8 Mar 2015

Somers-Hall, (0.6), Deleuze’s Difference and Repetition, ‘0.6 Incongruent Counterparts (13–14/15, 23–7/26–31)’, summary

Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own.]

Henry Somers-Hall

Deleuze’s Difference and Repetition.
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text



0 Introduction: Repetition and Difference

0.6 Incongruent Counterparts (13–14/15, 23–7/26–31)


Very Brief Summary:

We may distinguish many things by means of the parts’ relative positions to one another. However, a simple glove for example could fit on a left or a right hand, even though when both of the pair are worn together it can only be a left or a right handed glove. Its own conceptual distinctions, which are based on the relative positions of its parts, are not enough to distinguish its right or left handedness. Thus there are reiterations of things in our world – these incongruent counterparts – that are repetitions whose instantiations do not collapse into one another on account of their being conceptually indistinguishable.


Brief summary:

For there to be repetition, you need a number of instances of something, but they cannot all be one and the same, as you would have one thing never ceasing to be itself rather than repeating. But if there are no conceptually discernible differences between the instances, they would collapse into one another. However, if there are conceptual differences, then they are not reiterations but rather new things altogether each time. So to have repetition, it would seem we need a series of things which are not conceptually distinguishable (and thus do not collapse into one thing) but are also truly unique from one another (so that there is reiteration and not continuation). Deleuze offers examples of such cases. Here we look at Kant’s incongruent counterparts. If we imagine that the first thing invented was a plain and very simple glove, we would not know if it were left or right handed. For, you could flip it over and it could fit the opposite hand. But (assume that) God would only make a glove for either a left or a right hand. It must inherently be one or the other. [It is left handed on account of there being not the relative spatial relations of each part of the glove to the other parts, but rather that the glove takes up some absolute position in space, which perhaps is a place belonging either to a left or a right hand]. So because many things are different (like being left and right hand gloves) without any spatial relations to determine which is which, these incongruent counterparts are examples of repetitions without conceptual distinctions.



Previously we looked at examples of ‘natural blockages’ in atomism. Now we see ‘natural blockage’ in the case of Kant’s incongruent counterparts, Kant’s argument for which “is first introduced into a debate between Newton (and Clarke) and Leibniz on the nature of space” (16). Newton and Leibniz debated whether space was absolute or if it was relative to the objects it contains. Newton thinks we have both types and that we can distinguish them. Absolute space for him does not need anything external to it to be what it is, and it is “always similar and immovable” (SH 17, quoting Newton 1934: Defs., Scholium II). Relative space, however, is “some moveable dimension or measure of the absolute spaces.” Our senses determine it by means of its position in relation to bodies. It is also “commonly” thought to be an immovable space, as in the cases of “a subterraneous, an aerial, or celestial space, determined by its position in respect of the Earth” (SH 17, quoting Newton 1934: Defs., Scholium II).  Newton defines a frame of reference by inertia, “that is, by the fact that all objects within a frame of reference are moving at constant velocity” (SH 17). [The move to the next point is not clear to me. Maybe SH’s point is that if everything is determined within one frame of reference, then all things are spatially related in an absolutely consistent way, and thus it is very difficult to distinguish this relative space to absolute space.]  “On this basis, it is very difficult to even differentiate between a relative and an absolute frame of reference” (17). Nonetheless, Newton still argues that these relative spatial relations are only possible on the basis of an absolute frame of reference that is “logically prior to the existence of objects themselves. Absolute space is therefore essentially a metaphysical posit within Newton’s physics, which grounds the possibility of relations between objects” (17). [The reason why relative spatial relations depend on an absolute space is not given here.]

Leibniz does not think that space is absolute. Rather, it is “a secondary, derivative concept that emerges from the relations which exist between objects” (17). Leibniz gives three reasons why the notion of absolute space is problematic. 1) [Something needs to be either a substance or a property, but absolute space is neither]. It is not a substance, [because substances have causal powers, but] substance is causally inert. Yet, [properties do not precede the objects they are properties of, however] absolute space “precedes objects rather than depending on them” (18). 2) Leibniz holds that every event needs a reason or cause. [This could be his principle of sufficient reason. Now consider relative space. We can use physics to say why one thing is where it is on account of some physical cause. However,] “If space is independent of the things within it, it becomes inexplicable why the universe is where it is and not, for instance, three feet to the left of its current position” (18). 3) [Recall Leibniz’ identity of indiscernibles. Two things which cannot be distinguished are in fact really just one thing after all. But,] “if there is no way to distinguish one point of space from any other, then we can say that each point in space is identical to every other one, and so, as they are identical, space is just one point” (18).

So instead of the Newtonian view that there exists both absolute and relative space, Leibniz argues that space is relative in the same way time is. That is to say, space is “an order of co-existences as time is an order of successions” (SH 18, quoting Leibniz and Clark 2000, p.15). Leibniz does not think the concept of space tells us anything about the particular way things exist. So when we perceive objects in space, we do not perceive their absolute locations but rather just their spatial relations.  [Perhaps Leibniz means something like the following. When we perceive things in space, we do not perceive their absolute locations in some universal all encompassing space, as if we somehow stood outside our spatial context and could see all things exactly in their absolute places. On this basis of our spatial perception, perhaps, we would conclude that space itself is not absolute.]

[Since relative relations are conceptual and not physical determinations of things,] for Leibniz,

space is a distorted view of what are really conceptual determinations of objects. Space in this sense is therefore secondary to the ‘order of things’, and exists only in so far as it allows us to see the relations which obtain between these entities. Space emerges because the intellectual nature of the universe is only perceived confusedly by the finite subject. On this view, therefore, conceptual determinations precede space, which is in no way a real feature of the world, rendering Newton’s absolute theory of space false. (18)

This also means for Leibniz that monads lack spatial properties [in the absolute sense] but they do have spatial properties as “well-founded phenomena,” which are [somehow] “analogous with what are in reality conceptual properties” (SH 18). [Now recall the problem we have addressed in the recent sections. According to Leibniz’ law of the identity of indiscernibles, two things sharing the same (conceptual) properties are really identical (and thus perhaps not really two things in the first place). But repetition somehow involves one thing being repeated (under a certain view of repetition). However, that means that if all things are conceptually distinguishable, then repetition is impossible, as we only have a plurality of distinct things and not the reiteration of some one thing. Thus] SH says that the main point we take from Leibniz is that for him

all of the properties which we encounter in space can be understood purely in conceptual terms. If that is the case, then because each object will be conceptually distinct for every other, repetition is impossible.
(SH 18)

[SH now moves on to Kant.] In his Concerning the Ultimate Foundation for the Differentiation of Regions in Space, Kant tries to show that Newton’s view of [absolute] space is correct. [The paragraphs of Kant under discussion do not present his idea very readily. Kant will make the point that if only one hand is created, we cannot determine whether it is a left or a right hand merely by means of the relations of its parts, that is to say, merely by means of the spatial relativities of the individual parts like the fingers, palm, back-hand, and thumb. However, this is not so obvious, given that there is clearly a distinguishable front and back side of the hand (palm and back-hand), and the left hand is the one which, when looking at the palm side, the thumb is to the left of the fingers. This example is also sometimes explained using the idea of a glove, whose front and back side are not always distinguishable like the human hand is. It would be a glove which could fit perfectly on one hand, and if flipped around, can fit perfectly on the other hand. See for example Catherine Wilson’s Stanford Encyclopedia article, “Leibniz’s Influence on Kant,” http://plato.stanford.edu/entries/kant-leibniz/ . So consider if the first thing ever created were a glove symmetrical in this way. You could flip it over and it would turn from a right to a left hand glove. Hence the relative positions of its parts are not enough to determine a left from a right hand glove. Kant’s point might be that what would make that determination is a distinction in absolute space, with the left one being in one place and the right one being in another. Those absolute positions would then somehow determine its left or right handedness. I can only guess that this would be that the gloves somehow correspond to the absolute positions for the left and right hand on which they are worn. This absolute spatial determination would be internal to each glove, since its absolute location is a distinction internal to the object and not a matter of external relations of one to another. But this is not clear to me. Try to find your interpretation for this quoted Kant passage. According to SH, the main idea we take from this is that the conceptual determination of the glove in terms of the relation of its parts is insufficient for knowing whether it is a left or a right hand glove. The following first gives a block quote of Kant, and following after its citation is SH’s commentary.]

Let it be imagined that the first created thing were a human hand, then it must necessarily be either a right hand or a left hand. In order to produce one a different action of the creative cause is necessary from that, by means of which its counterpart could be produced.

If one accepts the concept of modern, in particular, German philosophers, that space only consists of the external relations of the parts of matter, which exist alongside one another, then all real space would be, in the example used, that which this hand takes up. However, since there is no difference in the relations of the parts to each other, whether right hand or left, the hand would be completely indeterminate with respect to such a quality, that is, it would fit on either side of the human body. But this is impossible. (Kant 1968: 42–3)

Kant’s point is that the conceptual determination of the hand, in this case, a set of relations between parts, is not sufficient to determine whether the hand is a left hand or a right hand. In both cases, the relations are identical, and so, conceptually, the hands are also identical. The fact that hands are left or right handed therefore means that there must be an ‘internal difference’ that is not a conceptual determination.
(SH 19, block quoting above Kant 1968: 42–3).

[SH’s next example is not entirely clear to me. I will take a guess at what he means with it. We are to consider a triangle being on a two-dimensional plane. In order to know if it is congruent with another triangle, which in this case is a mirror image of the first, we need a third dimension to flip it over, since rotating it two-dimensionally will only give us the triangle upside down. So if we stay in two dimensions and rotate it, we are only dealing with a relative concept of space, as the triangle’s parts retain their relations among one another, but the congruency between one triangle and its mirror image is not determinable on the basis of this presentation of the triangle that is limited to spatial relations. What is needed is the third dimension of space which allows us to flip the triangle over so to overlay its mirror image beside it. For some reason, this is a matter of absolute space, perhaps because the third dimension enables us to fix the locations in a way we are unable using just two dimensions. Thus (on the basis of some reasoning still not presented entirely by me here), it is not enough to only use relative space and its limited use of conceptual relations to determine whether or not a triangle can be congruent with its mirror image. Please read SH’s paragraph below to better understand how it is that this example demonstrates Kant’s argument for absolute space (internal differences) rather than relative space (external relations of parts).]

We can make this point clearer by noting that the property of handedness is intimately related to the nature of the space in which the object is placed. If, instead of a hand, we took the example of a triangle on a two-dimensional plane, it should be clear that it cannot be rotated so as to cover its mirror image. If we consider the same triangle in a three-dimensional space, however, we could ‘flip the triangle over’, thus making it congruous with its mirror image. The dimensionality of space therefore determines whether the counterparts are congruous or incongruent, meaning that handedness is a property of space, and not purely of conceptual relations. For this reason, Kant rejected his earlier Leibnizian interpretation of space in favour of a Newtonian conception. (SH 19)

Kant’s incongruence of counterparts “lays the groundwork” for Kant’s notion that space is an a priori intuition because it shows how “space cannot be understood in conceptual terms. Space is an intuition, or a mode of sensibility, by which we apprehend the world. In the transcendental aesthetic of the Critique of Pure Reason, Kant makes two claims about intuition: that it is a priori, and that it is non-conceptual” (20). Deleuze regards Kant’s notion that the structures of space and time are different in kind from our conceptual understanding as one of Kant’s greatest philosophical innovations. We will later see in the second chapter  something analogous in Deleuze’s thinking. (20)

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

Kant, Immanuel (1968), ‘Concerning the Ultimate Foundation for the Differentiation of Regions in Space’, in G. B. Kerferd and D. E. Walford (trans. and ed.), Selected Pre-Critical Writings, Manchester: Manchester University Press.


Leibniz, Gottfried Wilhelm and Clarke, Samuel (2000), Correspondence, ed. Roger Ariew, Cambridge: Hackett Publishing.

Newton, Sir Isaac (1934), Mathematical Principles of Natural Philosophy and his System of the World, trans. Felix Cajori, Los Angeles: University of California Press.

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