At several points the discussions of the list led us to hypothesis of
arithmetic truth. Bruno mentioned once that the basis for this hypothesis
was quite strong, requiring studies in logic to grasp.
But as a non-logician, I have some trouble wrapping my brain around Gödel
and Tarsky's Papers concerning this. What I do see is that Tarsky
generalizes the notion and its difficulties to all formal languages: truth
isn't arithmetically definable without higher order language. Post
attacking the problem with Turing degrees also resonates with this in that
no formula can define truth for arbitrarily large n.
My question as non-logician therefore is: don't these results weaken the
basis for such a hypothesis or at least make it completely inaccessible for
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