On Thursday, May 15, 2014 2:19:01 PM UTC-4, Bruno Marchal wrote: > > > On 15 May 2014, at 14:40, Craig Weinberg wrote: > > > > On Wednesday, May 14, 2014 6:34:55 PM UTC-4, Bruno Marchal wrote: >> >> >> On 14 May 2014, at 03:45, Craig Weinberg wrote: >> >> I'm showing that authenticity can be empirically demonstrated, and that >> the failure of logic to detect the significance of authenticity can be >> empirically demonstrated, but that neither authenticity or the failure of >> logic to detect it can be detected within logic. At least Godel shows >> logic's incompleteness, but that is just the beginning. What logic doesn't >> know about what logic doesn't know I think dwarfs all of arithmetic truth. >> >> >> Gödel has shown the completeness of first order logic, and this means >> that what we prove in a theory written in such logic, will be true in all >> interpretation of the theory, and what is true in all interpretations, will >> be provable in the theory. >> >> Then Gödel proved the incompleteness of *all* theories about numbers and >> machines, with respect to a standard notion of truth. >> >> This means that the truth about number and machines are above what >> machines can prove, and thus what human can prove, locally, if we assume >> computationalism. >> > But computationalism is a theory about numbers and machines, so we cannot truthfully assume it.
> > Does Wiles solution to Fermat's last theorem prove that humans can use > non-computational methods, in light of the negative solution to Hilbert's > 10th problem? > > > No. > Why not? I doubt I'll understand your answer but I might be able to get someone else to explain why he thinks you're wrong. > > > > Penrose thinks that it does: > > "The inescapable conclusion seems to be: Mathematicians are not using a > knowably sound calculation procedure in order to ascertain mathematical > truth. We deduce that mathematical understanding – the means whereby > mathematicians arrive at their conclusions with respect to mathematical > truth – cannot be reduced to blind calculation!" > > > Good. That's when Penrose is correct. No machines at all can use a > knowably sound procedure to ascertain a mathematical truth. > By adding "knowably" Penrose corrected an earlier statement. But then he > does not realize that now, his argument is in favor of mechanism, because > it attribute to humans, what computer science already attributes to machine. > If computer science attributes it to machines (and I would say that it is only some computer scientists who do so) then it cannot use a knowably sound procedure to do that, therefore it is a belief rather than a correct attribution. If we allow mechanism to be true by faith, I don't see how any argument within mechanism can be used to prove that mechanism cannot be disproved. > > > > > The arguments against Penrose seem to me pure unscientific bigotry: > > "Theorems of the Gödel and Turing kind are not at odds with the > computationalist vision, but with a kind of grandiose self-confidence that > human thought has some kind of magical quality which resists rational > description. The picture of the human mind sketched by the computationalist > thesis accepts the limitations placed on us by Gödel, and predicts that > human abilities are limited by computational restrictions of the kind that > Penrose and others find so unacceptable." - Geoffrey LaForte > > > Well, if you have evidence that we don't have those limitations, please > give them. > That's what I'm giving. I saw someone's exhibit at the consciousness convention a few weeks ago which included a musical translation of Wiles proof - a proof which he says would not be possible for a computer to produce, given the negative answer of Hilbert's 10th problem. > Are you able to solve and decide all diophantine equations? > I can't, but Wiles proves that humanity as a whole might. > > > > > > He seems to be saying "I don't like it when people imagine that being > human can ever be an advantage over being a machine. Machines must be equal > or superior to humans because of the thesis that I like." > > > > Being a machine is an advantage, for reproduction and use of information > redundancies. Instead of terraforming the neighborhoods we can adapt > ourselves in much more ways. We have more clothes, and ultimately we know > where they come from, and where we return. > You're saying that we are identical to machines on one hand but that if we are machines we will be able to be and do things that we could not do now. That says to me that you are 1) intuiting properties of non-machines that are not discoverable by math, and 2) attributing those properties to us because it is natural to assume that humans are not machines. > > > > >> >> Universal machine are always unsatisfied, and are born to evolve. There >> is a transfinite of path possible. >> > > But there are a lot of humans who seem quite satisfied. They actively > resist dissatisfaction and protect their beliefs, true or not. > > > Good for them. I guess they don't look inward or are not interested in the > search of truth. > Then either they aren't universal machines, or it doesn't mean anything to say that universal machines are always unsatisfied. > > > > > > >> >> And Gôdel completeness is what machine discover themselves quickly, they >> can justify it rationally. >> > > Yet some of what they justify is not merely justified within their own > experience or belief, but veridically in intersubjective experience over > many lifetimes. > > > That too, from passing from the arithmetical []p (and []p & <>p) to the > non arithmetical []p & p (and []p & <>p & p), with p sigma_1. > > I almost only translated what you said in arithmetical terms, and it works > very well, as this entials your insitence that sense is not formalizable in > arithmetic. (It also refute your statement that this fact refutes comp). > To me, what you're saying sounds like "I figured out that what you are saying is wrong." but then not explaining it. Craig > > Bruno > > > > > > Craig > > >> >> Bruno >> >> >> http://iridia.ulb.ac.be/~marchal/ >> >> >> >> > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-li...@googlegroups.com <javascript:>. > To post to this group, send email to everyth...@googlegroups.com<javascript:> > . > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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