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AbstractionismEssays in Philosophy of Mathematics$
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Philip A Ebert and Marcus Rossberg

Print publication date: 2016

Print ISBN-13: 9780199645268

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780199645268.001.0001

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Abstraction and Epistemic Entitlement: On the Epistemological Status of Hume’s Principle

Abstraction and Epistemic Entitlement: On the Epistemological Status of Hume’s Principle

8 (p.161) Abstraction and Epistemic Entitlement: On the Epistemological Status of Hume’s Principle

Crispin Wright

Oxford University Press

The abstractionist program of foundations for classical mathematical theories is, like its traditional logicist ancestors, first and foremost an epistemological project. Its official aim is to demonstrate the possibility of a certain uniform mode of a priori knowledge of the basic laws of arithmetic, real and complex analysis, and set theory. Traditional logicism aimed to show that mathematical knowledge could be accomplished using only analytic definitions and theses of pure logic and hence is not merely a priori if logic is but is effectively a proper part of logic. Abstractionism, however, adds abstraction principles to the base materials employed in the traditional logicist project—principles that, at least in the central, interesting cases, are neither pure analytic definitions nor theses of pure logic as conventionally understood. Thus, whatever significance they may carry for the prospects for logicism, the epistemological significance of technically successful abstractionist projects must turn on the epistemological status of the abstraction principles used, with any demonstration of a priority in particular being dependent on whether those principles can themselves rank as knowable a priori. My primary focus here will be on this natural thought.

Keywords:   abstraction principle, Abstractionism, a priori knowledge, entitlement, Hume’s Principle

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