Hi Bruno, what I undestand about the UD is that it generates all programs, a program being simply a number from the set N.(1)
There exists an infinity of program which generates a set of growing function (different set), all the computable growing function are generated by all these programs(taken as a whole). Is this correct ? Is this metaset also diagonalisable ? I said no, because if it was then there is a contradiction with the premises that said that we generate *all* the programs that compute growing functions, thus either we cannot generate those programs (but that would be strange, that would means N is not enumerable ?) or the "metaset" is not diagonalisable... Where do I fail in my understanding ? Thanks, Quentin (1) I still have another problem with that because a program to be run need also the coding scheme (the instruction set of the turing machine that run it), which instruction set the UD use ? or how it construct it ? Le Mercredi 7 Juin 2006 15:11, Bruno Marchal a écrit : > Le 06-juin-06, à 20:50, [EMAIL PROTECTED] a écrit : > > Given a > > (countably infinite) sequence of functions f1, f2, ..., you say that > > fn(n)+1 must either be in the sequence OR not in the sequence. > > I am just showing constructively that if f1, f2,f3, ... is a well > defined sequence of computable functions from N to N, then the > "diagonal" function g (i.e. the one defined by g(n) = fn(n)+1) for each > n) cannot belong to the sequence f1, f2, f3, ... > The proof is constructive in the sense that if you give me some fk > equal to g, I can generate a contradiction from that. The contradiction > being that g(k) will be equal to g(k)+1. > > > But I will take some of my rare spare time (which I always have by > > diagonalization) > > I hope you will explain to me how you do that :) > > > to think some more about this absoluteness of > > computability and Church Thesis, etc. and try to understand this and > > solve the puzzle of where your straw-man argument is wrong. > > OK, I let you think a little more then. > > > Speaking of straw-men, it seems you are saying that machines simply > > running programs, without axioms and inference rules, are like zombies. > > Where am I saying that? > > > Zombies are how I would traditionally think of machines, but you seem > > to be saying that the axioms and inference rules somehow breathe life > > into the machine. > > Not really. Axioms and inference rule just makes it possible for the > machine to develop (third person describable) beliefs. The relation > between computation and proof are subtle. Let us be sure everyone > understand Church thesis (and its non constructive price) before moving > on the subject of theories and chatting machines. I could say things > but it will adds confusions at this stage. > Also zombie is a concept in the philosophy of mind, but we are not yet > really talking about that. > > OK, i give the solution tomorrow. All right? (answer only if you prefer > I give you more time, or else to make any other comments of course, but > by default I give the answer tomorrow). > > 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 -~----------~----~----~----~------~----~------~--~---
