Re: Torkel Franzen on truth

Daryl McCullough wrote:
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.

Unfortunately mathematical reasoning isn't religion where "beliefs"
would be much relevant.


--
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 ...
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  • Re: Torkel Franzen on truth
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  • Re: Torkel Franzen on truth
    ... Maybe, but we don't know which are these axioms and rules in general, so it can be a controversial point of view to assume that they always characterize every kind of reasoning. ... and if it is "convincing" at all, then it is convincing BECAUSE OF its ... I obviously can agree with your view, but my point was another: I'm saying that we don't need to actually formalize an argument in ZFC, PA or any other formal system in order to be convinced. ...
    (sci.logic)
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