Oxford University Press (2004)

Authors
Michael Potter
Cambridge University
Abstract
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Keywords Set theory Philosophy
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Call number QA248.P675 2004
ISBN(s) 0199269734   9780199269730   9780199270415
DOI 10.1093/mind/fzi764
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Objectivity and Reliability.Justin Clarke-Doane - 2017 - Canadian Journal of Philosophy 47 (6):841-855.
The Iterative Conception of Set: A (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
The Deflationary Theory of Ontological Dependence.David Mark Kovacs - 2018 - Philosophical Quarterly 68 (272):481-502.
Set-Theoretic Pluralism and the Benacerraf Problem.Justin Clarke-Doane - 2020 - Philosophical Studies 177 (7):2013-2030.

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