Maximally Consistent Sets of Instances of Naive Comprehension

Mind 126 (502) (2017)
Download Edit this record How to cite View on PhilPapers
Abstract
Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a ‘one step back from disaster’ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGee’s Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of Naïve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable.
PhilPapers/Archive ID
INCMCS
Revision history
First archival date: 2014-12-17
Latest version: 2 (2014-12-19)
View upload history
References found in this work BETA
Truth.Horwich, Paul
Truth.Horwich, Paul
The Revision Theory of Truth.Gupta, A. & Belnap, N.

View all 25 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2014-12-17

Total views
344 ( #9,114 of 41,584 )

Recent downloads (6 months)
64 ( #8,767 of 41,584 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.