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] <javascript:>>
> 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."*
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.
- Philip Thrift
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