Synthese 170 (3):393-414 (2009)

Authors
Matti Eklund
Uppsala University
Abstract
A central element in neo-Fregean philosophy of mathematics is the focus on abstraction principles, and the use of abstraction principles to ground various areas of mathematics. But as is well known, not all abstraction principles are in good standing. Various proposals for singling out the acceptable abstraction principles have been presented. Here I investigate what philosophical underpinnings can be provided for these proposals; specifically, underpinnings that fit the neo-Fregean's general outlook. Among the philosophical ideas I consider are: general views on a priori justification; the idea of abstraction as reconceptualization, the idea that truth is prior to reference in the sense associated with Frege's context principle; and various broadly relativistic views. The conclusions are by and large negative.
Keywords Philosophy   Metaphysics   Philosophy of Language   Logic   Epistemology
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DOI 10.1007/s11229-007-9262-x
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References found in this work BETA

Truth and Objectivity.Crispin Wright - 1992 - Harvard University Press.
The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Warrant for Nothing (and Foundations for Free)?Crispin Wright - 2004 - Aristotelian Society Supplementary Volume 78 (1):167–212.

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Citations of this work BETA

Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
Higher‐Order Abstraction Principles.Beau Madison Mount - 2015 - Thought: A Journal of Philosophy 4 (4):228-236.
Negative Existentials in Metaphysical Debate.Alexis Burgess - 2012 - Metaphilosophy 43 (3):221-234.
Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction.Demetra Christopoulou - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):35-47.

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