By Penelope Maddy

Arithmetic depends upon proofs, and proofs needs to commence someplace, from a few primary assumptions. for almost a century, the axioms of set conception have performed this position, so the query of ways those axioms are adequately judged takes on a imperative value. imminent the query from a commonly naturalistic or second-philosophical perspective, *Defending the Axioms* isolates the ideal equipment for such reviews and investigates the ontological and epistemological backdrop that makes them acceptable. in spite of everything, a brand new account of the objectivity of arithmetic emerges, one refreshingly freed from metaphysical commitments.

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**Extra info for Defending the Axioms: On the Philosophical Foundations of Set Theory**

Russell, Bertrand [1907], ‘The regressive approach to studying the premises of mathematics’, repr. in his Essays in research, D. Lackey, ed. (New York: George Braziller, 1973), pp. 272–283. Shapiro, Alan [2002], ‘Newton’s optics and atomism’, in Cohen and Smith [2002b], pp. 227–255. one hundred forty four bibliog raphy Shapiro, Stewart [1997], Philosophy of arithmetic: constitution and Ontology (New York: Oxford collage Press). ——[2000], puzzling over arithmetic (Oxford: Oxford collage Press). Shapiro, Stewart, ed. [2005], The Oxford instruction manual of Philosophy of arithmetic and common sense (Oxford: Oxford college Press). Shoenﬁeld, J. R. [1977], ‘Axioms of set theory’, in J. Barwise, ed. , instruction manual of Mathematical common sense (Amsterdam: North Holland), pp. 321–344. Silverman, Allan [2003], ‘Plato’s center interval Metaphysics and Epistemology’, The Stanford Encyclopedia of Philosophy (Summer 2003 Edition), Edward N. Zalta (ed. ), URL=