Noûs 44 (2):329-339 (2010)

Authors
Marcus Rossberg
University of Connecticut
Abstract
Second-order axiomatizations of certain important mathematical theories—such as arithmetic and real analysis—can be shown to be categorical. Categoricity implies semantic completeness, and semantic completeness in turn implies determinacy of truth-value. Second-order axiomatizations are thus appealing to realists as they sometimes seem to offer support for the realist thesis that mathematical statements have determinate truth-values. The status of second-order logic is a controversial issue, however. Worries about ontological commitment have been influential in the debate. Recently, Vann McGee has argued that one can get some of the technical advantages of second-order axiomatizations—categoricity, in particular—while walking free of worries about ontological commitment. In so arguing he appeals to the notion of an open-ended schema—a schema that holds no matter how the language of the relevant theory is extended. Contra McGee, we argue that second-order quantification and open-ended schemas are on a par when it comes to ontological commitment
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1111/j.1468-0068.2010.00742.x
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: 51,232
Through your library

References found in this work BETA

Truth and the Absence of Fact.Hartry Field - 2001 - Oxford University Press.
Logic, Logic and Logic.George Boolos - 1998 - Harvard University Press.

View all 16 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-02-12

Total views
79 ( #116,742 of 2,329,878 )

Recent downloads (6 months)
1 ( #582,921 of 2,329,878 )

How can I increase my downloads?

Downloads

My notes