On 9 June 2014 09:16, Bruno Marchal <marc...@ulb.ac.be> wrote: > > On 08 Jun 2014, at 05:41, LizR wrote: >
> Yes comp strikes me as highly controversial, which is why have been trying >> to get to grips with it, to decide where I stand. But I have got stuck at >> the MGA and (I think) some Kripkean logic. >> > > If you get step 3 I am already glad. Step 7 needs the understanding of the > notion of universal number when written in some (Turing universal) base. > > I recall the number u is universal (in the base phi_i), if phi_u(<x,y>)= > phi_x(y). Such u is sigma_1 complete, and becomes Löbian when he proves p > -> []p for all p sigma_1. > > What you miss, and many miss, is the mathematical, actually arithmetical > definition of "beweisbar", the "[]p" hypostase which is the one which > explains the presence of all its "rivals", the "[]p & p", notably. > > The creative bomb is Gödel's theorem, and the discovery of the universal > machine (hated and loved by different mathematicians, and which does bring > some amount of mess in Platonia. > Well I believe I understand Godel's theorem - in its word-based form, at least. Understanding it arithmetically (i.e. properly) is more of a challenge. > I can't get even an infinity of computations to grok some of that stuff. > > Nobodies does. > Thank you for those kind words. (Also I feel "nobodies" is an interesting word and should be a crossword solution, because it contains quite a few other words ... no/bo/dies ... I will add it to my collection.) > > More precisely. No sigma_1 complete and pi_1 incomplete (machines) > entities does. > Pi_1 complete set (which are still arithmetical, but no more computable) > can solve much more, but are still incomplete with respect to the > arithmetical truth. > > But come on! All you need is a good diary, patience, and well, you might > have good manuals with you like the Mendelson, Boolos, Smorynski, and you > might need to see by your own eyes the equivalence between a bunch of > universal numbers/languages/machines/systems. > I haven't given up! But things keep happening ... distractions ... work, housework, children, husband ... I ask myself if the confusion between p->q and q->p should not be punished > by laws, as propaganda. > Probably, if stated a little more wordily. I encounter that often enough. > > Legalized drugs, make propaganda, and lies in advertising, punishable > perhaps ... > > Yeah! (Swinging sixties here I come!) -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
