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)? 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!) 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! 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. What you call ontological part of the theory are just the axioms you make explicit. I don't see how this make them ontological, and the implicit assumption epistemological. 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, but there is no notion of numbers without consciousness. 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. I can explain with words why humans have legs, this doesn't mean my words are the reason that humans have legs. Bruno Marchal wrote: > >> Consciousness is required for any meaning to exist, > > That is ambiguous. If you accept that some proposition can be true > independently of us, it can mean that some meanings are true > independently of us. If not you need some one to observe the big bang > to make it happen, or the numbers to make them existing. Well, independently of "small us", sure. But not independent of consciousness. 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? 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. The consciousness, that can be, in some way, represented in arithmetic, can develop meaning. 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! 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. 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. 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. Bruno Marchal wrote: > > On the contrary we need the numbers to address the question of how to > define the > higher level notion of subjectivity Why can't we define it with words? Bruno Marchal wrote: > > , and then we can make sense of > your correct sentence that an entity needs to have consciousness for > making sense, personnally, of the numbers. If not you will need an > observer outside the universe to make sense of the universe. Well, consciousness is not necessarily outside of numbers, but transcendent of them. 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, while we could probably agree that cars can function without invisible horses. 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? Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> You can't just >>>> ignore what you already know, by not making your assumptions >>>> explicit in >>>> your theory. >>> >>> It is just not an assumption in the theory, but a derived existence. >>> With comp, consciousness is implicit in the arithmetical truth. >> Maybe, but it seems arithmetical truth is implicit in consciousness >> also. > > This I doubt. But it is very ambiguous. Arithmetical truth is *very > big*. Consciousness needs only a tiny part of it, although matter > might need a much bigger part of it, yet both conscious and material > things will only scratch the surface of arithmetical truth. > > Hmm I might begin to see, below, what is your problem. And I begin to see what is your problem ;). 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? Again, you assume consciousness at the start, which is the internal you speak of here! Bruno Marchal wrote: > > That is why we don't need to suppose anything else ontologically. That > is a fundamental difference. It is the numbers who interpret the > numbers. Well, show me how this is done. Bruno Marchal wrote: > > An interpretation is itself a relation between numbers, a > complex one involving universal numbers, relative coding, etc. But > everything needed to that exists as a consequence of addition and > multiplication. An interpretation can be represented using numbers. But the interpretation itself is an experience, which can not be substituted with numbers. 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's true is that you can code dimensionality with arithmetics, as you explained above. 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. You almost said it yourself, the being is *represented* in arithmetics. This is not enough. Because the representation makes no sense without making sense of it. 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. 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. 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. 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. 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. 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. 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. Bruno Marchal wrote: > > With the numbers and addition only, I cannot represent all computable > functions. > With numbers and multiplication only, I cannot represent all > computable functions. > But it happens that with addition and multiplication I *can* represent > all computable functions. > This is done in the good textbook on theoretical computer science > (Boolos and Jeffrey, Epstein and Carnielli, Mendelson, for example) > The representation works through some coding, but the emulation is > represented through the coding and the laws of addition + > multiplication. REPRESENT! :D 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. Otherwise, show me how the numbers itself do it, without using consciousness. Of course this is not possible, or even meaningful. 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? 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. It does not contain languages, it just can represent them. Bruno Marchal wrote: > > We might have to delve a bit more deeply on the difference between coding > (a relatively > trivial notion), and representing something (a notion which needs more > familiarity in math and logic). In our case, we can replace > representations by emulations (exact simulations). You have to grasp > that the arithmetical (and statical) relations between numbers (made > true by the laws of addition and multiplication) does emulate the > computation of (all) observers, entirely by itself. Fine, but consciousness itself cannot be emulated, or at least I don't know what this would mean. 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. Bruno Marchal wrote: > > This makes not just 1+1=2 true independently of you and me, it makes > "Benjayk > believes 1+1=2" true, independently of you and me. "Benjayk believes 1+1=2" is true indepently of me? 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