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Topic: Torkel Franzen argues
Replies: 25   Last Post: May 17, 2013 3:52 PM

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scattered

Posts: 89
Registered: 6/21/12
Re: Torkel Franzen argues
Posted: Apr 25, 2013 8:10 PM
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On Thursday, April 25, 2013 3:58:56 PM UTC-4, FredJeffries wrote:
> On Apr 25, 8:25 am, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>

> > Newberry <newberr...@gmail.com> writes:
>
> > > Torkel Franzen argues that all the axioms of ZFC  are manifestly true
>
> > > the logic apparatus is truth preserving therefore all is good and the
>
> > > system is consistent.
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> >
>
> > Really??
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> >
>
> > Where did he make this claim?
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>
>
>
>
> In "The Popular Impact of Gödel's Incompleteness Theorem"
>
>
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> http://www.ams.org/notices/200604/fea-franzen.pdf
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>
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> he says:
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>
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> "we can easily, indeed trivially, prove PA consistent using
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> reasoning of a kind that mathematicians otherwise
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> use without qualms in proving theorems of
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> arithmetic. Basically, this easy consistency proof observes
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> that all theorems of PA are derived by valid
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> logical reasoning from basic principles true of the
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> natural numbers, so no contradiction is derivable in PA"


So it seems that perhaps he didn't make the claim regarding ZFC but only regarding the weaker system of PA; which is hardly surprising since PA is generally considered to be nonproblematic in a way that ZFC is not. Of course strict finitists such as Edward Nelson might be unconvinced, but such skeptics are in a small minority.




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