Philosophical Quarterly 54 (214):16 - 37 (2004)

Authors
Stewart Shapiro
Ohio State University
Abstract
Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics.
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DOI 10.1111/j.0031-8094.2004.00340.x
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
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Citations of this work BETA

What is Neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.
Is Unsaying Polite?Berislav Žarnić - 2012 - In Majda Trobok, Nenad Miščević & Berislav Žarnić (eds.), Between Logic and Reality: Modeling Inference, Action and Understanding. Springer. pp. 201--224.
Debating (Neo) Logicism: Frege and the Neo-Fregeans.Majda Trobok - 2012 - In Majda Trobok Nenad Miščević & Berislav Žarnić (eds.), Between Logic and Reality. Springer. pp. 83--98.

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