The New Logic by Anders WedbergReview by: Th. SkolemThe Journal of Symbolic Logic, Vol. 13, No. 2 (Jun., 1948), p. 122Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2267346 .

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122 REVIEWS

semiotic' overcomes its terminological obscurity it will not genuinely possess the status of being a science which can usefully "serve as a guide to many sciences."

ARTHUR FRANCIS SMULLYAN

ANDERS WEDBERG. Den nya logiken (The new logic). Studentf6reningen verdandis smAskrifter nos. 477, 478. Part I, 61 pp., and Part II, 71 pp.; Albert Bonniers Forlag, Stock- holm 1945.

This book gives a popular introduction to the most elementary and fundamental parts of modern symbolic logic. Indeed, symbolic logic is very little known in the Scandinavian countries. The author has therefore written this book with the intention of showing those who are acquainted only with the traditional Aristotelian logic how much more developed the new logic really is. In accordance with the popularizing purpose of the book, the author gives many illustrative examples, and he never enters upon technical difficulties. One may hope that this little book will convince its readers that modern logic is of great value and interest.

Part I deals with the calculus of propositions, the calculus of classes, the Aristotelian syllogisms from a modern standpoint, and the theory of relations.

In Part II the quantifiers are introduced. Further, the author explains the axiomatic method and formalization of theories. A chapter treats the relation between logic and mathematics. Here the criticism may be made that the author completely ignores intui- tionism. The incompleteness theorem of Godel and the theorem of Church on the non- solvability of the decision problem for the restricted functional calculus are briefly men- tioned. The book ends with considerations concerning the logical antinomies and the opposition between Platonism and conventionalism. TH. SKOLEM

ANDERS WEDBERG. Johdatus nykyiseen logiikkaan (Introduction to modern logic). Finnish translation of the foregoing by Otso Aalto, with a preface by Eino Kaila. Kustannu- sosakeyhtio Otava, Helsinki 1947, 150 pp.

DIMITRI RIABOUCHINSKY. Sur les nombres d'origine imaginaire et la notion de signe d'un nombre complete. Competes rendus hebdomadaires des seances de l'AcademiedesSciences (Paris), vol. 225 (1947), pp. 1104-1106. See Errata, ibid., vol. 226 (1948), p. 136.

Cf. XIII 55 (4,5). The indicated classification of this paper as "Logique Mathematique"' is erroneous, or at best extremely doubtful. ALONZO CHURCH

HANS A. LINDEMANN. Leibniz y la l6gica moderna. Anales de la Sociedad Cientifica Argentina, vol. 142 (1946), Pp. 164-176.

A semi-popular lecture, touching on Leibniz's project of a characteristics universalis. W. V. QUINE

ALDERTO E. SAGASTUME BERRA. Sobre filosoffa de las matemdticas. Ibid., pp. 177-192. A semi-popular lecture touching on the rise of modern geometry, the Cantorian infinities,

the antinomies, and the philosophical points of view of Kant, Poincar6, Russell, Hilbert, and Brouwer. W. V. QUINE

H. MEYER. On definitions in symbolic logic. Synthese, vol. 5 (1946), pp. 261-266, 353- 361.

The question is raised whether definitions in symbolic logic are mere abbreviations or "convey some specific concept which is indispendable for reasoning." Before attempting to answer this question, the author considers the nature of undefined terms. These he groups into three categories: (1) terms designating operations on symbols, (2) logical constants, (3) propositional functions. He is most concerned with the third category and seems to hold that propositional functions are to be identified with defining properties. Expressions designating classes are regarded as defined "in use" in such a way that the name of a class is always replaceable by the name of an extensional propositional function. There is much discussion of extensionality, contextual definitions, and Russell's theory of descriptions. There is also a somewhat elaborate illustrative example that deals with

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