Why anti-realists and classical mathematicians cannot get along

Topoi 20 (1):53-63 (2001)
Abstract
Famously, Michael Dummett argues that considerations concerning the role of language in communication lead to the rejection of classical logic in favor of intuitionistic logic. Potentially, this results in massive revisions of established mathematics. Recently, Neil Tennant (“The law of excluded middle is synthetic a priori, if valid”, Philosophical Topics 24 (1996), 205-229) suggested that a Dummettian anti-realist can accept the law of excluded middle as a synthetic, a priori principle grounded on a metaphysical principle of determinacy. This article shows that the for the anti-realist, the law of excluded middle entails that humans have wildly implausible abilities. The proposed synthesis between anti-realism and classical mathematics thus fails.
Keywords Philosophy   Philosophy   Philosophy of Science   Philosophy of Technology
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1010656826667
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,827
External links

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.

Add more references

Citations of this work BETA
The Objectivity of Mathematics.Stewart Shapiro - 2007 - Synthese 156 (2):337-381.

Add more citations

Similar books and articles
Added to PP index
2009-01-28

Total downloads
82 ( #69,180 of 2,210,672 )

Recent downloads (6 months)
5 ( #100,764 of 2,210,672 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature