By Raymond Pearl

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Conjoined, (2b) and (2a) imply: (2) Numbers and objects of any similar sort do not act on us. Conjoined, (2) and (1) imply (0). I offer this version as an ideal type to which the arguments sketched in the passages quoted above are approximate realizations (mostly more explicit about assumption (2) than about assumption (1». Penelope Maddy (most recently in her contribution to the present volume) has argued that any premise like (2) might be questioned or qualified without falling into pre-Fregean confusion or neo-Platonic superstition.

Does not help us to decide the relevant identity questions. Requiring identity questions to be always in principle decidable, Frege rather abruptly breaks off and introduces extensions. Was he right to do so? Given that extensions themselves had to be conventionally determined, and that the whole system was inconsistent, the answer is not obvious. Frege occasionally entertained the idea that classes and numbers were "unauthentic" objects for which the law of excluded 50 Frege [1884], § 64. Cf.

1973] "Mathematical Truth", Journal of Philosophy, 70, 661-79. Reprinted in Paul Benacerraf & Hilary Putnam, Philosophy of Mathematics, second edition, Cambridge: Cambridge University Press, 1983, 403-20. Benacerraf, Paul & Hilary Putnam [1983] Philosophy of Mathematics, second edition, Cambridge: Cambridge University Press. Bonevac, Daniel A. [1980] Reduction in the Abstract Sciences, Indianapolis: Hackett Publishing Company. Burgess, John P. [1983] "Why I Am Not a Nominalist", Notre Dame Journal of Formal Logic, 24, 93-105.