Thought: A Journal of Philosophy 2 (2):137-147 (2013)

Jonathan Payne
University of Sheffield (PhD)
Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles
Keywords free logic  abstractionism  Neo‐Fregeanism  set  abstraction principles
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DOI 10.1002/tht3.82
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References found in this work BETA

The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.
Abstract Objects.BOB HALE - 1987 - Blackwell.
Abstract Objects.John P. Burgess - 1992 - Philosophical Review 101 (2):414.

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Russell’s Paradox and Free Zig Zag Solutions.Ludovica Conti - forthcoming - Foundations of Science:1-19.

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