> On 16 Dec 2020, at 18:20, Telmo Menezes <[email protected]> wrote: > > > > Am So, 13. Dez 2020, um 17:11, schrieb Bruno Marchal: >> >>> On 10 Dec 2020, at 16:14, Telmo Menezes <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> Mindey asked a very interesting question, and I've been thinking about it >>> while following the discussion. I don't have a good answer, but I might >>> have a good question. I propose another take: the discussion so far has >>> been in terms of quanta, but what if we reframed it in terms of qualia? >>> >>> Imagine the "universe" in terms of the set of all first-person experience >>> moments of all of its inhabitants. Is there a limit to novelty here? Or can >>> qualia also display unbounded complexity? >> >> >> With Mechanism, we have to separate clearly the ontology, which is given by >> the minimal things that we have to assume because we cannot derive them from >> simpler thing, and which has to be enough rich to support a universal >> machine. There is some amount of latitude here, because we can assume any >> universal machinery(*). As everyone believe already in natural numbers and >> the laws of addition and multiplication, I use them (albeit in my course I >> prefer to use the combinators, but once we have them we have the >> numbers+laws, and vice versa. > > Still, don't you find it incredibly strange that such a thing exists to being > with?
The mystery is reduced to the arithmetical truth. Once you grasp that (Bp & p) behaves like a “predicate” of knowledge, which is not an arithmetical predicate (nor even definable), it seems that this explains completely consciousness, including why consciousness seems completely mysterious. Consciousness became “just” a believe in a reality (whatever that reality is conceived). The nice thing here is that incompleteness makes the Theaeteus’ definition of knowledge working very well. > >> Then, everything is explained, even imposed, by the fact that we get all the >> universal numbers, and that they all discover the nuance imposed on >> provability by incompleteness, which are the nuances between, truth, belief, >> knowledge, sharable observation (quanta) and the non sharable observation >> (qualia). >> >> First incompleteness separate truth (p) from provability ([]p), and it makes >> provability into a belief predicate, forbidding it to be a knowledge >> predicate (which can be proven to NOT exist, which is coherent with the fact >> that consciousness and qualia will not be definable by the machine, but >> still deferrable too indirectly assuming mechanism and some notion of >> (arithmetical) truth (itself not definable). This entails that >> provability-and-truth will obey a knowledge logic, not definable by the >> machine about itself, but still deferrable, just by using the original idea >> of Theaetetus: knowledge is true belief, and rational knowledge is true >> provable belief ([]p & p). Sharable Observation is given by []p & <>t (which >> leads to probability logic) > > The probability comes from <>t? Am I correct in reading <>t as: "it is > possible that the machine is consistent?” ? <>t = ~[]f = consistency. <>t can be read as the machine is consistent, or the machine’s beliefs are consistent. You can read <>p as p is consistent, or directly as “p is possible” for the machine. Consistency is the possibility predicate of the machine. > >> and private observation (qualia, and “unfortunately” also the quanta (which >> becomes first person plural, making physics a psychological reality) is >> given by applying Theatetus’ move again leading to []p & <>t & p. >> This gives 8 different mathematical theories, and the observable part >> (private and public) are testable, and can be said to fit rather well with >> physics, given that we get a many-histories interpretation of arithmetic, >> but also a quantum logic for the first person plural locally sharable >> quanta. In fact we get (up to some details I skip here) an intuitionist >> logic for the knower, a quantum logic for the observable, and an >> intuitionist quantum logic for the qualia. >> >> The logical explanation follows: >> >> NUMBER => CONSCIOUSNESS => PHYSICAL-LAWS >> >> We cannot start from consciousness, and we cannot start with matter, which >> are the notion that we have to explain from numbers, when we assume >> Mécanisme, and indeed, the universal numbers provide that explanation, and >> it is testable as it leads to number/machine physical laws, that we can >> compare with Nature. >> >> I would have preferred by far that the quanta appears at the []p & <>t level, > > Why would you prefer it? Because it would be less shocking for most people. It makes possible to conceive that the physical reality is one, and not many-wordy, and the physical reality would not be a pure first person notion (albeit plural). By appearing in the “… & p” modes, the physical reality is *only* due to the first person plural statistics, and "physically objective” is purely first person (plural), making it more idealistic than Mechanism suggests. To be sure, today, all the quantum tautologies of the three modes are verified by Nature, so this remains quite possible. > >> but they appear only in []p & p, and []p & <>t & p, making physics a first >> person plural construct (with p’s interpretation limited to the partial >> computable formula, which are the sigma_1 (true) sentences. >> >> You can see any universal number in arithmetic as the initialisation of a >> sheave of (aleph_0, or bigger) computational histories, in the universal >> dovetailing (aka the sigma_1 truth). Those are the differentiating histories >> which, from the pov of the machine, and below their substitution level, >> select a continuum of continuations obeying to different mathematics >> (intutionist, quantum, or both) corresponding to each self-referential modes >> imposed by incompleteness. >> >> This makes also the universal “virgin” (unprogrammed) machine) already >> maximally (somehow) conscious, > > Ok. I think I follow, except for the "maximally conscious". Can you explain > what you mean here? My intuition is that consciousness is a binary property, > an all-or-nothing kind of deal… I agree that “being conscious” is a binary all-or-nothing type of reality. "Maximally conscious” should perhaps better be “maximally awake”. It is a state of consciousness without any “wrong belief”, before something or someone lied to you. All babies are born that way, like all universal machine, but they will quickly forget that state. I don’t use this in the paper, but some mystic described well that state, like also in some report of salvia divinorum experience. It is a highly counter-intuitive state, as it is a consciousness state without time, and in fact without any content, yet it is felt as maximal, like we could see the shape of the abyssal ignorance, hidden usually by the theories/bodies. > >> but it is a highly dissociative sort of consciousness, out of time and >> space. Time and space should arise from the subjective time (canonically >> related to the intuitionist logic of the knower. (S4Grz and S4Grz1 can be >> see as a logic of evolving state of knowledge). >> >> The notion of universal machine (Post, Kleene, Turing, Church, Markov, >> arguably Babbage) structured canonically the classical (sigma_1) >> arithmetical reality in 8 internal modes, differentiating on their first >> person histories. >> >> Like in Neoplatonism, but also many eastern school of philosophy, Nature is >> the product of the universal number self-contemplation. >> >> The bomb here are the discovery of the universal number, mainly by Turing, >> and the incompleteness which results, and (the subtle point seen by Gödel, >> but made clear by Hillbert and Bernays, and Löb) that with enough induction >> axiom (like PA) the universal machine can reflect its incompleteness and its >> consequences, including that partial “free will”, the hesitations, and the >> unavoidable complications in the local neighbourhoods. The core of the low >> level, not reflective, consciousness is the fixed point of a semantical sum >> up of all histories, > > What do you mean by semantical here? A semantic in logic is the giving on a model. A model is a “reality” satisfying the axioms of a theory (and preserving that satisfaction through the inference rule). Usually that reality is itself render mathematically through some structure. The stucture (N, 0, +, *) where N is the set of natural numbers, and 0, + and * are interpreted in the usual way, is a model of both RA and PA. A semantical fixed point is when a theory is rich enough to embed the thinker/observer in the theory, which will include the representation of the model, and the representation of the representation of the model, etc. That leads (for some theories and models) to a fixed point, rather analogue to the place you are in front of a map of a city. The “you are here” is the same point on the map and in the models of reality, and, eventually to the point in the reality. This is an image, and it would be rather long to get enough of model theory to provide the details here. This relies on the first recursion theorem, which I use much less than the second recursion theorem, but the first recursion theorem has a role to explain consciousness. What is very important here is the completeness theorem (also proved by Gödel for the first order logic, and before by Post for the propositional calculus). The completeness theorem has two equivalent formulation: 1) a theory is complete iff it proves what is true in all models. 2) a theory is consistent iff it has at least one model. The fixed point appear when the theory is embedded in the model, and consciousness is an invariant for that transformation, a bit like your consciousness remains the same after the “doctor” put a digital transplant (but then it is the same for all version of you run in arithmetic, which leads to the first person indeterminacy). Much more should be said here... > >> a bit like all the numbers satisfy an empty set of equations, or that the >> unary intersection of the empty set is the collection or classe of all sets. >> Locally, the universal machine are never “completely” satisfied, but that’s >> why histories develop. It is a sort of “eternal” travel from G to G*, > > To be clear, qualia correspond to []p & <>t & p, independently of the G/G* > distinction, correct? The mathematics of the qualia is given by the mathematics of the “predicate” []p & <>t & p” which is provable by G*. The qualia themselves relies on G* minus G. Without the G/G* distinction, []p & p, and []p & <>t & p, but also []p itself would all collapse to p, like before Gödel most people would have said that, at least in arithmetic, p <-> []p. > What I don't understand is what you mean by this "eternal" travel from G to > G*, but I would like to know more. It's an eternal travel from provable truth > to general truth? Somehow, with a catch. Take Peano arithmetic (PA). It is consistent (as most people believe). Now, PA + (“PA is consistent”) is a NEW consistent theory of arithmetic, proving more theorems in arithmetic than PA, let us call it PA+. But PA+ is also a consistent theory, and thus obeys the same incompleteness than PA, and the logics G and G* are still the correct logic of both PA and PA+. Of course their box are different arithmetic predicate, the one is for PA, and the new one is for PA+, but they both obeys to G and G*. And you can continue this in the (constructive) transfinite. PA, PA+, PA+++, … PAomega+, … You get richer and richer theories for arithmetic, which get a bigger and bigger set of provable arithmetical truth, but their logic of (individual) provability will still obeys to G and G*. So adding your consistency, (which is a theorem of G*) iteratively provide a sort of path from G to G*, with the catch that your predicate of provability has changed, and the logic of G and G* still apply to all individual theories in that progression of theories. Note that PA + con(PA), that is PA + <>t, does not prove its own consistency. It proves the consistency of the previous theory in the iteration. But its own “<>t” is still not provable. By using the second recursion theorem, we can build a finite theory which does proves its own consistency. That is, there is a fixed point for a theory like PA + con(PA + con(PA + con(PA + con(PA + con(PA + …. …)))). But *that* theory is necessarily inconsistent, as it would prove its own consistency. (Paling it inconsistent by Gödel second incompleteness theorem) So no machine can consistently “really travel" from G to G*, but it can make giant leap, still letting his theology invariant. What change is the extensional meaning of the provability predicate “[]”. I hope I am not too quick, and well, I have to go. Ask anything, it is not an easy subject. Bruno > > Telmo. > >> and fake science/religion comes from confusing one made of self-reference >> with another. >> >> Bruno >> >> (*) I recall what those things are. Take any formal (Turing) universal >> programming language. Enumerate the functions with one input/variable, with >> repetitions, through the enumeration of all the programs, in the >> lexicographic order (by length, and then alphabetically for those having the >> same length). This gives the phi_i (that is all the (partial) computable >> functions phi_0(n), phi_1(n), phi_2(n), phi_3(n) … That is a universal >> machinery. They have an important property, related to the fact that this >> enumeration is itself computable, which is that there are numbers u such >> that phi_u(<n, m>) = phi_n(m). Here m is called the program/machine, m is >> called the data or input, and u is called the computer, or the universal >> machine, or the universal number, or the universal word, depending of the >> chosen universal machinery. >> >> If, given a universal machinery, you define on N (the set of all natural >> numbers), an operation * by n * m = phi_n(m), you make N into a combinatory >> algebra. So the combinators provide both a universal machinery, but also an >> abstract theory of all universal machineries. Same in presence of Oracle, >> and that plays some role in the measure problem. The measures associated >> with the first person point on view relies on all sigma_1(a), with a “real”, >> that is why it is a continuum, and the “sum on dreams” seems to be a >> Lebesgue integral…). The whole phenomenology can be formalised in ZFC + PD >> (ZF + Choice + Projective indeterminacy). >> >> >> >> >> >>> >>> Telmo >>> >>> Am Fr, 27. Nov 2020, um 18:35, schrieb Tomas Pales: >>>> The idea of an all-encompassing set (a set of all sets) is inconsistent, >>>> for example because the power set of a set (=the set of all subsets of a >>>> set) is an even bigger set. If a set is infinite then its power set has an >>>> even bigger infinite size. So there is no biggest set, just as there is no >>>> biggest number and no biggest infinity. There just seems to be a >>>> never-ending hierarchy of sets, from the empty set upward and maybe there >>>> are also sets that have no bottom, that is they contain sets that contain >>>> sets etc. without end. But everything needs to be kept consistent and I >>>> have heard that according to Godel's second incompleteness theorem there >>>> may be inconsistencies lurking in infinities which we may never be able to >>>> detect. >>>> >>>> >>>> On Thursday, November 26, 2020 at 6:57:47 PM UTC+1 Mindey I. wrote: >>>> Curiously, I found the Everything List, because I wanted to to create a "A >>>> Universe Where Everything Can Exist" ( https://mindey.com/world.pdf >>>> <https://mindey.com/world.pdf> ), which the Google search of 2007 returned >>>> me to my search query "How to create a universe, where everything can >>>> exist?" >>>> >>>> So, suppose that we create a universe, where everything exists, -- would >>>> that universe be a superset of all possible universes, or, just the same >>>> set? >>>> >>>> >>>> -- >>>> You received this message because you are subscribed to the Google Groups >>>> "Everything List" group. >>>> To unsubscribe from this group and stop receiving emails from it, send an >>>> email to [email protected] >>>> <mailto:[email protected]>. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/everything-list/00cbfe99-1fc6-478e-9ddb-6c8d177112bbn%40googlegroups.com >>>> >>>> <https://groups.google.com/d/msgid/everything-list/00cbfe99-1fc6-478e-9ddb-6c8d177112bbn%40googlegroups.com?utm_medium=email&utm_source=footer>. >>> >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send an >>> email to [email protected] >>> <mailto:[email protected]>. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/everything-list/57015210-0691-4544-8969-045b505ebc6e%40www.fastmail.com >>> >>> <https://groups.google.com/d/msgid/everything-list/57015210-0691-4544-8969-045b505ebc6e%40www.fastmail.com?utm_medium=email&utm_source=footer>. >> >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] >> <mailto:[email protected]>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/F3D80ADB-B2CE-41EF-83FE-064BE246C36E%40ulb.ac.be >> >> <https://groups.google.com/d/msgid/everything-list/F3D80ADB-B2CE-41EF-83FE-064BE246C36E%40ulb.ac.be?utm_medium=email&utm_source=footer>. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/ff175a8c-f597-4d61-9f27-049ed11903f9%40www.fastmail.com > > <https://groups.google.com/d/msgid/everything-list/ff175a8c-f597-4d61-9f27-049ed11903f9%40www.fastmail.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/8CED8BA1-82A0-4E02-AC72-10CBF01B734E%40ulb.ac.be.
