[FOM] A Question

[Max Weiss]

Substitution of a tautology for A in your (1) yields a T-schema, hence  
truth would be definable if your impl were.



On 9-Jun-09, at 11:55 PM, hdeutsch at ilstu.edu wrote:

> Let L be a language capable of expressing its own syntax.  Add to L a
> two place predicate 'impl' satisfying
>
> (1) impl ([A], [B]) < - > (A - > B),
>
> where terms such as [A] are standard names of sentences A or of their
> Godel numbers.
>
> Let p be an arbitrary sentence of the object language.  Then impl(v,
> [p]) is a formula in one free variable.  By Godel's diagonalization
> lemma, it follows that there is a sentence W such that
>
> (2) W < - > impl ([W], [p]).
>
> From here on the argument for Curry's paradox (using (1) and (2)) can
> be used to deduce p.
>
> Is this argument correct?  If so, is it "known" in the  sense at least
> of just "in the air," if not published?  If correct, does it not show
> that classical implication as a predicate expressed in terms of names
> of sentences (rather than a sentential operator) is not definable?
> Harry Deutsch
>
>
>
>
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