A reconstruction of G.E. Moore’s open question argument (Mark Kalderon)

This is Mark Kalderon’s reconstruction of G.E. Moore’s open question argument. I repeat his wording:

(1) If the universal closure of the biconditional “x is good iff x is F” is a definition, then good and F 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 questions: Q1 ‘Granted that x is F, is x good?’ and S2 ‘Granted that x is good, is x good’ differ only in the substitution of good for an occurrence of F.

(4) If good and F are synonymous, then Q1 and Q2 mean the same. From (2) and (3).

(5) If Q1 and Q2 mean the same, then if a competent speaker who understands Q1 lacks sufficient evidence to know its answer (in which case Q1 is open), then a competent speaker who understands Q2 lacks sufficient evidence to know its answer (in which case Q2 is open).

(6) Q1 is open.

(7) Q2 is not open.

(8) Q1 and Q2 do not mean the same. From (5), (6) and (7) by modus tollens.

(9) Good and F are non-synonymous. From (4) and (8) by modus tollens.

Therefore:

(10) The universal closure of the biconditional “x is good iff x is F” is not a definition. From (1) and (9) by modus tollens.

Reference

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

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