Introduction á la Philosophie. by Louis De Raeymaeker; Inleiding tot de Wijsbegeerte by L. DeRaeymaekerReview by: Alonzo ChurchThe Journal of Symbolic Logic, Vol. 14, No. 3 (Sep., 1949), p. 186Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2267063 .

Accessed: 11/06/2014 01:58

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to TheJournal of Symbolic Logic.

http://www.jstor.org

This content downloaded from 188.72.96.185 on Wed, 11 Jun 2014 01:58:10 AMAll use subject to JSTOR Terms and Conditions

186 REVIEWS

take for (Elx) (Ely) [Fx & Fy & Div xy]. A similar remark applies to the definitions of (E3x)Fx and (Emx)Fx. The negation-formulae of the definitions of (E2x)Fx and (E3x)Fx are also in need of correction.- The passage dealing with Lewis's strict implication and truth-tables on pages 113-115 is obscure. The author seems to imply that Lewis's system could be "built up" with the help of such (four-valued) tables in essentially the same way as the system of ordinary propositional logic can be built up from truth-tables. This, how- ever, is not correct (VI 37(4)).

There is a useful bibliography added. A forthcoming second volume will deal with the logic of relations, etc. G. H. v. WRIGHT

Louis DE RAEYMAEKER. Introduction a la philosophie. Troisibme edition revue et

corrigde. Editions de l'Institut Supdrieur de Philosophie, Louvain 1947, 277 pp. L. DE RAEYMAEKER. Inleiding tot de wijsbegeerte. Tweede, herziene uitgave. Uit-

geverij Het Kompas, Antwerp, and L. J. Veen's Uitgeversmij., Amsterdam, 1948, 271 pp. These are new editions of XIII 123(1, 2). Among other revisions, the footnote to which

the reviewer objected in the English edition has been amended to give the more acceptable list of names, Frege, Peano, Russell, Whitehead. ALONZO CHURCH

A. WOLF. Textbook of logic. Second edition revised and enlarged. George Allen &

Unwin, London 1938 (reprinted 1943, 1948), 455 pp. Like the first edition (1930), this is a textbook of traditional logic, and only some parts

of the Appendix (added in the second edition) are within the field of the JOURNAL.

Among the valid immediate inferences the author includes inversion of universal proposi-

tions. To this the suggested counter-example, "No novelist has written a completely satis-

factory novel"-whose inverse would be "Some person who is not a novelist has written a

completely satisfactory novel"-is discussed in the Appendix. The explanation is given that

the universe of discourse here is that of novelists, and inversion would involve trespassing

outside the universe of discourse; also that the inverse is self-contradictory. It seems to be

meant that inversion has an exception when the subject coincides with the universe of dis-

course.-However, no sufficient warning of such an exception is given when inversion is

treated in the body of the work. And the reviewer would add that (unless the author holds

that the subject always coincides with the universe of discourse) it is easy to modify the

counter-example to avoid the exception; e. g., "No one known to me has written a com-

pletely satisfactory novel," or "No nineteenth century novelist has written a completely

satisfactory novel." In the discussion of existential import which then follows, it is held that none of the four

traditional kinds of propositions (SaP, SeP, SiP, SoP) need imply existence, i. e., reality,

of the subject S. The example is cited, "Some of the cruisers for which provisions were made

in the last budget are not being constructed," to show that SoP may be true though S is not

real.-However, this is insufficient, if the purpose is to preserve the traditional inference

by subalternation from SeP to SoP. For this purpose the author should rather contend that

SoP and There are no S's may be true together (e. g., "Some of the cruisers provided for

in the budget are not being constructed" and "There are no cruisers provided for in the

budget"). But it is not clear that he means to do this. And such a contention would be at

least not very plausible (cf. Lewis Carroll 674). Another section of the Appendix is intended "to give a general idea of what Symbolic

Logic is about." But it falls short even of what might be done within the twelve pages allotted,

partly because the algebra of logic is emphasized rather than the logistic method proper,

partly because disproportionate space is given to the author's objections against such matters

as the use of the null class and of material implication. ALONZO CHURCH

W. H. WERKMEISTER. An introduction to critical thinking. A beginner's text in logic. Johnsen Publishing Co., Lincoln, Nebraska, 1948, xx + 663 pp.

Part III of this book (154 pp.) which would be of concern to readers of this JOURNAL covers

the truth tables and the calculi of propositions and propositional functions. A short chapter

handles the class calculus with a note on the paradoxes. All of these last (including the

This content downloaded from 188.72.96.185 on Wed, 11 Jun 2014 01:58:10 AMAll use subject to JSTOR Terms and Conditions