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. >
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? 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!" 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 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." > > 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. > > 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. 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-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
