Friday, October 19, 2007

Objection from non-sucky implicit aboutness standards

Williamson poses an argument to the effect that
(M) Mars was always either dry or not dry
is implicitly about language:

1) (M) is equivalent (truth functionally) to (ML) The sentence "Mars was always either dry or not dry" is true, which is explicitly about language
2) (1) -> (3)
3) (M) is implicitly about language

This argument is bad because truth functional equivalence is much too weak to be a standard for implicit aboutness. A similar argument could be run to the effect that (ML) is implicitly about Mars, or any other truth functionaly equivalent sentence for that matter. So, here's a better argument:

(IA) If a sentence S is truth-functionally equivalent to a sentence about language S', AND the initial justification for S includes the truth of S' then S is implicitly about language
4) (M) meets the conditions for (IA)
5) (M) is implicitly about language

As it turns out, I believe this second argument is also inadequate. In practice, when Williamson presents ways of answering (M), he never explicitly answers (ML). An additional argument would be needed to show that (ML) was implicitly answered and used as a hidden premise in the arguments that answer (M). I'm unconvinced that this is true, and even if it were true I'm not sure it could be shown to be true.

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