Frege: Tradition and Influence

This revised second edition of Frege's "Conception of Numbers as Objects" extends the discussion of the first edition in a number of directions. A detailed critical appraisal of Hartry Feild's Nominalism is included, and a response to Field's critical study of the first edition which appeared in the Canadian Journal of Philosophy in 1984. Discussions have been added of Frege's response to Russell's Paradox, and of the prospects for extending the variety of logicism canvassed in the first edition beyond formal number theory. A more fully formalised version of the second-order system sketched in the concluding part of the first edition is provided together with a proof of its consistency. New appendices have been added concerning the application of arithmetic, logicistically construed, and of the worries, voiced by several reviewers of the first edition, concerning the impredicativity of Frege's definition of the Ancestra and of the axiom, N=, stating the condition for the identity of numbers in terms of one-to-one correspondence between concepts. Collectively, the additions deepen and strengthen the case for a neo-Fregean philosophy of mathematics. Advanced undergraduate and graduate students of philosophy of mathematics and philosophy of language, and professional philosophers.