Relying on reason: A reliabilist account of a priori mathematical knowledge.
Item
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Title
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Relying on reason: A reliabilist account of a priori mathematical knowledge.
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Identifier
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AAI3083690
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identifier
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3083690
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Creator
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McEvoy, Mark Valentine.
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Contributor
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Advisers: Jerrold J. Katz | David M. Rosenthal
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Date
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2003
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Language
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English
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Publisher
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City University of New York.
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Subject
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Philosophy | Mathematics
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Abstract
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Because mathematical Platonism construes mathematical objects as existing outside of space and time, it precludes their having any causal interactions. This has led some to object that mathematical Platonism cannot explain how we know anything about such objects.;Process reliabilism sometimes evokes the converse objection. Since process reliabilism takes knowledge to be reliably produced true belief, it is sometimes said that the theory cannot explain the reliability of our mathematical beliefs, as we cannot interact causally with mathematical objects. If this were true, process reliabilism would be inadequate as a theory of knowledge, since it could not account for our mathematical knowledge.;My dissertation seeks to reconcile Platonism and process reliabilism by explaining the reliability of the processes which lead to our a priori knowledge of mathematics. Chapter One outlines and defends my conception of process reliabilism from Bonjour's counterexamples, from Feldman's "Generality Problem" and from evidentialist objections. Chapter two defends the notion of the a priori from Quine's arguments. Chapter Three offers a conception of mathematical proof according to which it is a reliable, a priori process. It defends this conception of proof from attacks due to Kitcher and Tymoczko. Chapter Four argues that, contra Casullo, reliabilism can answer Benacerraf's challenge, and provide a satisfactory account of mathematical knowledge. Chapter Five offers a reliabilist account of the a priori process of mathematical intuition, and defends it against various objections.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
