Cours de Logique by Marcel Barzin; La Relativite de la Logique by Louis RougierReview by: Alonzo ChurchThe Journal of Symbolic Logic, Vol. 11, No. 3 (Sep., 1946), p. 100Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2266775 .

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100 REVIEWS

ford with making this clear. C. I. Lewis has also remarked it in his recent Carus lectures. The first assumption, that free will is presupposed if regret is to be justified is mentioned rather than proved, and is I think, open to doubt. CHARLES A. BAYLIS

FREDERIC HAROLD YOUNG. Charles Sanders Peirce. America's greatest logician and most original philosopher. A paper delivered 15 October 1945, at Milford, Pennsyl- vania, before the Pike County Historical Society. Privately printed 1946, 8 pp.

A brief biography and an appreciation of Peirce's attainments in logic and philosophy; an estimate of his logical work by Paul Weiss, quoted from IV 38 (6). CHARLES A. BAYLIS

C. G. HEMPEL. On the nature of mathematical truth. The American mathematical monthly, vol. 52 (1945), pp. 543-556.

In an explanatory article that is clear, simple, and straightforward, the author "exhibits the system of mathematics [arithmetic, algebra, and analysis] as a vast and ingenious con- ceptual structure without empirical content." He first points out the major difficulties in the way of regarding mathematical propositions as either self-evident or empirical. He then shows how mathematics can be formulated as an axiomatized deductive system, and presents a brief account of Peano's axiom system for the natural numbers as an example. He indicates how the primitive concepts of this system can be derived from logical concepts and the primitive propositions from logical principles. CHARLES A. BAYLS

C. G. HEMPEL. Geometry and empirical science. Ibid., pp. 7-17.

MORRIS R. COHEN and ERNEST NAGEL. An introduction to logic and scientific method. Abridged edition. George Routledge & Sons, Ltd., London 1939, vii + 245 pp.

The abridged edition consists of Chapters VI-XVI, XIX, XX of the original edition (5251), page by page the same as the original chapters, and renumbered as Chapters I-XIII.

ALONZO CHURCH

MARCEL BARZIN. Cours de logique. Mimeographed. Volume I, 1939, 113 + II pp. Volume II, 1940, 65 pp. Maison Desoer, Liege. [Cf. IV 91 (l).]

Louis ROUGIER. La relativity de la logique. Revue de metaphysique et de morale, vol. 47 no. 3 (for 1940, pub. 1942), pp. 305-330.

This differs from V 124(2) only to the extent of a few very minor amendments, and some slight changes of notation. See further the author's VII 127(3). ALONZO CHURCH

G. BOULIGAND. Les crises de l'unite dans la Math~matique. Revue generate des sciences Pures et appliqudes, vol. 52 no. 11-12 (1945), pp. 215-221.

A popular discussion of the r6le of logistic formalization in the foundations of mathematics, the opposition between formalism and intuitionism, the logical antinomies, the Skolem paradox, and related topics.-The term "formalism" (which has frequently been used in reference to the Hilbert school, though not adopted by the Hilbertians themselves) is em- ployed by the author in an unusual sense, since he writes of the formalists that: "Ils r6- pudient completement l'opinion de Hilbert, qui dans la Mathdmatique, voyait des 6tres pr6existants, auxquels sont applicables les calculs de la logique."

Inevitably, in view of the length of the paper, the account of particular logistic systems- especially the functional calculus of first order and the Zermelo axiomatic set theory-is inadequate to support the general discussion. ALONZO CHURCH

K. CHANDRASEKHARAN. Partially ordered sets and symbolic logic. The mathematics student, vol. 12 (1944), pp. 14-24.

The first part of the paper is a brief historical summary of the development of symbolic logic, with mention especially of Boole and his successors, of Peano, Whitehead and Russell, Hilbert. Then the author turns to an outline, with emphasis on the lattice-theoretic view- point, of various propositional logics - classical two-valued, Lukasiewicz 's n-valued, Heyting's intuitionistic, Lewis's S5.

A few statements occur which, although authority can be found for them in the literature,

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