Scientific Confirmation and Naturalized Mathematical Realism

Andrew Steele

Date of Award

2010

Document Type

Thesis

Degree Name

Bachelors

Department

Humanities

First Advisor

Edidin, Aron

Keywords

Naturalism, Antirealism, Mathematical Realism, Nominalism, Philosophy of Mathematics

Area of Concentration

Philosophy

Abstract

My thesis addresses the issue of naturalized mathematical realism and the possibility of naturalized nominalism. What I call here �naturalized mathematical realism� is the position that, upon the adoption of a naturalized approach to philosophy wherein scientific methods and standards are taken as authoritative, we must subsequently fully accept the existence of mathematical objects. I argue for the possibility and legitimacy of rejecting mathematical realism while accepting just such a naturalistic starting point. Specifically, I argue against the naturalized mathematical realism of W. V. Quine on the basis the �entity realism� of Ian Hacking. Hacking�s position concerns the nature of scientific standards and procedure. It asserts that the knowledge of the existence of entities regularly manipulated in the course of physical experimentation, and the knowledge of the causal natures of these entities that allows for this manipulation, receives an especially strong degree of confirmation and stability. Further, Hacking believes that we might legitimately regard scientific knowledge not so described with an attitude of scientific anti-realism. I argue that, as scientists cannot manipulate mathematical entities in the necessary ways, Hacking�s conception of science would make possible a naturalized nominalism wherein one would accepted the experimental knowledge already described while rejecting the remaining scientific theory. It is this latter body of scientific theory which Quine argues is most truly committed to mathematical entities. An appendix sketches an extension of this argument to the naturalized mathematical realism of John P. Burgess and Gideon Rosen.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

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