> On 11 Aug 2019, at 18:07, John Clark <[email protected]> wrote: > > On Sat, Aug 10, 2019 at 1:09 PM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > > “Digital machine” is just an expression referring to the kind of machine > > defining Universal system. They are finite mathematical object. > > If it's a mathematical object then it's not a machine because machines change > and mathematics doesn’t.
Would you say that if the block universe view of general relativity happened to be correct, there would be no more any machine? Already some physicist think that time is an illusion. Obviously, in arithmetic, time is a relative concept, and the change of a machine is defined relatively to other universal machine and natural numbers (which is a discrete version of time already). Anyway, I don’t assume a physical reality, if only because its existence or appearance is what we have to explain from arithmetic once we bet on Digital Mechanism. > > > Finite object can be identified with their Gödel numbers without problem. > > Identified by who? By some universal number. > Identified by brains made of matter I will wait your answer to how that matter make a computation more real than the one already executed in arithmetic (executed in the sense of Church-Turing). > that obey the laws of physics that are inside the heads of mathematicians. > > >> You postulate physics every time you wish to get to the outer side but > >> refuse to step off the curb into the street if you judge that a physical > >> car moving at its current physical speed will intersect with your physical > >> body before you have time to get to the other side. And you are not the > >> only one, for the last 500 million years without exception every single > >> one of your ancestors has postulated physics or you wouldn't be here > >> today; I'm sure some animals ignored physics but they left no descendants. > > > Where is the physical assumption in the theory, which I recall can be put > > in the form: > 1) If A = B and A = C, then B = C > 2) If A = B then AC = BC > 3) If A = B then CA = CB > 4) KAB = A > 5) SABC = AC(BC) > I do not use any other assumption. > > I don't see any physics in the above either, that's why it can't change and > if it can't change it can't compute. > > > You can also assume classical logic + > 1) 0 ≠ s(x) > 2) x ≠ y -> s(x) ≠ s(y) > 3) x ≠ 0 -> Ey(x = s(y)) > 4) x+0 = x > 5) x+s(y) = s(x+y) > 6) x*0=0 > 7) x*s(y)=(x*y)+x > > Those squiggles are slightly different but I still don't see any physics in > them, and so it still can't change and it still can't compute. But it does. > > > In English: > 1) 0 is not the successor of a number > 2) Different numbers have different successors > 3) Except for 0, all numbers have a predecessor > 4) If you add zero to a number, you get that number > 5) If you add a number x to the successor of a number y, you get the > successor of x added to y > 6) If you multiply a number by 0, you get 0 > 7) If you multiply a number x by the successor of y, you get the number x > added to the multiplication of the number x with y > As everyone can see, there is no physical assumption. > > And as everyone can see there is no computation in the above without "you" to > actually *do* things, and "you" is made of matter that obeys the laws of > physics. That is simply false. > > >> People observed that whenever they added two physical things to two more > >> physical things they always got a invariant quantity, four physical > >> things. People then used inductive reasoning to conclude this would always > >> be true even when they are not observed, and at least until the discovery > >> of quantum mechanics this has all worked out fine. But if you wait long > >> enough induction will always let you down. > > > Let us use “inductive inference” in place of “induction” to avoid a > > confusion between mathematical induction and inductive inference. > > Why use different words when it's the same thing? Induction just says that > things usually continue and animals have been making very good use of that > fact for at least 500 million years. For a few hundred years mathematicians > have been using induction to generalize things by saying if they can prove > that something is true for integer n and if they can also prove its true for > integer n+1 then they have proven it is true for ANY integer larger than n. > And that line of reasoning all seems to work very well; but Bertrand Russell, > a man who knew a thing or two about mathematical logic and induction said: > > “The man who has fed the chicken every day throughout its life at last wrings > its neck instead, showing that more refined views as to the uniformity of > nature would have been useful to the chicken.” Mathematical induction is an axiom in some mathematical theories, like Peano arithmetic, or ZF, etc There is simple induction and transfinite inductions. Inductive inference is a technic to infer something about some reality. Machine’s inductive inference is a branch of IA, practical, and theoretical. There are obvious relations between both, but they are very different concepts. > > Mathematicians say that if n is prime then n+1 can not be prime because it is > divisible by 2, however if n+1 is a lot larger than 10^100^100^100 then the > entire multiverse may lack the computational resources needed to divide n+1 > by 2 or by any other number. So if n+1 can't be divided by any integer then > by definition both n and n+1 are prime. > > >> A theory must fit the facts and it's easy to do that with consciousness > >> because there are no facts about it to fit except that I John Clark am > >> conscious. > > > But there is an infinity of John Clark in arithmetic, > > An infinity? There may or may not be an infinity of John Clarks in the > Multiverse but there is not even one John Clark in arithmetic; Then the digital mechanist hypothesis is false. > I know this for a fact because I know for a fact that John Clark can change > and I know for a fact that arithmetic can’t. You confuse Joihn Clark belongs to arithmetic in the relative way, with John clark is arithmetic. In physics that would be like claiming that you cannot change because the block universe is static. > > > and you have to drive the appearance of matter from the first person > > indeterminacy > > First person indeterminacy is just your prosaic observation that people are > not omniscient, for some reason you think this is a revolutionary new > discovery but I feel no duty whatsoever to explain it. You think that it is revolutionary? Thanks, but it is just a modest step in a longer reasoning, which shows that with mechanism, physics is a real and persistent “illusion” in the mind of the universal numbers/machines. > > >> If the ability to change by interacting with time and space is magic then > >> yes, matter has a certain magic that numbers lack. But they explains already the existence of change in time and space, and that there are aware of this, without committing an ontological commitment. > > > Good! It is that magic which makes you not Turing emulable, once you link > > consciousness and piece of matter. > > That statement does not compute. I can change and if matter can change by > interacting with time and space then a material Turing Machine can emulate me. If they exist. But the John Clark in arithmetic makes the same reasoning, and we know a priori that it is false; and that invalidate your reasoning. It begs the question by using an ontological commitment. You have no evidence for a primitive matter, and with mechanism, such evidence are testable, but none have been given until now. > > > Textbook does not make calculation. > > I agree, so telling me to look at a textbook can not strengthen your > argument. To make a calculation you need 2 things: > 1) Matter > 2) Organization made in the way Turing described. And Turing showed that a lambda expression can emulate all Turing machine, so that a model of lambda calculus contains already the universal dovetailing, even the quantum universal dovetailing. It remains to show why it wins the “measure battle”, but the discovery of quantum logics where they are needed for this is a promising step in that direction. > > Textbooks only have one of those attributes, and pure numbers don't have any. > > > See Davis “computability and unsolvability” chapter 4 > > Davis “computability and unsolvability” chapter 4 is incapable of figuring > out what 2+2 is because Davis “computability and unsolvability” chapter 4 > never changes. You make again the rather low level confusion between a text and its meaning. > > > Read the chapter 4 of Davis’ book for all (tedious) details, or read > > Gödel’s 1931 paper. > > Davis’ book and Gödel’s 1931 paper are made of matter but it is not organized > in the way Turing described thus neither one has the ability to figure out > what 2+2 is. Bruno, I think your problem is that although you can follow each > individual step in a proof when you get to the end you really don't > understand what has just been proven. > > >> It the computations performed by a mathematical oracle are real then so is > >> the magic performed by Harry Potter. > > > No, because all mathematician and scientists agrees it is arithmetically or > > set theoretically real. > > Theoretically real? I don't know what that means. > > > I know nobody who take seriously the magic of Harry Potter, most would say > > it is only for entertaining. > > Harry Potter is English fiction, it answers the question what would happen if > a boy could do magic. Mathematical oracles are mathematical fiction, it > answers the question what would happen if a machine could solve problems that > a Turing Machine couldn't. > > >> I don't know what the definition of "mechanism" is in Brunospeak, > > >Please stop this bullying ad hominem absurdity. > > Ad hominem my ass! You persist in making up a new language and inventing > eccentric definitions for very common words like God and atheism (which is > somehow very close to Christianity) and theology and primitive and even the > personal pronoun "you"; and the truth is that in your language I really don't > know what "mechanism" means in Brunospeak or how it differs from > "materialism". > > > You already said yes to the doctor! I can have some admiration for that. > > Well thank you. Examples are better than definitions so does that mean I > believe in "mechanism"? Do I also believe in "materialism"? I'm not kidding, > I don't know if I believe in those things or not because I don't know what > the words mean in your unique language. You show that you believe in matter when you say that a computation has to be done by matter to be real. > > > You posit the existence of some god, that [...] > > And that is my cue to skip to the next paragraph because nothing interesting > ever follows. > > > following Aristotle theology [...] > > And that is my cue to say goodnight. OK. Good morning! 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 [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv1HjGc0fD%2BQ2DR%2B1WntQ3mh2mG8y_v2Bf6wrqKm1RBJtA%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv1HjGc0fD%2BQ2DR%2B1WntQ3mh2mG8y_v2Bf6wrqKm1RBJtA%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/2A98B030-AB3E-4AE2-A189-02DC227C6800%40ulb.ac.be.
