Authors
Ian Rumfitt
Oxford University
Abstract
[Ian Rumfitt] Frege's logicism in the philosophy of arithmetic consisted, au fond, in the claim that in justifying basic arithmetical axioms a thinker need appeal only to methods and principles which he already needs to appeal in order to justify paradigmatically logical truths and paradigmatically logical forms of inference. Using ideas of Gentzen to spell out what these methods and principles might include, I sketch a strategy for vindicating this logicist claim for the special case of the arithmetic of the finite cardinals. /// [Timothy Williamson]The paper defends the intelligibility of unrestricted quantification. For any natural number n, 'There are at least n individuals' is logically true, when the quantifier is unrestricted. In response to the objection that such sentences should not count as logically true because existence is contingent, it is argued by consideration of cross-world counting principles that in the relevant sense of 'exist' existence is not contingent. A tentative extension of the upward Löwenheim-Skolem theorem to proper classes is used to argue that a sound and complete axiomatization of the logic of unrestricted universal quantification results from adding all sentences of the form 'There are at least n individuals' as axioms to a standard axiomatization of the first-order predicate calculus
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1111/1467-8349.00053
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: 55,899
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

A General Theory of Abstraction Operators.Neil Tennant - 2004 - Philosophical Quarterly 54 (214):105-133.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
75 ( #131,330 of 2,401,863 )

Recent downloads (6 months)
2 ( #361,817 of 2,401,863 )

How can I increase my downloads?

Downloads

My notes