Bruno, In one sense those examples are things for which (finite) reasoning fails, but I would still say that they are governed by (finite) rules and possess a (finite) description-- the problem is "merely" that it takes infinite amounts of time to derive the consequences of those rules/descriptions.

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--Abram On Fri, Dec 26, 2008 at 11:49 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > > On 25 Dec 2008, at 22:27, Kim Jones wrote: > >> >> >> On 26/12/2008, at 5:23 AM, Bruno Marchal wrote: >> >>> >>> On 25 Dec 2008, at 08:05, Abram Demski wrote: >>> >>>> >>>> Bruno, >>>> >>>> I agree with Gunther about the two types of machine. The broader >>>> machine is any system that can be logically described-- a system >>>> that >>>> is governed by rules and has a definite description. >>> >>> Then Church thesis entails it is not broader, unless you mean that >>> the rules are not effective. >>> >>> >>> >> >> I might be missing something here, but somebody please give an example >> of a system that is NOT governed by rules and possesses NO definite >> description. > > Arithmetical truth. That is, the set of all true sentences of > elementary arithmetic. > The set of Gödel number, or description of never stopping programs or > machines. > The set of descriptions (in any universal language) of any non trivial > machines. > At the first order level: all the arithmetical hypostases. > Sigma_2 truth, Sigma_3 truth, Sigma_4 truth, Sigma_5 truth, Sigma_6 > truth, etc. (the union of which gives arithmetical truth) > Analytical truth (far beyond arithmetical truth). > Mathematical Truth (if that exists). > > Kim, all those exemples provide well defined set of objects, (except > the last one) but there is no way to generate them by any machine, nor > can we axiomatize them in any effective way. No effective complete > "Theory" for any of them. > > Alas, there is a need of some math to prove this. If you are patient, > when we get the seven step of UDA, I will have to give you at least a > tool (diagonalization) capable of easily showing the existence and the > non effectivity of those non mechanical mathematical realities. > > It is needed to be more precise on "effectivity" to discover the non- > effectivity. > Mechanism is not a reductionism, (as I explain often to John Mikes) > because Universal machines behaviors depends on those non effective > things. Creation and life appears on the border between the computable > and the non computable. It is similar to the border of the Mandelbrot > set. > > Bruno > > http://iridia.ulb.ac.be/~marchal/ > > > > > > > -- Abram Demski Public address: abram-dem...@googlegroups.com Public archive: http://groups.google.com/group/abram-demski Private address: abramdem...@gmail.com --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---