PhilosophyMathematics

George Boolos

2000.9.1HISTORY AND PHILOSOPHY OF LOGIC

DOI: 10.1080/01445340051095856

Abstract

Part 1 Studies on set theory and the nature of logic: the iterative conception of set reply to Charles Parsons' "Sets and Classes" on second-order logic to be is to be a value of a variable (or to be some values of some variables) nominalist platonism iteration again introductory note to Kurt Godel's "Some Basic Theorems on the Foundations of Mathematics and their Implications" must we believe in set theory?. Part 2 Frege studies: Gottlob Frege and the foundations of arithmetic reading the "Bergriffsschrift" saving Frege from contradiction the conspiracy of Frege's "Foundations of Arithmetic" the standard of equality of numbers whence the contradiction? 1879? the advantages of honest toil over theft on the proof of Frege's theorem Frege's theorem and the Peano Postulates is Hume's principle analytic? Die Grundlagen der Arithmetik 82-83 (Richard Heck) constructing Cantorian counterexamples. Part 3 Various logical studies and lighter papers: zooming down the slippery slope don't eliminate cut the justification of mathematical induction a curious inference a new proof of the Godel Incompleteness theorem on "seeing" the truth of the Godel sentence quotational amibguity the hardest logical puzzle ever Godel's Second Incompleteness theorem explained in words of one syllable.

Citation format

BOOLOS, George. Logic, logic, and logic. HISTORY AND PHILOSOPHY OF LOGIC, 2000, 21: 223–229.