Philosophical Studies 49 (1):37 - 61 (1986)

Authors
Christopher Menzel
Texas A&M University
Abstract
As the story goes, the source of the paradoxes of naive set theory lies in a conflation of two distinct conceptions of set: the so-called iterative, or mathematical, conception, and the Fregean, or logical, conception. While the latter conception is provably inconsistent, the former, as Godel notes, "has never led to any antinomy whatsoever". More important, the iterative conception explains the paradoxes by showing precisely where the Fregean conception goes wrong by enabling us to distinguish between sets and proper classes, collections that are "too big" to be sets. While I agree wholeheartedly with this distinction, in this paper I argue first that the iterative conception does not provide an explanation of all of the set theoretic paradoxes. I then argue that we need to reconsider the distinction between sets and proper classes rather more carefully. The result will be that ZFC does not capture the iterative conception in its full generality. I close by offering a more general theory that, arguably, does.
Keywords set theory  proper classes  iterative conception of set
Categories (categorize this paper)
DOI 10.1007/BF00372882
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,827
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

On Sets and Worlds: A Reply to Menzel.Patrick Grim - 1986 - Analysis 46 (4):186 - 191.
Frege Numbers and the Relativity Argument.Christopher Menzel - 1988 - Canadian Journal of Philosophy 18 (1):87-98.
Mundos posibles y paradojas.Guillermo Badía - 2013 - Areté. Revista de Filosofía 25 (2):219-229.
Antireductionism and Ordinals.Beau Madison Mount - 2019 - Philosophia Mathematica 27 (1):105-124.

Add more citations

Similar books and articles

Proper Classes Via the Iterative Conception of Set.Mark F. Sharlow - 1987 - Journal of Symbolic Logic 52 (3):636-650.
Iterative Set Theory.M. D. Potter - 1994 - Philosophical Quarterly 44 (171):178-193.
Boolos on the Justification of Set Theory.Alexander Paseau - 2007 - Philosophia Mathematica 15 (1):30-53.
Plural Quantification and the Iterative Concept of Set.Stephen Pollard - 1985 - Philosophy Research Archives 11:579-587.
Categoricity Theorems and Conceptions of Set.Gabriel Uzquiano - 2002 - Journal of Philosophical Logic 31 (2):181-196.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Are Species Sets?Bradley E. Wilson - 1991 - Biology and Philosophy 6 (4):413-431.
The Iterative Conception of Set.Thomas Forster - 2008 - Review of Symbolic Logic 1 (1):97-110.

Analytics

Added to PP index
2009-01-28

Total views
627 ( #9,848 of 2,432,727 )

Recent downloads (6 months)
6 ( #114,948 of 2,432,727 )

How can I increase my downloads?

Downloads

My notes