On 13 Jun 2016, at 03:22, Bruce Kellett wrote:
On 13/06/2016 7:12 am, 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.
Assuming arithmetic does not even account for mind,
(Sigma_1) Arithmetic is (Turing) equivalent with a universal
dovetailing, or any concept of universal machine. With digital
mechanism, you can define the mind by what universal machine do. To
express this, you need to assume a universal base, and number addition
and multiplication, learned at school, is basically enough.
of course, arithmetic per se does not account for the mind in any
obvious way. But that follows from the work of Gödel, Turing, Church,
and others. The sigma_1 arithmetical reality (a tiny part of bthe
arithmetical reality) account for the highly structured collection of
all computations. And that concept is made solid with the CHurch-
Turing thesis.
much less account for matter.
It does, and QM confirms the most shocking consequence (that our
consciousness relies on infinitely many computations). Just read the
papers. I think it is the first refutable theory which does it. in the
eighties, I was sure it would have been refuted before 2000. But the
evidence adds on both side, and primary matter will become the new
ether or phlogiston, I think.
Saying that consciousness is a computation is empty until one
specifies precisely what form of computation.
Here, it is the complete contrary which happens. No sound machine can
ever specify the computations which supports her first person
experience. That is a theorem. The *constructive* reduction of physics
to arithmetic is based on the necessarily non constructive theology of
the universal machine.
And why that form of computation rather than some other?
We can only bet that if we are copied at some level, we survive. This
provably require an act of faith. All sound machine knows that, soon
or later. Fundamentally, that bet is a private affair between you and
your doctor. Of course, high level copies are cheaper than low level
copies.
I don't see that computationalism actually solves anything
It shed light on the road, and so we can search the key we have lost.
Virtually nobody assumes the negation of computationalism today.
Except the wave collapse, there is no sign that there is anything not
Turing emulable in Nature.
-- the problems it leaves unanswered are every bit as difficult as
the problems one started with.
?
There are open mathematical problems, and the contrary would have been
quite astonishing, as the science is still only starting. yet, it
provides the whole shape of the solution of the mind body problem, and
people open to Everett can understand it more easily than others. The
rest is in the study of Gödel, Löb, ... Solovay.
At least with scientific realism, one has the objective external
world to underpin one's experience: i.e., one knows that it works,
even if one is not quite sure how.
Computationalism *belongs to*scientific realism.
It just happens that the physical appearances are explained by a
realist theory of the universal machines' dreams and the third and
first person logics and statistics.
The big discovery is Gödel discovery. With computationalism, that is
the discovery of the mathematician *in* arithmetic. All its dreams
belongs there too.
Bruno
Bruce
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