Bad Company and Neo-Fregean Philosophy

Synthese 170 (3):393 - 414 (2009)
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 Neo-Fregeanism  Hume’s principle  Bad company  Relativism  Epistemology  Mathematics  Crispin Wright  Bob Hale
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References found in this work BETA
Crispin Wright (2004). Warrant for Nothing (and Foundations for Free)? Aristotelian Society Supplementary Volume 78 (1):167–212.
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.

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Beau Madison Mount (2015). Higher‐Order Abstraction Principles. Thought: A Journal of Philosophy 4 (4):228-236.
Demetra Christopoulou (2014). Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):35-47.

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