On Jul 1, 2012, at 6:27 PM, meekerdb <meeke...@verizon.net> wrote:
On 7/1/2012 2:46 PM, Jason Resch wrote:
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?
But not perceived. They are part of the theory, i.e. the language.
Other branches of the wave function are not perceived either. They
are part of the theory though, so can be considered real.
Numbers and Turing machines are part of Bruno's theory. I don't see
the difference. Why can't Turing machines exist?
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.
Only metaphorically.
The whole "it's real if it kicks back" idea is a metaphor. I think
the point of the metaphor is that to be real something needs to have
its own properties which we have limited or no control over. It is
not malleable to our whims or will, but resists attempts to change it.
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.
Explain why Sherlock Holmes doesn't exist according to Conan Doyle's
model of reality.
Sherlock holmes does exist, but then what is Sherlock holmes? A
character described in some books.
Conan could have changed anything he wanted about Sherlock holmes, and
therefore he doesn't "kick back".
If you asked two people what properties Sherlock holmes has that were
not answered in the book there would be no agreement, and no way to
study Sherlock holmes as an objectively real object. Only the texts
can be studied.
This is not true of mathematical objects. Properties are not
enumerated in some text. They are not subject to be defined or
changed by some authority. Two mathematicians, whether on earth or on
different planets can make the same discoveries about the same objects.
Further, mathematical realism is a useful scientific theory. It
provides explanations for scientific questions. Why you don't see it
as a legitimate theory is a mystery to me.
If you don't support the theory, that is fine, but it seems like you
discount it's possibility altogether because only "real physical
things" can be real.
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.
He could say it, but he would be redefining what 'exists' means.
What is your definition?
To escape this we need some model of reality which postulates more
exists "out there" than can be found in one's mind.
Materialism generally postulates more than what exists in your
mind. That's how it explains the intersubjective agreement of
perceptions.
Right.
Your model seems to assume an external world exists, but it stops
exactly where our instruments and inferences from their
observations end.
Not at all. That's whole point of having a model and not just an
encyclopedia of data. A model makes predictions beyond the data on
which it was based.
I agree.
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.
I'm not a conservative.
Good to know.
Jason
Brent
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