LauLuna wrote: > > >For any Turing machine there is an equivalent axiomatic system; >whether we could construct it or not, is of no significance here.
But for a simulation of a mathematician's brain, the axioms wouldn't be statements about arithmetic which we could inspect and judge whether they were true or false individually, they'd just be statements about the initial state and behavior of the simulated brain. So again, there'd be no way to inspect the system and feel perfectly confident the system would never output a false statement about arithmetic, unlike in the case of the axiomatic systems used by mathematicians to prove theorems. > >Reading your link I was impressed by Russell Standish's sentence: > >'I cannot prove this statement' > >and how he said he could not prove it true and then proved it true. But "prove" does not have any precisely-defined meaning here. If you wanted to make it closer to Godel's theorem, then again, you'd have to take a detailed simulation of a human mind which can output various statements, and then look at the statement "The simulation will never output this statement"--certainly the simulated mind can see that if he doesn't make a mistake he *will* never output that statement, but he can't be 100% sure he'll never make a mistake, and the statement itself is only about the well-defined notion of what output the simulation gives, not in more ill-defined notions of what the simulation "knows" or can "prove" in its own mind. Jesse _________________________________________________________________ Get a preview of Live Earth, the hottest event this summer - only on MSN http://liveearth.msn.com?source=msntaglineliveearthhm --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
