Bruno Marchal wrote: > > On 08 Aug 2011, at 20:56, benjayk wrote: > >> >> >> Bruno Marchal wrote: >>> >>> >>> On 07 Aug 2011, at 21:50, benjayk wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> >>>>>> >>>>>> >>>>>> Bruno Marchal wrote: >>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Bruno Marchal wrote: >>>>>>>>> >>>>>>>>> Then computer science provides a theory of consciousness, and >>>>>>>>> explains how >>>>>>>>> consciousness emerges from numbers, >>>>>>>> How can consciousness be shown to emerge from numbers when it is >>>>>>>> already >>>>>>>> assumed at the start? >>>>>>> >>>>>>> In science we assume at some meta-level what we try to explain at >>>>>>> some >>>>>>> level. We have to assume the existence of the moon to try >>>>>>> theories >>>>>>> about its origin. >>>>>> That's true, but I think this is a different case. The moon >>>>>> seems to >>>>>> have a >>>>>> past, so it makes sense to say it emerged from its constituent >>>>>> parts. In the >>>>>> past, it was already there as a possibility. >>>>> >>>>> OK, I should say that it emerges arithmetically. I thought you did >>>>> already understand that time is not primitive at all. More on this >>>>> below. >>>> Yeah, the problem is that "consciousness emerging from arithmetics" >>>> means >>>> just that we manage to point to its existence within the theory. >>> >>> Er well, OK. But arithmetic explains also why it exist, why it is >>> undoubtable yet non definable, how it brings matter in the picture, >>> etc. >> Well, if I try to interpret your words favourably I can bring myself >> to >> agree. But I will insist that it only explains why it exists >> (ultimately >> because of itself), and does not make sense without consciousness. >> >> I am getting a bit tired of labouring this point, but honestly your >> theory >> is postulating something that seems nonsensical to me. Why on earth >> would I >> believe in the truth of something that *can never be known in any way* >> (namely, that arithmetics is true without / prior to consciousness)? > > Why do I believe that Benjayk exists, independently of me? I think because you have the sense of seperate existence and take that to be an accurate reflection of how the world works on the deepest level. I think it is an unfounded belief, ultimately. Our independence is relative. I believe we really are fundamentally the same being in different expressions.

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Bruno Marchal wrote: > > Why do some people believe in God? I guess because they need something to believe in that there is something beyond themselves. Which makes sense, as long as you think you are seperate from God. As you begin to see you aren't, there is no need to believe in God as an act of faith, because you aware that you already experience God. Bruno Marchal wrote: > > Why do some people believe in a physical universe, prior to the > apparition of life? Evidence seems to suggest that the physical universe existed before life appeared, so this is reasonable belief in my opinion. Bruno Marchal wrote: > > Why do some people believe that 17 is prime, prior to everything? I don't know, maybe because of treating numbers as some kind of God. I don't see how they could be prior to everything. I don't know what this would even mean. Bruno Marchal wrote: > > We cannot prove those statements, except in theories which postulate a > realm which transcend us. If we don't do that we fall into solipsism. Yeah, sure. "Ego solipsism" is riduculous, but "consciousness solispism" is obvious, honestly. "I am"ness (being oneself) is all that is - everything is itself. Bruno Marchal wrote: > > And about the truth of "17 is prime", you can know it by reflection, > if you agree with simple statement like 0 ≠ s(x), etc. > That why I postulate explicitly those little statements on which every > one agree, except sunday-philosopher (I am serious here). Sure, I agree with that. Bruno Marchal wrote: > > I think you are confusing (like all beginners in logic) the level and > the metalevel. The TOE I am isolating from the comp hypothesis does > not assume consciousness, because that would mean it would have some > sentence like "consciousness exists", but it contains only strings > like "0 ≠ s(x)", "s(x) = s(y) -> x = y", ... > The consciousness you mention is used implicitly at the meta-level, it > is not assumed in the theory. > I get that. But just because we don't explicitly assume something in theory, doesn't make the theory independent of that which isn't explicitly assumed, but assumed even before making the theory. You talk as if the meta-level can just be ignored within the theory, which doesn't work. The theory itself arises within the meta-level, and thus it is a mistake to pretend it can be conceived apart from it. Bruno Marchal wrote: > >> >> >> >> Bruno Marchal wrote: >>> >>>> We have no >>>> reason to suppose this expresses something more fundamental, that >>>> is, that >>>> consciousness literally emerges from arithmetics. Honestly, I don't >>>> even >>>> know how to interpret this literally. >>>> >>> >>> It means that the arithmetical reality "is full" of conscious >>> entities >>> of many sorts, so that we don't have to postulate the existence of >>> consciousness, nor matter, in the ontological part of the TOE. We >>> recover them, either intuitively, with the non-zombie rule, or >>> formally, in the internal epistemology canonically associated to >>> self- >>> referring numbers. >> But what you do is assuming consciousness (you have to!) > > Logician are literalist. My theory of everything is: > > 0 ≠ s(x) > s(x) = s(y) -> x = y > x+0 = x > x+s(y) = s(x+y) > x*0=0 > x*s(y)=(x*y)+x > > It does not assume consciousness. You just didn't write down that you assume consciousness. It's just putting the mystery under the carpet and saying it isn't there. If you didn't assume consciousness you couldn't even write the axioms down. So you can't say that you theory is independent of consciousness . How would you know that, if you already always assume consciousness? Bruno Marchal wrote: > > It assumes that zero is not a > successor (written 0 ≠ s(x)), it assumes that if two successor of > numbers are equal, then they are successor of the same number (written > s(x) = s(y) -> x = y), and it assumes the recursive laws of addition > and multiplication, and nothing else. Nope. You just failed to write down that you assume consciousness. Bruno Marchal wrote: > >> and then formulate >> a theory that claims itself to be primary and ontologically real that >> derives that consciousness is "just epistemlogically true", by >> virtue of >> hiding the assumption that consciousness already exists! > > You might demolish *all* attempts made by physicists to explain the > origin of planets, on the pretext that they are using a planet to > convey their theories to people. This is not the same. The physicists surely say that they assume the existence of the planet. It is an observation they made. And they try to make sense of that observation. No problem with that. You can make the theory that you observe that there is consciousness - and thus assume it within the theory - and try to make sense of that with numbers, this is fine with me. You could also not make explicit in the theory that you assume consciousness, but then you have to be careful to not talk as if the theory is independent of it. Bruno Marchal wrote: > >> It seems you are just bullshitting yourself by not mentioning >> consciousness >> as an assumption in the theory and then claim it follows "without >> assuming" >> it. > > UDA presupposes it, if only to explain what we have to explain. Then, > it isolates the TOE which does no more presuppose consciousness in the > ontology You continue to say that, yet I don't see how you do this. You need to presuppose consciousness, because there is no way not to. Bruno Marchal wrote: > >> >> What you call ontological part of the theory are just the axioms you >> make >> explicit. > > Not at all. The ontology is the natural numbers: 0, s(0), s(s(0)), > etc... It is captured in the theory by the infinity of theorems like > Ex(x =0), Ex(x = s(s(0)), Ex(x = s(s(s(0))), etc. OK. Wrong formulation. Not only the axioms themselves, but also what follows from them. Bruno Marchal wrote: > >> I don't see how this make them ontological, > > It is captured in the theory by the infinity of sentence like Ex(x > =0), Ex(x = s(s(0)), Ex(x = s(s(s(0))), etc. > The intended meaning of "E" is it exists. So why does the existence needs to be ontological? Why can't it mean "existing within the theory"? Like Harry Potter exists within the book. I am not saying numbers are fictional, but there is no need to postulate them as fundamental, either. Bruno Marchal wrote: > >> and the implicit >> assumption epistemological. > > Not at all. The epistemology is entirely derived. It is not assumed, > even implicitly. You say this without ever showing how you mange to not assume consciousness. Bruno Marchal wrote: > >> If anything, it would be the opposite. What is >> implicit in everything, ie that which cannot be removed, is >> ontological, and >> what can (apparently) be removed (or not mentioned) is >> epistemological. We >> can be conscious without any notion of numbers, > > Not with comp! If you say yes to the doctor, it is because you assume > that he will save your soul on a disk. That is a number, and it has to > make sense even when your (original) brain is destroyed. But we don't have to be aware that this can be represented as a number. I may just say yes regardless. Also, I'm not sure if I would accept COMP. Maybe I would say "yes" without really believing it will work. Bruno Marchal wrote: > >> but there is no notion of >> numbers without consciousness. > > I don't see why you are so sure that "17 is prime" needs > consciousness, to be true. Because I am unable to remove consciousness, it is just obvious that everything needs it. I just can't make sense of something being true without consciousness. How would I know what true means if there isn't consciousness? Bruno Marchal wrote: > > It needs consciousness to be known, but not > to be true. You are perhaps confusing truth and knowledge. Knowledge > presuppose a knower. Truth don't. Well, I think truth and knowledge in a very general sense are equivalent. What you usually call knowledge is much more narrow, though. If a truth is totally unkown, how can you know it's true, or false? Bruno Marchal wrote: > > Proton are made of quarks or are not > made of quarks independently of the humans, a priori. Even less > doubtable is that the number 6789279001 is either composite or prime, > independently of you knowing which alternative is true, or even ever > thinking on that question. Right. I just think consciousness always has implicit knowledge of this already. It is itself, and knows (experiences) that, and in this, all knowledge is already there in a compressed form. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> OK. That would be a real disagreement. I just assume that the >>>>> arithmetical relations are true independently of anything. For >>>>> example >>>>> I consider the truth of Goldbach conjecture as already settled in >>>>> Platonia. Either it is true that all even number bigger than 2 are >>>>> the >>>>> sum of two primes, or that this is not true, and this independently >>>>> on >>>>> any consideration on time, spaces, humans, etc. >>>>> Humans can easily verify this for little even numbers: 4 = 2+2, 6 = >>>>> 3+3, 8 = 3+5, etc. But we don't have found a proof of this, despite >>>>> many people have searched for it. >>>>> I can see that the expression of such a statement needs humans or >>>>> some >>>>> thinking entity, but I don't see how the fact itself would depend >>>>> on >>>>> anything (but the definitions). >>>> My point is subtle, I wouldn't necessarily completly disagree with >>>> what you >>>> said. The problem is that in some sense everything is already there >>>> in some >>>> form, so in this sense 1+1=2 and 2+2=4 is independently, primarily >>>> true, but >>>> so is everything else. >>> >>> The theory must explains why and how relative contingencies happen, >>> and it has to explain the necessities (natural laws), etc. >> OK. It can theoretically explain that, no doubt about that. But from >> this it >> doesn't follow that the means of explanation (numbers) are primary. > > We have to start by assuming that something exist, because we cannot > derive anything from nothing. This can be proved. people who derive > things from nothing assume a notion of set, which means that they > assume much more than nothing. Well, OK. By virtue of being able to formulate a theory, we always assume consciousness, so let's just make this explicit first. Bruno Marchal wrote: > >> I can >> explain with words why humans have legs, this doesn't mean my words >> are the >> reason that humans have legs. > > But numbers are infinitely richer than words, unless you add some > primitive laws. But every number relation can easily be expressed with words. Just say zero for 0, successor of zero for 1, plus for +, times for *,... Bruno Marchal wrote: > > Mathematics is not a language. Well it depends on what you mean with mathematics. If by math you mean what mathematical reasoning describes, OK, but I would regard math as the way of describing (and reasoning) itself. 1+1=2 is a statement in the language of math, but what it refers to is deeper than math. Bruno Marchal wrote: > >> Why? Because I fail to see what this might even mean. How >> could I know that there is meaning without anyone being able to see >> meaning? > > By having the intuition that 17 is prime is a truth which does not > depend on time, space, etc. If you believe that the primality of 17 is > human dependent, I will ask you to define what is a human, and to > explain the relation of dependence which make it impossible of > senseless that 17 might be prime without human. This is just a straw man, I didn't say that whether 17 is prime is human dependent. Bruno Marchal wrote: > >> >> >> >> Bruno Marchal wrote: >>> >>>> and ultimately is equivalent to it (IMO), so we derive from the >>>> meaning in >>>> numbers that meaning exist. It's true, but ultimately trivial. >>> >>> No, we derive from numbers+addition+multiplication a theory of >>> meaning, consciousness, matter. You should not confuse a theory, and >>> its meaning, interpretation, etc. >>> I happens that we can indeed explain how numbers develop meanings for >>> number relations, etc. >> But numbers aren't the kind of thing that can develop anything. > > Well, you really have to study some book on number and computer (universal > number). I guess I would understand that we can make up a story that says that numbers can develop something in a metaphorical way (by using an interpretative meta-level), but fundamentally numbers are just conceptual, and thus can't literally develop something. I just don't see how this is meaningful. Bruno Marchal wrote: > >> The >> consciousness, that can be, in some way, represented in arithmetic, >> can >> develop meaning. > > Yes. Numbers representation of consciousness, is not more intriguing > than a chemical brain representing you. So maybe they can represent consciousness, but this doesn't make them the cause of it. The word "consciousness" also represent consciousness, but certainly isn't the cause of it. Bruno Marchal wrote: > > Now, it is a bit more tricky, because consciousness is not > representable by numbers, it is lived by numbers relatively to > infinities of numbers. But this needs to be understood by following > all the details of the reasoning. I will not insist at this stage. You see, the reasoning doesn't really matter. In my view you make a category mistake at the start, by thinking concepts can live anything. They only can in metaphorical way, like characters in a movie can live something. Your reasoning only shows you can make a coherent story about numbers "living" something. Bruno Marchal wrote: > >> >> >> >> Bruno Marchal wrote: >>> >>>> That's why it makes little sense to me to say consciousness as such >>>> arises >>>> out of numbers. >>> >>> It means that we have a theory with some simple primitive terms, >>> actually 0, s(0), s(s(0), + the laws of addition and mulitiplication, >>> and from this, and only from this (not from our interpretation of >>> those symbols, just by applying the las of addition and >>> multiplication, + definitions), we can derive proposition concerning >>> observers, their consciousness, meaning, the mass of their body, etc. >> You just hide that you interpret the theory! > > But that is not part of the theory. Again, you would say to the guy > who explains the apparition of the solar system that he is hiding the > fact he is is using the solar system, indeed a place on earth, to > expose its theory. That is a big confusion of level. But the guy that explains the apparition of the solar system makes explicit that the solar system is already assumed to exist! He just tries to find a relation between this observation and our observations about the past. Bruno Marchal wrote: > >> Of course you can express >> everything with numbers if you interpret them the right way. But if >> you >> don't, they are just a bunch of meaningless numbers. >> Derivation itself is a kind of interpretation. > > Which is done in arithmetic itself, as shown by Gödel arithmetisation > of meta-arithmetic. But then you just represent the interpretation within arithmetic. The interpretation itself still doesn't ultimately happen within arithmetic! Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>> I might miss something, but your critics here resemble to "we cannot >>> understand how the brain function, because we need a brain to make >>> the >>> understanding". That problem has been solved *in* arithmetic. It is >>> not entirely obvious. >> Well, it has been solved in (or maybe more accurately with) >> arithmetic and >> with the help of the people that understand arithmetic. > > Not at all. It is really *in* (Peano) arithmetic. Or *by* Peano > arithmetic, but logicians prefer to say *in*, because they think > theory, where I think theorem provers. It is not at all "with", and > the fact that people understand arithmetic or not is not part of the > explanation. This is just your claim. It is not written down that this is the case, but this doesn't change that it is so. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> Subjectively we first need consciousness to make sense of >>>> numbers. >>> >>> Yes, but the numbers themselves does not need consciousness >>> primitively. They does not need we make sense of them. >> How do you know? This statement seems meaningless to me. > > How does a neurologist knows that a brain can exist without the > existence of its own brain? Well, I guess because he has the intuition that his brain is not primitive, that is, he could be without his brain (even if he is superficially unware of that). Bruno Marchal wrote: > > Science is always build on primary > *assumptions*. I assume numbers, and this is usually not considered > controversial by scientists. Then the theory *explains* how numbers > develops consciousness, entirely by virtue of the laws they obey to. Right. But you also assume consciousness. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> Bruno Marchal wrote: >>>>> >>>>>> Bruno Marchal wrote: >>>>>>> >>>>>>> Yet, consciousness is not assumed as >>>>>>> something primitive in the TOE itself. >>>>>> But this doesn't really matter, as we already assume that it's >>>>>> primitive, >>>>>> because we use it before we can even formulate anything. >>>>> >>>>> We already assumed it exists, sure. But why would that imply that >>>>> it >>>>> exists primitively? It exist fundamentally: in the sense that once >>>>> you >>>>> have all the true arithmetical relation, consciousness exists. So, >>>>> consciousness is not something which appears or emerges in time or >>>>> space, but it is not primitive in the sense that its existence is a >>>>> logical consequence of arithmetical truth (provably so when we >>>>> assume >>>>> comp and accept some definition). >>>>> >>>>> Sometimes I sketch this in the following manner. The arrows are >>>>> logico- >>>>> arithmetical deduction: >>>>> >>>>> NUMBERS => CONSCIOUSNESS => PHYSICAL REALITY => HUMANS => HUMANS' >>>>> NUMBERS >>>> I accept this deduction. But just because it can deduced does not >>>> mean it is >>>> more primary. To me there is no reason to suspect that consciousness >>>> does >>>> not exist primitively. >>> >>> That is like: I completely understand how a car engine function, >>> but I >>> do not see any reason why this would prevent car to be pulled by >>> invisible horses. >> Not at all. You failed to show that numbers make any sense absent >> consciousness, > > You fail to explain how the truth of "17 is prime" depends on > consciousness. Well, I would equate truth and consciousness, and of course the truth of "17 is prime" depends on truth. It is just obvious. There is no objective explanation of that. Either you get it, or not. I can just try to point to the obvious. Bruno Marchal wrote: > > You should be the one explaining to me why "17 would no more be prime" > in case humans or life disappear from the physical universe. I don't believe this at all. Bruno Marchal wrote: > >> while we could probably agree that cars can function without >> invisible horses. > > Yes, but this we cannot prove. We accept this because we prefer simple > explanation than complex one. Right. Bruno Marchal wrote: > > All the same for a theory of > consciousness. But to say that numbers exist without consciousness is not simple, but impossible, because you can't remove consciousness to see if numbers still exist. Part of a simple theory is that it makes explicit what it assumes, otherwise it is just confusing. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>> If the numbers can explain why the numbers believe >>> correctly in the existence of consciousness, without postulating >>> consciousness at the start, the theory NUMBERS is preferable to the >>> theory NUMBERS+CONSCIOUSNESS, especially that consciousness is hard >>> to >>> define, and is at the origin of controversies. It is just a use of >>> the traditional weak form of OCCAM in a theoretical framework. >> I repeat myself here, but what on earth do numbers mean without >> consciousness? > > What on earth *anything* could mean without consciousness? But *that* > meaning is used at the meta-level, not at the level of the theory. OK. But then we need to take the meta-level into account when discussing the the theory, as the theory does only exist in the context of this level. You just talk as if it doesn't exist. Bruno Marchal wrote: > > Give me a definition of the number five, and explain to me why you > need consciousness, not to make sense of it, but for its mathematical > property. Without sense there is no sense in mathematical properties. Bruno Marchal wrote: > >> Bruno Marchal wrote: >>> >>>> Bruno Marchal wrote: >>>>> >>>>> But you will need a richer language to >>>>> describe that bijection. >>>> But as you said below, the same it true for expressing points with >>>> natural >>>> numbers. It makes only sense if we encode the points in the numbers >>>> and have >>>> an external decoding mechanism. >>> >>> Not at all: the "external decoding" is, in the case of arithmetic >>> (number + the laws of addition and multiplication) entirely internal. >> What? How do you decode numbers with numbers? > > Excellent question! But you should understand that this is the non > trivial part of Gödel's proof of its 1931 theorem. > I am just hoping that people are familiar with computers so that they > can imagine how a program (a lisp interpreter, for example) can > interpret another list as a program. It is basically the same trick, > but with number+add+mult, instead of list+lambda. > That is obvious today for computer scientists, but Gödel showed this > phenomenon arises with numbers before computers were build. It is not > obvious because addition and multiplication are rather low level > procedures, so that a description of how numbers decode numbers with > numbers is rather long and tedious to describe. I might try if you > insist. Last year a student, like you, did not believe numbers can do > that, and I have been obliged to proof the fundamental theorem of > arithmetic, the chinese lemma, the beta function of Gödel, etc. Things > are already easier if you accept the exponential laws, but to show > that I need only RA, I could not use the exponential laws, nor the > induction axioms. Yet I succeed in convincing him that this is > possible. It has taken a full year of rather heavy math. > It is a miracle of the numbers, but if you accept comp, it is no more > astonishing than people using brain to study brains. Yes, relative > numbers can study relative numbers and get quite troubled by their own > abilities. But if you decode numbers with numbers you still have numbers and so failed to ultimately decode anything, if you don't use a meta-level, to decode the decoding. How can numbers decode numbers without using a meta-level, that is without arithmetization (because arithmetization assumes that someone assumed on a meta-level understand the arithmetization)? Bruno Marchal wrote: > >> >> >> >> Bruno Marchal wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> >>>>>> >>>>>> >>>>>> Bruno Marchal wrote: >>>>>>> >>>>>>>> but still it's not as powerful as the language it represents. >>>>>>>> >>>>>>>> Similarily if you use just natural numbers as a TOE, you won't >>>>>>>> be >>>>>>>> able to >>>>>>>> directly express important concepts like dimensionality. >>>>>>> >>>>>>> >>>>>>> Why? If you prove this, I abandon comp immediately. >>>>>> Hm, how do you express the point (3,4) on a two-dimensional plane >>>>>> with >>>>>> natural numbers? >>>>> >>>>> I might use a Gödel-like coding for the string "(s(s(s(0))), >>>>> s(s(s(s(0)))))", like coding "(" by 2, "s" by 3, "0" by 4 and ")" >>>>> by >>>>> 5, and then the string itself, using the prime numbers, by 2^2 * >>>>> 3^3 * >>>>> 5^2 * 7^3 * etc. That is each prime number exponent the code of the >>>>> particular symbol. Or something like that, where I can code an >>>>> axiomatic of the plane by a number too, etc. >>>> But then you faild to directly express the concept! You just >>>> represented it >>>> in a less rich language. >>> >>> The concept itself is expressed through some arithmetical relation, >>> that is a sentence build on the language of first order logic + the >>> symbols: s, +, * and 0. >> But those don't express dimensionality. Honestly, it seems to me you >> believe >> so much in arithmetic that you disregard it's actual power to express >> concepts. + doesn't imply any dimension, nor does * or 0. > > What do you mean by "express dimensionality"? An expression that can easily be seen to map to a dimensional space. That is, without using a meta-level of encoding. 3+4i expresses dimensionality just with the explanation that the real part is the x coordinate and the imaginary part the y coordinate. With numbers, there is no such short explanation. Bruno Marchal wrote: > > Do you agree that a > human can express dimensionality? Yes. Bruno Marchal wrote: > > Do you agree that a digital brain > can express dimensionality? Yes, if there is a way to convert the output of the digital brain into a intelligable format. Bruno Marchal wrote: > > If so, with comp, you can understand that > numbers can express dimensionality, even if you don't know the details. Numbers can express dimensionality on a meta-level (with additional interpretative layers), but they themselves don't. We first have to convert the output of the computations into something else than numbers. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> >>>>>> It seems we have to interpret the numbers in a certain way >>>>>> to do this, and can't express it directly. If we used gaussian >>>>>> integers we >>>>>> could simply describe the point as 3+4i. >>>>> >>>>> That's OK, but 3+4i can itself be coded, by 2^(code of 3)*3^(code >>>>> of >>>>> +)*5^(code of 4) *7^(code of i). >>>> But that's the point! It can be *coded*. But everything can be coded >>>> with >>>> the symbol "I" as well. In both cases we need some intelligent >>>> decoding to >>>> retrieve the meaning. >>>> >>> >>> No, we don't need it. The intelligent being is coded, but not just >>> coded, it is fully represented by arithmetical relations, and fully >>> emulated by arithmetical relations. So it has its personal points of >>> view, and from its points of view it does not matter how he is >>> represented. >> Again, you just implicitly assume the intelligent being, by >> attributing >> points of view to the numbers. But you don't provide any evidence >> that this >> point of view has anything to do with numbers in particular. > > ? have you read the second part of sane04. Well, I know it is concise, > and presuppose you read some of the papers in the reference. But the > whole things has been done in all details. Bp = the machine or Löbian > number (under consideration) believes p, and Bp is a pure arithmetical > relation (written only with the symbol s, 0, +, * + logical symbols). You just show you can represent points of views in numbers. Not that the points of view really belong to the numbers, in more than a metaphorical or representative way. Bruno Marchal wrote: > >> This >> is not enough. Because the representation makes no sense without >> making >> sense of it. > > That is like saying that a brain cannot think without a human making > sense on the notion of brain, or that the big bang makes no sense, > without the presence of a physicist to make sense of it, or that the > notion of dinosaur makes no sense, without a modern zoologist making > sense of it. Nope, it is like saying that a brain cannot think without anyone making sense of the brain, or that the big bang makes no sense, without anyone make sense of it, or that the notion of dinosaur makes no sense, without anyone making sense of it. The one making sense of it is consciousness. Bruno Marchal wrote: > > But a LISP intepreter can interpret a LISP program independenltly of > any humans, Yes, but the final interpretation is always done by consciousness. It works on a representative level, but no more. Bruno Marchal wrote: > > and I show, in the comp frame, that numbers makes sense of > themselves; just by virtue of the + and * laws, without any need of > humans or aliens to make sense of it. If you have some idea how a > computer work, this should be not so hard to understand. The computer shows fairly obviously that he can make no sense of himself. We always need some tools to output it's compuations in a usable way an a user, even if the user is only watching. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> >>>> Bruno Marchal wrote: >>>>> >>>>>> >>>>>> >>>>>> Bruno Marchal wrote: >>>>>>> >>>>>>> From comp you can >>>>>>> derive the whole of physics, and this should be easy to >>>>>>> understand if >>>>>>> you get the UDA1-7. >>>>>> Well, I get that if we accept COMP we need to associate sheafs of >>>>>> computations to mind-states, but I have no clue how natural >>>>>> numbers >>>>>> can be >>>>>> used to derive physics, or even formulate anything related to >>>>>> physics, >>>>>> without using a meta-level of interpretation. It seems we always >>>>>> need a more >>>>>> powerful language to do that. >>>>> >>>>> So physics becomes a first person uncertainty calculus >>>>> associating to >>>>> each computational state a collection of computations, hopefully >>>>> with >>>>> a reasonable measure (which has to be derived by the self-reference >>>>> logic. >>>>> >>>>> The meta-level of comprehension can be embedded in the arithmetical >>>>> truth, in the same way that Gödel discovered that metamathematics >>>>> can >>>>> be embedded in (and retrieved from) arithmetic. >>>> It all comes down to the same thing, that we encode statements in >>>> arithmetic. But for this to make sense we need some external thing >>>> to make >>>> sense of the encoded statements. >>> >>> I see you miss the "real thing", which is tedious to explain (but >>> well >>> understood by logicians). You don't need to interpret the coding and >>> the decoding. The coded entities do it by themselves. >> What you miss is that coded entity is consciousness itself, and it >> doesn't >> emerge out of the coding but is postulated at the start. > > It is not. I repeat that the toe is: > > 0 ≠ s(x) > s(x) = s(y) -> x = y > x+0 = x > x+s(y) = s(x+y) > x*0=0 > x*s(y)=(x*y)+x > > + some logic. Where is consciousness assumed? :D Well of course nowhere, because you didn't write you assumption down. Bruno Marchal wrote: > >> The coding is just >> coding the entity. You have it backwards, because you focus your >> attention >> on arithmetic and miss the consciousness that's already here, before >> any >> theory can be formulated. > > Same confusion of level. I assume consciousness at the metalevel, like > the physicist assume the existence of the planet earth to organize a > conference where he will explain how the planet earth has emerged in > the solar system. You can't destroy the theory by asserting that he is > presupposing the existence of earth at the start. He might presupposes > only a giant cloud of gaz, in its theory. Likewize I presuppose only: > > 0 ≠ s(x) > s(x) = s(y) -> x = y > x+0 = x > x+s(y) = s(x+y) > x*0=0 > x*s(y)=(x*y)+x > > and I explain how consciousness appears from that. Of course I do > presuppose that humans are conscious, can think, so that they will > eventually grasp how consciousness is explained by the axioms just > above, if only to accept some attributes of knowledge and > consciousness, so as to recognize that it is explained entirely by the > axiom above. I already stated above why the physicist anology doesn't work. I don't confuse the level, I am just insisting that it makes no sense to ignore the meta-level, as if it didn't exists, or is somehow secondary to the theory. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> >>>>>> >>>>>> >>>>>> Bruno Marchal wrote: >>>>>>> >>>>>>> Comp remains incomplete on God, consciousness and >>>>>>> souls, and can explain why, but physics, including dimensionality >>>>>>> is >>>>>>> entirely explained. To be sure comp is still "hesitating" between >>>>>>> dimension 2 and dimension 24 for the shadow of the notion of >>>>>>> space, >>>>>>> but this is a very complex mathematical problem, and it assumes >>>>>>> that >>>>>>> the Z1* logic (the "divine" third person plural points of view) >>>>>>> give >>>>>>> rise to some mathematical structure (Temperley-Lieb algebra, >>>>>>> braid >>>>>>> groups). >>>>>> But how can you formulate dimension 2 / 24 or Z1* logic in >>>>>> arithmetic? >>>>> >>>>> Z1* is the logic of Bp & Dt & p; the p are arithmetic proposition >>>>> and >>>>> the B and D are the Beweisbar arithmetical predicate and its dual >>>>> (D = >>>>> ~B~). The Gödel-like arithmetization does the remaining work. >>>> But then the result of the arithmetization makes no sense by itself, >>>> doesn't >>>> it? >>> >>> Arithmetisation makes sense *in* arithmetic. It makes sense for the >>> internal creatures. >> But there are no internal creatures in arithmetic. There are just >> creatures >> encoded in arithmetic. > > But then there are no creatures on earth. They are just creatures > encoded in chemical physics. Well, but creatures on earth can be plainly seen to be creatures. They have bodies, legs, eyes,... Numbers don't have any of that. Bruno Marchal wrote: > >> The "internal creatures" are just the consciousness >> that you knew before the definition of numbers. Show me a creature >> made of >> numbers and I will change my mind. > > The whole point is that creature are not made of numbers. Matter is > not made of numbers, consciousness is not made of numbers. OK, I already get that this is a consequence of COMP. But it just works because we already assume consciousness, and this is my point. So if you don't assume consciousness you should be able to show how consciousness is made of numbers. Bruno Marchal wrote: > > How can I explain? > Suppose you play a video game like "second life", or supposed that you > discover that our reality is fake, and that we are already second-life > players of some kind. Then you know, like Douglas in SIMULACRON III, > that the sun you see is not a big ball of fire, but that your sun > perception is the result of some programs (number relations) in some > hardwired super-computer in some higher level, or lower level, of > reality. I think this would be a category error. Perceptions cannot be a result of a program, they can only be a results of an interpretation of a program. Bruno Marchal wrote: > > You know that such a sun is not made of numbers, but results from > number relation in a computer. > Then what I say, is that this is already the case no matter what. > Arithmetical truth executes all video games, and physical reality is > the result of a non trivial competition between all the games leading > to your state at or below your computationalist level of substitution. > Necessarily so if you assume comp. That physical reality is a "result" of the computations is only a interpretation of COMP. Just because it is derived in the theory, doesn't mean that it is in fact, literally, the result of it. Bruno Marchal wrote: > > Then you can bet, with OCCAM, that > we don't have to postulate more than arithmetic to explain how that > matrix works. Occam cannot be used to get rid of assumption which cannot be gotten rid of. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> So natural numbers are not sufficient after all? It seems to me we >>>> have >>>> to know how the arithmetization worked, and what it arithmetized to >>>> make >>>> sense out of it. >>> >>> No, the sense of it is an internal building by the creature itself. >>> To >>> assume that we need an external observer would be like to say that >>> your brain can function only if it is observed by ... another >>> observer- >>> with-a-brain, and that leads to a infinite regression or a god of the >>> gap, which is ridiculous in the comp theory: brain and self- >>> referential numbers does the job by obeying only to the laws of >>> addition and multiplication (which is Turing universal). >> Well, maybe a brain is just an appearance within that which observes >> itself. > > Exactly. And with comp, *that* needs no more than what you can derive > in any Sigma_1 complete theory, like the following theory: > > 0 ≠ s(x) > s(x) = s(y) -> x = y > x+0 = x > x+s(y) = s(x+y) > x*0=0 > x*s(y)=(x*y)+x > > from those axioms I can prove (non constructively, which means that I > use the logical law A V ~A) the existence of Benjayk, Bruno, this > conversation, and even that they are both correct when they assert "I > am conscious". You can only prove it with the help of your consciousness, which is pressuposed. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> >>>>> Remember that: I do assume comp, and whatever is your conception of >>>>> space and dimension, this is already represented in your brain >>>>> through >>>>> neuronal relations (say), and those neuronal relations are >>>>> themselves >>>>> represented, even emulated, in arithmetic. >>>> So, they are represented? But you can represent anything with >>>> anything. >>> >>> Not at all. The representation have to be faithful and as rich as >>> what >>> they represent. >> But this is not the case with numbers, as you showed yourself. > > ? > I am no sure to what you are alluding too. Your attempt to express dimensionality with numbers. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>> My body represents me in this reality, and your body represents you. >>> It is the same with the numbers. Perhaps I shoud explain this >>> explicitly, but then you will have a lot of math work for your >>> holiday. I guess by conversing I might point exactly on what you seem >>> to precisely still misunderstand. >>> You are confusing coding and representation. I think. >> I think you are confusing representation and reality. Just because >> numbers >> represent consciousness in some way, it doesn't mean that the >> numbers itself >> are conscious. > > I have never said that a number is conscious. You said numbers develop meaning, and just consciousness can do that,. Bruno Marchal wrote: > >> Bruno Marchal wrote: >>> >>>> This >>>> is just trivial. I can just say that this letter "A" represents the >>>> axioms >>>> of peano arithemtic, and that's my TOE. Of course, arithmetic >>>> representation >>>> is much more clever and expressive, but that's beside the point. >>> >>> The big, enormous, ultra-fundamental difference, is that arithmetic >>> represents itself, and all observers, without any further ado. The >>> codings themselves exist in arithmetic, independently of any >>> observer. >>> The numbers code and decode themselves, because they obey precise >>> laws >>> we agree on (+ and *). The letter A only just does nothing, without >>> the lexicon saying that "A is PA", and the human who can understand >>> this. >> The numbers do also nothing without someone saying how the >> arithmetization >> works. > > False for mathematician. True for you given that you believe that a > human is needed for 1+1=2 being true. I never said that. Bruno Marchal wrote: > > But I assume 1+1=2 at the start > (well I assume: > > 0 ≠ s(x) > s(x) = s(y) -> x = y > x+0 = x > x+s(y) = s(x+y) > x*0=0 > x*s(y)=(x*y)+x > > from which we can derive that 1+1=2). > > And, like I can prove that 1+1=2 from the axiom above, I can prove > that the numbers do all their duties, without saying to anyone how the > arithmetization works. You can prove that you can represent it arithmetic. This doesn't mean much at all! It doesn't mean numbers really do their duties in a concrete way. Bruno Marchal wrote: > > Like I don't have to explain to you how your > brain work for you being able to use it. Because I already know it, on some level. Not how it works in it specifics, but how it used. Bruno Marchal wrote: > >> Otherwise, show me how the numbers itself do it, without using >> consciousness. Of course this is not possible, or even meaningful. > > Sigh. You have to study Gödel's 1931 paper. During 30 years of my > life, logicians criticized my papers because I took too much time in > explaining all this, but I realized since that the very basic idea of > Gödel are still not understood by anybody, but the logicians. Well, with regard to this debate it doesn't really matter what Gödel showed. Whatever he proved he could only prove with the help of consciousness, and to claim otherwise is to miss the obvious. Bruno Marchal wrote: > > Let me try this. > If physicalism is true, you can understand that the complete behavior > of the physicist is entirely explained by the Schroedinger equation. I am not so sure. Bruno Marchal wrote: > > Let us accept Stathis non-zombie principle. Then we can attribute > consciousness to those physicists emulalted by the wave equation, OK.. Well, we have to be careful. The consciousness doesn't really belong to the physicists. Both the physicist and the wave equation are an appearance within consciousness. Bruno Marchal wrote: > > Now, if you study logic and arithmetic, you can see that the relation > between numbers emulated also the brain of those physicists and > everyone. If we apply the non-zombie principle, we can attribute them > consciousness. OK? I don't think so. They can represent consciousness, but they aren't conscious themselves, because they need to be interpreted by something transcendent of them. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> Bruno Marchal wrote: >>>>> >>>>> I am not proposing an explanation of "reality", on the contrary, I >>>>> show that a very common hypothesis, mechanism (made clear through >>>>> Church thesis and computer science) makes the mind body problem two >>>>> times more difficult than it is usually understood. >>>>> It makes the physical laws more mysterious, it leads to a purely >>>>> arithmetical body problem. >>>>> And at first sight, it does look like a refutation of comp, because >>>>> if >>>>> we just look at the computations, we can expect an inflation of >>>>> possibilities (the white rabbit problem). It looks like even if we >>>>> were in one winning computation, perhaps physical, we are >>>>> immediately >>>>> at first send in a solipsistic mental space, and then get >>>>> dissolve in >>>>> white noise. And that, admittedly is not confirmed by the >>>>> experiments >>>>> nor experience, except with salvia perhaps :). >>>> OK.... Well everything you said was natural language, not numbers, >>>> so in >>>> some sense you unfortunately missed my point (even though it was >>>> interesting) :). It seems to me it is impossible to formulate this >>>> in >>>> arithmetic without postulating some more powerful language first, >>>> and then >>>> represent it in arithmetic. But in this case arithmetic is hardly >>>> fundamental anymore. >>> >>> It is here that you *might* be deadly wrong, or not. The point is >>> that, accepting that the truth of 1+1=2 is independent of any >>> observers, >> This is probably the crux of our disagreement. What does 1+1=2 mean >> absent >> observers? > > That is the crux, apparently. > What would it mean that a proton is made of three quarks without a > physicists? Well, we could say it means that a proton is made of three quarks. I can imagine this being true without there being a physicist to assert it. I can still be felt by consciousness, without an ability to express it directly. Bruno Marchal wrote: > > If you agree that a proton can be made of three quarks, > even before a physicist appears, why would it be difficult to assume > that 1+1=2 before a mathematician discover that fact? This isn't diffifcult to assume at all. I am always refering to consciousness as the source of meaning, not mathematicians. What is difficult about assuming that 1+1=2 is true without consciousness, is that in my mind consciousness is meaning itself, so what could 1+1=2 mean without meaning? Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>> what you call the more "powerful languages" are in fact the >>> internal Löbian machines/numbers. They exist *in* arithmetic >>> independently of any external observer, and they do their job of >>> coding, decoding, interpreting, finding meaning, ... >> But arithmetic IS a language. > > > Ah! I predicted it, I was beginning to sense that you believe in > mathematical conventionalism. "Einstein's error". > This has been almost abandoned by all philosophers of math. I guess by > just understanding a bit more of math. Mathematician does not believe > in it (except the week-end, for some). > Arithmetic has nothing to do with language, except that , like with > everything, you need some language if you want talk about it. OK, then you don't treat arithmetic as our expression of the underlying meaning, but the underlying meaning itself. I am fine with that, so OK, arithmetic is not a language. Then my point is that arithmetic cannot contain powerful languages, as arithmetics does not contain anything. It is just a system for quantifying things. Bruno Marchal wrote: > >> It does not contain languages, it just can >> represent them. > > Then you could say that the physical world does not contains > observers, it just represent them biochemically. Right. The observer contains the physical world, that contains "observers". Bruno Marchal wrote: > > I don't exist, the > world just represent me. You do exists, but you are not the biochemical representation. You are consciousness. Bruno Marchal wrote: > >> The number relations can only be known to be equivalent to the >> computations >> because consciousness can interpret them in a way that they can be >> conceived >> of as being equivalent. > > Right, and it is the number relation which do the interpretation. No > need of an external observers. Like you don't need an external > observer of a brain, to make a people conscious through that brain. OK, no need of an external observer. But a transcendent observer. Indeed a brain makes no sense without the transcendental consciousness, that is beyond the brain. Bruno Marchal wrote: > > Of course, if you need the existence of Benjayk to have 1+1=2, there > is nothing I can do for explaining to you that the existence of > Benjayk, or Bruno, is a truth of arithmetic, that is, independent of > Benjayk and Bruno. > I don't think the manifest existence of me is necessary to have 1+1=2, though in some sense I am a necessary part of truth, and in this sense indeed I (and everybody else) is needed to have 1+1=2. benjayk -- View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32233504.html Sent from the Everything List mailing list archive at Nabble.com. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. 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