Reference for neo-Fregeans
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Reference for neo-Fregeans David E. Taylor1 Received: 3 December 2019 / Accepted: 25 July 2020 © Springer Nature B.V. 2020
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. Keywords Neo-Fregeanism · Neo-logicism · Reference · Hume’s principle · Deflationism Neo-Fregeanism, as I will understand it here, is a family of positions in the philosophy of mathematics. What binds its members together is a common adherence to a combination of (a certain type of) platonism about mathematical abstracta and (a certain type of) logicism regarding the foundations and epistemology of mathematics. Under its heading I include not only the seminal work of Hale (1987) and Wright (1983), but also more recent work by Cook (2009, n.d.) and Rayo (2013).1 Despite the important
1 Øystein Linnebo’s (2018) view could naturally count as neo-Fregean as well. But it is different enough from the views mentioned above that I will save discussion of it for another time.
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David E. Taylor [email protected] Minnesota Center for Philosophy of Science, University of Minnesota, 831 Heller Hall, 271 19th Ave S, Minneapolis, MN 55455, USA
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differences among these views, each can reasonably be seen as a version of what I’m calling neo-Fregeanism (henceforth, “NF”).2 Since its inception, proponents and critics of NF alike have largely agreed that the view, though primarily one directed at mathematics, presupposes a broader, Fregeaninspired picture about the general relationship between language and world. The basic contours of this picture are clear enough, but many important details remain unresolved (and perhaps can be filled out in different ways by different versions of NF). The question I’d like to address in this paper is concerned with one such unresolved issue. Specifically: What sort of theory of reference (for singular terms) can (should) the proponent of NF be com
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