David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Topoi 20 (1):53-63 (2001)
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||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
Stewart Shapiro (2007). The Objectivity of Mathematics. Synthese 156 (2):337 - 381.
Karin Katz & Mikhail Katz (2012). A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science 17 (1):51-89.
Similar books and articles
Josh Parsons & Jon Cogburn (2005). Wrestling with (and Without) Dialetheism. Australasian Journal of Philosophy 83 (1):87 – 102.
Imogen Dickie (2010). Negation, Anti-Realism, and the Denial Defence. Philosophical Studies 150 (2):161 - 185.
Jon Cogburn (2005). The Logic of Logical Revision Formalizing Dummett's Argument. Australasian Journal of Philosophy 83 (1):15 – 32.
Bernhard Weiss (2007). Truth and the Enigma of Knowability. Dialectica 61 (4):521–537.
Robert G. Hudson (2009). Faint-Hearted Anti-Realism and Knowability. Philosophia 37 (3):511-523.
Feng Ye (2010). What Anti-Realism in Philosophy of Mathematics Must Offer. Synthese 175 (1):13 - 31.
Neil Tennant (1996). The Law of Excluded Middle Is Synthetic A Priori, If Valid. Philosophical Topics 24 (1):205-229.
Added to index2009-01-28
Total downloads33 ( #55,791 of 1,099,914 )
Recent downloads (6 months)2 ( #190,037 of 1,099,914 )
How can I increase my downloads?