Philosophia Mathematica:nkv033 (2015)

Authors
Graham Leach-Krouse
Kansas State University
Abstract
In this paper, I present a class of ‘structural’ abstraction principles, and describe how they are suggested by some features of Cantor's and Dedekind's approach to abstraction. Structural abstraction is a promising source of mathematically tractable new axioms for the neo-logicist. I illustrate this by showing, first, how a theorem of Shelah gives a sufficient condition for consistency in the structural setting, solving what neo-logicists call the ‘bad company’ problem for structural abstraction. Second, I show how, in the structural setting, we can measure the logical strength of abstraction principles using categories of interpretations between theories.
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DOI 10.1093/philmat/nkv033
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References found in this work BETA

The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.
Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
Structuralism and the Notion of Dependence.Øystein Linnebo - 2008 - Philosophical Quarterly 58 (230):59-79.

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Citations of this work BETA

The Structuralist Thesis Reconsidered.Georg Schiemer & John Wigglesworth - 2019 - British Journal for the Philosophy of Science 70 (4):1201-1226.
The Structuralist Thesis Reconsidered.Georg Schiemer & John Wigglesworth - 2017 - British Journal for the Philosophy of Science:axy004.

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