11 Aug 2015

Somers-Hall, (3.8), Deleuze’s Difference and Repetition, ‘3.8 The Postulate of the Proposition (153–6/191–5)’, summary

Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text


Chapter 3. The Image of Thought

3.8 The Postulate of the Proposition (153–6/191–5)

Brief summary:
The sixth postulate of the problematic image of thought is of logical function or of the proposition. Consider the proposition, “it is raining” outside. If it is true, then it corresponds to the state of affairs of it actually raining outside. If it is false, it does not correspond, since outside it is not raining. This correspondence to a true state of affairs is its denotation or designation. This assertion also has a “sense,” which refers to the belief of the speaker that it is raining. The sentence has sense even if it is false, since the speaker supposedly does in fact have the belief that it is raining. This also means that the sense is broader than the denotation, since the sense refers more generally to possible states of affairs (either that it is or is not raining) while the designation refers supposedly only to one actual state of affairs. In the sixth postulate, designation is problematically given the primary status, and so sense is understood in terms of how it may be captured in propositional form. But this creates various problems. One is that we already said that sense is broader and thus more fundamental than the proposition, so we cannot ground sense in it. The other problem comes if we explicate sense in propositional form. This will produce a sentence with yet a new sense. The regress either terminates in a fundamental proposition like Descartes’ cogito, which as we noted in a prior section is problematic. Or the regress is infinite and thus fails to find a ground.






[Recall the postulates of the image of thought that we have covered so far: 1) our reason judges an object that was 2) processed by the faculties working in common, and which is 3) recognized and also which 4) is a representation. One way 5) error arises is through misrecognition. We turn now to the sixth postulate of the proposition.] Besides truth and falsity, the image of thought also needs the notion of sense.

As Deleuze notes, ‘Teachers already know that errors or falsehoods are rarely found in homework . . . Rather, what is more frequently found – and worse – are nonsensical sentences, remarks without interest or importance, banalities mistaken for profundities, ordinary “points” confused with singular points, badly posed or distorted problems – all heavy with dangers, yet the fate of us all’ (DR 153/191).
(SH 122)

SH turns to Bertrand Russell’s account of significance  to elaborate what Deleuze means by sense. [This section is a bit complicated. Let us begin with the Russell quotation. We first distinguish two sorts of states, inner subjective states and outer objective states of affairs. Inner states, or beliefs, can exist in a person even without words expressing them. An assertion has both subjective and objective sides. Let us suppose that it is raining outside, and we say, “it is raining outside”. This assertion has the subjective side, our belief that it is raining, which can be there whether we say it or not. (It also would seem that the objective state of affairs would exist whether we say it or not, and thus it is not clear if this issue makes a difference.) Since it is raining outside, then the statement indicates a fact. But if it were not raining outside, it would not indicate a fact, even though it is intending to. Now imagine that we say to ourselves, “I believe that I am hungry.” Here both the subjective state that is expressed (my belief in my hunger) and the objective state of affairs that the assertion indicates (my body being in a state of hunger and being aware of that situation) are identical. But normally these two things which may be indicated are different. Russell then defines ‘significance’ as what the sentence expresses. It seems that Russell assumes all assertions are made in good faith and that they express one’s own beliefs, thus all true and false statements are equally significant. However, a string of words that do not express a speaker’s beliefs are nonsensical. The following quotes Russell:]

An assertion has two sides, subjective and objective. Subjectively, it ‘expresses’ a state of the speaker, which may be called a ‘belief’, which may exist | without words, and even in animals and infants who do not possess language. Objectively, the assertion, if true, ‘indicates’ a fact: if false, it intends to ‘indicate’ a fact, but fails to do so. There are some assertions, namely those which assert present states of the speaker which he notices, in which what is ‘expressed’ and what is ‘indicated’ are identical; but in general these two are different. The ‘significance’ of a sentence is what it ‘expresses’. Thus true and false sentences are equally significant, but a string of words which cannot express any state of the speaker is nonsensical. (Russell 1940: 171)
(SH 122-123).

[Next let us turn to SH’s commentary. He says that Russell makes a distinction between a proposition’s truth value and its meaning. If the proposition is true, it successfulyl indicates or denotes, and if false, it fails to. So designation occurs when the proposition’s structure mirrors states of affairs in the world. Then SH seems to equate significance with sense, and he says truth and falsity cannot capture sense, because, it seems, all propositions that have sense already correspond adequately to a belief, even if they are false. However, truth can capture denotation, perhaps since it is only true statements which can denote a state of affairs. Thus we must separate the notions of truth and sense.]

Russell here is making a distinction between the truth value of a proposition (whether it is true or false), and the meaning of a proposition. Truth or falsity determine whether something is successfully indicated (in Russell’s terms) or designated (in Deleuze’s terms) by a proposition. Designation is simply a relation whereby either the structure of the proposition mirrors a state of affairs in the world (and hence is true), or does not (and hence is false). For Russell, truth and falsity cannot capture the significance, or sense, of a proposition, because what a proposition expresses is not a correspondence between a state of affairs and a proposition, but rather the beliefs of the speaker who asserts the proposition. While whether a proposition succeeds in indicating a fact or not depends on the truth or falsity of a proposition, since the sense of a proposition depends on the psychological beliefs of the speaker, its significance or lack thereof is not dependent on truth or falsity. A proposition can still ‘make sense’, even though it is false. Thus, we have to be able to separate sense from truth.
(SH 123)

Deleuze thinks that the sort of account that Russell gives provides “a transcendental model of the conditions of the possibility of a proposition being true or false” (123) [I am not sure, but perhaps the idea here is the following. The transcendental conditions for an assertion being true or false are that the structures of language be capable of indicating the structures of states of affairs in the world such that they may be said to correspond or not.] Deleuze also thinks that this Russellian model has the same problems as Kant’s transcendental model of experience (123). SH then notes a couple similarities in their accounts. [In the following material I get a little confused. I thought that from the quotation and commentary above that sense is significance, and significance is what is expressed, and what is expressed is subjective belief. Here is what SH writes:]

First, sense is abstract and broader than the propositions it relates to: ‘the condition [sense] must retain an extension larger than that which is conditioned [the true or false]’ (DR 153/191). As Russell notes, ‘we may say that whatever is asserted by a significant sentence has a certain kind of possibility’ (Russell 1940: 170). That is, whereas designation aims at an actual state of affairs, sense for Russell operates according to possible states of affairs. Something is significant if it could be the case.

[I am confused how the sense (which relates to the belief) is broader than the proposition it relates to. I also do not understand very well how significant sentences (ones that express a belief) deal with possible rather than with actual states of affairs. Perhaps an example would be helpful to explain these things, but I am not sure how to use the raining example from above in this case. So, we believe it is raining. The statement “it is raining” has a sense, which refers to or expresses that belief. How is this a possible state of affairs? Perhaps it is possible, since it could be raining or not, but either way, the sense holds. And thus maybe that is why it is broader that the proposition, since the sense refers to more than just an actual state of affairs, but the proposition (at least its denotation) refers only to an actual state of affairs.] [The second point is that sense repeats the structure of the proposition at a higher level. This is very complicated, and I will not be able to get it right, so I will quote it first:]

Second, and a consequence of this, sense merely repeats | the structure of the proposition at this higher level. Whereas Kant’s categories have structural parallels with the functions of judgement, the sense of a proposition actually is itself a proposition. In the case of Russell’s model, the sense of the proposition, ‘x is the case’ is the statement, ‘I believe x is the case’. In this manner, the sense of a proposition does not explain what makes a proposition true or false, in that sense is understood in propositional terms, and therefore already presupposes the true and the false. Sense for Russell is therefore much like common sense, in that it guarantees the fact that all significant propositions we encounter will either be true or false, just as common sense guaranteed that all states of affairs would be amenable to judgement.
(SH 124)

[The first idea above seems to be that since both the sense and denotation are about states of affairs, and since the sense more broadly refers to possible ones, that the sense repeats the structure of the proposition at a higher (broader) level. The next point I do not get, but perhaps it is the following. For Kant, we make judgments, which have a subject-predicate structure, and our categories of judgment themselves have such a subject-predicate structure. Therefor, the structures in each are parallel (or isomorphic), but perhaps for some reason they are not identical. But in Russell, the sense of the proposition and the proposition itself are both propositions. And I suppose the important difference is that it is not that their structures are isomorphic but rather that they are one in the same. The next point is also very difficult. It seems we begin by recalling Kant’s common sense, which assumes that anything we encounter can be processed in such a way that we may form a judgment of it. In a similar vein, Russell thinks that all significant propositions can be either true or false. There might be more to it, so please refer to the quotation above.] [The third and final parallel between Russell and Kant is also hard for me to grasp. Let me quote it first:]

Finally, ‘The true and the false are supposed to remain unaffected by the condition which grounds the one only by rendering the other possible’ (DR 153/192). That is, sense does not explain the genesis of the true and the false, but merely conditions them, just as Kant fails by not providing a truly genetic transcendental account.
(SH 124)

[Perhaps the idea is the following. Sense holds whether it objectively is true or false. But since it is about the possibility of the state of affairs, it somehow “conditions” (creates the conditions for) the true and the false. Yet, there is another matter to be concerned with, namely, the question of how truth and falsity come about in the first place. Russell’s account does not explain how this happens. In a similar vein, Kant does not provide a genetic transcendental account of synthesis.] The Russellian account presents certain difficulties. And they become apparent when on its basis “we try to give some kind of grounding to sense” (124). There are two ways we might do so. 1) [The idea here seems to be the following. We are taking sense to be at a higher level than the proposition that expresses it, perhaps since the proposition refers merely to an actual state of affairs but sense more broadly to possible ones. One possible way for grounding sense would be somehow to specify it by rendering it into propositional form. But that is not grounding it, since sense is already on a more basic level than the proposition. Let me quote, since I probably have it wrong:] “Deleuze specifies two ways in which we might do this: ‘We are then in a strange situation: having discovered the domain of sense, we refer it only to a psychological trait or a logical formalism’ (DR 153/191–2). That is, we might take the latter case, and simply specify sense in terms of the proposition itself, but this just involves repeating the proposition at a higher level without explaining it” (124). 2) [I again am not following the second way, as it seems similar to my interpretation of the first. It seems there is another way, which is to explicitly state in propositional form the sense. So if we believe that it is raining, then we might write with quotation marks, “I believe it is raining.” But this proposition refers to more than merely the sense that I believe it is raining, because now we are saying that I believe (I have a subjective belief) that I believe (objectively speaking) that it is raining. Now, since we are trying to explicate the root sense in propositional form, we now would write, “I believe that ‘I believe that it is raining’”.Then there are two problematic possibilities that might follow. One is that this regresses infinitely and thus never reaches a root sense. The other possibility is that the regress reaches a fundamental proposition of consciusness, like Descartes’ cogito. But we saw already that this is problematic, on account of “difficulties of common sense with which we began the chapter” (I am not sure how they apply here, but perhaps because such a fundamental proposition is representational but for some reason should not be. I am just guessing). Let me quote, as I am not sure here:]

Otherwise, we might try to find the root of the sense of propositions. As the sense of a proposition is itself another proposition, then, Deleuze notes, we quickly fall into a regress, as we attempt to determine the sense of the sense of the proposition, and so on. Either this regress is infinite, or we stop with a ‘first proposition of consciousness’ (DR 155/194), such as Descartes’ cogito, thus leading us back into the difficulties of common sense with which we began the chapter. As we can see, Russell takes up this Cartesian solution when he notes that expression and indication are identical in reflective belief statements.
(SH 124)

[The next paragraph is also hard for me to grasp. It seems we merely need to note the following. Deleuze has a solution to prevent this problematic regress. That solution has something to do with his notion of the Idea, which we deal with in the next chapter. What we need to know now is that “what will give sense to propositions is something that is different in kind from the propositional, responsible for the constitution rather than simply the conditioning of truth”. I quote:]

In order to avoid the kind of regress that threatens the Russellian model of sense, Deleuze instead proposes a difference in kind between the transcendental and empirical operations of sense: ‘from this point of view, sense is the veritable loquendum, that which in its empirical operation cannot be said, even though it can be said only in its transcendental operation’ (DR 155/193). While it is ‘easier to say what sense is not than to say what it is’, (DR 155/193), Deleuze makes clear in this section | that it is ‘like the Idea which is developed in the sub-representative determinations’ (DR 155/193). We will deal with this notion of the Idea in the next chapter, but for now, we can note that what will give sense to propositions is something that is different in kind from the propositional, responsible for the constitution rather than simply the conditioning of truth (‘truth is a matter of production, not of adequation’ [DR 154/192]), and no wider than that which it conditions.
(SH 124-125)

Citations from:

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

Or if otherwise noted:

Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.


Russell, Bertrand (1940), An Inquiry into Meaning and Truth, London: George Allen and Unwin.



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