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Papers in philosophical logic. (English) Zbl 0914.01028

Cambridge Studies in Philosophy. Cambridge: Cambridge University Press. vi, 234 p. £12.95, $ 17.95/pbk; £35.00, $ 54.95/hbk (1998).
This collection of previously published, satisfyingly brief articles in philosophical logic is the first of a three-part reprint series by the author. They address a wide range of subjects including formalisms of natural language, model-theoretic investigations of intensional logic, and issues raised by Nelson Goodman, Carnap’s Aufbau, and anti-mechanistic arguments based on Gödel’s theorem. In “Mathematics is Megethology” Lewis picks on the unwritten “axioms” of set theory and wittily depicts the difficulties of arriving at an understanding of the odd nature of the singleton set and the imperviousness of mathematics to such merely philosophical criticisms. His rich alternative to the usual development of set theory is not one, as he acknowledges, that will be taken up by mathematicians; his critique, however, is one which should interest anyone who has had doubts about how set theory is presented.

MSC:

01A75 Collected or selected works; reprintings or translations of classics
00A69 General applied mathematics
51-XX Geometry
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