David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Oxford University Press (2004)
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|
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Citations of this work BETA
Justin Clarke-Doane (2013). What is Absolute Undecidability?†. Noûs 47 (3):467-481.
Luca Incurvati (2012). How to Be a Minimalist About Sets. Philosophical Studies 159 (1):69-87.
Andrew Arana (2010). Proof Theory in Philosophy of Mathematics. Philosophy Compass 5 (4):336-347.
Tim Button (2011). The Metamathematics of Putnam's Model-Theoretic Arguments. Erkenntnis 74 (3):321-349.
Alex Oliver & Timothy Smiley (2006). What Are Sets and What Are They For? Philosophical Perspectives 20 (1):123–155.
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