> On 9 Aug 2019, at 23:40, John Clark <[email protected]> wrote: > > On Fri, Aug 9, 2019 at 7:54 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > >> Without the notion of multiplication and division "a prime number" would > >> have no meaning, and multiplication and division is something ONLY physics > >> can do. > > > First that is false. Any universal digital machine can add and multiply, > > Yes a universal digital machine can add and multiply, and a universal > digital machine just like any machine is made of matter that obeys the laws > of physics.
“Digital machine” is just an expression referring to the kind of machine defining Universal system. They are finite mathematical object. Which one is not relevant. Turing used finite sets, but usually people use (mathematical) words, or just numbers. Finite object can be identified with their Gödel numbers without problem. > > > Second, the expression “physics can do” is so terribly vague that I can > > interpret it it many different ways, > > The statement "physics can do X" may be vague in the Brunospeak language but > it isn't in the English language . You mean such expression is not English. I agree. > > > But I explicitly do not postulate physics. > > I know for a fact that is untrue. 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. Of course I do use the physical reality to send this too you, but that is different from a postulate assuming something physical. It would like saying that group theory assumes the existence of blackboard and chalks … (a confusion of level). 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 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. A physical assumption would be the hypothesis that some particles or fields exist, or a physical “universe”, etc. > > > Without physics no statement in arithmetic would be true and none would be > > false either, they would just be meaningless squiqles. > > > If that is true, 2+2=4 would be a theorem in some physical theory > > No theory was involved. 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. Then what you describe is how the humans discovered the numbers, but with mechanism, we need to assume the numbers, or anything equivalent, and then to derive the physical reality appearance from the computations. That is what the main reasoning proves, and what both math and the empirical reality confirms, up to now. > > > you need to explain how an arithmetical John Clark is not conscious, > > I was talking about intelligence, I have not proposed any consciousness > theory not because it is hard but because it is easy. It is certainly easier that matter. But with mechanism, matter must be explained from that theory of consciousness, and that works very well. > 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, and you have to drive the appearance of matter from the first person indeterminacy on that infinity. That works. > > > How does you God, [...] > > And that is my cue to skip to the next paragraph because I believe in the > value of induction and you've never said anything intelagent after that. Judgment weaken your point a lot. > > >> I don't know how to be clearer or more unambiguous. As I've said more > >> than once, a real calculation can be used to buy a Bitcoin but your > >> pretend phantom calculations lack that property. > > > How can the arithmetical John Clark distinguish between an arithmetical > > bitcoin and a physical bitcoin? > > Distinguish? The arithmetical John Clark can't *do* any distinguishing, > arithmetical John Clark can't *do* anything at all because doing involves > change and arithmetic never changes, but matter that obeys the laws of > physics does. Appearance of change are explained from within arithmetic. Indeed S4Grz1 is a logic of subjective time. > > > You just repeat your credo, without providing explanations or > > justifications. You seem to imbue a lot of magic in your notion of matter. > > If the ability to change by interacting with time and space is magic then > yes, matter has a certain magic that numbers lack. Good! It is that magic which makes you not Turing emulable, once you link consciousness and piece of matter. > > >> Speak for yourself. Maybe you lack the ability to deduce the fact that a > >> non physical thing can't emulate a computer or emulate anything else but > >> I'm smart enough to have figured it out; and I'm not bragging because it > >> takes very little brain power to figure it out. > > > A point which is simply contradict by the facts. The only problem is that > > you don’t open the textbook. > > I don't have to open my computer for it to make a calculation, why do I have > to open a textbook for it to make a calculation? Textbook does not make calculation. I refer to those textbook so you can see that you are the only person believing that a Turing machine or a digital machine, or a program, or a lambda expression is a physical object, or need a physical reality to be implemented. I say that the number x emulate the number y on the number z when phi_x(y,z) = phi_y(z), and that relation is definable in pure arithmetic (usually this is done using Kleene’s predicate). See Davis “computability and unsolvability” chapter 4, where it is done in detail, or ask me to show it here. (By phi_i, I = 0, 1, 2, …) I mean a computable enumeration of all partial computable function, corresponding to the comptable enumeration of the codes of the machines or programs is a fixed universal system. I gave examples like the combinators, the coffee bar machines, the Turing machine, etc. It is “easy" to show that the operation # defined by a#b = phi_a(b) transform N into a combinatory algebra, making the combinator formalism both a very low level language and a very high level language (which explains its importance in theoretical computer science and constructive mathematics, proof theory, etc.). Now the relation phi_x(y) = z is shown, in those textbooks to be an arithmetical relation, by the use of the “well known” predicate of Kleene T(a, b, c), T(a, b, c) says that there is a Turing machine with number a which applies on input b leads to the (halting) computation c. phi_x(y) = z is z = U(min c T(x,y,c). Read the chapter 4 of Davis’ book for all (tedious) details, or read Gödel’s 1931 paper. You need to understand that once you accept the church-Turing thesis, then the code of the total functions canot be mechanically ordered, so that the universal machine is confronted quickly to a non computable reality in arithmetic. > > Arithmetic implement also the computation with oracle. > > 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. Depending on the oracle, we might need richer theory, but that is necessarily the case in arithmetic as the arithmetical reality is far above what any effective theory, or machine, can say about it (by incompleteness). I know nobody who take seriously the magic of Harry Potter, most would say it is only for entertaining. But the non computable distribution of the code of the total computable functions is not a convention; it is the hard price of all universal machineries phi_i, be it combinators, Turing machine, or sigma_1 arithmetical relations, or even just polynomial Diophantine relations. > > >> It has been proven that the truth or falsehood of the Continuum hypothesis > >> makes no difference to our current set theory; and in a similar way if the > >> entire multiverse lacks the resources to calculate a prime number bigger > >> than 10^(10^1000), and it probably does, then the existence or > >> nonexistence of that enormous number has nothing to do with reality. > > > With your conception of reality, which is inconsistent with mechanism. > > Maybe so but I'm not sure because I don't know what the definition of > "mechanism" is in Brunospeak, Please stop this bullying ad hominem absurdity. Mechanism is CT + YD, and you have shown some understanding of both. Indeed, you are the only computationalist practitioner. You already said yes to the doctor! I can have some admiration for that. My point is just that we cannot have mechanism and materialism (both in rather weak sense) together. Then the physical facts (quantum mechanics) add evidences to Mechanism, I would say. > although I have a feeling it would contain words like "primitive" and > "fundamental" which seem pretty irrelevant on a discussion about mind. It is relevant when we discuss on the relation between mind, matter, and number. > > >> . I and my entire world might be a simulation, but if so I am NOT the > >> product of a computation in arithmetic, > > > How do you know? > > I explained how I know that immediately after the comma: > > "I am the product of a computation made in a Physical Turing Machine because > matter that obeys the laws of physics can change but arithmetic lacks that > ability and you can't have computation without change.” Knocking table argument, already shown to be invalid. The arithmetical John Clark in similar histories claims the same things. You posit the existence of some god, that you call matter, and by its magical ability, it transforms all the John Clark in arithmetic into zombie, except one, just for you or perhaps us. That is worst than “a miracle occur”. If that matter has a role in consciousness, either it is Turing emulable, but then it is in arithmetic, or it is not Turing emulable, and you will not survive with the digital brain. If you survive in a physical yet digital emulation, you survive in the digital emulations, and those are run out of time and space in arithmetic, in the relative way apparently confirmed by the observation. > > > Even in many physical theories, like GR, change is relative to the subject. > > Well duh, change is always relative to something. In physics 2 object change > their orientation in space with time, but the change between 2 and 3 is > always one everywhere. Physical stuff changes, mathematical stuff doesn't, > And mind needs change. > > > I am waiting for your explanation, avoiding terms like "real”, of why the > > arithmetical John Clark are zombies. > > There is only one thing I know for certain about zombies, I am not one; other > than that my ignorance on that subject is total. Of course talk of the p-zombies. This might illustrate your lack of interest in the domain, but that should be the reason to be more modest when you identify reality with what we see/observe/measure, which is just following Aristotle theology. Today, only a con scientist could claim has decided between Plato and Aristotle. Aristotle’s idea was fertile, but when looking closer we have reason to doubt and not take it for granted. The Church Turing thesis rehabilitates Pythagorus, with the gift of some vaccine against the reductionist conception of the person. 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/CAJPayv1YODVEDo-Fk15Q9cQVa2UX0KJOp_bRWmSvphcSKPTd_g%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv1YODVEDo-Fk15Q9cQVa2UX0KJOp_bRWmSvphcSKPTd_g%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/4C6224C8-60C3-4073-99BB-F212BEB06380%40ulb.ac.be.
