> 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 >> <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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/F3D80ADB-B2CE-41EF-83FE-064BE246C36E%40ulb.ac.be.
