What is wrong with classical negation?

Grazer Philosophische Studien 92 (1):51-86 (2015)

Abstract

The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, I shall grant Dummett his general bias towards verificationism, encapsulated in the slogan 'meaning is use'. The second general assumption I see no need to question is Dummett's particular breed of molecularism. Some of Dummett's assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inference in the Dummettian framework.

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References found in this work

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Tractatus Logico-Philosophicus.Ludwig Wittgenstein - 1956 - Revista Portuguesa de Filosofia 12 (1):109-110.

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