A reconstruction of Frege’s puzzle (Mark Kalderon)

This is Mark Kalderon’s reconstruction of Frege’s puzzle. I repeat his wording:

(1) If the meaning of a name is the object that it denotes, then if Hesperus and Phosphorus denote the same object, then Hesperus and Phosphorus are synonymous.

(2) Compositionality: Let e and e’ be expressions of the same grammatical category. If S[…e…] and S[…e’…] are sentences free of quotation contexts and S[…e…] is the result of substituting e for an occurrence of e’ in the sentence S[…e’…], then if e and e’ are synonymous, then S[…e…] and S[…e’…] mean the same.

(3) The sentences: S1 ‘Hesperus is visible in the evening’ and S2 ‘Phosphorus is visible in the evening’ differ only in the substitution of Phosphorus for an occurrence of Hesperus.

(4) If Hesperus and Phosphorus are synonymous, then S1 and S2 mean the same. From (2) and (3).

(5) If S1 and S2 mean the same, then if a competent speaker possesses sufficient evidence in a context c to accept S1, then that speaker possesses sufficient evidence in c to accept S2 as well.

(6) Competent speakers possess sufficient evidence in c to accept S1.

(7) Competent speakers lack sufficient evidence in c to accept S2.

(8) S1 and S2 do not mean the same. From (5), (6) and (7) by modus tollens.

(9) Hesperus and Phosphorus are non-synonymous. From (4) and (8) by modus tollens.

(10) Hesperus and Phosphorus denote the same object. Empirical premise.

Therefore:

(11) The meaning of a name is not the object it denotes. From (1), (9) and (10) by modus tollens.

Reference

Kalderon, M. 2004. Open Questions and the Manifest Image. Philosophy and Phenomenological Research 68: 251-289.

Note: premise (4) in the original article says From (2) and (5), but I think this is a slip and Kalderon actually meant from (2) and (3).

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