> On 2 Sep 2018, at 21:32, Philip Thrift <cloudver...@gmail.com> wrote: > > > > On Sunday, September 2, 2018 at 8:15:01 AM UTC-5, Bruno Marchal wrote: > >> On 30 Aug 2018, at 01:04, Philip Thrift <cloud...@gmail.com <javascript:>> >> wrote: >> >> >> >> On Wednesday, August 29, 2018 at 4:55:12 PM UTC-5, Brent wrote: >> Do you have some evidence for doubting CT? It seems that it's >> essentially a definition of digital computation. So you could offer >> some other definition, but it would need to be realisable. >> >> Brent >> >> On 8/29/2018 12:12 PM, Philip Thrift wrote: >> > also thought by some in what I call the UCNC gang >> >> Also thought WHAT? >> >> >> >> >> In terms of theory, Joel David Hamkins @JDHamkins >> <https://twitter.com/JDHamkins> (the set-theorist now at Oxford) considers >> infinite-time TMs to be a part of "computation": >> >> http://jdh.hamkins.org/ittms/ <http://jdh.hamkins.org/ittms/> >> >> If computation is the fundamental "substrate" of nature, and ITTMs are >> "natural" extensions of TMs, there is no reason to exclude ITTMs. >> > I have explained in this list, and in my papers, that Church’s thesis (with > Mechanism) entails that matter and nature are non computable. Elementary > arithmetic realise/emulate all computations, and physics is reduced into a > statistic on all computations, which is not something a priori computable. If > mechanism is refuted some day, it will be by showing that nature is “too much > computable”, not by showing that nature is not computable. Mechanism in > cognitive science is incompatible with Mechanism in physics. Now, it could be > that the only not computable things is just a random oracle, but this does > not change the class of computable function. It would change the class of > polynomial-time computable function, as we suspect nature do, but that > confirms mechanism which predicts this. > > > > >> >> But what does the presence of ITTMs mean for the CT thesis? Whether ITTMs >> are "realizable" remains to be seen. >> > > The CT thesis identifies human intuitively computable functions with > functions programmable on a computer. It is a priori neutral on what the > physical reality can compute. With mechanism, CT entails the existence of non > emulable phenomena by computer “in real time”. > > > >> >> In terms of practice, UCNC people think that computers made with >> non-standard materials, e.g. "live" bioware produced by synthetic biology, >> could have novel computational (behavioural) abilities not equivalently >> replicable in a simulation. >> >> > > Quantum computer can emulate some piece of matter more quickly than a > classical computer. But that was a prediction of mechanism. You can read the > basic explanation in my paper here if interested. > > > B. Marchal. The Origin of Physical Laws and Sensations. In 4th International > System Administration and Network Engineering Conference, SANE 2004, > Amsterdam, 2004. > http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html > <http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html> > (sane04) > > > The key notion if the “first person indeterminacy” which is just the fact > that if we are machine, we are duplicable, and duplicated in arithmetic, and > whatever we predict about our first person experience is indeterminate on the > set of all computations (in arithmetic) which go through our local and actual > state of mind (that is: an infinity). Physicalism is refuted with mechanism, > and becomes a branch of machine psychology, or better machine theology (the > study of the non provable true propositions). > > I am just know writing a post on why Church’s thesis is a quasi-miracle in > mathematics and epistemology. In particular it entails the incompleteness > phenomenon, from which we can derive mathematically the physical laws. That > makes Mechanism testable, and indeed, we recover already the quantum logical > core of the formalism. > > Bruno > > > > This is very interesting. (I've written about the irreducibility of "matter" > to physics, e.g., > [ https://codicalist.wordpress.com/2018/06/20/materialism-vs-physicalism/ ].)
I will take a look, but feel free to explain the basic. > > > > Do you see what role a "multiverse perspective of mathematical truth" could > play in your theory? > > https://en.wikipedia.org/wiki/Joel_David_Hamkins#Philosophy_of_set_theory > https://arxiv.org/abs/1108.4223 > I am not sure why you say that the the universe of set is well defined. To be franc, although I am realist on arithmetic, I am not for set theory, nor analysis, second ordre arithmetic. Most set theories that I know are first order theory, ans thus they have infinitely many non-isomorphic models, including enumerable one. A problem here is that we call set theory, well set theory or theory of sets, when we should say “theory of universes” (in the math sense of universes of set), if we use “of” like in theory of groups, or we should call “theory of groups” a theory of vectors, or a theory of transformation. That gives the feeling that set theory admit one clear model, but it has many. Arithmetic also has many non-isomorphic models, but most people agree on a notion of standard model, which lacks for set. Also, there are many set theories, which all have different models, but quite different theorems too. In Quine set theory (New Foundations, NF), the universes can belong to themselves, which is not the case in Zermelo-Fraekel of Von Neuman Bernays Gödel set theories. That is a reason why I prefer to put “set theory” in the catalog of the mind of the universal machine looking at itself. Once we postulate Mechanism, the “cardinality” of the mathematical "universe" becomes undecidable, and it is simpler to use enumerable models. In fact, the standard model of arithmetic is already too much big, and we can decide to postulate only the “sigma_1 truth”, or the “PI_1 truth”, that is the truth of the proposition having the shape ExP(x,y) with P decidable (and their negations). That is, we need only the notion of computation (which provably exists in any Sigma_1 complete (= Turing universal) theory. We do get a constructive “multiverse” of some sort, which I call Universal Dovetailer. It is a program which generates all programs, and executes them all, in a dovetailed way, pieces by pieces to avoid being stuck in non terminating computations (something that I have just explained to be non predictable in advance). From this I have extracted the mathematics of a physical multiverse, but that structure is phenomenological: it exist only in the mind of the machines (naturally implemented in arithmetic). Physics becomes a statistics on computations, and the math fit well with some version of Quantum Mechanics, until now. More on this later, very plausibly. Bruno > - pt > > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
