On Wed, May 3, 2017 at 4:51 PM, Bruno Marchal <[email protected]> wrote: > > On 03 May 2017, at 15:21, Telmo Menezes wrote: > >>>>> I think that mechanism gives the most of what we can hope for an >>>>> explanation >>>>> of what consciousness is. >>>>> >>>>> A number e can refer to itself and develop true belief about itself, >>>>> including some guess in its relative consistency. >>>> >>>> >>>> >>>> I can understand self-referentiality, and at the same time that there >>>> is "something" to it that is profound but not fully graspable -- as >>>> Hofstadter talks about with his "strange loops". >>>> >>>>> Then the theory explains >>>>> why any Gödel-Löbian machine can access to the truth that such belief >>>>> can >>>>> be >>>>> correctly (but that is not seen by the machine, only by god/truth) >>>>> related >>>>> to the truth, but only in a non communicable way. So the machine knows >>>>> truth, that she is unable to justify, and can only seem mysterious. >>>> >>>> >>>> >>>> I am ok with this. >>> >>> >>> >>> Then, it is weirder for me why you are not convinced by the machine's >>> explanation of consciousness. >> >> >> But you conclude yourself, that the machine knows truth, that is >> unable to justify, and can only seem mysterious. The fact that I find >> consciousness mysterious isn't exactly what you would expect? > > > Yes. But now we are in the Gödelian trap. Interpret (momentarily) > "consciousness" by "consistency" (<>t), and justify x by "prove x" ([]x). > > We seem to agree with ~[]<>t (we cannot > justify/explain/rationally-believe-in consciousness, so there is a mystery) > > Then the machine explanation comes: <>t -> ~[]<>t (the machine proves that > if she is consistent then she cannot prove it), and similarly, my > explanation of the "mystery" is that if we are conscious we can understand > that we cannot justify it.
Ok, I have no problem with any of this. > So there is a mystery (a non justifiable truth), but in the cadre of the > mechanist hypothesis, we can explain why there is necessarily a mystery. The > mystery remains "lived" from the first person perspective, but we can > understand, even in the 3p view, that if mechanism is true then it is > expected that we feel it as mysterious. Eventually, it is no more mysterious > than our belief in numbers. But our belief in numbers is pretty mysterious, no? > > > > > >> >>> >>>> >>>>> That does not explains the whole of consciousness, but that reduce its >>>>> mystery to the mystery of our belief in anything Turing universal, like >>>>> the >>>>> numbers. >>>>> >>>>> But then again, the numbers explains, by themselves, why if you belief >>>>> in >>>>> anything less than them, you cannot get them, and so justify their >>>>> mysterious character. We don't know, and it is the fate of any machine >>>>> to >>>>> not know that. >>>>> >>>>> Don't mind to much. I am not sure if what you miss is a part of >>>>> mathematical >>>>> logic, or something about consciousness. >>>> >>>> >>>> >>>> Again, I am convinced by your explanation of why the mystery exists. >>> >>> >>> >>> The mystery is our understanding or belief (in apparently a finite time) >>> of >>> elementary arithmetic. >>> >>> >>> >>> >>>> For me, the hard problem remains: you talk about mathematical >>>> constructs. >>> >>> >>> >>> Only half of the time, unless you put mathematical truth in the >>> mathematical >>> construct, something typically impossible to do, except for some >>> approximation, for theories much simpler than ourself. I guess you know >>> the >>> difference between the true fact that 2+2=4, and the much weaker fact >>> that >>> some machine or theory believes or prove that 2+2=4. In fact the word >>> "mathematical construct" is a bit ambiguous. The semantic in general is >>> not >>> a construct, when we do mathematics, but partial semantic can be >>> associated >>> to mathematical construct, when we do metamathematics (mathematical >>> logic), >>> but this is due to the fact that we approximate meaning by "mathematical >>> construct" (which are most often infinite and non computable mathematical >>> object). >>> >>> >>> >>> >>>> Physicalists talk about emergence from complex >>>> interactions of matter. I remain baffled and ask you the same question >>>> that I ask physicalists: what is the first principle from where >>>> consciousness arises? >>> >>> >>> >>> Truth. That cannot be a mathematical construct (provably so if >>> computationalism is true). It is not 3p definable. >> >> >> Aren't you just renaming the mystery? > > > Truth is much more general than consciousness. All logicians and > mathematicians believe in (arithmetical) truth, but few would even dare to > use a term like consciousness. Truth has been very well treated by Tarski, > and I use that (sometimes implicitly, sometimes more explicitly). It is a > key notion, which is on the side of semantic, or model theory, unlike > provable and consistency, which admit arithmetical definition. Arithmetical > truth can still be treated mathematically, at the meta-level, using set > theory or second-order logic. Consciousness/knowledge remain more > problematical, and mix syntax and semantics, like with the Theaetetus' > definition []p & p. We cannot define this in arithmetic. We would need []p & > true(p), but if true p was definable, we would be able to get a sentence k > provably equivalent with its falsity (PA would prove p <-> ~true(p), leading > to inconsistency). Ok. The salient thing for me here is that you tend to place consciousness and knowledge as very close concepts. While I agree that consciousness is a form of knowledge, for me the big mystery is closer to asking "who knows?" or "what knows?". >> >>> The whole key is in the theorem that ([]p & p) does not admit a predicate >>> definable to any machine from which "[]p & p" is (meta)defined. >> >> >> I understood this as a key to understanding why certain things cannot >> be known, but not to knowing them... > > > Well, "[]p & p" obeys to the logic of knowledge. So PA knows all its > theorem, for example. The difficulty with consciousness, is that it is close > to consistency (<>t) in the 3p view, and close to the triviality (<>t v t) > in the 1p view. That makes consciousness "obvious" for the machine, and > unprovable, once the machine approximates it by any third person notion. Ok. > > > >> >>> >>>> >>>> I confess I have a hard time formulating the question correctly. I >>>> feel that what I am trying to ask is so fundamentally simple that it >>>> becomes hard to write the real question. >>> >>> >>> >>> That is common when we dig on notion like truth and consciousness. Those >>> notion are too much obvious from the 1p view, and almost non intelligible >>> in >>> the 3p view, which explains why materialist want to eliminate them. >> >> >> Ok. >> Yes, I came across this over and over. Materalists want to eliminate >> the question because they can sense that it is subversive to their >> belief system. > > > Plausibly so. > > > > > >> >>>> >>>>> The core of the explanation is in >>>>> the G/G* separation, and its inheritance by the intelligible and >>>>> sensible >>>>> matter. We might come back at this some day or another. I am of course >>>>> very >>>>> interested in trying to see what you miss here. The explanation is like >>>>> the >>>>> cow koan: the head of the cow go through the window, like the legs and >>>>> the >>>>> truncs, but not the tail. That will play a role also in the fact that >>>>> computationalism is a theology: the soul of the machine cannot >>>>> understand >>>>> rationally that she will be resurrect. That is the fun of it: the soul >>>>> of >>>>> the machine says "no" to the doctor, until some leap of faith in some >>>>> situation. >>>> >>>> >>>> >>>> This is harder for me to follow, but I think I follow you on the >>>> "barriers to knowledge". >>>> >>>> I definitely don't understand the cow koan! >>> >>> >>> >>> The idea is that about truth and consciousness we can explain everything, >>> except for a tiny detail. But with computationalism, we can explain why >>> they >>> should remain a tiny detail which has to be NOT explainable from the >>> machine's pov. >> >> >> Ok, thanks! It's a nice koan :) >> >>> >>> >>>> >>>>> Maybe I will just ask you this. 1) Do you agree that consciousness is a >>>>> form >>>>> of knowledge? >>>> >>>> >>>> >>>> I'm not sure. I think that I know that I am consciousness, but that >>>> consciousness itself is unlike anything else that I can talk about. >>>> >>>> I am inclined to think that consciousness = existence. Perhaps it's >>>> such a simple and fundamental thing that it becomes almost impossible >>>> to talk about it. >>> >>> >>> >>> Consciousness is the 1p feeling that there is something real. I am not >>> sure >>> why consciousness would be existence. There are things which exists and >>> are >>> not conscious. >> >> >> What I mean is more along the lines of: are there things that exist >> outside of the content of someone's consciousness? >> Call it collective solipsism, maybe... > > > With mechanism, we need to believe that phi_i(j) is defined or is not > defined independently of us, for any choice of an acceptable enumeration of > the partial recursive function. We need to be platonist/realist on the > sigma_1 (and pi_1, the negation of sigma_1) propositions. We need to believe > in the consequence of Robinson Arithmetic (at least). > > > >> >> But the reason why I wrote it has to do with the radical simplicity >> that I attribute to consciousness. It exists, and I don't know what >> else I can say about it (from my 1p experience). > > > Yes, here you talk like the subject described by S4Grz. It is basically <>t > v t. It is "there is a reality of (0 = 0)". But the machine cannot equate > that consciousness with this, unless she buy mechanism (against its first > person instinct) and try to make a theory. In that case you add something > highly non trivial to your consciousness, which is the bet that it is > sustained by some relative digital processing, and maintained through the > doctor's brain transplant. Is it fair to call comp a theory? Do you think it can be falsified? I believe we talked about this before, sorry in that case. >> >>> Consciousness is more what we need to give meaning to word like >>> "meaning". >>> It is on the semantical side, like truth. >>> >>> Do you agree that consciousness is undoubtable and unjustifiable. I >>> cannot >>> doubt consciousness because doubt requires consciousness, and I cannot >>> justify consciousness (cf the conceptual existence of philosophical >>> zombie). >> >> >> I agree that it is undoubtable. In fact, I think that it is the only >> thing I can think of that is undoubtable. > > > That is very nice, as it would make its undoubtability useful for an > axiomatic definition of consciousness. It would be define by what is true > and undoubtable. Ok, nice. >> I don't know if I agree that it is unjustifiable. I feel you are using >> "unjustifiable" as a technical term that perhaps I don't fully >> understand. > > > I mean that you cannot rationally convince another conscious entity that you > are conscious. You will need poetry, music, art, etc. There are no 3p > discourse, nor 3p test which would prove that some entity are conscious. Of > course, we can add evidence for betting that some entity is conscious, and > we have some instinctive empathy, it seems, for our human fellows. Ok, then I agree. > > > > > >> >>> >>> >>> >>> >>>> >>>>> 2) that knowable obeys the S4 axioms? >>>>> >>>>> S4 = >>>>> >>>>> [](A->B) -> ([]A -> []B) K >>>>> []A->A T >>>>> []A -> [][]A 4 >>>>> >>>>> Then incompleteness explains why this works with "[]" payed by >>>>> provability, >>>> >>>> >>>> >>>> I don't understand this sentence, what do you mean by "payed by >>>> provability"? >>> >>> >>> >>> I meant "played by provability". Sorry for the typo. It means that "[]" >>> is >>> for Gödel's provability predicate. It is Gödel's incompleteness which >>> makes >>> the box behaving like a belief, and unlike a knowledge. >> >> >> Ok. >> >>> Imagine that incompleteness would have been false. Then we would have >>> "[]p >>> <-> []p & p" not only true, but provable by the machine, and the logic of >>> the 3p self would have been the same as the logic of the 1p-self, making >>> impossible to associate to a machine a different notion for its 1p and 3p >>> points of view. >> >> >> Ok. >> >>> It is because []p -> p is NOT provable by the machine, that the logics of >>> []p and []p & p differs. Without incompleteness the 8 hypostases would >>> collapse. >> >> >> Ok. >> >>> >>> >>> >>>> >>>>> and gives a temporal non nameable subject, which cannot identify itself >>>>> with >>>>> any third person notion. Looks like my poor soul to me :) >>>> >>>> >>>> >>>> I agree that what I call "consciousness" is something that cannot >>>> identify itself with third person notions. This is what leads me to >>>> suspect that it is not something that can be studied scientifically. >>> >>> >>> >>> When doing science, we cannot invoke first person notion (or god, or >>> truth), >>> but there is no reason why we cannot make a 3p theory *on* those notion, >>> and >>> do the 3p reasoning and the 3p experimental verification for the >>> 3p-sharable >>> part of the theory. >>> >>> That is exactly the case with computationalism. We cannot define >>> consciousness, but we know pretty well what it means for each of us, and >>> can >>> make hypothesis on it (like "yes doctor"), and study the consequence. >> >> >> Ok, this is how you convinced me that computationalism and physicalism >> are incompatible. > > > OK. > > > >> >>> Similarly, Pean arithmetic cannot define arithmetical truth, and cannot >>> define knowledge, but can simulate truth by the assertative p, and >>> conjunct >>> it, for each arithmetical sentence to its boxed presentation, and so even >>> PA >>> can see that it obey S4, which is usually a good axiomatics for >>> knowledge. >>> And that explains why, if the machine tries the Maharshi koan "Who am I", >>> she might get the ineffable point. In fact, if she succeeds to remain >>> correct all along the introspection, she cannot avoid the "ineffable >>> answer". >> >> >> I have to think about this, but I believe I see your point. >> >> Brent argues that AI will dissolve the hard question. I think that >> people know intuitively that it will not. This is what pop-culture >> works such as "Blade Runner" are about. > > > Like Minski, or McCarthy, I think that not only the problem will not > dissolve, but the machines will work on it, and have hard time with it. Of > course, we can dissolve the problem by burning the machine alive when they > contradict the government theory, which is the usual human method. Yes, this is more or less what happens in Blade Runner, except that they shoot the machines. > > > > >> >>> I think that what you need to keep in mind, and understand, is that >>> despite >>> its simple 3p meta-aspect, "[]p & p" refers to something which does not >>> admit any 3p explicit definition. That is also the reason why I insist so >>> much that "[]p & p" is a theological notion, and why saying "yes" to a >>> doctor is a theological act of faith. The machine is simply unable to >>> prove >>> for each p that []p and []p & p are equivalent. Only its own G* knows >>> that. >> >> >> I feel that, in the end, this is all I was saying. That you don't have >> a 3p definition of consciousness, although you might be able to show >> why such a definition is not possible. > > > OK. Then the point is in the consequence of what I call the third theorem of > Gödel, which is that PA (or Gödel's Principia Mathematica) can prove its own > second-incompleteness theorem. Gödel announced it in his 1931 paper, but it > was proved by Hilbert and Bernays later, and embellished and generalized by > Löb. > > It might be useful to have in mind the four theorems of Gödel > > 0) 1930: the completeness theorem for predicate calculus. A first order > theory is consistent iff it has a model (equivalently if a first order > theory proves some formula A, then A is true in all models of that theory). > > 1) 1931: first incompleteness theorem: If T is a "rich enough" theory there > will be an undecidable sentence (yet true in the standard model of the > theory) > > 2) 1931: second incompleteness theorem if T is rich enough and consistent T > cannot prove that (personal) consistency. > > 3) The Gödel-Hilbert-Bernays-Löb theorem: if T is rich enough, T proves <>t > -> ~[]<>t (the formalisation of the second theorem made by or in T). > > The "machine theory on machine consciousness" uses them all, and others, but > the most important one is the "3)". It can be used quickly to refute > Luca/Penrose type of argument based on Gödel's incompleteness against > Mechanism. It shows that the machine PA found Gödel's incompleteness before > Gödel, so to speak. The only thing that confuses me here is the direct use of t. I can follow: <>p -> ~[]<>p Intuitively this makes sense if I say, for example, that p means "I am sane". I understand things like t -> f in the context of reductio ad absurdum, but the direct use of t in the expression above still baffles me. Telmo. > Bruno > > >> >> Telmo. >> >>> Bruno >>> >>> >>> >>> >>> >>> >>>> >>>> Telmo. >>>> >>>>> >>>>> Bruno >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>>> >>>>>> What I don't like about your position is this: just because science >>>>>> cannot address (or as not so far been able to address) a mystery, >>>>>> doesn't mean that this mystery becomes irrelevant or that we can >>>>>> pretend it doesn't exist -- or worse, that we should pretend that we >>>>>> have a viable theory when we don't. This is essentially what makes me >>>>>> agnostic instead of an atheist: I recognise that the big mystery is >>>>>> there. Labelling people that recognise that the mystery is there as >>>>>> lunatics does not serve intellectual rigor. >>>>>> >>>>>>>> >>>>>>>> Then we can talk about evidence. >>>>>>>> >>>>>>>>> Second. An argument from authority is not necessarily a reason to >>>>>>>>> reject >>>>>>>>> that argument. Because life is short and we cannot be experts in >>>>>>>>> absolutely >>>>>>>>> everything, we frequently have to rely on authorities -- people who >>>>>>>>> are >>>>>>>>> recognized experts in the relevant field. I am confident that when >>>>>>>>> I >>>>>>>>> drive >>>>>>>>> across this bridge it will not collapse under the weight of my car >>>>>>>>> because I >>>>>>>>> trust the expertise of the engineers who designed and constructed >>>>>>>>> the >>>>>>>>> bridge. In other words, I rely on the relevant authorities for my >>>>>>>>> conclusion that this bridge is safe. An argument from authority is >>>>>>>>> unsound >>>>>>>>> only if the quoted authorities are themselves not reliable -- they >>>>>>>>> are >>>>>>>>> not >>>>>>>>> experts in the relevant field, and/or their supposed qualifications >>>>>>>>> are >>>>>>>>> bogus. There are many examples of this -- like relying on President >>>>>>>>> Trump's >>>>>>>>> assessment of anthropogenic global warming, etc, etc. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> I agree that arguments from authority are necessary to save time, >>>>>>>> but >>>>>>>> in the context of a debate about a mystery of nature for which no >>>>>>>> strong and widely-accepted scientific theories exist, it is >>>>>>>> nonsensical to invoke authority. >>>>>>>> >>>>>>>> Also, this is not a place where people come to have their car >>>>>>>> repaired, or their doctor appointment. This is a discussion forum >>>>>>>> about the unsolved deep mysteries of reality. >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> Which is exactly the point. Because their mechanic can repair their >>>>>>> car >>>>>>> they suppose we have explained cars - but we have only found the >>>>>>> Lagrangian >>>>>>> that described them. When we can write the programs that produce >>>>>>> "conscious" behavior of whatever kind we choose, cheerful, autistic, >>>>>>> morose, >>>>>>> lustful, humorous,..., then most people will think we have explained >>>>>>> consciousness. Mystics will still claim there's a "hard problem". >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> This feels like thought policing. Of course the mystery is still >>>>>> there, and it's huge! Why am I conscious? I can't think of a more >>>>>> compelling mystery. Why is it so hard to say: "I don't know"? >>>>>> >>>>>> Congrats on your daughter's wedding! >>>>>> >>>>>> Telmo. >>>>>> >>>>>>> Brent >>>>>>> >>>>>>> >>>>>>> -- >>>>>>> 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 post to this group, send email to >>>>>>> [email protected]. >>>>>>> Visit this group at https://groups.google.com/group/everything-list. >>>>>>> For more options, visit https://groups.google.com/d/optout. >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> -- >>>>>> You received this message because you are subscribed to the Google >>>>>> Groups >>>>>> "Everything List" group. >>>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>>> an >>>>>> email to [email protected]. >>>>>> To post to this group, send email to [email protected]. >>>>>> Visit this group at https://groups.google.com/group/everything-list. >>>>>> For more options, visit https://groups.google.com/d/optout. >>>>> >>>>> >>>>> >>>>> >>>>> http://iridia.ulb.ac.be/~marchal/ >>>>> >>>>> >>>>> >>>>> >>>>> -- >>>>> 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 post to this group, send email to [email protected]. >>>>> Visit this group at https://groups.google.com/group/everything-list. >>>>> For more options, visit https://groups.google.com/d/optout. >>>> >>>> >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups >>>> "Everything List" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an >>>> email to [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at https://groups.google.com/group/everything-list. >>>> For more options, visit https://groups.google.com/d/optout. >>> >>> >>> >>> http://iridia.ulb.ac.be/~marchal/ >>> >>> >>> >>> -- >>> 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 post to this group, send email to [email protected]. >>> Visit this group at https://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/d/optout. >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at https://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > 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 post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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