Bemerkungen zur Hypothesenwahrscheinlichkeit by Hans ReichenbachReview by: Ernest NagelThe Journal of Symbolic Logic, Vol. 5, No. 3 (Sep., 1940), p. 124Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2266882 .

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124 REVIEWS

hypotheses (e.g., of the hypothesis that the probability of getting heads with a coin is on the evidence of 100 trials showing 49 heads). It turns out that the problem is one

in inverse probabilities and requires the use of Bayes' Theorem. Dr. Geiringer carefully explains that when the requisite initial probabilities are supplied (e.g., the initial proba- bilities of randomly selected coins falling heads uppermost with a probability of p), a unique and valid solution is obtainable.

Most of the paper, however, is given over to a criticism of writers like Reichenbach who maintain that the mathematical theory makes possible the calculation of the probability of such a theory as the quantum theory, and who believe that the traditional problems of induction and of the application of axiomatized theories to experience are to be settled by appeal to the calculus of probability. Dr. Geiringer's criticisms are trenchant and, to this reviewer, in the main conclusive. She points out that Reichenbach's definition of "the probability of scientific theories" does not correspond to the ordinary meaning of this phrase, that the assumptions required on that definition before probabilities can be calcu- lated are not warranted by the facts in the case, that his Probability Logic and Inductive Rule are not sufficient for estimating the validity of theories, and that the Anwendungs- problem is not a question which is "fundamentally" a matter for probability theory.

ERNEST NAGEL

HANs REICHENBACH. Bemerkungen zur Hypothesenwahrscheinlichkeit. Ibid., pp. 256-260.

This is a reply to the above article by Dr. Geiringer. Reichenbach finds little merit in the points directed against him, and reaffirms his views on the probability of theories.

ERNEST NAGEL

Louis ROUGIER. La relativity de la logique. Ibid., pp. 193-217. M. Rougier defends his thesis of the relativity of logic against two forms of absolutism,

the absolutism of Aristotle and the absolutism of Wittgenstein. He traces briefly the changes in the conception of logic from Aristotle to Hilbert, showing how the notion of logical principles as self-evident propositions, true in themselves, has given way to the notion of a hypothetico-deductive system, in which no statements are essentially undemon- strable. He finds untenable the radical empiricism of Wittgenstein, based upon an absolute classification of statements as tautological, contradictory, synthetic, or meaningless. He maintains that Wittgenstein's thesis is valid only for a two-valued logic, that is to say, for only one type of logic amongst an infinite variety. Classifying these logics as multi- valued logics, modal logics, weakened forms of the two-valued logic, and logic conceived in the most general way possible, he gives a clear statement of the relations of these dif- ferent types and suggests uses for them in physics, mathematics, and probability-logic. Although he succeeds in showing that the decision to call a given sentence contradictory or meaningless, and so on, depends on the vocabulary and syntax of the language in which it occurs, he seems to stress unduly the purely relative aspect of logic. The successful handling of the subject-matter must still be a factor in the choice of one's syntactical rules, and Wittgenstein's empiricistic thesis can be adapted to any one of M. Rougier's infinite variety of logics. M. W. GROSS

J0RGEN JORGENSEN. Reflexions on logic and language. Ibid., pp. 218-228. The main purpose of this article is "to suggest the possibility of a peculiar kind of

logic which I call semantical logic and which I believe is the very thing which the advocates of a so-called intentional logic (at least in one sense of this word) have in mind when they assume such a logic to be a necessary foundation for the extensional systems of logic." Mr. J0rgensen excludes such terms as the logical constants and the logical copula as being

expressive linguistic phenomena and semantically superfluous, thus leaving only nouns or

names. He formulates the task of logic as follows: "State the rules by which simple or compound nouns may be constructed from other nouns without observation of the phe- nomena which are represented by the names." He gives three rules, analogous to the rules of simplification, adjunction, and commutation, and defines the relation of entail-

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