Am So, 13. Dez 2020, um 17:11, schrieb Bruno Marchal: > >> On 10 Dec 2020, at 16:14, Telmo Menezes <[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? > 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?" ? > 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? > 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... > 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 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? 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? 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 ), >>>> 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]. >>> 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]. >> 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]. > 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. 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