On Jul 1, 2012, at 2:07 PM, meekerdb <meeke...@verizon.net> wrote:
On 7/1/2012 11:50 AM, Jason Resch wrote:
On Sun, Jul 1, 2012 at 1:20 PM, meekerdb <meeke...@verizon.net>
wrote:
On 7/1/2012 4:59 AM, Bruno Marchal wrote:
On 01 Jul 2012, at 09:41, meekerdb wrote:
On 7/1/2012 12:17 AM, Bruno Marchal wrote:
On 30 Jun 2012, at 22:31, meekerdb wrote:
On 6/30/2012 12:20 PM, Bruno Marchal wrote:
On 30 Jun 2012, at 18:44, Evgenii Rudnyi wrote:
I think that you have mentioned that mechanism is incompatible with
materialism. How this follows then?
Because concerning computation and emulation (exact simulation) all
universal system are equivalent.
Turing machine and Fortran programs are completely equivalent, you
can emulate any Turing machine by a fortran program, and you can
emulate any fortran program by a Turing machine.
More, you can write a fortran program emulating a universal Turing
machine, and you can find a Turing machine running a Fortran
universal interpreter (or compiler). This means that not only those
system compute the same functions from N to N, but also that they
can compute those function in the same manner of the other machine.
But the question is whether they 'compute' anything outside the
context of a physical realization?
Which is addressed in the remaining of the post to Evgenii.
Exactly like you can emulate fortran with Turing, a little part of
arithmetic emulate already all program fortran,
Turing, etc. (see the post for more).
Except neither fortran nor Turing machines exist apart from
physical realizations.
Of course they do. Turing machine and fortran program are
mathematical, arithmetical actually, object. They exist in the same
sense that the number 17 exists.
Exactly, as ideas - patterns in brain processes.
Brent,
What is the ontological difference between 17 and the chair you are
sitting in? Both admit objective analysis, so how is either any
more real than the other?
You might argue 17 is less real because we can't access it with our
senses, but neither can we access the insides of stars with our
senses. Yet no one disputes the reality of the insides of stars.
We access them indirectly via instruments and theories of those
instruments.
Are numbers not also inferred from theories of our instruments?
For example, computers are instruments that let us observe and study
the properties of various Turing machines, which themselves are
mathematical objects.
You might argue the chair is more real because we can affect it,
but then you would have to conclude the anything outside our light
cone is not real, for we cannot affect anything outside our light
cone.
You can kick it and it kicks back.
Math kicks back too. If you come up with a proposition, it kicks back
with either true or false.
Of course there are many events outside one's lightcones which one
infers as part of a model of reality based on the events within
one's lightcones, e.g. I suppose that the Sun continues to exist
even though the photons I from which I infer it's existence are from
it's past.
Explain then why one is mistaken in supposing mathematical objects
exist, when they can be inferred according to some models of reality.
Also, how do you know the chair is anything more than a pattern in
a brain process?
How do you know you're not a brain in a vat? or a pattern in
arithmetic?
This was my point. You say math exists only in our minds. But an
immaterialist could say the same of the chair.
To escape this we need some model of reality which postulates more
exists "out there" than can be found in one's mind.
Your model seems to assume an external world exists, but it stops
exactly where our instruments and inferences from their observations
end.
Humanity's model of reality has over the centuries, been repeatedly
extended. Therefore I think it is more conservative to believe there
is more "out there" than we can see or imagine.
Jason
Brent
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