# In Defense of Mathematical Inferentialism

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

**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**

**Categories**

(categorize this paper)

**PhilPapers/Archive ID**

PARIDO-3

**Revision history**

References found in this work BETA

Image and Mind.Kosslyn, Stephen M.

The Indispensability of Mathematics.Colyvan, Mark

The Scientific Image.Friedman, Michael

Mathematics as a Science of Patterns.Resnik, Michael D.

View all 15 references / Add more references

Citations of this work BETA

Two Criticisms Against Mathematical Realism.Park, Seungbae

Can Mathematical Objects Be Causally Efficacious?Park, Seungbae

**Added to PP index**

2017-03-11

**Total views**

214 ( #18,985 of 47,115 )

**Recent downloads (6 months)**

52 ( #15,030 of 47,115 )

How can I increase my downloads?

**Downloads since first upload**

*This graph includes both downloads from PhilArchive and clicks to external links.*