Inferentialism and Structuralism: A Tale of Two Theories

Logique Et Analyse 61 (244):489-512 (2018)

Authors
Ryan Mark Nefdt
University of Cape Town
Abstract
This paper aims to unite two seemingly disparate themes in the philosophy of mathematics and language respectively, namely ante rem structuralism and inferentialism. My analysis begins with describing both frameworks in accordance with their genesis in the work of Hilbert. I then draw comparisons between these philosophical views in terms of their similar motivations and similar objections to the referential orthodoxy. I specifically home in on two points of comparison, namely the role of norms and the relation of ontological dependence in both accounts. Lastly, I show that insights from this purported connection can address certain objections to both theories respectively.
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References found in this work BETA

Making It Explicit.Isaac Levi & Robert B. Brandom - 1994 - Journal of Philosophy 93 (3):145.
Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.
The Logical Basis of Metaphysics.Michael Dummett, Hilary Putnam & James Conant - 1991 - Philosophical Quarterly 44 (177):519-527.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.

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