> On 7 Jun 2019, at 20:22, Philip Thrift <[email protected]> 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 > <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 > <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. > > > @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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/71fdd53d-c433-4c6d-9c9a-347ee44103da%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/71fdd53d-c433-4c6d-9c9a-347ee44103da%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/18971B7B-4115-4F9B-BC6F-1FFAA4815441%40ulb.ac.be.
