On Mon, Sep 10, 2018 at 4:59 AM Bruno Marchal <[email protected]> wrote:
>>In the physical world induction is just a rule of thumb that usually >> works pretty well most of the time, but it seldom works perfectly and never >> works continuously, eventually it always fails. > > >*? You seem to confuse mathematical induction, and adductive inference.* > I assume you mean abductive inference, but that says you should look for the simplest explanation and that is not induction. Induction is not about explanations. Every animal with a nervous system employs induction, even snails. Evolution has programmed snails to assume things usually continue, when they don't continue, such as a sudden change in the light level or in background noise then danger often follows so precautions need to be taken, like withdrawing into its shell. The snail has no explanation as to why something changed it just knows that something did and that's usually not a good sign. >>Turing explained exactly precisely how to build one of his machines but >>> you have never given the slightest hint of how to build a "Löbian machine" >>> or even clearly explained what it can compute that a Turing Machine can’t. >> >> >> >*?* >> > ! > > *I have given a lot of example. Peano arithmetic is a Löbian machine. > Zermelo-Fraenkel Set Theory is a Löbian Machine,* > Machines are made of matter as is our brains, Peano arithmetic can be run on a machine as can Zermelo-Fraenkel Set Theory, but neither is a machine because neither is made of matter. > *Here is another definition*: [...] > I'm not interested, definitions are a dime a dozen, you're never going to define your way to the truth. If you want to understand something you got to figure out how to build it, at least in principle. >>Step 3? Ah yes I remember now, that's the one with wall to wall personal >> pronouns without a single clear referent in the entire bunch. > > > *No, you have agreed on each definition. * > John neither agrees nor disagrees because it was never made clear what the personal pronoun "you" means in a world with "you" duplicating machines, all Bruno will say is it's unique and the duplicating machine can't duplicate it for some reason never specified. And thus Bruno simply stated at the start of the "proof" the very thing Bruno was trying to prove. Both know this is true because Bruno is totally unable to state the idea without copious personal pronouns and continues to use those pronouns exactly as Bruno always has as if the existence of a personal pronoun duplicating machine made no difference and it was all business as usual. > >>> *The notion of Löbian machine is easy to construct,* >> >> > > >>The notion of a Perpetual Motion machine is also easy to construct as >> is the Clark Machine that can solve the Halting Problem, but Turing did far >> more than dream up a magical universal calculating machine, he showed >> exactly how to make one. > > > *>Yes, it did that too, but that does not change the fact that his > recovery was in pure mathematics at first. Then later it has been shown to > be in already pure arithmetic.* > Both Church and Turing independently proved the Halting Problem didn't always have a solution but Turing's accomplishment was greater because unlike Church he proved it has significance for the physical world. I'm not alone in this, Gödel also felt that Turing's discovery was more profound than Church's. http://www.cs.umd.edu/~gasarch/BLOGPAPERS/soareturing.pdf > *Universal machine have important logical limitation, and Löbian machine have the same limitation, but are aware of those limitation,* I see no reason why Turing's proof couldn't be encoded to run on a Turing Machine and the conclusion recorded on the tape, so if you asked the machine to prove that it was consistent it wouldn't even try just would just tell you that was a stupid command. > *I recall to you that by machine theology I just meant the modal logic > G*. It is the logic of the true proposition that a machine can or cannot > prove about itself.* > Just like a human a computer can prove that it s consistent if and only if it is inconsistent. So if humans are "Löbian machines" then so is my iMac. John K Clark -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
