On 9 June 2014 09:16, Bruno Marchal <[email protected]> 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
