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Wittgenstein and Quine on the Problem of Intensionality
By: Tamela Ice

Ludwig Wittgenstein and W. V. O. Quine attempt a similar resolution to the problem of the logical form of intensional propositions (often referred to as prepositional attitudes or reported speech). Some examples of intensional propositions include “Genet said that crime is the highest form of sensuality”, “Mary thinks that Henry is in love with her”, or “Amy believes Tom is a killer.” Intensional propositions are mental states, that is, what is stated is the thought of the speaker. The problem at issue in this paper is how Wittgenstein and Quine attempt to establish the logical form of intensional propositions. Although there are differences in the proposed resolutions of Wittgenstein and Quine, both philosophers want to make intensional propositions assertions of a fact, thus eliminating the speaker (or believer, etc.) from the proposition. I will first explicate the proposed resolution of each philosopher. Next, although there are numerous problems with the resolutions proposed by Wittgenstein and Quine, I will only bring to the reader’s attention what I perceive as the most obvious difficulties. I will point out that it is not clear that the end result is a molecular proposition, that Moore’s paradox raises a problem for intensional propositions, and that the logical form of the proposition, if we consider it a molecular proposition, does not show what is said. Finally, I will present for consideration alternate ways of thinking about intensional propositions. My position is that logic is an incomplete system, that is, there are some propositions whose truth cannot be determined by the rules of logic. Moreover, a truth-relative stance may be the only way to deal with intensionality.

In his Tractatus Logico-Philosophicus, Wittgenstein says, “Propositions are truth-functions of elementary propositions.” This is generally understood to mean that all molecular propositions are truth functional. Truth-functional propositions have a definite truth-value and depend only on the truth-values of the atomic components of the propositions. For example, P&Q is true only when both P and Q are true.

At 5.541-5.542 in the Tractatus, Wittgenstein admits that there are some propositions that do not appear to fit the schema of truth-functional propositions, such as, for example, “A believes p”. Wittgenstein says that “it appears superficially as if the proposition p stood to the object A in a kind of relation … But it is clear that “A believes that p”, “A thinks p”, “A says p”, are of the “’p’ says p”: and here we have no co-ordination of a fact and an object.”

It has been argued that there are two problems with intensional propositions. That is, there is a problem concerning the violation of extensionality with these types of propositions and the problem of establishing the logical form of intensional propositions. Russell contends that Wittgenstein is concerned with the second of these problems, that of the “logical form of belief, i.e., what is the schema representing what occurs when a man believes.” It is important to note that Wittgenstein does not view intensional propositions as problematic because, in the Tractatus, he accepts the theory of extensionality. Moreover, Wittgenstein thinks the problem of logical form disappears as a result of this theory. The theory of extensionality alleges that
… once our language has been purged of nonsense, obscurity and confusion, intensional contexts will be eliminated. The extension of every compound expression will be entirely determined by the extension of its components: especially, the truth-value of every compound statement will be entirely determined by the truth-values of its components.

Now, what Wittgenstein has done in making “A believes p” synonymous with the assertion “p says p”, is to guarantee the truth-functionality of the proposition. That is, if p is true, the proposition is true. Likewise, if p is false, then the proposition is false. Thus, for Wittgenstein, extensionality is assumed and the problem of logical form is only a perceived problem.
Further explanation of Wittgenstein’s position is provided by Russell in the Introduction to the Tractatus. According to Russell’s understanding of Wittgenstein, the problem arises because, with regard to all intensional propositions,
… it seems natural to express the phenomenon [i.e., intensional propositions] in the form “A doubts p,” “A desires p,” etc., which makes it appear as though we were dealing with a relation between a person and a proposition. This cannot, of course, be the ultimate analysis, since persons are fictions and so are propositions, except in the sense in which they are facts in their own account. A proposition, considered as a fact on its own account, may be a set of words that a man says over to himself, or a complex image, or train of images passing through his mind, or a set of incipient bodily movements. It may be any one of innumerable different things. The proposition as a fact on its own account, for example the actual set of words the man pronounces to himself, is not relevant to logic. What is relevant to logic is that common element among all these facts, which enables him, as we say, to mean the fact which the proposition asserts [italics mine] … What does concern [the logician] in this problem of belief is the logical schema. It is clear that, when a person believes a proposition, the person, considered as a metaphysical subject, does not have to be assumed in order to explain what is happening. What has to be explained is the relation between the set of words that is the proposition considered as a fact on its own account, and the “objective” fact that makes a proposition true or false. This reduces ultimately to the question of the meaning of propositions, that is to say, the meaning of propositions is the only non-psychological portion of the problem involved in the analysis of belief. This problem is simply one of the relation of two facts, namely, the relation between the series of words used by the believer and the fact which makes these words true or false [italics mine] … the meaning of a proposition results from the meaning of its constituent words … Accordingly, the proposition as a whole does not really enter into what has to be explained in explaining the meaning of a proposition.

This lengthy quote reiterates and elaborates on the theory of extensionality. In addition, it is clear that the role of the person expressing the proposition is eliminated from the proposition. That is, the proposition “Aristotle believes that the life of contemplation is the best life” becomes, for Wittgenstein, “The life of contemplation is the best life.” The fact that Aristotle believes the assertion is irrelevant for Wittgenstein.

Mark Platts, in his Ways of Meaning, says that schema of intensional propositions is, as noted in Wittgenstein, ‘A said that p’ … and ‘p’ is a full declarative sentence … the content-sentence.” Platts reiterates the problem Wittgenstein alleges as “superficial,” that these types of sentences are relational, that is, that the speaker stands in relation to the sentence asserted. Platts does not want to reject this relation. Indeed, his concern is how Quine attempts to resolve the problem of the second term in the relation. In other words, how does Quine deal the ‘A says (believes, desires, etc.)’ part of the proposition?

Quine’s proposed resolution to the problem of the logical form of intensional propositions is similar to Wittgenstein’s conclusion. Platts sets up Quine’s proposed resolution by offering for consideration the proposition, “Genet said that crime is the highest form of sensuality.” Platt says that
… all we initially feel entitled to conclude is that Genet said something, that somebody said that crime is the highest form of sensuality, and that someone said something. In the first and third of these inferences, we feel entitled to draw the same conclusion no matter which saying of Genet’s is being reported; while in the second, there is no structure within the content-sentence involved and the same pattern of inference would work whichever saying of Genet’s was being reported. The content-sentence, as regards inference, seems unstructured and inert.

Since, as Platt contends, “there seem to be no intuitively acceptable inferences involving the structure within the content-sentence, Quine saw no point in assigning logical structure to that sentence.” Quine’s suggested resolution is to “combine ‘said that’ and the content-sentence (that which is said) “to form a one-place predicate ‘said-that-p, true or false of utters, of persons.”

It seems, at least to me, that what Wittgenstein and Quine both end up with is an atomic proposition. If, in the case of Wittgenstein’s resolution, ‘A believes (says, thinks, etc.) that p’ is of the form ‘p says p’, then all that is being asserted is p. Similarly with Quine’s resolution. In combining the subject and predicate to make a one-place predicate, all that is being considered is the predicate. The truth or falsity of an atomic proposition is determined by whether there is some fact in the world that corresponds to the proposition. Consider the proposition ‘Mary says Tom is a killer.’ On Quine’s account, we have a tacit understanding that a person asserts ‘Tom is a killer.’ If it is the case that Tom has killed, then the proposition is true. If Tom has not killed, then the proposition is false. However, it does not simply matter that we understand this to be an utterance of a person. It matters that who said it. The proposition cannot be understood to be true of all utterers. Nor can the proposition be determined as true or false for some utterers. The relevant portion of the proposition is that Mary says it. Without a subject, it seems odd to consider intensional propositions as molecular. What is in need of explanation is not the truth or falsity of the predicate, but the truth or falsity of the subject, ‘Mary says …’

Wittgenstein mentions G. E. Moore’s problem with establishing the logical form of intensional propositions. This has come to be called Moore’s paradox, which is stated as follows.

A person, A, who says ‘p, but I do not believe that p’ has asserted that p, and that implies that he believes that p. But he has also asserted that he does not believe that p. So, what he says implies a contradiction. But, on the other hand, what he says clearly does not imply a contradiction, since p need not contradict a statement to the effect that A does not believe that p.

This is a problem with regard to establishing the logical form of intensional propositions if the person who asserts the fact is included in the symbolization of the proposition. With a contradiction as the result, there is no information conveyed about p.

Wittgenstein says that “The truth of tautology is certain, of propositions possible, of contradiction impossible.” I see no other way of considering ‘p says that p’ than as a tautology or a contradiction, if we allow for intensional propositions to be counted as molecular propositions. For Wittgenstein, ‘A says that p’ is “senseless if p is a tautology.” Wittgenstein further states that “all propositions of logic say the same thing. That is, nothing.” It is plausible to assume that this includes intensional propositions.

Quine concedes that his resolution of combining the subject and predicate into a one-place predicate proposition does not apply to all intensional propositions. So, truth-functionality, and thus a logical form, cannot be established for intensional propositions.

It seems that both Wittgenstein and Quine admit that their resolutions are perhaps convenient, but not an ultimate solution to the problem of intensional propositions. It appears to be the case that logic is an incomplete system. That is, there are some propositions whose truth or falsity cannot be adequately determined by the rules of logic. This may be a difficult concept for logicians to consider, but it does not hail the end of philosophy. Logic is a useful tool of philosophy. However, we need not accept that if logic cannot adequately deal with particular types of propositions that these statements have no place in philosophy. We may want to reconsider the position of the medieval philosophers and consider whether intensionality belongs to the realm of faith rather than reason. We may also want to consider whether, with regard to intensional propositions (especially those concerned with belief) a truth-relative stance is preferable. Truth relativism is the view that
… a belief or opinion cannot be said to be true simply, but only true relative to a species a conceptual scheme, a social practice, a social group, or a person. To illustrate with the last mentioned kind: whenever a person, X, says or thinks: ‘p is true’, this can only mean ‘p is true for X’.

There is a problem with this view, namely that it has “the absurd consequence that if A believes that p is true and B believes that p is not true, there is no contradiction between what A and B believe!” Still, outside the realm of logic, it matters who asserts the claim.

There are numerous responses to the problem of the logical form of intensional propositions. My purpose in this paper has been to bring the issue under consideration, explicate two similar proposed resolutions, and consider some of the more obvious (perhaps even trivial) problems with the resolutions. It may be the case that logicians will find an adequate way of dealing with such propositions. Until then, I do not think we want to ignore the significance of the subject in such propositions, namely, the person who makes the claim.

Article Source: http://journal.ilovephilosophy.com

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