> On 6 Sep 2018, at 21:48, Philip Thrift <[email protected]> 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] <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/ >>>>>> <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/ >>>>> <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://en.wikipedia.org/wiki/Joel_David_Hamkins#Philosophy_of_set_theory> >>>>> https://arxiv.org/abs/1108.4223 <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/ >>>> <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/ >>>> <https://plato.stanford.edu/entries/incommensurability/> >>>> http://depa.fquim.unam.mx/sieq/Documentos/floresgallegosgarritzgarciaincommensurabilityse2007.pdf >>>> >>>> <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 >>> <https://en.wikipedia.org/wiki/S._Barry_Cooper> ]: >>> >>> Incomputability after Alan Turing >>> [ https://arxiv.org/abs/1304.6363 <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 >> <https://twitter.com/philipthrift/status/1029079439190228992> >> Mathematical pulp fictionalism [ >> https://codicalist.wordpress.com/2018/08/26/mathematical-pulp-fictionalism/ >> <https://codicalist.wordpress.com/2018/08/26/mathematical-pulp-fictionalism/> >> ] >> ref: https://plato.stanford.edu/entries/fictionalism-mathematics/ >> <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.
I accept classical first order logic. If 2+2=4, I can deduce Ex(x+2=4). It is neutral if 2 is an object or an idea (which is also an object of some sort). I am not sure I can understand 2+2=4 if 2 does not exist in a way or another. This means that you are not using classical logic. What logic are you using? Frankly, I tend to believe in 2, and not in vampire (when these words are used with their usual meaning. Of course I believe in bats!). I can explain that mechanism leads to physical fictionalism. Numbers (and combinators, Turing machine, …) belongs to what I doubt the less. All humans agree on all their properties. Again, if you think that Mechanism is false, then there is some place for a possible ontological matter, but we loss the computationalist explanation of matter appearance and mind, provided by any introspecting universal machine (well, the Löbian one, i.e. they know that thy are universal, like Peano Arithmetic, or the humans). Bruno > > - 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > 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 [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.
