[FOM] Deflationism and the Godel phenomena

[Aatu Koskensilta]

On Feb 16, 2005, at 12:58 PM, Joseph Vidal-Rosset wrote:

> Jeffrey Ketland a écrit :
>
> | (ii) The Adequacy Condition (adding truth axioms should give a proof 
> of
> | reflection principles, and in particular "All theorems of S are 
> true").
>
> Do we need at this point to grow up to the second order? I believe it.

Only if we want to be able to define the truth predicate explicitly. 
Otherwise it suffices to add a predicate True to the language of the 
theory T under consideration. To the axioms of T one adds axioms saying 
that True is a truth predicate (for the original language of T) - these 
are the usual inductive clauses of Tarski's definition of truth - and 
extends all schemata of T to apply to formulae in the extended 
language.

-- 
Aatu Koskensilta (aatu.koskensilta at xortec.fi)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus