On Mon, Sep 19, 2016 at 04:18:21PM +0200, Bruno Marchal wrote:
> 
> On 18 Sep 2016, at 23:54, smitra wrote:
> 
> >https://www.youtube.com/watch?v=nK6XawDE8_U
> 
> 
> I was hoping seeing Nelson's more or less recent proof of the
> inconsistency of Peano Arithmetic, which was enough convincing to
> require some good logician to find out the precise error, that
> Nelson immediately acknowledges.
> 
> Now, this was different and not entirely uninteresting but it is
> just obvious that by assuming there is a physical universe, and that
> it is finite, and by defining some notion of physical numbers, you
> can show that the axioms of Peano will not work for those physical
> numbers.
> 
> It is just that what PA, and Euclid, Pythagorus, Gauss, Fermat,
> Dedekind, Peano, etc.  talk about is something which has nothing to
> do a priori with the sort of numbers this physicalist believer
> (apparently) is talking about. Of course, with computationalism they
> become related: the "physical numbers" would belong to partially
> sharable 3-p-computations/1-p dreams of the natural numbers.
> 
> But I guess this was a bit of a joke, lol.
> 
> Bruno
> 

Norm is one of the preeminent latter-day ultrafinitists. He is quite
persuasive when he talks. And he has done a lot of work in presenting
"trigonometry" using rational functions that avoid the need for
infinite quantities. I gather that ultrafinitism still lacks a
rigorous foundation, however...

Cheers

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Visiting Senior Research Fellow        hpco...@hpcoders.com.au
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