Set Theory and its Philosophy: A Critical Introduction

Oxford University Press (2004)
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
Categories (categorize this paper)
Buy the book $140.25 used (15% off)   $165.00 direct from Amazon   $165.00 new    Amazon page
Call number QA248.P675 2004
ISBN(s) 0199269734   9780199269730  
DOI 10.1093/mind/fzi764
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,224
External links

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.

Add more references

Citations of this work BETA
The Iterative Conception of Set: A (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
How to Be a Minimalist About Sets.Luca Incurvati - 2012 - Philosophical Studies 159 (1):69-87.
Understanding Programming Languages.Raymond Turner - 2007 - Minds and Machines 17 (2):203-216.

View all 18 citations / Add more citations

Similar books and articles
A Brief Introduction to Algebraic Set Theory.Steve Awodey - 2008 - Bulletin of Symbolic Logic 14 (3):281-298.
Issues in Commonsense Set Theory.Mujdat Pakkan & Varol Akman - 1995 - Philosophical Explorations.
On Interpretations of Bounded Arithmetic and Bounded Set Theory.Richard Pettigrew - 2009 - Notre Dame Journal of Formal Logic 50 (2):141-152.
Sets, Classes, and Categories.F. A. Muller - 2001 - British Journal for the Philosophy of Science 52 (3):539-573.
Is Any Set Theory True?Joseph S. Ullian - 1969 - Philosophy of Science 36 (3):271-279.
Naïve Set Theory is Innocent!A. Weir - 1998 - Mind 107 (428):763-798.
Notes on Logic and Set Theory.P. T. Johnstone - 1987 - Cambridge University Press.
Added to PP index
2009-01-28

Total downloads
58 ( #93,069 of 2,192,001 )

Recent downloads (6 months)
4 ( #59,432 of 2,192,001 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature