Hi Bruno, Thank you for the information. I understand these parts for the others it seems I need to search in archives of the list for some keywords that I do not understand. I'm not an old member. I just wanted to say, most of links in your page lead to nowhere!(Error), It would be nice if you fix them.
Mohsen Ravanbakhsh On 5/23/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > > > Hi Mohsen, > > Le 22-mai-07, à 12:20, Mohsen Ravanbakhsh a écrit : > > > > Hi Bruno, > > > > My sixth sens says you're talking about something important :) but I > > don't get it. > > > Note that it could help me if you could be a little more specific. OK I > see another post of you. > > > > > > It could have been of much more interest, if you could elaborate, or > > provide us with some references for each part of your > > > So you are able to make sense of the fact that > [LOGIC+ADDITION+MULTIPLICATION] gives already a Universal Turing > Machine. This is no more astosnishing than the fact that the K and S > combinators provides already turing-universality, or that the Conway > Game of Life is already turing universal. > The advantage of [LOGIC+ADDITION+MULTIPLICATION] is that (universal) > computability is seen as a particular case of provability. > > What is more long to explain in details is that > [LOGIC+ADDITION+MULTIPLICATION + INDUCTION] is already lobian. But I > will first look to your other post which title refer to incompleteness. > > > > > argument.(Beginning from the 'OBVIOUS IMPORTANT QUESTION' it > > becomesvague for me) > > > The key point consists in understanding the difference between > computability/simulability and provability. I will come back on this, > but the idea is that, assuming comp, I can simulate Einstein's brain > exactly, and still not share his beliefs. Similarly the very non > powerful Little-Robinson-arithmetic can simulate rich theories like > PEANO or ZF, but cannot prove the theorem of PA or ZF. > > For example PA can prove that ZF can prove the consistency of PA, yet, > PA cannot prove the consistency of PA. > > Bruno > > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- Mohsen Ravanbakhsh, Sharif University of Technology, Tehran. --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---