David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
|Buy the book||$154.55 new (7% off) $165.00 direct from Amazon $165.78 used Amazon page|
|Call number||QA248.P675 2004|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
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.
Simon B. Duffy (2009). The Role of Mathematics in Deleuze's Critical Engagement with Hegel. International Journal of Philosophical Studies 17 (4):563 – 582.
Similar books and articles
Steve Awodey (2008). A Brief Introduction to Algebraic Set Theory. Bulletin of Symbolic Logic 14 (3):281-298.
A. Weir (1998). Naïve Set Theory is Innocent! Mind 107 (428):763-798.
Joseph S. Ullian (1969). Is Any Set Theory True? Philosophy of Science 36 (3):271-279.
F. A. Muller (2001). Sets, Classes, and Categories. British Journal for the Philosophy of Science 52 (3):539-573.
Gabriel Uzquiano (2005). Review of M. Potter, Set Theory and its Philosophy: A Critical Introduction. [REVIEW] Philosophia Mathematica 13 (3):308-346.
Richard Pettigrew (2009). On Interpretations of Bounded Arithmetic and Bounded Set Theory. Notre Dame Journal of Formal Logic 50 (2):141-152.
Mujdat Pakkan & Varol Akman (1995). Issues in Commonsense Set Theory. Philosophical Explorations.
P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
Added to index2009-01-28
Total downloads35 ( #71,879 of 1,696,807 )
Recent downloads (6 months)1 ( #346,744 of 1,696,807 )
How can I increase my downloads?