On Sun, Dec 13, 2020, 14:11 Bruno Marchal <[email protected]> wrote: > > 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. > > 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) 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, 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, 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, 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*, 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> > . >
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