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||Philosophy Philosophy Philosophy of Science Philosophy of Technology|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography.Karin Katz & Mikhail Katz - 2012 - Foundations of Science 17 (1):51-89.
Similar books and articles
Wrestling with (and Without) Dialetheism.Josh Parsons & Jon Cogburn - 2005 - Australasian Journal of Philosophy 83 (1):87 – 102.
Negation, Anti-Realism, and the Denial Defence.Imogen Dickie - 2010 - Philosophical Studies 150 (2):161 - 185.
The Logic of Logical Revision Formalizing Dummett's Argument.Jon Cogburn - 2005 - Australasian Journal of Philosophy 83 (1):15 – 32.
What Anti-Realism in Philosophy of Mathematics Must Offer.Feng Ye - 2010 - Synthese 175 (1):13 - 31.
The Law of Excluded Middle Is Synthetic A Priori, If Valid.Neil Tennant - 1996 - Philosophical Topics 24 (1):205-229.
Added to index2009-01-28
Total downloads76 ( #66,958 of 2,153,332 )
Recent downloads (6 months)13 ( #39,982 of 2,153,332 )
How can I increase my downloads?