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 -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
