hume's account of extension than thissimple aggregational picture suggests. In fact, what has been omitted sofar is the central feature of his account of the ideas of space and time,namely, that they are constituted by an order or disposition (not simply anaggregate) of points. In short, Hume advances a relational view, where (inthe case of space) the relata are these colored or tangible points, whichpossess intensive but not extensive, magnitude. 13 Correlatively, in the


5/36






case of time, which we shall consider in more detail in the next section, therelata are all perceptions and the idea concerns their successive manner ofappearing.

Hume gives an indication of the complexity of his position later in theTreatise in the context of his discussion of the immateriality of the soul.Although he rejects the views of both materialists and immaterialists, theportion of Hume's analysis that interests us here concerns his insistence(against the materialist) on the nonextendedness of all impressions otherthan those of sight and touch. Considering a desire as an example of sucha nonextended impression, Hume remarks (by way of demonstrating theabsurdity of the supposition) that [I]n that case twou'd be possible, by theaddition of others, to make two, three, four desires, and these dispo'd andsituated in such a manner, as to have a determinate length, breadth and

thickness' (T1.4.5.9; SBN 235).The first part of the remark suggests that extension is simply a matter ofaggregation and that the absurdity consists in the assumption that desirescould be aggregated in that manner, thereby attaining what no singledesire possesses, namely, a determinate extension. The final part, however,indicates that it is rather as the result of being dispos'd and situated in acertain manner, that the points constitute a determinate length, breadthand thickness. In other words, extension, including its three dimensionality,is constituted by the order or arrangement of the aggregated points, notsimply by their aggregation.

The immediate problem is that whereas the order or arrangement of theparts can easily explain shape or configuration (in all three dimensions) andsituation, it seems much more difficult to understand how it could explainsize or distance. In fact, this is a general problem for relational theories ofspace, (p. 42 ) which Clarke had raised against Leibniz. 14 Unfortunately,Hume fails to discuss the problem in these terms; but it does appear froma consideration of the resources available to him that he must fall back onsheer aggregation. In other words, he seems committed to the view thatboth the size of an object and the distance between two or more objects

are determined by the number of the colored or tangible but extensionlesspoints. But, with this we seem to be back to the problem with which webegan, namely, how to generate a determinate extension from extensionlesspoints.

In addressing this question, I shall borrow a suggestion from C. D. Broadconcerning Hume's understanding of contiguity. The significance of Hume's


6/36






treatment of this concept for his views on extension is nicely illustrated by apassage (cited by Broad), in which Hume attempts to answer the objectionthat, in his view, all matter would interpenetrate, since any simple andindivisible atoms that touched one another would do so completely and

therefore penetrate. Against this, Hume replies that A blue and red pointmay surely lie contiguous without any penetration. And, continuing in thesame paragraph, he asks whether one would not perceive that from theunion of these points there results an object, which is compounded anddivisible, and may be distinguish'd into two parts, of which each preservesits existence distinct and separate, notwithstanding its contiguity to theother? (T1.2.4.6; SBN 41).

In analyzing this response, Broad points out first that the difference of thecolor of the two points is irrelevant and second, and more important, that

contiguity in the case of points cannot mean contact, since, as the objectionto which Hume is responding insists, indivisible points (not having parts)would completely coincide with one another if they touched. Consequently,Broad suggests that the contiguity of these points must be understood interms of an intrinsic minimum distance, such that two points cannot benearer together than this. And, he goes on to add, Two points which were atthe intrinsically minimal distance apart might be said to be contiguous. 15

Although the introduction of this idea may seem like a desperate expedient,and was clearly taken as such by Broad, it appears to provide a neat solutionto Hume's problem. For if we assume such a distance between contiguous

points, then we can easily see how the aggregation of these points couldproduce an extensive magnitude, even though the points, taken singly, areextensionless. Moreover, since contiguity is a relation or, in Hume's terms,a manner in which the points are dispos'd and situated, this also providesa model for understanding how a relational theory might account for sizeand distance. Here the basic point is not simply that contiguous points areseparated by an intrinsically minimal distance, but that the minimal nature oftheir separation (p. 43 ) constitutes their contiguity. In short, the relation ofcontiguity is a limiting case of extensive magnitude.

Apart from the fact that there is no clear evidence that this reflects Hume'sactual thinking, there remains the matter of the viability of the conception ofan intrinsically minimal distance. Indeed, this is the target of Broad's critiqueand he raises three objections: (1) The conception is inconsistent with thenotion of distance. (2) It is impossible, on general Humean principles toaccount for the idea that there is a certain distance such that no two points


7/36






can be nearer together than this, and that any two points must be separatedeither by this distance or by some integral multiple of it. (3) The doctrineleads to paradoxical geometrical consequences. 16

Taking these objections in reverse order, the third can be quickly set asideon the grounds that Hume would readily admit the charge but deny its force.As we shall see in the next chapter, he fully acknowledges that his accountof geometry has certain consequences that are contrary to the standardview; but he defends it as necessary in order to avoid the true paradoxesgenerated by the doctrine of infinite divisibility.

Broad's second objection turns on the question of the kind of necessity Humemight claim for an intrinsically minimal distance, that is, for the propositionthat there is a distance x, such that no distance smaller than x can beconceived. Ruling out the analytic variety (since it is not a matter of therelation between ideas), Broad concludes that, according to Hume's officialtheory, the proposition (and belief) must concern a matter of fact based on auniform past experience. But since (as Hume himself admits) we are seldom,if ever, capable of discriminating individual points, which would be requiredin order to be aware of this minimal distance, it cannot be the latter either. 17

I believe that this line of objection reflects a level confusion on Broad's part.The question is not whether there is an ordinary belief in something like anintrinsically minimal distance (Hume has no need to assume this any morethan in the case of the other minima), but whether there is an experiential

basis for incorporating such a conception into a science of human nature.And here Hume would be in a position to appeal to experiments such as thedisappearing impression of the ink spot he used to support the doctrine ofa minimum visibile. 18 This is not to defend Hume's position on this matter,but merely to suggest that introducing the conception of an intrinsicallyminimal distance need not create any new problems for him, since it wouldsimply be a matter of another kind of perceptual minimum determined bythe recognitional capacities of human beings.

At first glance, the first objection appears more serious, since there does

seem to be something incoherent in the notion of an intrinsically minimaldistance. (p. 44 ) After all, may not anydeterminate distance, no matter howsmall, be conceived as divisible ad infinitum? And does this not preclude thevery possibility of an intrinsically minimal distance? So formulated, however,it becomes clear that this likewise is not a new problem, but merely theold problem of a minimal size applied to distance. In short, if the notion of


8/36






perceptual minima is coherent, then so is that of an intrinsically minimaldistance and vice versa.

What this shows, I think, is that, while Broad's objections point to real

difficulties in Hume's account, they are not new difficulties, above andbeyond those connected with his radically finitistic position. Accordingly,given this position, Hume could well have appealed to the conception ofan intrinsically minimal distance in support of his system of colored ortangible points as a distinct and viable alternative to the three views onthe composition of the continuum offered by Bayle. Moreover, in closingthis section, I wish to point out that Hume's conception of space and timeas manners or orders of appearings is not dependent upon his thesis thatthe relata are perceptual minima or aggregates thereof. A case in point isLeibniz, for whom space is an order of coexisting phenomena, while these

phenomena (and extension) are themselves infinitely divisible.19

II

Emphasizing the relational nature of Hume's doctrine of space and timebrings to the fore the problem of its compatibility with the Copy Principle.This might not be an important issue, save for the fact that Hume insistsupon their connection. Indeed, he states that his intent is to apply thisprinciple in order to discover farther the nature of our ideas of space andtime (T1.2.3.1; SBN 33). And, in an attempt to illustrate this application, hesuggests that it is essentially a matter of looking. As he initially puts it, Upon

opening my eyes, and turning them to the surrounding objects, I perceivemany visible bodies; and upon shutting them again, and considering thedistance betwixt these bodies, I acquire the idea of extension (T1.2.3.2;SBN 33).

This suggests that the application of the Copy Principle to the ideas of spaceand time is a fairly straightforward matter. Moreover, Hume reinforces thisview when he remarks that since every idea is derived from an impressionwhich is exactly similar to it, there must be some impression (of eithersensation or reflection) from which the idea of extension is derived. And

quickly ruling out reflection, Hume concludes that only the senses canconvey to us this original impression (T1.2.3.3; SBN 33).

(p. 45 ) It soon becomes apparent, however, that the situation is morecomplex than these remarks suggest. In particular, there are twocomplicating factors. First, the ideas in question are abstract, which meansthat Hume must show both how ideas of particular spaces and times arise in


9/36






experience and how they can function as universals through their connectionwith naming and custom. Second, it turns out that there are no distinctsimple impressions to which these ideas are exactly similar. In fact, Humelater describes the impressions from which particular ideas of extension are

supposedly derived as compound (T1.2.3.15; SBN 38), thereby indicating amore complex genealogy.

The latter point emerges with Hume's attempt to isolate the impressionfrom which an idea of extension is copied through an examination of what isactually given to the mind in sense perception. To this end, he considers arepresentative instance of such perception, that of a table, about which hewrites:

The table before me is alone sufficient by its view to give methe idea of extension. This idea, then, is borrow'd from, and

represents some impression, which this moment appears tothe senses. But my senses convey to me only the impressionsof color'd points, dispos'd in a certain manner. If the eye issensible of any thing farther, I desire it may be pointed out tome. But if it be impossible to show any thing farther, we mayconclude with certainty, that the idea of extension is nothingbut a copy of these colour'd points, and of the manner of theirappearance. (T1.2.3.4; SBN 34)

Although we are prepared for it by the preceding analysis, when viewed inlight of Hume's seemingly commonsensical preliminary account of the origin

of the idea of a distance between objects, this is surprising; for it indicatesthat what is actually seen is not the threedimensional object of commonlife (the table), but a set of colored points, dispos'd in a certain manner.This, then, constitutes the sensory data, the pure given, considered apartfrom any interpretation. Consequently, it must also characterize the contentof the compound impression from which the idea of the table's extension isderived.

The problem is to understand how the Copy Principle is supposed to applyin the case of such compound impressions, which include not simply

the colored points, but also the manner in which they are dispos'd or,equivalently, the manner of their appearance. Can the latter be said toform part of the content of an impression? Moreover, the same questionapplies, mutatis mutandis, to Hume's account of time, which he claimsarises altogether from the manner in which perceptions appear to the mind[successively] without making one of their number (T1.2.3.10; SBN 36).


10/36






But, before turning to that issue, it will be useful to consider Hume's accountof how the mind proceeds from the particular idea that mirrors a certaindisposition of colored points to the idea of space or extension in general.

(p. 46 ) Hume begins by inviting the reader to suppose that the coloredpoints from which the mind allegedly derives its idea of extension are allpurple. It follows, he reasons, that with every repetition of this idea [thearrangement of purple points] the mind would not only place the points inthe same order, but also bestow on them the same color. But, he continues,after experiencing points of different colors and finding a resemblance inthe disposition of colour'd points of which they are compos'd, the mind isable to set aside the difference of color and form an abstract idea merelyon that disposition of points, or manner of appearance, in which theyagree (T1.2.3.5; SBN 34). Hume's point, which amounts to a straightforward

application of his theory of abstraction, is that, in spite of the particularity ofits ideas, the mind is able to set aside differences of color and attend merelyto a structural resemblance in the disposition of two or more differentlycolored sets of points.

As we have seen, this accords with what Hume said in T1.1.7 regardingdistinctions of reason, where his concern was to show how the mindis capable of distinguishing in thought items that are not separable inimagination or reality, e.g., the color and figure of an object, and onthis basis to take notice of resemblances between distinct objects, e.g.,different colored globes. What he is now suggesting is that a similar analysis

applies to the disposition of the colored points. Thus, even though thisdisposition is not separable from the points themselves and their color, themind (by a distinction of reason) can consider the former separately andframe the idea of a disposition or order shared by distinct sets of pointsof different colors. And, by parity of reason, by considering that differentdispositions or orderings of points of various colors resemble each other inbeing dispositions of colored points, the mind can set aside the differencesand arrive at a general idea of extension consisting of an indeterminatedisposition of points of indeterminate color. Or, more precisely, it can let oneparticular set of points disposed in a certain way stand for any disposition of

points of any color.

Although Hume only hints at the latter, such a development is both implicitin his analysis and required to account for the idea of extension or spacein general. Moreover, he does explicitly discuss how this analysis can beextended from intra to intersensory modalities (from vision to touch). As


11/36






Hume puts it, in an attempt to call attention to the fact that he is making asignificant amplification of his argument, Nay even when the resemblanceis carry'd beyond the objects of one sense, and the impressions of touch arefound to be similar to those of sight in the disposition of their parts; this does

not hinder the abstract idea from representing both, upon account of theirresemblance (T1.2.3.5; SBN 34).

The notion that a single idea can represent both visible and tangibleextension serves to differentiate Hume's view sharply from Berkeley,who emphasized (p. 47 ) the radical heterogeneity of the two speciesof extension. 20 Moreover, since tangible extension is obviously threedimensional, this strongly suggests that Hume was committed to a thesisthat was denied by both Locke and Berkeley, namely, that visible extensionis likewise threedimensional. In other words, on the Humean view we see

threedimensional objects, such as the table referred to earlier, ratherthan flat surfaces, which are interpreted as having a third dimension.21 Admittedly, Hume never quite says this explicitly and it seems to becontradicted by his remark that, Tis commonly allow'd by philosophers, thatall bodies, which discover themselves to the eye, appear as if painted ona plain surface, and their different degrees of remoteness from ourselvesare discover'd more by reason than by the senses (T1.2.5.8; SBN 56). 22

Nevertheless, I believe that there are two compelling reasons why we shouldnotregard the latter passage as a statement of Hume's considered view onthe nature of visual perception.

The first is Hume's view of compound impressions. Once he has bittenthe bullet and claimed that some impressions are extended, there is nofurther obstacle to claiming that visual as well as tactile impressions canbe extended in three dimensions, that is, as Hume himself says, havethickness as well as length and breadth. Thus, his account is at leastcompatible with visual impressions being threedimensional. Furthermore,there is phenomenological support for such a view, which would carry someweight with Hume, since, contrary to what the above passage suggests,visual experience usually seems to be threedimensional. 23 Thus, thequestion becomes the basis for this appearance, and for Hume there are

only two possibilities: either it is immediately perceived, which means thatwe have threedimensional visual impressions, or it is a fiction producedby the imagination, presumably on the basis of an associative relationwith tactile perceptions. But, in spite of his fondness for fictions of theimagination, Hume nowhere makes any such claim for threedimensionalvisual extensions, as it seems reasonable to assume he would have done


12/36






had he regarded the idea as a fiction. 24 Moreover, Hume could not sayat this point that the third dimension is inferred, since at issue is not thedimensionality of physical objects but of visual perceptions qua visual.Accordingly, if it were inferred, it would have to be from visual evidence,

which is just the impression.

My second reason is that I can see no other plausible way to understandHume's claim that the abstract idea of extension, which is itself merelya particular order of disposition of points (either visible or tangible), canrepresent indifferently either visible or tangible extension. Granted, similarityis not identity; but when Hume claims that the impressions of sight andtouch are found to be similar in the disposition of their parts, he presumablymeans a similarity sufficient to generate an idea of extension, which willsuffice (p. 48 ) for representing or calling to mind tokens of either species.

And assuming that tangible extension is threedimensional, it follows that avisible extension that is capable of representing tokens of tangible extensionmust itself be threedimensional, which, given Hume's theory of ideas,further requires that this idea be derived from a threedimensional visualimpression. In other words, Hume seems to be suggesting, though he neverquite says, that there is something like a common spatial order (or mannerof disposition) accessible to both sight and touch, and with it presumablyalso a common geometry (even if it be an inexact science). Otherwise, theresemblance could not be carried over from the visible to the tangible andthe abstract idea of extension could not represent what is common to both.

In order to appreciate the significance of this, we need to see Hume'sanalysis against the backdrop of William Molyneux's famous questionto Locke: could a person born blind and thus possessing only a tactileawareness of spatial relations, but who later gained sight through anoperation, then recognize visually the same relations that were previouslygrasped through touch? 25 More specifically, could a blind person who hadlearned to distinguish a cube from a sphere by touch, be immediately able todistinguish these figures visually, if somehow granted sight?

Since it concerns the relationship between two distinct orders of perception,

the question served as something of a watershed separating empiricistand rationalist epistemologies. The former, exemplified by Locke andBerkeley, answered the question in the negative. Denying anything like anintrinsic affinity between the two orders, they claimed that it is only throughexperience that the mind comes to associate the visible with the tangible.26 Conversely, a rationalist such as Leibniz, while admitting that a person


13/36






suddenly receiving sight through an operation could not at first distinguishanything by purely visual means, nonetheless insists that such a personcould discern them by applying rational principles to the sensory knowledgewhich he has already acquired by touch. And this, for Leibniz, is because

there is only a single geometry, that is, a single set of ideas, which must besharply distinguished from the quite distinct images received through thedifferent sensory modalities. 27

Where, then, does Hume stand on the issue? Since he does not addresses itdirectly (or even refer to it), one cannot be sure; though it would be naturalto assume that his sympathies lie in the empiricist camp. Indeed, this isparticularly true in view of his imagistic conception of thought. Nevertheless,if we take seriously the possibility that for Hume both sight and touchyield an awareness of a common threedimensional order or disposition

of points, then Hume's position would be closer to Leibniz's rather thanthe empiricists'. And if, as is assumed in Molyneux's question, the newlysighted person, has a clear (p. 49 ) tactile grasp of the tangible order (coulddifferentiate a sphere from a cube by touch), it is hard to see, at least onHumean grounds, why (setting aside certain psychophysiological factorssuch as adjusting to the light) such a person could not likewise differentiatebetween these figures visually.

In view of this somewhat unexpected result, let us return to the question ofthe compatibility of Hume's account of the ideas of space and time with theCopy Principle. The answer suggested by the text involves the combination

of an appeal to the analysis of distinctions of reason in T1.1.7.18; SBN 25,with the account of the given in perception in T1.2.3.4; SBN 34. We haveseen that in attempting to account for the possibility of such distinctions,Hume appeals to the example of variously colored globes. The perceptionsof these globes are there regarded as simple impressions, the shapes ofwhich are nonetheless separable in thought from the colors, and vice versa.Accordingly, we may be said to have an impression of their shapes as wellas their colors, even though these are not distinct impressions. We have alsoseen that the analysis of the perception of the table purportedly shows thatthe shapes appealed to as primitive in the earlier account are really nothing

more than dispositions of colored points, which suggests that all Hume needsin order to account for the possibility of impressions of particular extensionsis to apply the initial result to the later analysis. In other words, just as wecan have an impression of an object's shape, even though it is not distinctfrom its color, so we can have an impression of the disposition of its points,


14/36






since this is just what its shape really amounts to. 28 This impression is,therefore, the source of the corresponding idea.

This line of thought may well reflect Hume's actual position and explain

the confidence with which he appeals to the Copy Principle, but it hardlyprovides a complete solution to the problem. In particular, it ignores thesalient fact that whereas shape is initially treated as a simple impression,Hume now explicitly characterizes the impression of colored (or tangible)points disposed in a certain manner as compound. Moreover, I do notbelieve that Hume holds that the disposition is a part of the compoundimpression in the sense of being one of its constituent elements. 29 On thecontrary, in characterizing the content of the impression from which theideas of particular extensions are supposedly derived, Hume tells us thatit consists of several lesser impressions that are indivisible to the eye or

feeling, and may be call'd impressions of atoms or corpuscles endow'dwith colour and solidity (T1.2.3.15; SBN 38). In other words, the indivisiblepoints are the only components of the impression and what makes theimpression compound is not that it has different aspects that may beconsidered separately, but, rather, that it is composed of a number of theseperceptual atoms, each one of which supposedly constitutes a distinct simpleimpression.

(p. 50 ) Accordingly, the question is whether, as the Copy Principle requires,a mental representation of points disposed in a certain manner counts as animpression in Hume's sense, that is, a lively content passively perceived by

the mind and copied by an idea that is exactly similar in everything saveits FLV. Impressiontalk may appear to be in order at the commonsenselevel at which Hume begins, where he refers to an impression of the shapeof a colored globe; but it becomes much more problematic when we learnthat what was initially viewed as simple (though having different aspects)is really a compound of distinct impressions. At issue is the very notion of acompound impression; and at the heart of the problem is the passivity of themind, which is criterial for an impression (simple or complex). This requiresthat the mind not only receives a compound set of data (simple impressions),but that itperceives it as such, that is, as an array of impressions with a

certain manner of appearing.

Although it applies to his account of space as well, the underlying difficultyis best illustrated by Hume's analysis of the idea of time, which he claimsarises altogether from the manner, in which impressions appear to the mind,without making one of the number. In explaining this, Hume remarks, Five


15/36






notes play'd on a flute give us the impression and idea of time, tho time benot a sixth impression, which presents itself to the hearing or any others ofthe senses. Nor is it a sixth impression, which the mind by reflection findsin itself (T1.2.3.10; SBN 36). Here Hume emphatically denies that there

is a distinct impression of time. All that is given to the mind are the fivesuccessive impressions; there is no additional impression of the successionitself, that is, of the notes manner of appearing. Moreover, Hume goeson to reinforce this point, remarking that in contemplating the successionof notes, the mind does not feel some new original impression arise, butonly takes notice of the manner, in which the different sounds make theirappearance (T1.2.3.10; SBN 37).

Hume is clearly correct in denying that there is a distinct impression of themanner of appearing of these notes, which is somehow perceived together

with the five successive notes. Where he runs into trouble is in trying toexplain how the mind could take notice of this manner of appearing andform an idea of a determinate stretch of time (that constituted by thesuccession of the notes) without having an impression of it. If all that isgiven to the mind are the five successive notes, how does the awarenessof their successiveness, which just is their manner of appearing, arise? Letus assume that the fifth note of the sequence is currently being perceived;in which case its perception takes the form of an impression. At this point,however, the previous four notes have already vanished into the past andare replaced by memoryimages, which are ideas for Hume and which needto be combined with each other and the (p. 51 ) present impression in orderto form a representation of the succession, which just is their manner ofappearing. In short, the manner of appearing cannot be regarded as simplypassively received and then copied in the form of an idea. On the contrary,unless one attributes temporal thickness to impressions, it seems thatsomething like Kant's synthesis of apprehension is required in order toperceive a determinate succession. 30

For reasons similar to those suggested above, Hume's attempt to link histreatment of the ideas of space and time with the Copy Principle, like histreatment of the ideas themselves, has been widely rejected in the literature.

31 More recently, however, Hume's attempted linkage has been defendedby Lorne Falkenstein, who argues that Hume's account of the ideas ofspace and time constitutes an amendment to this principle rather than anexception. 32 In fact, according to Falkenstein, it is an exceedingly friendlyamendment, which far from weakening or qualifying the principle extendsits scope beyond the sphere to which Hume himself limited it, namely,


16/36






simple impressions, to the compound (or complex) impressions that Humeclaims to be the sources of our ideas of space and time. 33 In arguing for thisview, Falkenstein maintains that the latter consist not merely of the simpleimpressions, but of an array or order thereof. 34 Thus, in contrast to the view

suggested above, he effectively maintains that this order constitutes partof the content of these impressions, which means that there is nothing toprevent it from being faithfully copied in the corresponding compound idea.As he puts it at one point, That this manner or disposition of parts should becopied over into the idea is ultimately no more mysterious . . . than that aphotocopier should reproduce not only the letters on a printed page, but theexact order in which they are printed. 35

Falkenstein's defense of this thesis rests on two prongs. First, he callsattention to Hume's claim that both impressions of extension and their

corresponding ideas are themselves extended.36

Although this seemsdeeply paradoxical and is often dismissed as manifest nonsense, we haveseen that the extendedness of some impressions (those pertaining to sightand touch) is a consequence of Hume's view of impressions and that, giventhis, the extendedness of their corresponding ideas follows from the CopyPrinciple.

Second, and more controversially, Falkenstein defends the plausibility ofthis view and with it the applicability of the Copy Principle to the ideasof space and time, by attributing to Hume a distinctive conception ofrepresentation. In this vein, he suggests that what makes Hume's claim

that ideas of extension are extended seem paradoxical is the imposition onhim of a conception of representation (which Falkenstein associates withReid) according to which ideas are intentional acts that take impressions astheir objects. 37 Since, according to Falkenstein, ideas for Hume are objectsrather than acts of thinking and (p. 52 ) represent their objects by mirroringthem rather than by intending them, it is perfectly natural to view ideas ofextension as themselves extended. 38

Inasmuch as Falkenstein claims merely that this view is not an obviouslyincoherent one, 39 I shall not discuss its intrinsic merits. Instead, I shall call

attention to two points. First, his analysis glosses over what I take to be themain point, which is the extendedness ofimpressions. Second, the denialof the intentionality of consciousness, which his reading implies, does notfit well with crucial aspects of Hume's overall position. A case in point isHume's account of distinctions of reason. As we have seen, these distinctionssupposedly arise through the mind considering separately aspects of its


17/36






impressions that are inseparable in the impression, which, in turn, makes itpossible to note resemblances or similarities between distinct impressions.It seems clear, however, that this capacity presupposes that the mind doesnot simply have resembling ideas that mirror resembling impressions, but

also has an awareness of them as resembling. In addition, it seems equallyclear that the consideration of aspects of impressions and the noting ofthese resemblances are acts of the mind regarding its perceptions and arethemselves conditions of the application of a name. Thus, pace Falkenstein,I do not see how Hume's theory of ideas precludes the intentionality ofconsciousness, even though it may very well be true that it is unable toprovide a satisfactory account of it. 40

III

If our ideas of space and time are not copies of impressions what are they?Presumably, for Hume the only alternative would be to characterize them asinnate, which would be anathema to him as it was to his fellow empiricists.And this, I believe, is why Hume stuck to his Copy Principle in spite of theabovementioned difficulties in applying it to these ideas. I also believe,however, that it is just at this point that a comparison of Hume's account ofspace and time with Kant's becomes illuminating. 41

Admittedly, at first glance, such a comparison does not appear to be aparticularly apt, since Hume's views on the topic are diametrically opposedto Kant's in at least two essential respects. First, whereas Hume attempts

to provide our ideas of space and time with an empirical foundation, Kantemphasizes their apriority, and assigns them the status of pure intuitions.Second, whereas Hume's account is based on the denial of their infinitedivisibility, which leads him also to deny (at least in the Treatise) the apriori nature of geometry, Kant prides himself on the fact that his doctrineaccounts for the possibility of the synthetic a priori status of geometry, aswell as the infinite divisibility of space and time.

(p. 53 ) Nevertheless, there are at least two significant similarities, which Ibelieve make such a comparison worthwhile. The first is methodological:

both thinkers arrive at their conclusions by rejecting all the alternativesthen currently thought to be available and introducing a radically newalternative, which transforms the framework in which the question hadpreviously been posed. For Hume, following Bayle, the question was thecomposition of the continuum and the possible alternatives, spelled out byBayle: mathematical points, physical points, and infinite divisibility. Largely


18/36






accepting Bayle's criticisms of these alternatives, Hume attempts to avoidthe latter's sceptical conclusion by introducing his new alternative (coloredor tangible points), which supposedly enabled him to preserve the existenceof extension (and succession) from Bayle's dialectic and the validity of

geometry (reinterpreted as an empirical science of physical extension).Similarly, Kant (for whom the problem was framed in terms of the greatdebate between the absolutist Newtonians and the relationist Leibnizians)rejected both views and introduced his own critical alternative, accordingto which space and time are a priori forms of human sensibility. This likewisetransformed the nature of the debate, since rather than being conceivedas either themselves quasithings or relations that hold between thingsindependently of their epistemic relation to the human mind, space and timeare reconceived as ways of cognizing things or, as I have elsewhere termedthem, epistemic conditions. 42

Second, there is at least a partial agreement between the two thinkersconcerning the nature of the representations of space and time. Althoughas a dedicated antischolastic Hume eschews any use of the term form,we have seen that he characterizes the perceptions (both impressions andideas) of space and time by means of locutions such as [points] dispos'd in acertain manner, the manner of their appearance, the disposition of pointsor manner of appearance (T1.2.3.4; SBN 34), the manner in which differentsounds make their appearance (T1.2.3.10; SBN 37), and the manner ororder in which objects exist (T1.2.4.2; SBN 40). Accordingly, space andtime for Hume are the manner or order in which objects appear (or exist)rather than themselves objects that appear (or exist), which, in spite ofthe terminological differences, is quite close to Kant's view. In fact, therecognition of this similarity has led Falkenstein to suggest that both thinkersbe viewed as formal intuitionists, by which he means that they regard spaceand time as expressions of the manner in which sensory data are given toor received by the mind in experience rather than being themselves eitherdistinct sensory data or products of an intellectual or imaginative activityperformed upon these data. 43

The salient difference stems from the fact that for Kant form, while

sometimes meaning way or manner, primarily means condition; so thatfor (p. 54 ) him the form in which things appear is itself a condition of theirappearing in this manner (as related in space and time). Moreover, this formreflects the nature of the human mind (in Kant's terms its peculiar formsof sensibility) rather than the nature or relations of things as they are inthemselves. Naturally, Hume would reject the latter aspect of Kant's position,


19/36






since it runs directly counter to his thoroughgoing empiricism. Nevertheless,given the failure of the Copy Principle, it becomes difficult to see how Humecould maintain his thesis that space and time are manners of appearingwithout adopting something close to the Kantian position.

In an attempt to substantiate this thesis, I shall here consider Hume's viewsin light of the central arguments of Kant's Metaphysical Expositions ofthe concepts of space and time in the Transcendental Aesthetic. Althoughthese arguments are addressed mainly to the Newtonian and Leibnizianviews, they have a direct bearing on the issues separating Kant and Hume.Kant has a twofold goal in these expositions: he wants to show that therepresentations of space and time are both a priori and intuitive, from which(together with the Transcendental Exposition, which in the case of space isan argument from the synthetic a priori nature of geometry) he concludes

that space and time themselves are nothing but forms of human sensibility,which is the central thesis of transcendental idealism. Having discussedKant's idealism in considerable detail elsewhere, I shall here set aside thatissue and focus instead on Kant's arguments for the apriority and intuitivenature of these representations. And, inasmuch as these arguments arelargely parallel, I shall reverse the usual procedure and focus mainly (thoughnot exclusively) on time. Not only will this help to avoid redundancy, itwill also make it possible to build upon the preceding analysis of Hume'streatment of time.

Kant offers two arguments for the apriority of the representation of time.

Since they are both quite short, I shall cite them in full and then commentbriefly upon their bearing on Hume:

(1) Time is not an empirical concept that is somehow drawnfrom experience. For simultaneity or succession wouldnot themselves come into perception if the representationof time did not ground them a priori. Only under itspresupposition can one represent that several things exist atone and the same time (simultaneously) or in different times(successively).

(2) Time is a necessary representation that groundsall intuition. In regard to appearances in general onecannot remove time, though one can very well take theappearances away from time. Time is therefore given apriori. In it alone is all actuality of appearances possible. Thelatter could all disappear, but time itself (as the universal


20/36






condition of their possibility) cannot be removed. (A 301/B46)

(p. 55 )

Since the first argument denies that time is an empirical concept, itobviously applies to Hume's as well as to classical empiricists' accounts ofthe origin of the idea such as Locke's. 44 Kant's justification for this claimis contained in the second sentence, which notes that the very relations towhich one might appeal in order to explain the origin of the representationof time, namely, simultaneity and succession, already presuppose it.Accordingly, any attempt to derive this representation from the perception ofsuccessive objects or events is inherently circular. 45

The problem with Hume's account that is captured by Kant's argument canbe easily seen from a consideration of his discussion of the five successive

notes. We have already seen that we cannot regard these notes as given ina single, compound impression, which is then copied by an idea, because,as successive, they do not exist atthe same time, though they succeed eachother in the same time. Thus, in order to form the compound idea of the fivesuccessive notes, it is necessary to bind them together in the imagination. Ifthe notes were played simultaneously on different instruments this would notapply; but Hume's, as well as most treatments of time, leave out the notionof simultaneity. 46 Quite apart from the function of the imagination, however,it is clear that the attempt to derive the idea of time from the perception ofsimultaneity would be hopeless, since by the latter is meant existence at the

same time. Moreover, the same applies, mutatis mutandis, to succession, bywhich is understood existence at successive times. Accordingly, unless timewere presupposed as the medium or framework in which this succession isperceived, one could not be conscious of the notes as successively occurringin it, which is to say that the representation of time is a priori. In fact, it is apriori not merely in the negative sense that it is not empirical, but also in thepositive sense that it functions as a condition of the empirical representationof time, which is the point that Kant makes in the third and final sentence ofthe argument.

Kant's second apriority argument is also applicable to Hume, though ina less direct way. It turns on the allegedly asymmetrical nature of thedependence relation between time and appearances in time. Basically, itaffirms that one may take (in thought) appearances out of time, but nottime out of appearances, which means in effect that time is a conditionof the manner of appearing of these appearances. 47 This argument hasAristotelian roots and falls under the following schema: if x can be (or be


21/36






represented) without A, B, C and their mutual relations, while A, B, C cannotbe (or be represented) without x, then x must be viewed as a condition ofthe possibility of A, B, C and their mutual relations (or the representationthereof). 48 In the case of Hume's successive notes, the claim would be that

we could have the representation of the time in which this succession occurswithout these successive notes, but (p. 56 ) not the succession of noteswithout the representation of time as the condition of the representation oftheir succession, which again makes it a priori.

Hume would agree that we could have the idea of time apart from thesuccession of the five notes, since he used them merely as an illustrationof how we arrive at the idea of a particular duration (or stretch of time).Thus, any succession of phenomena would do equally well and enable Humeto explain how, by abstracting from the content and attending only to the

successiveness (the manner of appearing), we come to form for ourselvesa general idea of time or duration, which is applicable to all instances. Hewould, however, reject the thesis that we could somehow represent timewithout appearances. In fact, one of the avowed consequences of Hume'sview, which is partially eclipsed by the attention that he devotes to thedenial of a vacuum, is the rejection of the possibility of an idea of an emptytime, understood as one in which there was no succession or change in anyreal existence (T1.2.4.2; SBN 40). Accordingly, we need to take a look atHume's reasoning behind this claim.

Unfortunately, Hume's treatment of this topic is extremely perfunctory and

basically comes down to two points. The first is the familiar challenge toproduce the impression. Appealing to the ubiquitous Copy Principle, Humeconcludes that since there is no impression there can be no idea of an emptytime (T1.2.5.28; SBN 645). The second is the equally familiar strategy ofproviding a psychological explanation of why we erroneously come to believethat we have such an idea (T1.2.5.29; SBN 65).

As far as the first point is concerned, its force depends entirely on the CopyPrinciple, which we have already seen does not appear applicable to theideas of space and time. And if this is true, the impossibility of having or

locating an impression of empty time, though it cannot be gainsaid, is besidethe point. Nevertheless, it should be noted that to some extent the twophilosophers are speaking past one another here, since they seem to meandifferent things by an empty time. For Kant it is one devoid of appearances,whereas for Hume it is one in which there was no succession or change inany real existence, that is, a time through which some entity is experienced


22/36






as enduring without undergoing any perceived change or succession. 49

Clearly, if there were no appearances there could be no change, since therewould be nothing to change; but this does not preclude appearances thatendure withoutchange, which is just what Hume denies. Or, more precisely,

he denies that the perception of such a duration could give rise to the idea oftime.

Inasmuch as Hume identifies time with duration rather than succession(just as he identifies space with extension), it might seem surprising thathe would deny that the perception of duration could of itself give rise to theidea of time. 50 Nevertheless, this becomes understandable if we keep inmind that for Hume (p. 57 ) successiveness is the manner of appearing thatgives rise to, indeed constitutes, the idea of time or duration. In response,however, Kant could point out that both duration and succession (together

with simultaneity) are modes of time, which, as such, presuppose time.51

Ishall return to this point below.

Hume's psychological explanation of the genesis of the fictitious belief ina time in which something endures without change amounts to a highlytruncated version of the far more elaborate explanation he provided of thefictitious belief in empty space or a vacuum. 52 It seems clear, however, thatHume is offering it as an application of the principle, which he describes asa general maxim in this science of human nature, that wherever there is aclose relation betwixt two ideas, the mind is very apt to mistake them, andin all discourses and reasonings to use the one for the other (T1.2.5.19;

SBN 60). In the case of a purportedly empty space or vacuum, the twoideas were that of a real visible or tangible extension and an imaginaryempty one; in the case of time, they are the perceptions of a changing anda putatively unchanging object. The close relation is not between the ideasof the two objects, but between the ways in which the mind entertains themwith respect to time. In both cases, there is, Hume tells us, a continualsuccession of perceptions in our mind; so that the idea of time being for everpresent with us . . . , from which it supposedly follows that in considering astedfast object at two points of time, the mind proceeds in much the sameway as it does in considering one that changes (T1.2.5.29; SBN 65). In other

words, the similarity in the manner of perceiving (successively) leads themind falsely to assign a temporal duration to an object in which no change isperceived.

This explanation appears to turn on the abovenoted point regarding thedependence of the perception of a duration on that of a succession or


23/36






change. As such, it suffers from the same defect as Hume's explanationof the similarly fictitious idea of a vacuum, namely, it involves apetitioprincipi. Moreover, this is not surprising inasmuch as it is intended as anexact parallel. In the case of the vacuum, Hume attempted to explain how,

due to certain resemblances, we tend to conflate our idea of an imaginaryempty space with a real filled one (constituted by an array of colored ortangible points); and the problem is that the possibility of this conflationpresupposes that we already have an idea of such an empty space, whichis the very thing that Hume wants to deny being possible. 53 Similarly, inthe case of an empty time, understood as one in which something endureswithout change, Hume's account presupposes that we have such an idea,which, again, is precisely what he wants to deny.

In addition to this internal difficulty in Hume's explanatory account, there

are two further problems in his treatment of the idea of an empty time,when (p. 58 ) considered from a Kantian point of view. First, it suffers fromthe previously noted identification of time with duration, thereby ignoringthe key point that duration, together with succession and simultaneity, aremodes of time. In order to understand the Kantian position, however, itis important to keep in mind that by this expression Kant does not meanproperties of time itself but of things in time. In other words, things andevents are experienced as enduring, succeeding, and as being simultaneousor coexistent with one another in time, which means that such experiencepresupposes time, not as a distinct object of experience (here Kant is inessential agreement with Hume), but as the presupposed framework inwhich such experience is possible. Second, and as a direct consequenceof this, the representation of time is a priori. Indeed, Hume comes as closeto recognizing this as his empiricistic commitments will permit, when heremarks that the idea of time is for ever present with us.

If sound, Kant's metaphysical exposition up to this point has establishedthe apriority of the representation of time. As such, it is compatible withit being an a priori concept, which for Hume (though not for Kant) wouldmean that it is an innate idea. Kant goes further, however, arguing notmerely that time (like space) is a priori, but also that it is an a priori or

pure intuition. Within the broader framework of the Critique, this move ismotivated by Kant's concern to link space and time with sensibility ratherthan the understanding and it is, therefore, inseparable from his discursivitythesis and transcendental idealism. It is also central to Kant's polemic withLeibnizian rationalism, as well as his attempt to ground the synthetic a prioristatus of mathematics. At the same time, however, his arguments for the


24/36






intuition thesis shed additional light on Kant's relation to Hume regarding thenature of space and time and it is from this limited point of view that I shallconsider them here. 54

As with the case of space, Kant offers two arguments for the intuitive natureof the representation of time, both of which assume the conceptintuitiondistinction and maintain, albeit on somewhat different grounds, that it mustbe an intuition because it cannot be a concept. Or, more precisely, since Kantdoes recognize that we have spatial and temporal concepts, for example, theconcepts of a yard and a year, the claim is that these concepts presupposean underlying intuition. As Kant put it at one point, space is inuitus, quemsequitur conceptus. 55 He could have said the same for time.

Kant's initial argument turns on the singularity of time. He points out thatthis accords with the nature of intuitions as singular representations. If thissingularity is to bear the weight assigned to it, however, more has to besaid. In particular, the reason why there is only a single time cannot be likethe reason why there is only a single tallest man in the world, since thatwould hardly support Kant's claim that it is a pure intuition. Rather, the(p. 59 ) key point underlying Kant's characterization is a peculiar feature oftime (and space), namely, that Different times are only parts of one and thesame time (A 31/B 47). Moreover, as Kant makes explicit in his discussionof space, but surely wishes to say of time as well, [T]hese parts cannot as itwere precede the allencompassing space [time] as its components (fromwhich its composition would be possible), but rather are only thought in it.

It is essentially single; the manifold in it, thus also the general concept ofspaces [times] in general, rests merely on limitations (A 25/B 39).

The conclusion that Kant immediately draws from this is that therepresentations of space and time cannot be classified as concepts becausethe partwhole relation they embody is distinct from that which pertains toconcepts. Whereas in the case of space and time the whole precedes andis a condition of the parts, which is why they are essentially single, in thecase of concepts the reverse holds. As general representations, Kantianconcepts are composed of other concepts, termed partial representations

or marks (Merkmale), which constitute their intension or sense. Forexample, the marks of gold include metallicness, yellowness, malleability,solubility in aqua regia, etc. These also determine the properties of the classof things that fall under or constitute the extension of the concept. And thisagain differs from the representations of space and time, since in their case


25/36






particular spaces and times are contained in rather than falling undertherepresentation.

Although Hume's theory of ideas has no place for Kantian concepts,

his complex ideas do share one important feature with them, namely,the wholepart relation. This becomes clear as soon as one notes that,though particular, Hume's complex ideas are produced by the combination(through the associative mechanisms of the imagination) of simple ideas.Consequently, in their case the parts likewise precede and are conditionsof the whole. Moreover, while for Hume the compound ideas of variousbits of extension or stretches of time are supposedly copied from theircorresponding compound impressions, it is evident from the compositionalistpicture that Hume presents in the first part of his system that the sameapplies to the latter as well.

By contrast, if we turn to the second part of this system, wherein spaceand time are characterized as manners of appearing, a quite differentpicture emerges. First, this manner is apprehended immediately ratherthan constructed or inferred, which satisfies Kant's immediacy criterion foran intuition. 56 Second, though this is a point that Hume would challenge,we have seen through a consideration of Kant's apriority arguments, thatthe apprehension of this manner presupposes the representations of asingle space and time. From this point of view, what the intuition argumentconsidered above adds is an explanation ofhow the representations of spaceand time are presupposed, (p. 60 ) namely, as the a priori frameworks in

relation to which spatiotemporal determinations are made. For example,when Hume talks about a determinate extension as a disposition of pointsor a manner of appearance, this must already be understood in spatialterms, say as contiguous or as located a certain distance from each other,from which it follows that it cannot be the source of our idea of extension.Similarly, if we wish to introduce the previously discussed notion of anintrinsically minimal distance as the basis for Hume's construction ofextension from an aggregation of colored or tangible points, we are obviouslyalready importing a spatial notion (distance), which returns us to thepreviously noted circularity. And the same applies, mutatis mutandis, to the

idea of time.

What this examination of Hume's system regarding space and time throughKantian spectacles shows is the deep tension between the two parts ofthis system. To be sure, Hume himself was not aware of any tension, sincehe presented the second part as a consequence of the first. Nevertheless,


26/36






we have seen that the first part effectively construes space and timeas compound ideas that track compound impressions, while the secondconsiders them as manners of appearing, which, as such, not only resembleKantian intuitions, but also forces one to regard them as a priori. Lacking

anything like Kant's conceptintuition distinction, the problem could not haveappeared to Hume in those terms; but he arguably should have noted thetension between his account of space and time as manners of appearing withthe Copy Principle.

The relevance of Kant's second intuition arguments stems primarily from thefact that they deal with the infinitude of space and time and, by implication,their infinite divisibility. In the case of time, Kant states that its infinitudesignifies nothing more than that every determinate magnitude of time isonly possible through limitations of a single time grounding it. The original

representation time must therefore be given as unlimited (A 32/B 478).57 Accordingly, time and space are infinite not in the sense that they arecomposed of an infinite number of parts, which is the only sense of infinitythat Hume allows, but in the quite different sense of being boundless, sothat however large a segment one assumes, it will always be encompassedby more of the same. 58 For Kant this entails that space and time areintuitions, since this again is incompatible with the partwhole relation thatpertains to concepts; and this is the use to which he puts this analysis in theTranscendental Aesthetic.

Finally, it must be noted that this analysis entails the infinite divisibility of

space and time; for the same process operates in reverse. In other words,just as every extent of space and time is bounded by more of the same,which makes them boundless, so every slice of space and time, no matterhow small, (p. 61 ) always contains within it further spaces and times,which means that they are infinitely divisible without being composed of aninfinite number of parts. To be sure, Kant was not the originator of the ideathat space and time could be infinitely divisible without being composedof an infinite number of parts, but his account of them as pure intuitionsconstituted an advance in understanding this possibility. In particular, itenabled Kant to claim that a moment is a limitrather than apartof time,

from which it follows that the indivisibility of a moment, which like that of apoint is a conceptual truth, has no bearing on the indivisibility of any portionof time. 59


27/36






IV

In conclusion, I would like to add a word about a distinct but closely relatedissue that is suggested by the preceding analysis. The issue concerns Kant's

Second Antinomy, more particularly the antithesis of this antinomy, whichaffirms infinite divisibility through a denial of simplicity. Since Kant wasapparently not aware of this aspect of Hume's thought, it is not surprisingthat the antithesis contains no reference to his arguments against infinitedivisibility and for simplicity. Nevertheless, it has been suggested that thismarks a significant defect in Kant's argument; indeed, that it fails becauseit ignores the alternative solution offered by Hume to a similar dialectic inBayle, namely, that extension is composed of indivisible (colored or tangiblepoints), which are located in and occupy space, but are not extended. 60

In considering the question of whether the antithesis of the Second Antinomysucceeds in eliminating the Humean alternative, it is essential to recognizethat the argument is divided into two parts. The first part asserts that Nocomposite thing in the world consists of simple parts, and the second thatnowhere in it [the world] does there exist anything simple (A 435/B 463).The first part appeals to the concept of substance and consists of a reductioof the assumption that a composite substance consists of simple parts. Thenerve of the argument is the premise that such a composition is possibleonly in space, from which it follows that there must be as many parts ofspace as there are parts of the composite that occupies it. But since (asshown in the intuition arguments) space itself consists of spaces rather thansimple parts, it likewise follows that the presumed simple must occupy aspace. The problem, however, is that everything real or substantial thatoccupies a space must itself contain a manifold of elements external to oneanother, that is, be composite. And this generates the contradiction that thesimple is a substantial composite (A 435/B 463).

(p. 62 ) It is clear from the fact that this argument concerns the compositionof substances in space that it does not address the Humean view. It is alsoclear that Hume would reject the premise that space consists of spacesrather than simple (nonextended) parts. The situation appears quite

different, however, when one turns to the second part of the argument,which, as Kant puts it in his conclusion, does away with the simple inthe whole of nature (A 438/B 466). 61 Here Kant's argument is purelyepistemological, turning on the principle, which Hume would certainlyaccept, that in order for such a simple (which Kant characterizes as atranscendental) idea to be established empirically, the empirical intuition


28/36






of some such object would have to be recognized, an intuition containingabsolutely no manifold whose elements are external to one another andbound into a uni

Documents

2 Humes Theory of Space and Time