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.

Keywords: concrete adequacy; mathematical fictionalism; mathematical inferentialism; mathematical realism

How to cite: Park, Seungbae (2017), “In Defense of Mathematical Inferentialism,” Analysis and Metaphysics 16: 70–83.

Received 22 February 2017 • Received in revised form 9 March 2017
Accepted 9 March 2017 • Available online 25 March 2017


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Division of General Studies,
Ulsan National Institute of Science and Technology,
Ulsan, Republic of Korea

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