Re: Torkel Franzen on truth

In article <qERcj.21015$DP1.9137@pd7urf2no>,
Nam D. Nguyen <namducnguyen@xxxxxxx> wrote:
Nam D. Nguyen wrote:
tchow@xxxxxxxxxxxxx wrote:
in response to Daryl McCullough's comment:

So, for example, a proof in PA + the negation of Goldbach's conjecture
would not be very convincing, because we have no reason to believe that
the negation of Goldbach's conjecture is true.
[...]
At this point in time, when there's no proof, the belief that the
negation of Goldbach's conjecture is not true is of the nature of
religion belief, which is quite irrelevant to reasoning: reasoning
requires proof not belief. Wouldn't you think so?

In fact, DMC's whole statement above is a religion statement, dressed in
formalism! A proof is supposed to be the only reason for belief.
One could disprove a proof by proving the negation and proving the
theory is consistent. But one should *not* dismiss a proof simply because
one already has the opposite belief, *without* a proof!

Your remarks here are even more absurd than your remark that belief is not
relevant. Daryl McCullough is not asserting that

the negation of Goldbach's conjecture is not true

He asserts only that

we have no reason to believe that the negation of Goldbach's conjecture
is true

That is, he is withholding belief in the negation of Goldbach's conjecture,
because there is no proof of that statement. In other words, he is behaving
in exactly the way that you say he should. So what are you complaining about?

Obviously you're just not reading what he wrote very carefully.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.

Relevant Pages

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  • Re: Torkel Franzen on truth
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  • Re: Torkel Franzen on truth
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    (sci.logic)
  • Re: Torkel Franzen on truth
    ... So, for example, a proof in PA + the negation of Goldbach's conjecture ... A proof is supposed to be the only reason for belief. ... *any* proof of ~GC in PA would be not convincing, ...
    (sci.logic)
  • Re: Torkel Franzen on truth
    ... we have no reason to believe that the negation of Goldbach's conjecture ... I am no asserting that the negation ...
    (sci.logic)
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