Episteme 10 (4):351-367 (2013)

Authors
Michaelis Michael
University of New South Wales
Abstract
Classical logic is explosive in the face of contradiction, yet we find ourselves using inconsistent theories. Mark Colyvan, one of the prominent advocates of the indispensability argument for realism about mathematical objects, suggests that such use can be garnered to develop an argument for commitment to inconsistent objects and, because of that, a paraconsistent underlying logic. I argue to the contrary that it is open to a classical logician to make distinctions, also needed by the paraconsistent logician, which allow a more nuanced ranking of theories in which inconsistent theories can have different degrees of usefulness and productivity. Facing inconsistency does not force us to adopt an underlying paraconsistent logic. Moreover we will see that the argument to best explanation deployed by Colyvan in this context is unsuccessful. I suggest that Quinean approach which Colyvan champions will not lead to the revolutionary doctrines Colyvan endorses
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DOI 10.1017/epi.2013.31
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References found in this work BETA

Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Ontological Relativity.W. V. Quine - 1968 - Journal of Philosophy 65 (7):185-212.
On What There Is.Willard Van Orman Quine - 1948 - Review of Metaphysics 2 (5):21-38.
Popper’s Qualitative Theory of Verisimilitude.David Miller - 1974 - British Journal for the Philosophy of Science 25 (2):166-177.

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In Pursuit of the Non-Trivial.Colin R. Caret - 2021 - Episteme 18 (2):282-297.

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