Bruno, Are you asserting this based on published findings concerning provability logic? If so, I would be very interested in references. If not, then your results obviously seem publishable :). That is, if you can show that huge amounts of set theory beyond ZFC emerge from provability logic in some way...

Anyway, I'd definitely be interested in hearing those ideas. --Abram On Fri, Dec 5, 2008 at 4:20 AM, Bruno Marchal <[EMAIL PROTECTED]> wrote: > > > On 05 Dec 2008, at 03:56, Russell Standish wrote: > >> >> On Wed, Dec 03, 2008 at 04:53:11PM +0100, Bruno Marchal wrote: >>> >>> I really don't know. I expect that the mathematical structure, as >>> seen >>> from inside, is so big that Platonia cannot have it neither as >>> element >>> nor as subpart. (Ah, well, I am aware that this is counter-intuitive, >>> but here mathematical logic can help to see the consistency, and the >>> quasi necessity with formal version of comp). >>> >> >> This point rather depends on what Platonia contains. If it contains >> all sets of cardinality 2^{\aleph_0}, then the inside view of the >> deployment will be conatained in it. > > I am not sure. In my opinion, to have a platonia capable of describing > the first person views emerging from the UD entire work, even the > whole of Cantor Paradise will be too little. Even big cardinals (far > bigger than 2^(aleph_0)) will be like too constrained shoes. Actually > I believe that the first person views raised through the deployment > just escape the whole of human conceivable mathematics. It is big. But > it is also structured. It could even be structured as a person. I > don't know. > > >> >> >> I do understand that your concept of Platonia (Arithmetic Realism I >> believe you call it) is a Kronecker-like "God made the integers, all >> the rest was made by man", and so what you say would be true of that. > > > Yes the 3-Platonia can be very little, once we assume comp. But the > first view inside could be so big that eventually all notion of 1- > Platonia will happen to be inconsistent. It is for sure unameable (in > the best case). I discussed this a long time ago with George Levy: the > first person plenitude is big, very big, incredibly big. Nothing can > expressed or give an idea of that bigness. > > At some point I will explain that the "divine intellect" of a lobian > machine as simple as Peano-Arithmetic is really far bigger than the > "God" of Peano-Arithmetic. I know it is bizarre (and a bit too > technical for being addressed right now I guess). > > Have a good day, > > 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 [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---