In Defense of Mathematical Inferentialism

Analysis and Metaphysics 16:70-83 (2017)
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Abstract

I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over mathematical realism and fictionalism.

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Seungbae Park
Ulsan National Institute Of Science And Technology

Citations of this work

Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (3):247–255.

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References found in this work

From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
The aim and structure of physical theory.Pierre Maurice Marie Duhem - 1954 - Princeton,: Princeton University Press.
Image and Mind.Stephen Michael Kosslyn - 1980 - Harvard University Press.
The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.

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