Somers-Hall, (0.5), Deleuze’s Difference and Repetition, ‘0.5 Extension and Comprehension (11–16/13–18)’, summary

by 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

0.5 Extension and Comprehension (11–16/13–18)

Summary

Very Brief Summary:

True repetition is not the reiteration of something self-same. Representation, then, is not repetition, since it is a matter of genericized reiterations. So whatever is repeating is not doing so in terms of conceptual representation. Such instances would need to be distinguishable in reality but not conceptually. An example is an atom. All atoms have the same conceptual determinations, but differ non-conceptually in terms of spatio-temporal determinations.

 

Brief summary:

We might normally think of something repeating as being a reiteration of the same thing. In this sense, we are thinking of repetition in terms of generality, since the thing being repeated is understood as something general that is reiterated in a number of particularities. Yet, Deleuze is formulating a concept of repetition which is not based on generality. Representation is also often understood in terms of generality, and thus representation is not for Deleuze a sort of repetition. There are two processes involving representation that Deleuze addresses: representational memory (which represents objects no longer present) and recognition (which compares present objects with internal representations). These representations often take a structure which makes them only representative of certain objects and not others. This structure can be understood as having a comprehension and extension. The comprehension is the conceptual description which delineates the essential attributes of the thing. The extension are the variety (or singularity) of things that the representation includes.  [“the comprehension of the idea triangle includes extension, figure, three lines, three angles, and the equality of these three angles to two rigid Angles, &c.” and “the idea of triangle in general extends to all the different sorts of triangles” (Arnauld 1850: 49).] The more we add to the comprehension, the more restrictive it gets, and thus more comprehension results in less extension, and vice versa. At the extreme where the extension is one thing, that means the comprehension has expanded to the infinite. Deleuze then addresses a problem this raises when we take into consideration Leibniz’ identity of indiscernables: “if two things share the same properties, they are in fact identical” (15). This implies that two objects cannot share the same properties, as they would really be one identical thing. But if repetition is understood as the reiteration of the same, then this sort of repetition would be impossible. However, if we have a reiteration of things which cannot be conceptually distinguished, then we would have a repetition without them collapsing into one self-same thing. But in order to have Deleuze’s sort of repetition, we need on the one hand to have things which are reiterations but on the other hand not be reiterations of things which conceptually collapse into one another. To progress to such examples, we need first to note the concept of blockages. All things within a generalized concept are the same and thus they all collapse into one another. All mammals if not further specified are conceptually indistinguishable. In order to distinguish some of those mammals from others, we need to stop the application of the term in certain cases, or to put it another way, we need to instate ‘blockages’, which are conceptual determinations. This allows us to have ‘horses’ and ‘cows’ be repetitions of the concept of ‘mammal’. We can further divide horses using other artificially instated blockages. But what we want are natural blockages where the differences are inherent to the things while also they cannot collapse conceptually into one self-same thing.  One case would be things which are conceptually indistinguishable (with that concept having an extension of 1) but differ only in spatial temporal determinations (which cannot be part of the conceptual determination). Atoms for example are like this. Another example of this is using the same word in many cases. They have the same conceptual determination but different contextual variations.

 

Summary

The Introduction to DR is about how real repetition is opposed to generality. First we saw how this is so with regard to natural law. Then we saw it with respect to moral law [here and here]. Now in this section we learn how they are opposed in terms of representation. Deleuze is critical of two processes, representational memory and recognition. In both of them, the representation of objects plays a central role. We need the representation of objects when we remember them, because they are in the past and are no longer presented. And when we recognize something, we need to “compare our internal representation of the object with the object itself” (14). We wonder, how do we structure these representations? (14) We often do so by defining the representation so that it corresponds only to those objects (or that object) it means to represent.

We normally see objects as composed of substances and properties, and we describe these objects using the parallel conceptual terms of subjects and predicates. Depending on how many predicates we ascribe to a subject, we can determine which objects fall under that concept. For example, we can restrict the application of a concept by stipulating that it only applies to objects which have a certain property. So the concept of an animal applies to only those entities with the property of animality. By adding further predicates, we can narrow down the group of entities which fall under the concept. Thus the concept of a rational animal covers a subset of both of the groups to which those predicates are attributed. It therefore circumscribes a smaller collection of entities (traditionally taken to be mankind).
(14)

We now turn to the ‘comprehension’ and ‘extension’ of the concept. These terms were defined in Arnauld’s then standard logic text the Port Royal Logic. The comprehension of the concept includes all its essential distinguishing features.

I call the COMPREHENSION of an idea, those attributes which it involves in itself, and which cannot be taken away from it without destroying it; as the comprehension of the idea triangle includes extension, figure, three lines, three angles, and the equality of these three angles to two rigid Angles, &c.
(15, see Arnauld citation below)

The extension are the things [and subcategories] that are included as instances of that concept.

I call the EXTENSION of an idea those subjects to which that idea applies, which are also called the inferiors of a general term, which, in relation to them, is called superior, as the idea of triangle in general extends to all the different sorts of triangles. (Arnauld 1850: 49)
(SH 15, quoting: Arnauld, Antoine (1850), Logic or the Art of Thinking, being the Port Royal Logic, trans. Thomas Spencer Baynes, Edinburgh: Sutherland and Knox.)

[Now, think of a very general concept, like ‘thing’. It refers to a great many objects, since it is so vague. Its comprehension is small but its extension is great. Instead think “living whales”. It refers to a far smaller number of items. So its comprehension is large but its extension is small.] “Now, it should be obvious that the extension and the comprehension of a concept are inversely proportional. That is, the more we specify a concept, the fewer objects will be subsumed by it” (15). This means that if the extension is 1, then the comprehension is infinite, since “the extension and the comprehension of a concept are inversely proportional” (15). [This part is not entirely clear to me. What does it mean for the comprehension to be infinite? Does it mean that it has an infinity of essential distinguishing traits? Why would it be infinite? Would it be infinite because any one particular thing must be distinguished from an infinity of other things and thus have an infinity of determining / particularizing traits? Would not many of them be accidental? Also, why is it if we decrease the extension and thereby increase the comprehension does the comprehension become infinite when the extension is 1, and not instead it just become a very large finite number? So why is it that for a concept with an extension of 1 and another concept with an extension of 2 that their difference in comprehension be on the scale of the infinite rather than the finite?] Now note Leibniz’ identity of indiscernables: “if two things share the same properties, they are in fact identical” (15). [Regarding extension and comprehension, if two things have no differences in their comprehensions, then they must have the same extension. The important concept here is that we begin by distinguishing two things, but in the end we conclude there never were two things but instead only one. But for repetition in the classic sense of reiteration of the same, then we cannot have repetition of the same, since there would only be one object continuing as itself rather than an another instantiation of it. The next move in Somers-Hall’s explanation is not clear to me, but it seems he is saying that, on this basis, in order to have repetition, we need to be able to distinguish each object conceptually (comprehensionally), but we might have reason to doubt that this is really possible. I will quote these passages for your interpretation:]

the more we specify a concept, the fewer objects will be subsumed by it. If we are to remember a particular event, or recognise a particular object, then the extension of that concept must be 1, i.e. it must only refer to the particular experience or object under consideration. But this implies, as extension and comprehension are inversely proportional, that the comprehension of the concept must be infinite. Deleuze refers to the idea that every object can be uniquely specified by a concept as a ‘vulgarized Leibnizianism’ (DR 11/13). By this, he means that it implies something like a principle of identity of indiscernibles (that if two things share the same properties, they are in fact identical). If it were impossible for two different objects to have the same properties, then repetition itself would be impossible. So the question is, is it possible to distinguish each object from every other conceptually?
(15)

[Note how we define concepts we arbitrary set cut-offs for what items will be included under it and which will not, and we set those cut-offs by means of setting limitations in the generalities of the concept.] When we limit an extension, we do so by setting up ‘blocks’ in our conceptual determination.

When we define a species, for instance, we attribute a set of properties to a thing. For instance, we might define a horse by the properties of being a mammal, having hoofs, being a herbivore, etc. In this case, we don’t want to develop a concept that defines an individual, since we want a concept that allows us to talk about a group of individuals at the same time (horses). Rather than carrying on until we have specified a particular horse, we introduce what Deleuze calls an ‘artificial blockage’ (DR 12/14) by stopping this process of determination. Depending on where we introduce the artificial blockage, we will get more or less general concepts. Thus, by | adding more determinations to the concept of mammal (and thereby increasing its comprehension), it will apply to a more and more specific class of mammals (its extension will decrease).
(16)

[Somers-Hall seems to be saying in the following that we cannot have repetition among the items of a concept, because everything within it is the same thing. For there to be repetition, you need conceptual difference. In order to make this difference, you need additional conceptualization, another concept, which can specify that thing more. So within mammals you cannot have repetition, since there is only one concept and thus only one extension (one general class, even though we may place many things into that class. We do not distinguish those things from one another conceptually, so we just have one thing, ‘mammal’). In order to get something new, we need to add blockages to obtain for example horse. Then we might say that we have a repetition of mammal in the horse. Please interpret the Somers-Hall text for yourself:]

Here we can relate repetition to difference, since purely in terms of these concepts of ‘horse’ or ‘mammal’, repetition is grounded in a difference which falls outside of the concept in question (DR 13/15). That is, in so far as we are only talking about the concept, ‘horse’, repetition is possible, as all particular horses are horses in exactly the same way. The difference between them is not in the concept, ‘horse’, but in another concept (perhaps they are different colours or sizes, or are used in different roles). Repetition is therefore difference without, or outside of, the concept.
(16)

[The next part is also a little unclear to me. In the above he says that the distinctions are found in external concepts, but now he says that by specifying further we bring the difference within the concept. Perhaps he is saying that when we create a blockage, we create an internal difference within ‘mammal’ for example, thereby creating two or more concepts external to one another, like ‘horse’ and ‘sheep’. Then he says that the internal differentiation is an artificial rather than a natural blockage. This seems to mean that we can explicate the difference between the objects conceptually, because we have conceptually made that distinction in the first place. The horse we say has different properties than the sheep. Now we need to think of ‘natural’ blockages which create a difference that is not conceptualizable.]

In this case, we could have carried on specifying the concept further and by doing so brought the difference within the concept, hence it being an artificial blockage; but the question is, are there natural blockages, that is, cases where it is impossible for us to capture the difference between two objects conceptually?
(16)

Deleuze offers three examples of these natural blockages: atomism, (psychic) repression, and Kant’s incongruent counterparts (16). Since Deleuze deals at greater length with the topic of repression in the second chapter, Somers-Hall will focus now on atomism and incongruent counterparts.

SH warns us that Deleuze’s account of atomism is “rather obscure” (16). [The basic reasoning that SH gives seems to be the following. We divide up the world into parts of parts of parts and so on until we arrive at fundamental parts. Now, what distinguishes one thing from another? Well, it has different parts, different constitution. But what if something has no parts? It will not have any distinguishing traits conceptually speaking. It will only be distinguishable from other atomic parts on the basis of temporal and spatial differences, which are not conceptual in the same way that constitutional differences are conceptual. Thus here we have natural blockages which say this atom is not that atom, but we have no conceptual way to distinguish them.]

He [Deleuze] suggests [the following up to citation is block quotation]:

Let us suppose that a concept, taken at a particular moment when its comprehension is finite, is forcibly assigned a place in space and time – that is, an existence corresponding normally to the extension = 1. We would say, then, that a genus or species passes into existence hic et nunc [here and now] without any augmentation of comprehension. (DR 12/14)

Rather than a species just being a convenient grouping, it would now be something that had a definitive existence, with each of the objects falling under the concept being absolutely identical. Deleuze is thinking of something like an atom here. Atoms are identical to one another (conceptually indistinguishable) in spite of the fact that they are separate individuals. While in the case of a species, we could add further determinations if we wished to distinguish particular members of a species, there simply are no further conceptual distinctions that can be made between | different atoms. In this case, each atom is a repetition of the one before precisely because they differ, but still fall under the same concept.
(SH 16-17)

We also have natural blockages in case of word usage. We use the same word many times each [presumably] denoting the same concept and thus being conceptually indistinguishable, while in fact [on account of non-conceptualizable contextual variations] each instance of the word is unique and distinguishable non-conceptually. (17)

While we might question whether atoms really are identical with one another, Deleuze claims that the case is much more decisive in the case of words, where we can repeat the same word. This is because each particular instance of the word is conceptually indistinguishable from each other. In this situation, we cannot specify each instance conceptually, and so the ‘vulgarized Leibnizianism’ of complete conceptual determination breaks down.
(17)

 

Citations from:

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