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] <javascript:>> > 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 -- 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.
