Abstract

This collection of twenty-three papers from the period 1934-1960 is concerned with formal number theory and syntax, axiomatic set theory, truth functions, and quantification theory. In the first group appear "Concatenation as a basis for arithmetic" and "Definition of substitution," among others; the second includes "Set-theoretic foundations for logic," "On ω-inconsistency," and "Element and number." Quine's important articles "Completeness of the propositional calculus" and "Cores and prime implicants of truth functions" are in the third section; the last one includes "A proof procedure for quantification theory" and "Church's theorem on the decision problem". These are but a few of many important articles. All the articles have been reset in a new, perspicuous type-face which makes study easier. Several important papers which were omitted should, in the reviewer's opinion, have been included, but this is a minor quibble. Quine's stature in modern logic can be gauged by examining these papers.—P. J. M.