### Re: [Fis] _ Re: _ Re: re Gödel discussion

Cari Terrence, Louis, Maxine e Tutti, premetto che sono un "poverino esponenziale" che non ha la pretesa di menare alcun vanto. Ma mi pare di aver capito dalla triangolazione dei tre colleghi,che non credo si sia conclusa, quello che: - Rosario Strano, un valente matematico dell'Università di Catania, tenendo una conferenza su "Goodel, Tarski e il mentitore" alla fine ha affermato: "In chiusura concludiamo con un'osservazione 'filosofica' suggerita durante la conferenza dal collega F. Rizzo: una conseguenza che possiamo trarre dai teoremi su esposti è che la ricerca della verità, sia nella matematica che nelle altre scienze, non può essere ingabbiata da regole meccaniche, nè ridursi a un calcolo formale, ma richiede estro, intuizione e genialità, tutte caratteristiche proprie dell'intelletto umano ("Bollettino Mathesis" della sezione di Catania, Anno V, n. 2, 28 aprile 2000); - anche a me è capitato, per difendere la scienza economica dall'invadenza o dominio del calcolo infinitesimale, di dichiarare che i modelli matematici assomigliano a dei simulacri, in parte veri (secondo la logica) e in in parte falsi (secondo la realtà): cfr. ultimamente, Rizzo F., ..."Economi(c)a", Aracne editrice, Roma, aprile 2016; -nella teoria e nella pratica economica il saggio di capitalizzazione "r" della formula di capitalizzazione V = Rn. 1/r si può determinare o ricorrendo alla "quantità qualitativa" di hegel ("La scienza della logica") oppure ai numeri complessi o immaginari che, fra l'altro consentirono al matematico polacco Minkowski, maestro di A. Einstein, di aggiustare la teoria della relatività generale, tanto che ho scritto: "I numeri immaginari e/o complessi usati per concepire l''universo di Minkowiski' che trasforma il tempo in spazio, rendendo più chiara ed esplicita l'influenza isomorfica che lo spazio-tempo esercita sulla formula di capitalizzazione e sull'equazione della relatività ristretta, forse possono illuminare di luce nuova la funzione del concetto di co-efficiente di capitalizzazione" (Rizzo F., "Dalla rivoluzione keynesiana alla nuova economia", FrancoAngeli, Milano, 2002, p. 35). Come vedete il mondo sembra grande ma in fondo spetta a Voi e, anche ai poverini come me di renderlo o ridurlo alla dimensione adeguata per comprendere (ed essere compreso) da tutti. Nel ringraziarVi per l'opportunità che mi avete dato, Vi saluto con amicizia intellettuale ed umana. Francesco 2016-05-03 5:28 GMT+02:00 Louis H Kauffman: > Dear Folks > I realize in replying to this I surely reach the end of possible comments > that I can make for a week. But nevertheless … > I want to comment on Terrence Deacon’s remarks below and also on Professor > Johnstone’s remark from another email: > > "This may look like a silly peculiarity of spoken language, one best > ignored in formal logic, but it is ultimately what is wrong with the Gödel > sentence that plays a key role in Gödel’s Incompleteness Theorem. That > sentence is a string of symbols deemed well-formed according to the > formation rules of the system used by Gödel, but which, on the intended > interpretation of the system, is ambiguous: the sentence has two different > interpretations, a self-referential truth-evaluation that is neither true > nor false or a true statement about that self-referential statement. In > such a system, Gödel’s conclusion holds. However, it is a mistake to > conclude that no possible formalization of Arithmetic can be complete. In a > formal system that distinguishes between the two possible readings of the > Gödel sentence (an operation that would considerably complicate the > system), such would no longer be the case. > ” > I will begin with the paragraph above. > Many mathematicians felt on first seeing Goedel’s argument that it was a > trick, a sentence like the Liar Sentence that had no real mathematical > relevance. > This however is not true, but would require a lot more work than I would > take in this email to be convincing. Actually the crux of the Goedel > Theorem is in the fact that a formal system that > can handle basic number theory and is based on a finite alphabet, has only > a countable number of facts about the integers that it can produce. One can > convince oneself on general grounds that there are indeed an uncountable > number of true facts about the integers. A given formal system can only > produce a countable number of such facts and so is incomplete. This is the > short version of Goedel’s Theorem. Goedel worked hard to produce a specific > statement that could not be proved by the given formal system, but the > incompleteness actually follows from the deep richness of the integers as > opposed to the more superficial reach of any given formal system. > > Mathematicians should not be perturbed by this incompleteness. Mathematics > is paved with many formal systems. > > In my previous email I point to the Goldstein sequence. > https://en.wikipedia.org/wiki/Goodstein%27s_theorem >

### [Fis] _ Re: _ Gödel discussion

Dear Friends, I was so struck by the group's focus on Gödel's theorems that I went back to John R. Lucas who originated the idea that Gödel's insights imply that the human miind is not a machine - and therefore capable of genuine phenomenal experience. You may find the ideas in the following informative and useful https://en.wikipedia.org/wiki/John_Lucas_(philosopher) https://en.wikipedia.org/wiki/Minds,_Machines_and_Gödel I noted particularly that I have used complexity (which Lucas mentions towards the end of MM) to establish that organisms are not machines, and out of that I identify the form of information which may explain various aspects of experience. I found Minds, Machines and Godel very useful to read since it seemed to confirm aspects of my offering to you all. On 3 May 2016 at 07:49, Francesco Rizzo <13francesco.ri...@gmail.com> wrote: > Cari Terrence, Louis, Maxine e Tutti, > I state that I am a "exponential poor" who do not claim to lead any claim > whatsoever. But I think I have understood from the triangulation of three > colleagues, I do not think it is concluded, that: > - Rosario Strano, a mathematician at the University of Catania, lecturing > on "Goodel, Tarski and liar" in the end he said: "In closing, we conclude > with a remark 'philosophical' suggested during the conference by fellow F. > Rizzo : a result that we can draw from the theorems of exposed is that the > search for truth, both in mathematics and in other sciences, can not be > caged by mechanical rules, nor reduced to a formal calculation, but it > requires inspiration, intuition and genius, all features own human > intellect ( "Bulletin Mathesis" section of Catania, Year V, n. 2, April 28, > 2000); > - Also it happened to me, to defend the economic science from encroachment > or domain of the infinitesimal calculus, to declare that the mathematical > models resemble simulacra, partly true (according to the logic) and partly > false (according to reality) : see. lately, F. Rizzo, ... "Bursars (c) > to" Arachne publishing, Rome, April 2016; > -in theory and in economic practice the capitalization rate "r" of the > capitalization formula V = Rn. 1 / r can be determined or resorting to > "qualitative quantity" of Hegel ( "The Science of Logic") or to complex or > imaginary numbers that, among other things, allowed the Polish > mathematician Minkowski, master of A. Einstein, to adjust the general > theory of relativity, so much so that I wrote: "the imaginary and / or > complex numbers used to conceive the 'Minkowiski of' universe that > transforms time into space, making it clearer and more explicit the > isomorphic influence that space-time exercises the capitalization formula > and equation of special relativity, maybe they can illuminate with new > lights the function of the concept of co-efficient of capitalization "(F. > Rizzo," from the Keynesian revolution to the new economy ", Franco Angeli, > Milan, 2002, p . 35). > How you see the world looks great but basically it is up to you and even > to poor people like me to make it, or reduce it to the appropriate size to > understand (and be understood) by all. > Thank you for the opportunity you have given me, I greet you with > intellectual and human friendship. > Francesco > > 2016-05-03 5:28 GMT+02:00 Louis H Kauffman: > >> Dear Folks >> I realize in replying to this I surely reach the end of possible comments >> that I can make for a week. But nevertheless … >> I want to comment on Terrence Deacon’s remarks below and also on >> Professor Johnstone’s remark from another email: >> >> "This may look like a silly peculiarity of spoken language, one best >> ignored in formal logic, but it is ultimately what is wrong with the Gödel >> sentence that plays a key role in Gödel’s Incompleteness Theorem. That >> sentence is a string of symbols deemed well-formed according to the >> formation rules of the system used by Gödel, but which, on the intended >> interpretation of the system, is ambiguous: the sentence has two different >> interpretations, a self-referential truth-evaluation that is neither true >> nor false or a true statement about that self-referential statement. In >> such a system, Gödel’s conclusion holds. However, it is a mistake to >> conclude that no possible formalization of Arithmetic can be complete. In a >> formal system that distinguishes between the two possible readings of the >> Gödel sentence (an operation that would considerably complicate the >> system), such would no longer be the case. >> ” >> I will begin with the paragraph above. >> Many mathematicians felt on first seeing Goedel’s argument that it was a >> trick, a sentence like the Liar Sentence that had no real mathematical >> relevance. >> This however is not true, but would require a lot more work than I would >> take in this email to be convincing. Actually the crux of the Goedel >> Theorem is in the fact that a formal system that >> can handle basic number