Epistemic Modality: The Problem of a Logical Theory of Belief Statements

  • Nicholas Rescher
Part of the Synthese Library book series (SYLI, volume 17)


This discussion is of an exploratory nature. It does not attempt the presentation of any accomplished theory of the logic of belief statements. Rather, its objectives are of a more limited scope. The present chapter merely attempts to examine some of the problems and difficulties that confront the construction of such a theory. Despite this limitation, the purpose of these considerations is constructive rather than negative, because their main aim is to determine some of the characteristic features which must inevitably form a part of any adequate theory of belief able to overcome these difficulties.


Belief Statement Logical Theory Logical Relationship Rational Belief Philosophical Logic 
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  1. 1.
    Analysis of Mind (London, 1921), p. 231.Google Scholar
  2. 2.
    A great many complexities inhere in the conception of ‘acting as though’. The man who ‘acts as though’ he had a headache simply acts the way people generally do when they have headaches. But the man who ‘acts as though’ the building were on fire acts the way people generally do when they believe the building to be on fire. In many or most cases ‘acting as though’ involves an inherent reference to beliefs. This is why it seems to me unworkable to adopt alternative (i) and explicate the concept of belief in terms of ‘acting as though’.Google Scholar
  3. 3.
    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).Google Scholar
  4. 4.
    ‘Belief and Propositions’, Philosophy of Science 24 (1957) 123–136.Google Scholar
  5. 5.
    Actually, (R1) is almost certainly too strong as it stands. Note that it is equivalent to:Google Scholar
  6. (i) ~(p→q)→(∃x) ◊ [B(x,p)&~ B(x,q)].Google Scholar
  7. If we assume, as surely we must, that, if p is a contingent proposition, we can have ~ (p → [p & q]), then (i) entails, (∃x) ◊ B(x,p). 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:Google Scholar
  8. (ii) □ (∀x) [B (x,p) → B(x,q)] (pq.Google Scholar
  9. 6.
    This conception of an ‘obvious consequence’ has a close relationship to the conception of a ‘surface tautology’ introduced into the logic of belief (for purposes quite similar to ours) by Jaakko Hintikka. See his papers “‘Knowing Oneself” and Other Problems in Epistemic Logic’, Theoria 32(1966) 1–13 (see especially p. 3) and ‘Are Logical Truths Tautologies?’ in Existenz und Analytizität: 4. Forschungsgespräch des internationalen Forschungszentrums für Grundfragen der Wissenschaften, ed. by P. Weingartner (Salzburg, 1966).Google Scholar
  10. 7.
    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. The distinction between the source of the belief statement (its assertor) and its subject (the person about whose beliefs the assertion is made) is crucial here. If in the source’s language, say, ‘vixen’ and ‘female fox’ are synonyms, then he has said the same thing when he says ‘Smith saw a vixen’ and ‘Smith saw a female fox’. If source wants to claim (say) that ‘Smith does not realize that a female fox is a vixen’ then he (source) had best say ‘Smith does not realize that a female fox is also called a “vixen”’. Otherwise the familiar use-mention puzzles will arise in this context.Google Scholar
  11. 8.
    It follows by (C) it 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 10 (1949) 1–7. This paper occasioned lively controversy, much of which is cited in Goodman’s subsequent paper ‘On Some Difference about Meaning’, ibid., 13 (1953) 90–96.Google Scholar
  12. 9.
    The starting point of this debate was Alonzo Church’s criticism (‘On Carnap’s Analysis of Statements of Assertion and Belief’, Analysis 10 (1950) 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. Scheflier, ‘An Inscriptional Approach to Indirect Quotation’, Analysis 14. (1954) 83–90; H. Putnam ‘Synonymity and the Analysis of Belief Sentences’, Analysis 14 (1954) 114–122. See also A Church, ‘Intensional Isomorphism and Identity of Belief’, Philosophical Studies 5 (1954) 65–73.Google Scholar
  13. 10.
    This chapter is a somewhat expanded version of the author’s paper of the same title in Philosophy of Science 27 (1960) 88–95. It was thus written some years before the appearance in 1962 of Jaakko Hintikka’s highly interesting but controversial book, Knowledge and Belief (Ithaca, 1962), perhaps the principal defect of which resides in just the point at issue here — viz., in enunciating rules for a logic of belief in the absence of the development of a prior test-criterion for the acceptability of such rules.Google Scholar

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© Springer Science+Business Media Dordrecht 1968

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  • Nicholas Rescher

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