> On 7 May 2018, at 00:28, John Clark <johnkcl...@gmail.com> wrote: > > On Sun, May 6, 2018 at 2:56 PM, Bruno Marchal <marc...@ulb.ac.be > <mailto:marc...@ulb.ac.be>> wrote: > > > Peano Arithmetic (PA) can already prove the existence of all computation. > > I don't need Peano or Plato to know that computations exist because I can > produce one right now, 2+2=4; but then unlike stuff in Plato's mystical > universe I am made of matter that obeys the laws of physics.
I don’t need Plato’s mystical universe. I need only very elementary arithmetic to get all computations emulated. You are the one invoking a supplementary assumption that there is some mystical primary stuff capable of disrupting the “consciousness flux” that the (sigma_1) arithmetical reality determines. You invoke your God “Matter” to avoid testing the consequence of an hypothesis. > > > It is not a matter of choice. Everett use mechanism, one we have the > quantum, phase randomisation explains the white rabbit away, but with > mechanism, we have to to justify the quantum from the sum on all > computations, not just the quantum one. > > I don't have a clue what that means and I doubt anyone else does either. Yes, OK. I summed up what follows from after step 3. > > > > Study the first chapter of Martin Davis > > > Only if the first chapter of Martin Davis's book can calculate 2+2 as well as > I just did. > > > Sometimes I have the feeling that you take for granted a physical > ontology, but that is automatically doubtful once you understand that the > notion of computation does not require any physical assumption. In fact K, S > and the combination (x y): (K K) …(S S), ((K K) K) ((K K) S), … with only the > two laws > > ((K x) y) = x > (((S x) y) z) = ((x z)(y z)) > > Is enough. > > Don't tell me, tell INTEL that they've been wasting their time all these > years making microchips when all they needed was those two lines. Those two lines have made some people building LISP machines already. Your remarks are distracting and non relevant for the logical point. > > > (3^3) + (4^3) + (5^3) = (6^3) is either true or false independently of > you verifying this or not. > > I agree, but verifying is what calculation is all about, Good inside. The whole point of Gödel-… Kleene is that the numbers can do those verifications, they are called “programs” or “digital machine”, and the notion of “doing by a universal machine” is explained entirely in term of any elementary universal system, and it happens that elementary arithmetic, without the induction axioms is such a system. Those axioms are used by all physical theories. I explain that if you assume mechanism, we have the task assume much less than usual, and to retrieve the physical from a statistics defined internally by the universal machine. You just make fun of mathematical logic and computer science. > and to do that you need physics. In your theory. But then you should not say yes to a future “doctor” as you did. I’m afraid you are inconsistent. > And that's why I say physics is more fundamental than mathematics, physics > can do math but math can't do physics. Only because you ignore the history of the universal machine. You just impose your god by mocking those who are skeptical. > Correct calculations are not the only things that exist, incorrect ones do > too, to sort the correct from the incorrect you need physics, In your religion. > you need INTEL's microchips. They would not exist if their cousins were not discovered before (in arithmetic, combinator logic, etc.). You say a truism: to get a universal physical number, we need the physical. No one doubt this. It is neutral on what will be derived from what. Everett use mechanism, so it has to justify the quantum universal dovetailing from the sum on all dovetailing in arithmetic. Then I explain my contribution in that direction, and your negative comments are not helping. If you believe that a universal machine can distinguish from its first person point of view (without external clues) if she is run by a physical reality or an arithmetical reality, you are the one having to explain how the physical can do that, and what is it? > > > > You seem also to have a problem to distinguish a description of > computation, which also exist in arithmetic, and the fact that participating > to some true arithmetical relations, a computation is truly emulated. That > confuse syntax and semantic, and is well explained in mathematical logic > textbooks. > > And yet, as I've pointed out over and over again and over again. every one of > those mathematical logic textbooks would get a big fat F on a first grade > arithmetic test because they can't make even the simplest calculation, but if > math was more fundamental than physical mechanism and more real as you claim > then those books certainly should be able to. Why would any book be able to do a computation? That does not follow at all. A book is a physical token having finite static amount of information (at human’s disposal). That has nothing to do with computations and number relations, which are Turing universal infinite (even in inductive) reality. And what those things can do, and not do, is the subject of the Davis book, so going at the meta-level here is like just asserting “No, I will not do my homework”. I know,, some students are like that. <sigh>. > I can make a calculation because the atoms in my brain are organized in a way > than enables me to do so but the atoms in those textbooks are not. Sure. But if you succeed in understanding the chapter 4 of the Davis book, you would understand that the tiny fragment of the arithmetical reality emulates all computations, and now, you have to describe me the “physical oracle”, and how a universal machine/number/cominator can test its presence. Bruno > > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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. 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