George Levy wrote: > > >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
The dovetailer is only supposed to generate all *computable* functions though, correct? And the diagonalization of the (countable) set of all computable functions would not itself be computable. Jesse --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
