> "But thanks to that crashing, *Church thesis remains consistent*. I > would just say "An existence of a universal language is not ruled out". > > > > I am ok with you. Consistent (in math) means basically "not rule out". > "Formally consistent" means "not formally ruled out", or "not refutable". > > That is: > > "Consistent(p") is the same as "~ Provable(~ p)" " ~" = negation > > like "Provable(p)" is equivalent with "~ Consistent( ~ p)"
All right... Now, let me just rephrase few points of the key post one more time. I will try to be picky with wording. Points which are not mentioned - I fill comfortable with. 1\ There is no language/algorithm/procedure/machine which can describe/execute all total computable functions. 2\ There exists non-empty set of all machine computable functions (inevitably includes both total and strict partial functions). Let us call this set MC (machine computable). 3\ Church himself *defined* the set of so-far-known-computable-functions as those computable by lambda calculus. 4\ What we use to call a *Church thesis* today says, that MC is in fact equal to the set of functions computable by lambda calculus. 5\ Church thesis is refutable. > * * * > > Something else: > > to us verify MM = SII(SII) does crash the system: > > SII(SII) = I(SII)(I(SII)) = SII(SII) = I(SII)(I(SII)) = SII(SII) = > I(SII)(I(SII)) = SII(SII) = I(SII)(I(SII)) = SII(SII) = ... (crashing). > Working with SK combinators, I had a bit problems with omitted parenthesis. Also it was not clear to me what is the meaning of eg. (SKK) since S is expected to take three arguments. What helped me was the unlambda language (http://www.madore.org/~david/programs/unlambda/) So here is my crashing sequence (yep, yours is shorter) (I don't expand the I term to keep it short) SII(SI(S(KI)I)) a reference implementation in unlambda: ```sii``si``s`kii the ` stands for 'apply' operation, aka left parenthesis. with a small modification ```sii``si``s`k.ui we can achieve the computer to print uuuuuuuuuuuuu.... in an endless loop. .u is a special function with a side effect of printing the character u. Best, Mirek --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
