A solution to Frege's puzzle

Abstract
This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is also used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality.
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DOI 10.2307/2214115
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Chad Carmichael (2016). Deep Platonism. Philosophy and Phenomenological Research 91 (3):307-328.
Chad Carmichael (2010). Universals. Philosophical Studies 150 (3):373-389.
Bjørn Jespersen (2008). Predication and Extensionalization. Journal of Philosophical Logic 37 (5):479 - 499.

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