Bryan Pickel

Does Semantic Relationism Solve Frege’s Puzzle?

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.

Structured propositions and trivial composition

Structured propositions are often invoked to explain why intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. As the semantics is standardly developed—for example, in Salmon (Frege’s puzzle. Ridgeview, Atascadero, CA, 1986 ), Soames (Philos Top 15(1):47–87, 1987 ) and King (Noûs 29(4):516–535, 1995 ), the semantic value of a complex expression is an ordered complex consisting of the semantic values of its components. Such views, however, trivialize semantic composition since they do not allow for independent constraints on the meaning of complexes. Trivializing semantic composition risks “trivializing semantics” (King and Stanley, in: Szabó (ed) Semantics versus pragmatics, Oxford University Press, Oxford, 2005 ). Yet, proponents of structured propositions suggest a route to reimpose substantive compositionality. While the mapping from a sentence to the structured proposition it expresses is trivially compositional, there is a non-trivial mapping from the structured proposition to its truth-value. This non-trivial level of semantic composition allows the meanings assigned to complex expressions to impose substantive constraints on the meanings of the simple ones. I first articulate the basic desiderata: an account of structured propositions capable of explaining attitude attributions and of delivering a non-trivially compositional semantics. I then show that the two-stage semantics proposed by standard proponents of structured propositions does not satisfy these joint goals.

Unity through truth

Renewed worries about the unity of the proposition have been taken as a crucial stumbling block for any traditional conception of propositions. These worries are often framed in terms of how entities independent of mind and language can have truth conditions: why is the proposition that Desdemona loves Cassio true if and only if she loves him? I argue that the best understanding of these worries shows that they should be solved by our theory of truth and not our theory of content. Specifically, I propose a version of the redundancy theory according to which ‘it is true that Desdemona loves Cassio’ expresses the same proposition as ‘Desdemona loves Cassio’. Surprisingly, this variant of the redundancy theory treats ‘is true’ as an ordinary predicate of the language, thereby defusing many standard criticisms of the redundancy theory.

Complex Predication and the Metaphysics of Properties

The existence of complex predicates seems to support an abundant conception of properties. Specifically, the application conditions for complex predicates seem to be explained by the distribution of a sparser base of predicates. This explanatory link might suggest that the existence and distribution of properties expressed by complex predicates are explained by the existence and distribution of a sparser base of properties. Thus, complex predicates seem to legitimize the assumption of a wide array of properties. The additional properties are no explanatory addition to the sparse base. I argue, however, that construing complex predicates as expressing properties undermines the explanatory links between simple and complex predications. The argument explores a variety of accounts of complex predicates currently on offer and develops a number of themes from the work of Herbert Hochberg.