Reference for neo-Fregeans

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Abstract

Neo-Fregeanism (NF) is a family of positions in the philosophy of mathematics that combines a certain type of platonism about mathematical abstracta with a certain type of logicism about the foundations and epistemology of mathematics. This paper addresses the following question: what sort of theory of reference can/should NF be committed to? The theory of reference I propose for NF comes in two parts. First, an alethic account of referential success: the fact that a term ‘a’ succeeds in referring to something depends on facts about truth. Second, a deflationary account of referential specification: given that ‘a’ refers to something, the fact that ‘a’ refers to b specifically follows from the disquotational schema for reference (‘a’ refers to x iff x = a) together with the fact that b = a. In the first section of the paper I argue that NF should be committed to the first part of this theory. This a point on which there is already (some) agreement. The bulk of the paper is therefore devoted to arguing that NF should be committed to the second part, given that it is committed to the first part. I close the paper by indicating some significant implications and a possible problem for this theory of reference.

Original languageEnglish (US)
Pages (from-to)11505-11536
Number of pages32
JournalSynthese
Volume198
Issue number12
DOIs
StatePublished - Dec 2021

Bibliographical note

Funding Information:
Some of the central ideas in this paper grew out of the many discussions of neo-Fregeanism that I had the pleasure of participating in over the past several years during meetings of the Foundations Interest Group at the Minnesota Center for Philosophy of Science. I thank the participants at those meetings for lively and stimulating discussion of these topics. An earlier version of this paper was presented at the Fifth Philosophy of Language and Mind Conference at the University of St Andrews in August of 2019. Thanks to the participants at that conference for their helpful questions and feedback. Finally, I?d like to pay special thanks to the following people for providing me with thoughtful comments on earlier drafts of this work: Samuel Asarnow, Roy Cook, Manuel Garc?a-Carpintero, Peter Hanks, Carlos N??ez, and two anonymous referees for this journal.

Publisher Copyright:
© 2020, Springer Nature B.V.

Keywords

  • Deflationism
  • Hume’s principle
  • Neo-Fregeanism
  • Neo-logicism
  • Reference

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