On 13 Jun 2016, at 22:08, Brent Meeker wrote:
On 6/13/2016 8:32 AM, Bruno Marchal wrote:
On 12 Jun 2016, at 23:12, Brent Meeker wrote:
On 6/12/2016 10:27 AM, Bruno Marchal wrote:
William S. Cooper, "The Origin of Reason" makes an argument that
mathematics is a way of brains thinking about things that was
found by evolution, just like mobility, metabolism,
reproduction,...and a lot of other functions. Bruno doesn't
like that story though because it means mathematics only exists
as instantiated in brains.
It is not a question of liking this or not. It is just that
Cooper, and many contemporaries, assumed some physical universe,
and that this assumption put the mind-body problem under the rug.
It is like saying God made it. They don't push enough their own
Darwinian logic.
That's begging the question. You assume arithmetic; which sweeps
the mind-body problem under the rug by making the "body" part
hard. Everybody starts by assuming something. Assuming physics
and providing an evolution based account of the development of
mind and minds development of arithmetic is just as legitimate as
starting with arithmetic and trying to derive matter and mind.
I should not have said that Cooper put the mind-body problem under
the rug by assuming the physical universe (and a primary one by
default). I should have said that this just don't work when we
assume Mechanism, and that QM confirms mechanism, not materialism.
I assume arithmetic, but everyone does. What axioms of Robinson
Arithmetic are you disagreeing with?
Why would I disagree with them? They're axioms.
But in applied science, like we are doing here, we have an intended
model in mind, and the axioms are supposed to be sound with respect to
that model. In the case of mathematics, axioms are chosen from some
introspective work. For elementary arithmetic there is a general
consensus that the axioms of RA and PA are quite reasonable, yet, even
here there are (rare but respectable) mathematicians who reject some
axioms. The most commonly rejected axiom of RA and PA is probably the
excluded middle axiom, leading to the Heyting intuitionist Arithmetic
HA. Nelson rejects the scheme of induction axioms, (leading to
something called predicative arithmetic, like RA is) and never cease
to hope showing that PA, and thus the induction axioms, are
inconsistent.
Then I get the body problem, but I solved it, in the sense that I
show that Arithmetic (+ Mechanism) implies physics (the body) is
reduced to statistics on infinitely many computations,
But it doesn't imply that in the sense of logical entailment.
? (it does).
Within arithmetic+mechanism you don't even have a derivation of
matter. It only "implies" it in the sense that "If my theory is
going to work it must be true that...."
No, even if false, it implies it.
with a measure given by the logic of some self-referential
modalities, imposed by UDA and its translation in arithmetic, and
we get quantum logic. I think it is the first explanation of where
physics and the quantum come from. may be it is wrong, but that
remains to be verified.
And where is this spelled out?
In most of my papers. Thanks to Solovay theorem, it takes not much
line. Of course, it leads to many open problem to compare that
universal machine's physics with observation, but that theory is not
yet refuted. On the contrary the physicalist theories are refuted at
once (in the computationalist frame: that is what is showed by the
UDA), (with some technical nuances due to the different possible use
of Occam and its weakening when we do fundamental applied science).
Bruno
Brent
If Mechanism is true, we just cannot assume any particular
universal system, including physical one. That gives them ad hoc
non Turing emulable role, and hides the necessary non Turing
emulable part of physics.
Now, if you have a better theory of mind than digital mechanism,
let me know. But with mechanism we have indeed that body problem,
but also the means to solve it, and this satisfy my interest in the
origin of the physical (or of its appearance).
Yet, even without Digital Mechanism, I would not be happy with
assuming a primary physical universe, because that is like giving
an answer before formulating a problem. But, as I said, once we
assume mechanism, it is not a matter of choice. You might reread
UDA, and I mean the 7 steps, and then I can better explain the
translation of the UDA in the arithmetical language, and the
relation with the RA, and also with PA and other Löbian machines.
Bruno
Brent
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