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.
Highlights
In a series of recent works, Fine [7, 8] has sketched a novel solution to Frege’s puzzle
Frege [9] claimed that sentences differing by the substitution of coreferential proper names such as (1) and (2) differ semantically, arguing that (2) expresses a valuable extension of our knowledge, while (1) doesn’t
We have by and large restricted our attention to the substitution of coreferential names in simple sentences such as (1) and (2)
Summary
In a series of recent works, Fine [7, 8] has sketched a novel solution to Frege’s puzzle. MINIMAL PAIR: Sentences (1) and (2) differ only by the substitution of ‘Cicero’ for ‘Tully’—all other inputs to semantic evaluation coincide. Current philosophical thinking on Frege’s puzzles has reached an impasse, with strong theoretical arguments in favor of [DIFFERENCE] and strong intuitive arguments in favor of [SYNONYMY] and yet no apparent way to choose between them This suggests that we should perhaps take more seriously the possibility of rejecting the assumption of [COMPOSITIONALITY] that puts them in conflict. By enriching the input to semantics, Rxx and Rxy are no longer a minimal pair, differing only by the substitution of variables ‘x’ and ‘y’. Fine’s solution is not to deny COMPOSITIONALITY but instead to deny that (1) and (2) are MINIMAL PAIRS differing only by the substitution of co-referential proper names. The correct characterization of Fine’s solution fits him more comfortably among familiar solutions to the puzzle
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