Truths of Logic by William KnealeReview by: Charles A. BaylisThe Journal of Symbolic Logic, Vol. 12, No. 3 (Sep., 1947), p. 101Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2267242 .

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REVIEWS 101

less" because so many statements would become undecidable. He proposes treating a predicate applicable to such a vague impression or image as an indeterminate set of more precise predicates, "-. -p, q, r..- ." The properties of such a set would resemble an incom- plete disjunction, "- *p v q v r*** ," save that the set could be true though the values of all disjuncts were indeterminate. Though these are alternatives to the traditional logic, none of them contradicts it for in each of them some crucial term such as "true" or "proposi- tion" undergoes modification.

Waismann suggests that our preference for Aristotelian logic may be due to the exigencies of living which require us to make decisions. Hence we tend to fashion our statements in such a way that the largest possible range of them shall be decidable. But under other cir- cumstances we might prefer a logic which stresses undecidability. CHARLES A. BAYLIS

WILLIAM KNEALE. Truths of logic. Ibid., pp. 208-234. In what seems to this reviewer a sound discussion of some philosophical aspects of logic,

Kneale proposes a unification of two theories of the nature of (propositional) logic: (1) that it is the science of the principles of valid inference, i.e., a system of entailment assertions, and (2) that it is a system of logically necessary truths or truisms such as p-or-not-p. In each case the science includes a higher order and minimal set of principles of inference by which from certain members of the lower order set the others are derived. After defending Lewis's system of strict implication, Kneale brings the two theories together by pointing out that not only can entailment be defined in terms of logical necessity, as Lewis does, but also that, instead of saying "It is logically necessary that p or not p," we can say "Auy proposition whatsoever entails the proposition that p or not p." Thus, "The two traditional accounts of logic are therefore equivalent and it seems to be only a matter of convenience whether we say that the truths of logic are principles of entailment or principles of necessity." This view is not novel-it is at least implicit in Lewis's own work-but it is well presented with clear and cogent discussion of the relevant factors.

Kneale next tries to clarify the term "proposition," distinguishing it carefully both from "sentence" and from "thought." He urges that truths about propositions are truths about the concepts involved. He points out some of the difficulties of Wittgentstein's language view of logic as it is presented in 2812, and of Carnap's exclusively syntactical view as stated in IV 82. Accepting instead Carnap's later semantical view as presented in his VIII 36, he

urges that any satisfactory logic must deal with propositions, and that its fundamental language conventions must be adapted to the relations among these designata of sentences. While challenging Carnap's identification of the logical and the a priori, Kneale accepts his conclusions that it is possible to formulate logic absolutely in terms of entailment, and that such a system is like that of Lewis in that it includes modality and is non-extensional.

CHARLES A. BAYLIS

FRIEDRICH WAISMANN. Verifiability (Part II of a symposium). Aristotelian Society, supplementary volume XIX (1945), pp. 119-150.

Waismann urges that one important difference between an a priori and an empirical con- cept is that the latter has an open texture (Porositat) which always leaves it subject to fur- ther specification. He distinguishes this characteristic from vagueness which involves equivocal usage which can be avoided by more precise definitions. Definitions of open terms on the other hand are always subject to emendation in respects not previously delimited. As a consequence of this, he maintains, no material object statement, containing as it must

one or more open terms, can be fully specified in terms of possible sense-data verifications. It is not merely the existence of an unlimited number of tests which prevents conclusive

verification of empirical statements, he argues, but also the open texture of the terms in-

volved. Open texture operates again, he urges, in the relation between an alleged law of nature

and its verificatory experiences. Since we recognize that no one observation disproves such a law, it cannot be that the law strictly implies these observational consequences. It is at most the law plus a host of additional suppositions which implies a set of observable conse-

quences. But these extra suppositions not only are not usually specified, but cannot be, he maintains, because the class of them also has an open texture. CHARLES A. BAYLIS

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