On Sunday, June 9, 2019 at 10:11:37 AM UTC-5, Bruno Marchal wrote: > > > On 7 Jun 2019, at 20:22, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Friday, June 7, 2019 at 11:54:42 AM UTC-5, Bruno Marchal wrote: >> >> >> On 6 Jun 2019, at 19:34, 'Brent Meeker' via Everything List < >> [email protected]> wrote: >> [... *stuff on libertarianism*] >> >> I'm reminded of Bruno's theory that everything is computation… >> >> >> Just to be exact. My working hypothesis is “Indexical Digital Mechanism”. >> It is “YD + CT” to sum it all. >> >> My contribution is a theorem: which says that if we assume Mechanism, it >> is undecidable if there is more than the additive and multiplicative >> structure of the natural numbers, or Turing equivalent. >> >> But most things are not computation. The mixing of the codes of the total >> computable functions and the strictly partial one IS NOT computable, yet >> “arithmetically real” and this will have a role in the “first person >> indeterminacy” measure problem. >> >> If Mechanism is true, very few things are computable, or even deducible >> in powerful theory. Both consciousness and matter are typically not >> computable, yet absolutely real, for all Lôbian machines, from their >> phenomenological perspective. >> >> Every is numbers, or computations, which means we can limit the >> arithmetical reality to the sigma_1 sentences eventually, but that means >> only that the fundamental ontology is very simple. The interesting things, >> including god, consciousness and matter all get their meaning and laws from >> the phenomenological perspective. >> >> So, to say that with mechanism, that 'everything is computation’ is a bit >> misleading, as the phenomenologically apprehensible things will all be non >> computable, and yet are *real*, as we all know. >> >> For consciousness you need only to agree that it is >> >> True, >> Knowable, >> Indubitable, >> (Immediate), >> >> And >> >> Non-definable, >> Non Rationally believable >> >> Together with the invariance for some digital transformation at some >> description level. >> >> >> >> >> and so everything must be explainable in terms of computation. >> >> >> In terms of addition and multiplication, you can understand where >> consciousness come from, why it differentiates, and the transfinite paths >> it get involved into, and why Reality is beyond the computable, yet >> partially computable, partially and locally manageable, partially >> observable, partially and locally inductively inferable. Etc. >> >> Even just the arithmetical reality is far beyond the computable, but from >> inside, the sigma_1 (ultra-mini-tniy part of that reality) is already >> bigger than we could hope to formalise in ZF or ZF + Large cardinal. >> >> Digital mechanism, well understood (meaning with understand the quasi >> direct link between the Church-Turing thesis and incompleteness, (which I >> have explained many times, but I can do it again), is constructively >> antireductionist theory. The Löb-Gödelian machines, those who obeys to the >> probability/consistency laws of Solovays (cf G and G*) can defeat any >> complete theory anyone could conceive about them. >> >> Only numbers at the ontological level, OK, but the crazily interesting >> things appears at the phenomenological levels, where things are no more >> very computable at all. >> >> Bruno >> >> >> > Today is the last day of *UCNC 2019*. > > Program: http://www.ucnc2019.uec.ac.jp/program.html > > What the conference is about can be summed up as > > *What is computing* > if the CT thesis [ > https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis ] is *false*? > > > > If CT is false, it means that we miss some human computable operation on > the natural numbers that a Turing machine, or a combinator, (…) cannot > imitate. > > In that case, two things are possible: > > 1) that the new operation is still a mathematical operation, like an > oracle à-la Turing, in which case we might still have a purely mathematical > theory of computations, we might get a new notion of universal machine, > stronger in abilities than any Turing machine, and we would keep the > “measure problem” formulation of the mind-body (1p/3p, 1pp/3p) problem, but > enlarged on more rich part of arithmetic/mathematics. Instead of sigma_1 > completeness, we would be pi_1 complete, or perhaps complete on the > analytical hierarchy, or perhaps not (many things remains possible, some in > relation with “older” notion of computability, some totally new. There are > no evidences for such human ability. > > 2) much more speculative would be that the new operation is not amenable > to mathematics at all. It would be like a way to compute a function from > N to N, needing consciousness for example. A zombie would be unable to > imitate the computation. That is highly speculative, and bad scientific > play: as it assumes the complicated in absence of evidences. Note that the > first person experience is of that kind, by the indeterminacy on its > histories, but that does not lead to computable function (the first person > indeterminacy on the histories below the substitution level is not > computable, albeit it could obeys precise statistical laws). > > The evidence for CT is strong, and, Imo, it should be provable that CT is > equivalent with the belief that second order arithmetic make sense, or just > that the notion of standard natural numbers is well understood, or that the > notion of “finite” is well understood. > > The main evidences for CT are that all attempts to define the computable > functions from N to N leads to the same class of total and partial > computable functions (from N to N), and then the “Miracle of Gödel”, that > is, the fact that the set of partial computable functions is closed for > Cantor “transcendental” diagonalisation technique, which brings down the > willing of universality on most epistemic-like predicate, like provability, > definability, etc. > > Such closure property remains correct for the relativized theory, with > oracles, and the “machine’s theology” is valid for large class of > relativised notion of computability.It is what makes possible to apply the > general theory to the machines embedded in their “cones” of computations > (there infinitely many “past” and “futures” steps in the universal > dovetailing on all computations. > > The finite and the infinite have deep relations, related to the relation > between the computable and the non computable. Universal machines exploit > their creativity on the frontiers between the computable and the non > computable. The flux of consciousness is not solely related to the > computations, but to where the person survives, all the modes of the self > structured the space of accessible and relatively stable histories.. > > > Bruno > > PS I have given more than three mathematical definition of computation and > computable, the last one was by using the combinators. I might give another > one soon and explains a relation between combinators, arithmetic, and > computer science. >
Close to 2) above is what is called "intrinsic computing": *A layered architecture based on **intrinsic computing** of physical systems avoids objections to a computationalism in the form of symbol manipulation.* The Architecture of Mind as a Network of Networks of Natural Computational Processes <https://pdfs.semanticscholar.org/48ed/85597914902cd5a7270f56fbfff9ff83e60a.pdf> Gordana Dodig-Crnkovic <https://www.chalmers.se/en/staff/Pages/gordana-dodig-crnkovic.aspx> It wouldn't be fair to say it's (completely) non-mathematical. It's a different mathematics perhaps that is more morphological and topological in nature. The key is that *intrinsic computing* is not reducible to Turing computing (but it has nothing to do with oracles in the hyperarithmetical sense). It is phenomenological computing (the hole in science left by Galileo - *Galileo's Error*: Foundations for a New Science of Consciousness, Philip Goff). Gordana Dodig-Crnkovic (above) and Robert Prentner* are two *intrinsic computing* people. * Consciousness and Topologically Structured Phenomenal Spaces Robert Prentner https://psyarxiv.com/at53n/ @philipthrift -- 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/b8989ddf-8d09-422e-aad0-6aee3390fdca%40googlegroups.com.
