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What Anit‐realist Intuitionism Could Not Be
Author(s) -
Shieh Sandford
Publication year - 1999
Publication title -
pacific philosophical quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.914
H-Index - 32
eISSN - 1468-0114
pISSN - 0279-0750
DOI - 10.1111/1468-0114.00074
Subject(s) - intuitionism , epistemology , philosophy , argument (complex analysis) , meaning (existential) , realism , relation (database) , constraint (computer aided design) , intuitionistic logic , scientific realism , classical logic , mathematics , computer science , propositional calculus , linguistics , chemistry , biochemistry , geometry , database
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.