Curry’s Critique of the Syntactic Concept of Formal System and Methodological Autonomy for Pure Mathematics

Aaron Lercher

doi:10.14394/filnau.2023.0002

Authors

Aaron Lercher Louisiana State University Libraries https://orcid.org/0000-0002-6994-5833

DOI:

https://doi.org/10.14394/filnau.2023.0002

Keywords:

Haskel Curry, mathematical structuralism, philosophy of mathematics

Abstract

Haskell Curry’s philosophy of mathematics is really a form of “structuralism” rather than “formalism” despite Curry’s own description of it as formalist (Seldin 2011). This paper explains Curry’s actual view by a formal analysis of a simple example. This analysis is extended to solve Keränen’s (2001) identity problem for structuralism, confirming Leitgeb’s (2020a, b) solution, and further clarifies structural ontology. Curry’s methods answer philosophical questions by employing a standard mathematical method, which is a virtue of the “methodological autonomy” emphasized by Curry (1951, 1963) and more recently with greater clarity by Maddy (1997, 2007).

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