David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Aristotelian Society Supplementary Volume 73 (1):181–203 (1999)
[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)|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Harvey Friedman (1977). On the Derivability of Instantiation Properties. Journal of Symbolic Logic 42 (4):506-514.
Vittorio Morato (2006). Propositions and Necessary Existence. Grazer Philosophische Studien 72 (1):211-231.
Kit Fine (2006). Relatively Unrestricted Quantification. In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. 20-44.
Bob Hale & Crispin Wright, Focus Restored Comment on John MacFarlane's “Double Vision: Two Questions About the Neo-Fregean Programme”.
Philip Percival (2011). Predicate Abstraction, the Limits of Quantification, and the Modality of Existence. Philosophical Studies 156 (3):389-416.
Timothy Bays (2009). Skolem's Paradox. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy.
Ian Rumfitt & Timothy Williamson (2000). Logic and Existence [Corrected Portion of an Article Appearing in Proceedings of the Aristotelian Society Supplementary Volumes, Vol. 73 (1999)]. [REVIEW] Proceedings of the Aristotelian Society 100:321 - 343.
Ian Rumfitt (1999). Logic and Existence: Ian Rumfitt. Aristotelian Society Supplementary Volume 73 (1):151–180.
Added to index2009-01-28
Total downloads81 ( #21,273 of 1,692,644 )
Recent downloads (6 months)5 ( #46,145 of 1,692,644 )
How can I increase my downloads?