Philosophical Quarterly 54 (214):16 - 37 (2004)
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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References found in this work BETA
Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility.Stewart Shapiro - 2003 - British Journal for the Philosophy of Science 54 (1):59--91.
Frege Meets Dedekind: A Neologicist Treatment of Real Analysis.Stewart Shapiro - 2000 - Notre Dame Journal of Formal Logic 41 (4):335--364.
Citations of this work BETA
On the Exhaustion of Mathematical Entities by Structures.Adrian Heathcote - 2014 - Axiomathes 24 (2):167-180.
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