FOM: Pratt on truth
John Mayberry
J.P.Mayberry at bristol.ac.uk
Thu Feb 5 04:47:04 EST 1998
Vaughn Pratt takes exception to my claim that without truth
there can be no proof. Pratt writes
Your premise seems to be that every axiom of every proof system is
absolutely true. For if not you would have proofs of theorems with no
basis for inferring that the proved theorems were absolutely true.
Of course my argument does not depend on such a premise. If you prove
that A follows from the axioms B,C,...,D, then you prove, not that A is
true, but that if B,C,...,D are true then A is true. If we are talking
of formal axiomatics here, then you have proved that in any
interpretation under which B,C,...,D are all true A is also true.
In any case, why should Pratt think me to be committed to the
view that "every axiom of every proof system" is true? Why those
*everys*? Does he think that all of mathematics consists in drawing
formal consequences from "arbitrarily posited" axioms on whose behalf
we make no truth claims whatsoever, not even claims that they are true
under suitable interpretations? In that case it seems to me that he is
profoundly wrong, and, indeed, has embraced Butz's views on truth, the
absurdity of which was the subject of my earlier posting. I stand by
what I said there.
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John Mayberry
Lecturer in Mathematics
J.P.Mayberry at bristol.ac.uk
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