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The Problem of a Logical Theory of Belief Statements

Published online by Cambridge University Press:  14 March 2022

Nicholas Rescher
Nicholas Rescher*
Affiliation:
Lehigh University
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Abstract

It is shown that the logical theory of belief statements must be prepared to take into account relationships among statements which are subtler and more delicate than is requisite in other contexts. It is necessary here to draw distinctions (of a modal and semantical character) which the standard assertory logic can ignore with impunity. This is due to the fact that it is entirely possible to be in ignorance of various logical relationships (eg., entailment, equivalence, etc.) that in fact obtain among believed statements, and so, for example to believe the premisses of a valid deductive argument, and yet disbelieve the conclusion which follows from them. The implications of such difficulties for the logic of belief statements are examined.

Type
Research Article
Information
Philosophy of Science , Volume 27 , Issue 1 , January 1960 , pp. 88 - 95
Copyright
Copyright © 1959 by Philosophy of Science Association

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References

1 Analysis of Mind (London, 1921), p. 231.

2 Where confusion cannot result, I adopt the practice of antonymous use of symbols. Also, it should be noted that throughout, the arrow “→” is used to represent logical entailment or strict implication (and not material implication).

3 “Belief and Propositions,” Philosophy of Science, vol. 24 (1957), pp. 123-136.

4 Actually, P1 is almost certainly too strong as it stands. Note that it is equivalent to:

If we assume, as surely we must, that, if p is a contingent proposition, we can have . Thus (i) has the consequence of asserting that any contingent proposition is a possible object of belief for some person. This, it seems clear, can scarcely be advanced as a strictly logical truth. Thus P1 must surely in any event be weakened to:

5 This presupposition of a (complete) knowledge of the language, i.e., of meaning relationships, is, of course, far more plausible and defensible than a presupposition of a (complete) knowledge of all logical relationships. Just this consideration justifies acceptance of (C) below in the face of a rejection of an unqualified (Q-ii) above.

6 It follows by (C) if it is logically possible that a person x can believe “...” and yet not believe (or even disbelieve) “- - -”, then “...” and “- - -” cannot be synonymous. This would swiftly lead to the conclusion that no two symbolically (inscriptionally) distinct propositional expressions can by synonymous, were it not for our stipulation of a complete knowledge of the language. Just this failure to stipulate a knowledge of the language had led several writers into the anomalous position of a categorical denial of synonymy among inscriptionally distinct expressions. See N. Goodman, “On Likeness of Meaning,” Analysis, vol. 10 (1949), pp. 1-7. This paper occasioned lively controversy, much of which is cited in Goodman's subsequent paper “On Some Difference about Meaning,” ibid., vol. 13 (1953), pp. 90-96.

7 The starting point of this debate was Alonzo Church's criticism (“On Carnap's Analysis of Statements of Assertion and Belief,” Analysis, vol. 10 [1950], pp. 97-99) of the analysis of belief statements proposed by R. Carnap in Meaning and Necessity (Chicago, 1947). Church presents an argument—whose force is, to my mind, conclusive—directed “against alternative analysis [of statements of assertion and belief] that undertake to do away with propositions in favor of such more concrete things as sentences”. Attempts to answer Church include: I. Scheffler, “An Inscriptional Approach to Indirect Quotation,” Analysis, vol. 14 (1954), pp. 83-90; H. Putnam, “Synonymity and the Analysis of Belief Sentences,” Analysis, vol. 14 (1954), pp. 114-122. See also A. Church, “Intensional Isomorphism and Identity of Belief,” Philosophical Studies, vol. 5 (1954), pp. 65-73.