- One of the two major parts of Dummett’s defense of intuitionism is the rejection of classical in favor of intuitionistic reasoning in mathematics, given that mathematical discourse is anti-realist. While there have been illuminating discussions of what Dummett’s argument for this might be, no consensus seems to have emerged about its overall form.
- In this paper I give an account of this form, starting by investigating a fundamental, but little discussed question: to what view of the relation between deductive principles and meaning is anti-realism committed?
- The result of this investigation is a constraint on meaning theoretic assessments of logical laws. Given this constraint, I show that, surprisingly, a consistent anti-realist critique of classical logic could not rely on the rejection of bivalence. Moreover, a consistent anti-realist defense of intuitionism must begin with a radical rejection of the very conception of logical consequence that underlies realist classical logic.
- It follows from these conclusions that anti-realist intuitionism seems committed to proceeding by proof theoretic means.
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