Philosophical Studies

, Volume 150, Issue 2, pp 161–185 | Cite as

Negation, anti-realism, and the denial defence



Here is one argument against realism. (1) Realists are committed to the classical rules for negation. But (2) legitimate rules of inference must conserve evidence. And (3) the classical rules for negation do not conserve evidence. So (4) realism is wrong. Most realists reject 2. But it has recently been argued that if we allow denied sentences as premisses and conclusions in inferences we will be able to reject 3. And this new argument against 3 generates a new response to the anti-realist argument: keep 1 and 2, avoiding 4 by rejecting 3. My aim in this paper is to see how much work in the fight against anti-realism this new response can really do. I argue that there is a powerful objection to the response: 2 is in tension with the claim that denied sentences can be premisses and conclusions in inferences. But I show that, even given this objection, the new response has an important role to play.


Classical negation Intuitionist attack on classical negation Anti-realist argument from the intuitionist attack on classical negation Denial Realism Anti-realism Dummett 



Thanks to Diana Raffman and to audiences at the University of Western Ontario and Carleton University for discussion of earlier versions. Thanks to Ranpal Dosanjh for a physicist’s perspective on the material in Sect. 3.3. Many thanks to Philip Kremer for extensive comments on an earlier draft and multiple helpful discussions of this subject matter. Many thanks also to an anonymous referee for Philosophical Studies for extremely useful comments.


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.University of TorontoTorontoCanada
  2. 2.New York UniversityNew YorkUSA

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