Does Semantic Relationism Solve Frege’s Puzzle?

Abstract

In a series of recent works, Kit Fine (The Journal of Philosophy, 100(12), 605-631, 2003, 2007) has sketched a novel solution to Frege's puzzle. Radically departing from previous solutions, Fine argues that Frege's puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given this enrichment, we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine's proposed solution to Frege's puzzle. We argue that Fine has mis-diagnosed his own solution-his attempted solution does not deny compositionality. The correct characterization of Fine's solution fits him more comfortably among familiar solutions to the puzzle.

Relational approaches to Frege's puzzle

“…That is, we must hold that there are semantic relations that are not reducible to semantic properties. The rules for the language must, in addition to assigning semantic properties to individual occurrences of variables, assign semantic relations to sequences of variables (for critical discussion, see (Pickel & Rabern, , )).…”

“…For discussions of Relationism and compositionality, see (Taschek, ), (Fine, , p. 26), (Pickel & Rabern, ).…”

Frege's Puzzle is About Identity After All

“…The merits of this solution are hotly debated and I won't enter the fray on that question here (Heck 2014;Lawlor 2010;Salmon 2012;Soames 2010;Pickel & Rabern 2017). From the present perspective, relationism is most interesting because it calls for di erent solutions to dyadic and monadic versions of Frege's puzzle.…”