On 14/10/2015 3:11 am, Bruno Marchal wrote:
On 13 Oct 2015, at 12:40, Bruce Kellett wrote:
On 13/10/2015 8:40 pm, Bruno Marchal wrote:
On 13 Oct 2015, at 07:37, Bruce Kellett wrote:
Has computationalism predicted spin? Special relativity? Quantum
field theory? General relativity?
Computationalism is used implicitly in the theory of evolution, in
biology, and in physics once we abandon the collapse of the wave.
Non-computationalism is only a collection of incompatible, often
vague, ideas. There is not yet any working theory.
Then computationalism explains both consciousness and matter
appearance already. Physics do not even try, it assumes them, and
some identity link. It works well to make local prediction, but it
fails on consciousness (when it does not eliminate it).
Physics is not a science addressing those questions.
Theology is the original science addressing those question, and
indeed computationalism explains why neoplatonist theology fit
better the most obvious facts (existence of mind and matter
appearance) than physics, when physics is seen as a theology
(Aristotle idea).
You just seem to be not interested in "philosophy" of mind or
theology, and at the same time you argue that physics is the only
correct theology, but then give us what is your non-computationalist
theory of mind.
Give me your computationalist account of why the world we observe
around us has three spatial dimensions and one dimension of time,
with these dimensions obeying the laws of special relativity (or
general relativity). And not just some wishy-washy claptrap such as,
"if computationalism.... then these things must be so." Derive the
actual facts of existence.
I might first ask you the same task with your apparently
non-computationalist theory. You will perhaps tell me that in physics
we assume such facts of existence, and so are dispensed to explain
them. But then your account of the facts of existence is no better
than "God made it".
Brute facts are like that -- they have no more fundamental explanation.
And there are always going to be some brute facts of experience. But the
great advantage of physics is that we can take some facts about the
world, model them, devise laws describing them, and then use these
models and laws to predict other things. As this process has developed
over several hundred years, we have come to the point where we have a
very good understanding of, and explanations for, most of the facts of
our everyday experience -- based on very few irreducible 'brute facts'.
I see nothing to be ashamed of in this. And I think it is disingenuous
of you to simply dismiss all physical explanation as nothing better than
"God did it".
Second, it is my job of logician of explaining that there is a problem
with computationalism: we have to explain physics from numbers. That
is the main result, except that when I discovered Gödel's theorem, I
realized that the tools exists to begin the derivation, or at least to
formulate the math problem to solve to do so.
Now, you do point on an interesting problem that we cannot avoid with
computationalism, which is that we have to derive physics, but cannot
know exactly the difference between physics and geography by observation.
Yes, you have to derive physics from computationalism. Until you can do
this, you have nothing more than the hope of a theory -- you do not
actually have a viable theory. As to your second point, that is again
disingenuous. Physics is very good as distinguishing between things that
have to be regarded, for the moment, as "brute facts", from those things
that current theory can successfully explain.
But that is interesting and provide some idea to distinguish physics
from geography. Indeed, we might decide to *define* physics by the
universal laws of the Turing machine's observable. Then any local
incarnation or particular instantiation of such laws will only differ
from the geographico-historical points of view.
But then we might fear that perhaps physics will become a triviality,
and that everything is geographico-historical.
But we already know that that is not the case. Not everything is
geographical -- much can be explained and understood on the basis of
very few unexplained inputs. All of our everyday experience can be
explained in this way, even the phenomenon of consciousness.
Bruce
That was actually a prevision made by some opponents a long time ago.
They predicted that all the modalities would collapse into G or even
into propositional classical logic. This would have entailed that the
physical laws are not laws at all, but special local geographical truth.
But then why not do the math? The UDA motivates for three possible
type of physical laws, or three possible way to make exact prediction,
by the Universal machine. All we need to make prediction, in
particular to have a "certain" prediction (a measure one on the
consistent computational continuations) is that we have the modal
principle []p -> <>p. This is a common modal axiom for all measure of
uncertainty, like probability, credibility, etc. I recall that []p
means here Gödel's beweisbar('p'), with 'p' denoting the Gödel number
of some arithmetical proposition.
[]p means, by Gödel's completeness (NOT INcompleteness) result: "true
in all (accessible) models", and this can work for "all consistent
computational extensions" when we limit p to the UD or sigma_1 true
propositions.
Unfortunately, that does not work, because []p is "trivially" verified
in the cul-de-sac world, and so []p cannot work for a "certainty"
notion. You can't say that you will win the lottery with probability 1
just because you will die before the game is over.
To get the []p -> <>p (that is that if p is certain then p is
consistent, or by Gödel's completeness, p is verified by at least one
model) needed for probability or credibility, we have thus three solution:
[1]p = []p & p (this will entail [1]p -> <1>p. Ask if you have a
problem with this)
[2]p = []p & <>t (this will entail [2]p -> <2>p, even more simply)
[3]p = []p & <>t & p (this will entail [3]p -> <3>p, as simply than
for [2]).
"[]p -> p" was an axiom of almost all modal logics, and the first
edition of some notable textbook in modal logic made it part of all
modal systems, but by incompleteness, we know that if []f -> f, then
that fact is not provable by the machine itself. And this does not
just prevent the collapse of [1] into G, but it prevents the collapse
of [2] and [3] as well.
In fact all modalities does collapse, but only in the mind of (the
second) God (G*). It is true (in Plato heaven), or put in another way
G* proves that
[]p <-> [1]p <-> [2]p
but the machine itself cannot prove that, nor know that, nor observe
that, nor feels that. The following are true in G* too:
~[] ([]p <-> [1]p <-> [2]p)
~[1] ([]p <-> [1]p <-> [2]p)
~[2] ([]p <-> [1]p <-> [2]p)
~[3] ([]p <-> [1]p <-> [2]p)
And the miracle occurs: such logics does provide a quantization when p
is restricted to the universal dovetailing, emulated through the truth
of the sigma_1 sentences. It is given by [i]<i>p with i in {1, 2, 3}
and p sigma_1.
This makes the "quantum" into a physical law, a common fact on the
possible observable of any arithmetically sound machine.
But my modest goal was to show that we have to extract physics from
arithmetic (assuming comp).
The fact that we detect already the logic of alternating histories,
having a quantization is just a promise that we might get a Gleason
theorem justifying the unicity of the computationalist measure.
Then to get the number of dimensions, we can hope that the quantum
leads to it by itself. I know that some people are working on such
tasks. My feeling about this might need the graded variants of [2]p
and [3]p, perhaps [1]p:
[2']p = []p & <><>t, more generally [i]^n p @ <i>^m t with m smaller
than n (they get quantization too)
Those might obey sort of Reidemeister formal relations, associating a
Temperly Lieb algebra to the structure, and it makes a relation
between quantum group theory and the invariant of knots, the von
Neuman projectors, from which the dimension might be explainable. In
fact due to the special role of the number 24 in gravity and geometry,
it is not unreasonable to hope to get gravitation and perhaps some
string theory, and to explain all breaking of symmetries and birth of
forces through Temperley-Lieb recoupling theory (à-la Kaufmann, in his
book: "Temperely-Lieb recoupling Theory and Invariants of 3-manifolds.
The problem is that my poor concrete implementations of G* is unable
to verify the Reidemeister moves. I think it might be necessarily non
tractable classically, but not quantum computationally. Z1* and X1*
might be tractable by a quantum algorithm, given that what they
describes are basically statistical interfering informations.
So you ask an interesting question, which, if computationalism is
true, admits solutions,. That is my point.
But we are not yet there to see the details of the solutions. That
asks for a lot of work.
The nice points is that the view from G and from G* differs on [2]p
and [3]p, and this does provides a way to dismantle the quanta from
the qualia, i.e. the sharable unconscious measurable thing from the
non sharable personal experience the machine can live when
contemplating the quanta.
The goal is not to compete with physics, but only to get a rational
understanding of what we are living, that is a theory which explains
the prediction and does not eliminate consciousness and the person.
Then this approach happens to provide an arithmetical clean
interpretation of Plotinus and the Neoplatonist understanding of the
"one". Actually, I have just discovered a much earlier (-1 century)
Neopythagorean theologian, Moderatus, who might even be closer to the
discourse of the universal machine (except that we have lost his
texts, and this comes from remarks made by Simplicius, also lost (I
think) commented by Porphyry in his Life of Plotinus).
Bruno
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