Bruno Marchal wrote: >Meanwhile, I >would like to ask George and the others if they have a good >understanding of the present thread, that is on the fact that growing >functions has been well defined, that each sequence of such functions >are well defined, and each diagonalisation defines quite well a precise >programmable growing function (growing faster than the one in the >sequence it comes from). >Just a tiny effort, and I think we will have all we need to go into the >"heart of the matter", and to understand why comp makes our "universe" >a godelized one in the Smullyan sense. > >
To speak only for myself, I think I have a sufficient understanding of the thread. Essentially you have shown that one cannot form a set of all numbers/functions because given any set of numbers/functions it is always possible, using diagonalization, to generate new numbers/functions: the Plenitude is too large to be a set. This leads to a problem with the assumption of the existence of a Universal Dovetailer whose purpose is to generate all functions. I hope this summary is accurate. George --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
