On Sunday, September 2, 2018 at 8:15:01 AM UTC-5, Bruno Marchal wrote: > > > On 30 Aug 2018, at 01:04, Philip Thrift <[email protected] <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/ > > 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 > (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/ ].) 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 - 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
