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olcott <polcott333@gmail.com> wrote:You just said that the current foundation of logic leads to a contradiction. Too many negations you got confused.
The assumption that ~Provable(PA, g) does not mean ~True(PA, g)It is an assumption which swifly leads to a contradiction, therefore must
cannot correctly be the basis for any proof because it is only
an assumption.
be false.
But you don't understand the concept of proof by
contradiction, and you lack the basic humility to accept what experts
say, so I don't expect this to sink in.
*He never proved that they cannot be identical*We know, by Gödel's Theorem that incompleteness does exist. So the
initial proposition cannot hold, or it is in an inconsistent system.Only on the basis of the assumption thatNo, there is no such assumption. There are definitions of provable and
~Provable(PA, g) does not mean ~True(PA, g)
of true, and Gödel proved that these cannot be identical.
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