Re: Torkel Franzen on truth

Newberry says...

So noted. I also note that most people do not find Gentzen's proof
very convincing. And I still do not see how a proof in a stronger
system could be more convincing than a proof in the system itself.

The *strength* of the system is not relevant so much as whether the
axioms are themselves intuitively true. A proof in a theory whose
axioms are intuitively true is more useful and interesting than
a proof in a theory whose axioms are not intuitively true.

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.

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: Torkel Franzen on truth
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  • Re: Torkel Franzen on truth
    ... system could be more convincing than a proof in the system itself. ... axioms are themselves intuitively true. ... Why is a consistency proof of a theory in a stronger theory ...
    (sci.logic)
  • Re: Torkel Franzen on truth
    ... Daryl McCullough wrote: ... system could be more convincing than a proof in the system itself. ... axioms are themselves intuitively true. ...
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  • Re: Why an inconsistent ZF may be desirable, and should be welcome.
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  • Re: Torkel Franzen on truth
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