[FOM] A Question

[William Tait]

On Jun 9, 2009, at 3:55 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),

 From what you write, it seems that you are starting with a theory T  
and then adding the constant impl and the above axiom schema to obtain  
a theory bT'.

impl([0=0], [B]) <-> B

is derivable in T'. I.e. T' has a definition of truth for itself. From  
the remainder of the message, T is assumed strong enough to support  
the Diagonalization Lemma. So T' is inconsistent.

Bill Tait