Graduate studies at Western
Philosophical Studies 49 (1):37 - 61 (1986)
|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)|
|Through your library||Configure|
Similar books and articles
Pierluigi Miraglia (2000). Finite Mathematics and the Justification of the Axiom of Choicet. Philosophia Mathematica 8 (1):9-25.
Mark F. Sharlow (1987). Proper Classes Via the Iterative Conception of Set. Journal of Symbolic Logic 52 (3):636-650.
M. D. Potter (1993). Iterative Set Theory. Philosophical Quarterly 44 (171):178-193.
Alexander Paseau (2007). Boolos on the Justification of Set Theory. Philosophia Mathematica 15 (1):30-53.
Stephen Pollard (1985). Plural Quantification and the Iterative Concept of Set. Philosophy Research Archives 11:579-587.
Gabriel Uzquiano (2002). Categoricity Theorems and Conceptions of Set. Journal of Philosophical Logic 31 (2):181-196.
Adam Rieger (2011). Paradox, ZF and the Axiom of Foundation. In D. DeVidi, M. Hallet & P. Clark (eds.), Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell. Springer.
George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.
Bradley E. Wilson (1991). Are Species Sets? Biology and Philosophy 6 (4):413-431.
Thomas Forster (2008). The Iterative Conception of Set. Review of Symbolic Logic 1 (1):97-110.
Added to index2009-01-28
Total downloads23 ( #60,278 of 739,396 )
Recent downloads (6 months)1 ( #61,680 of 739,396 )
How can I increase my downloads?