On 14 Sep 2009, at 19:02, Flammarion wrote:
> > > > On 13 Sep, 18:12, Bruno Marchal <marc...@ulb.ac.be> wrote: >> Marty, >> >>> Could you please clarify to a non-mathematician why the >>> principle of excluded middle is so central to your thesis (hopefully >>> without using acronyms like AUDA, UD etc.). >> >> Without the excluded middle (A or not A), or without classical logic, >> it is harder to prove non constructive result. In theoretical >> artificial intelligence, or in computational learning theory, but >> also >> in many place in mathematics, it happens that we can prove, when >> using >> classical logic, the existence of some objects, for example machines >> with some interesting property, and this without being able to >> exhibit >> them. > > What you are proving is only existence in the mathematical sense. Indeed. > The philosophical quesiton of whether backwards-E should be taken > literally (Platonism) or only metaphorically (formalism) is left > unadresses > by the PEM. Of course. that is why there is the MGA. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
