On Thursday, September 6, 2018 at 2:48:53 PM UTC-5, Philip Thrift wrote: > > > > On Thursday, September 6, 2018 at 11:47:46 AM UTC-5, Bruno Marchal wrote: >> >> >> On 6 Sep 2018, at 17:04, Philip Thrift <[email protected]> wrote: >> >> >> >> On Thursday, September 6, 2018 at 4:23:23 AM UTC-5, Bruno Marchal wrote: >>> >>> >>> On 5 Sep 2018, at 18:58, Philip Thrift <[email protected]> wrote: >>> >>> >>> >>> On Wednesday, September 5, 2018 at 9:12:49 AM UTC-5, Bruno Marchal wrote: >>>> >>>> >>>> On 5 Sep 2018, at 11:54, Philip Thrift <[email protected]> wrote: >>>> >>>> >>>> >>>> On Wednesday, September 5, 2018 at 2:28:39 AM UTC-5, Bruno Marchal >>>> wrote: >>>>> >>>>> >>>>> On 2 Sep 2018, at 21:32, Philip Thrift <[email protected]> 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 <[email protected]> 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/ >>>>> ].) >>>>> >>>>> >>>>> >>>>> 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 >>>>> >>>>> >>>>> >>>> On the reduction of all matter to physics: >>>> >>>> I consider "all matter" to include everything studied by natural >>>> sciences: physics, chemistry, biology, etc. I cite in some of my Notes* >>>> the >>>> concept that there may be "laws" of chemistry (or biology) that cannot be >>>> "reduced" to "laws" of physics. >>>> >>>> * e.g. 87. Backward and Downward! >>>> https://codicalist.wordpress.com/2018/07/06/backward-and-downward/ >>>> (the references there to "downward causation") >>>> >>>> There is another term: Incommensurability of the sciences >>>> https://plato.stanford.edu/entries/incommensurability/ >>>> >>>> http://depa.fquim.unam.mx/sieq/Documentos/floresgallegosgarritzgarciaincommensurabilityse2007.pdf >>>> >>>> The idea is that the spectrum of matter (from particles to people) has >>>> a spectrum of laws. >>>> >>>> >>>> On a (computational) universal dovetailer and its relationship to >>>> conscious matter: worth finding out more. >>>> >>>> >>>> >>>> I can explain that IF we assume that the brain or the body is Turing >>>> emulable, then everything can be reduced to arithmetic. Note that >>>> arithmetic is not a computable thing (the computable part of arithmetic is >>>> a very tiny part of arithmetic). It makes machine theology becoming the >>>> fundamental science. In particular physics and the natural science get >>>> reduced to “machine theology”, and this has been proven constructively: so >>>> that physics is deducible from arithmetical self-reference. That makes >>>> mechanism testable by comparing the physics deducible from theology with >>>> the physics inferred from observation. This works (until now), where >>>> physicalism does not work (as most people grasping the mind)body problem >>>> are more or less aware since long). >>>> >>>> I can agree that there is a spectrum of laws, that is the natural case >>>> in computer science. To understand a brain by studying neurons cannot >>>> work. >>>> It would be like trying to understand Big Blue strategy to win Chess game >>>> by studying the electronic gates. That might explain how some strategy is >>>> implemented, but that will not put light on which strategy is used. >>>> >>>> I am skeptical on (primary) matter. That is not used in physics, only >>>> in metaphysics, and its use is more like the use of God in some >>>> theologies: >>>> to prevent the search of theories and make people stopping asking >>>> question. >>>> >>>> What is matter? If I may ask? What are your evidence for all is matter? >>>> And are you open to the mechanist theory of mind? (The idea that there is >>>> no magic operating in a brain, or the idea that we could survive with a >>>> digital brain transplant, obtained by copying it at some level of >>>> description). Mechanism is my working hypothesis, and it makes primary >>>> matter very doubtful. We get a simpler explanation of both mind and >>>> matter-appearances without it, as matter, nor a god, can select a >>>> computation in arithmetic. >>>> >>>> The notion of computation is a purely mathematical (arithmetical) >>>> notion. It should not be confused with the notion of physical computation, >>>> which will appear to be a very special case, observable by the average >>>> universal (digital) machine/number from inside arithmetic. >>>> >>>> Bruno >>>> >>>> >>> >>> >>> I have mainly followed the perspective of the late Turing scholar S. >>> Barry Cooper >>> [ https://en.wikipedia.org/wiki/S._Barry_Cooper ]: >>> >>> *Incomputability after Alan Turing* >>> [ https://arxiv.org/abs/1304.6363 ] >>> >>> >>> I appreciate very much Barry Cooper. He invited me at one of the >>> European Meeting on Computability (CiE). >>> It is there that I prenseted my Plotinus paper (accessible on my URL >>> frontage). >>> >>> >>> >>> >>> Basically: We don't know the full nature of physical [ that is, material >>> ] computation. >>> >>> >>> OK. But Feynman and Dutch, like Landauer and Bekenstein did great >>> advances. Of course many great questions remain unsolved. >>> >>> >>> >>> Corollary: We don't know the full nature of matter. >>> >>> >>> I can explain in all details that “matter” (in its usual occidental >>> sense of primary substance) does not make sense once we postulate (Digital) >>> Mechanism. To put it simply: matter do not exist. There is no physical >>> universe, … or Mechanism is false, but there are no evidence for that. On >>> the contrary, modern physics sides more and more with the immaterialist >>> theology/metaphysics. The more we observe nature, the more we guess the >>> deep mathematical reality at its origin. >>> >>> >>> >>> >>> >>> Computation without matter, even though we don't know completely what >>> matter is (like Kant's noumenon) remains a ghostly entity, >>> >>> >>> Here I disagree. Unless you mean that 2+2=4 is a ghostly truth (in which >>> case I invite you to convince my taxe inspector! >>> The (arithmetical) notion of computation is a astonishingly clear >>> mathematical notion thanks to Church thesis. It admit an infinity of >>> apparently very different definitions, yet they can be shown equivalent, >>> and indeed equivalent to very simple definition of them, like I illustrate >>> with the combinators. It is a unique fact in the history of mathematics: an >>> epistemological (computable) notion which get a precise mathematical (even >>> arithmetical) definition. I am as sure about the existence of computations >>> than I am about the existence of prime numbers. I am less sure of >>> Mechanism, but then that is why I proposed an experimental testing >>> procedure, and as I said, physics confirms Mechanism (up to now at least, >>> thanks mainly to quantum-mechanics-without-collapse). >>> >>> >>> >>> >>> one where there is no real experientiality (like the pleasure of eating >>> a candy bar). >>> >>> >>> On the contrary, the logic of self-reference explains both qualia and >>> quanta, and link them without using the brain-mind identity thesis, which >>> has been debunked in the frame of Mechanism. Why would there be no real >>> experience, and how could you know that? Yet, your position might be >>> coherent: if matter exist and play a role in consciousness, then we cannot >>> be digital machine, and there must be actual infinities in nature. But that >>> seems rather speculative, given the absence of evidence for both actual >>> infinite in Nature, and the evidences for mechanism (Darwin theory of >>> evolution uses mechanism quasi explicitly, for example). >>> >>> So, you would not accept a digital brain transplant (in theory, in >>> practice me too!). That seems to me like invoking something more complex >>> that what we want to explain, to avoid searching an explanation. Matter is >>> a speculative hypothesis in metaphysics without evidences, and which hides >>> more the problem than clarifying it, I think. I prefer to assume Mechanism, >>> and see if we are lead to absurdity or to facts contradicted by nature. But >>> the most startling fact predicted by Mechanim, —the fact that physics is a >>> statistic on many computations is somehow confirmed by Quantum Mechanics >>> (without collapse). Then it took me 30 years to confirms this >>> mathematically (using the self-reference logics of Gödel, Löb and Solovay). >>> >>> Bruno. >>> >>> >>> >> >> My own (hypothetical) course in Philosophy of Mathematics would begin >> with this slide: >> >> *"There are no such things as mathematical objects.”* >> >> >> >> With mechanism, we are mathematical object, and the physical reality is a >> mathematical phenomenon, so there is no physical object per se. That does >> not threat the existence of the moon, of galaxies, or bosons and fermions, >> but such existence becomes phenomenological, yet more universal in the >> sense that the core of the physical laws is the same for all universal >> machine, the rest becomes historico-geographical differentiations. >> Mechanism makes it possible to delineate the indexical geography from what >> are genuinely univarsable laws for the universal machine observable. >> >> >> >> >> >> >> cf. https://twitter.com/philipthrift/status/1029079439190228992 >> *Mathematical pulp fictionalism* [ >> https://codicalist.wordpress.com/2018/08/26/mathematical-pulp-fictionalism/ >> ] >> ref: https://plato.stanford.edu/entries/fictionalism-mathematics/ >> >> That being the first principle, I would say what does exist are material >> objects. And then proceed from there. >> >> >> You will have to say “no” to the doctor proposing you a digital brain >> transplant. If we survive such transplants, we survive in the infinitely >> many continuations that are emulated in arithmetic, and the laws of physics >> are determined by what is provable in all such continuations, which is >> then mathematically recovered by nuances on provability logic imposed by >> incompleteness. It works actually, until now, formally, and intuitively if >> you agree with QM-without collapse. >> >> I avoid as much as possible to use any hypothesis in philosophy of >> mathematics, as the Mechanist Hypothesis in ogive science is so strong as >> to reset what we can sought on this. Contrary to what many people think, >> Mechanism is incompatible with Materialism. It explains the observable >> without any ontological commitment other than what is needed to define the >> notion of computation (and this requires nothing more than what is required >> in elementary arithmetic, or combinator theory, or anything equivalent with >> respect to computability). >> >> It uses only arithmetical realism, and recently I have discovered that it >> works even with some form of ultrafinitism. My “theory” seems to be the >> common base of all possible theories. A non arithmetical realist is someone >> who disbelieve that it is false that a digital machine stops or not. >> >> I doubt less 2+2=4 than F=ma or the SWE, or the existence of the moon, or >> my body, which are among what I try to explain from simple things, like >> "x+2 = 9 has a solution”. >> >> When you say “there is no mathematical object?” What do you mean. Please >> make your point here, and refers only for more detailed and lengthy >> treatment. To me, even without Mechanism, it seems that the notion of >> physical object is far less clear than mathematical object. I am not sure >> modern physics can define what is a physical object: you need a “theory of >> everything physical” for that, but gravitation and the quantum makes the >> big picture still not accessible. Mechanism does not (yet) seem to imply >> that the physical reality is, or not, immune to diagonalisation, so some >> universal number can still play some role in the physical reality, but we >> are far to know that, and the theory would still be a description of number >> relations. With mechanism, we can associate minds only to infinities of >> computations. Assuming physical object gives them a magical ability to >> deflect your consciousness in arithmetic, in a way which is not explainable >> when we assume Mechanism. >> >> Just to say that at some point you will need some non mechanist theory of >> mind, if you really want to have physicalist primary objects. Of course, I >> will also ask you some theory about those objects. >> >> Assuming Matter is a bit like assuming God. I can accept that things like >> that exists phenomenologically, and perhaps ontologically. But even in that >> case, invoking them does not help to explain them. I prefer to start from >> what I am the closest to certainty, like 2+2=4, or SKKK = K. >> >> Bruno >> >> >> > > By *"There are no such things as mathematical objects”* (quoted from the > SEP article "Fictionalism in the Philosophy of Mathematics") I mean that > in the language(s) of mathematics (including arithmetic), the objects > referred to are fictional and do not exist; as in vampire stories, the > vampire is a fictional object that does not exist. So the 2 in "2+2=4" is a > fictional object: it does not exist. > > - Philip Thrift >
On "digital machines", of course all material machines have to stop operation eventually given that this universe won't go on forever (unless "fictional" black hole computers are possible). - Philip Thrift -- 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.
