It is not a question of existence but of definability. For example you can define and prove (by Cantor diagonalization) the existence of uncountable sets in ZF which is a first order theory of sets. Now "uncountability" is not an absolute notion (that is the Lowenheim-Skolem lesson). Careful: uncomputability is absolute.
Bruno Le 03-nov.-06, à 13:43, Saibal Mitra a écrit : > uncompoutable numbers, non countable sets etc. don't exist in first > order logic, see here: > > http://www.earlham.edu/~peters/courses/logsys/low-skol.htm > > > "[EMAIL PROTECTED]" <[EMAIL PROTECTED]>: > >> >> Ah the famous Juergen Schmidhuber! :) >> >> Is the universe a computer. Well, if you define 'universe' to mean >> 'everything which exists' and you're a mathematical platonist and >> grant >> reality to infinite sets and uncomputables, the answer must be NO, >> since if uncomputable numbers are objectively real (strong platonism) >> they are 'things' and therefore 'part of the universe' which are by >> definition not computable. >> >> But if by 'universe' you just mean 'physical reality' or 'discrete >> mathematics' or you refuse to grant platonic reality to uncomputables >> or infinite sets (anti-platonism or weaker platonism) then the answer >> could be YES, the universe is a computer. 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 firstname.lastname@example.org 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 -~----------~----~----~----~------~----~------~--~---