On Sep 24, 2011, at 1:12 AM, Roger Granet <[email protected]> wrote:
Bruno,
Hi. My responses are:
>Mathematical truth is in the mind of persons. And assuming we are
machine, mathematical truth is in the mind >of numbers relatively to
numbers. Of course we have to assume all elementary arithmetical
truth, like "17 is ><prime". Do you doubt them?
Roger: When you say "Mathematical truth is in the mind of persons",
this was the very point I was making. I don't think there can exist
mathematical truths in some platonic realm somewhere. They're in
the mind, which is a physical thing, and humans created them as a
way of describing physical things. But, as you know, many
physicists and others think that mathematical and physical laws
exist independent of all else. When they can show us where they
exist, I'll be willing to accept their argument.
In the same way an idea of a chair is not the same thing as a chair.
The number 17 is not the same thing as any human's conception of it.
Regarding this object we call 17 I ask you at what point it became
prime?
Do you believe there exist an infinite number of integers? If so I
ask you why should these very large numbers exist if they require a
physical basis? There are numbers we cannot physically coceive of by
virtue of their size and the finite size of the observable universe.
If these large numbers exist, they have no mental or physical
existence here.
A final consideration: do you believe Pi has such a value that when
Euler's number is raised to the power of (2*Pi*i) the result is 1? Pi
has a value which no human has determined, as determinig it requires
infinite time and memory. If only those mathematical things known to
humans exist, then Pi's true value does not exist.
You ask us to point out the hidden cavern containing scribblings by
god for all mathematical truth before you can accept its human-
independent existence. But as a scientist do you believe the past
exists? How about the space beyond the cosmologicsl horizon? Other
branches of the wave function? Other universes implied by string
theory? If so, why do you believe in them when it is provably
impossible for anyone to point them out for your eyes to see?
You asked why it is that whatever serves as the basis of reality
exisys rather than nothing. Arithmatic truth such as the pimality of
17, or the oddness of 9 cannot be any other way. These perfectly
clear statements about the numbers must be either true or false, the
status of the truth cannot be undefined or non-existent. Or do you
disagree?
Thanks,
Jason
I'm not sure where you're getting that I don't accept truths like
"17 is prime". I didn't say that. All I'm saying is that these
truths don't have independent existence outside of everything else
that exists. If the truths exist, they're just one part of the
overall set of existent things that is what we're all trying to
figure out.
~~~~~~~~~~~~~~~
>To ask that a number should be somewhere is a category error.
Numbers are not space-time object. It means >also that you assume
space and time, which is a more complex notion than numbers.
Roger: See above.
~~~~~~~~~~~~~~~~~
>So, while nobody can disprove the existence of these things, we
can't really do much with them either it seems >to me. There just
more of the things people claim to exist but can provide no evidence
for. However, I admit >that I can also never directly prove my
ideas about what used to be called "non-existence" because no person
>or minds would be present there. All we can do is use our
unprovable, but hopefully logical, hypotheses to >build internally
consistent models that are consistent with known facts and that
eventually can make testable >predictions. This is where I want to
work towards because otherwise, it's all just talk.
>OK. But then you have to build a sufficiently precise theory, so
that we can criticize it. The problem with >nothingness is that it
is, a priori, just a word, indeed, and to make it precise requires
some theory. For example, >the quantum vacuum needs the quantum
theory. The empty set needs set theory, 0 needs number theory, etc.
Roger: This is what I just said in the comment you were responding
to.
~~~~~~~~~~~~~~~~~
>In regards to consciousness, I feel pretty much the same.
Consciousness is just the output of all the neurons, >neural
circuits, ion gradients, etc. in your brain.
>This is extremely ambiguous. But from the UDP (the universal
dovetailer proof), or UDA UD Argument, >either the neurons, neural
circuits, ion gradients, etc. in your brain, are Turing emulable,
and in this case >physicalism is refuted, or there are not, in which
case you are developing a non mechanist theory (which is >something
I respect, although I expect such theories to be very complex one,
and quite different from >everything we know from observation and
logic).
Roger: How is this ambiguous? No one yet knows exactly the
biochemical mechanisms that produce consciousness, but it's clear to
most biochemists, at least, that consciousness is a product of the
physical stuff inside the head.
~~~~~~~~~~~~~~~
> Again, if it's something else, I'd say: Show me where this
consciousness/mind is that's not in the brain.
>It belongs, assuming mechanism, to the infinite number relations
that you can derive from addition and >multiplication alone.
Roger: Hmm
~~~~~~~~~~~~~~~~
>For trying to think of why there is something rather than nothing,
I don't think there can be any postulated >conscious observer other
than some physical property intrinsic to whatever existent state
we're considering. > >Otherwise, that doesn't explain where the
observer comes from.
>I am afraid you are begging the question by assuming something
physical. Where does *that* come from. >What is it. Mechanism can
explain were both matter/space/time, and subjectivity arise come
from. They are >derived from the addition and multiplication laws of
natural numbers. The origin is not direct, nor physical in >any
sense, but is made possible by the self-referential ability that
some numbers display. The details of that >explanation needs some
amount of theoretical computer science. But the argument showing the
incompatibility >of mechanism and weak materialism (the doctrine
saying that primitive matter exists) is accessible to anyone >with
enough patience + a passive understanding of Church thesis.
>You might try to understand the 8 steps proof given >here
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
Roger: I don't have time to read your whole paper, but from near
the beginning, it looks like it's based on the comp idea which
assumes arithmetical realism:
"This is the assumption that arithmetical proposition, like
‘‘1+1=2,’’ or Goldbach conjecture, or the inexistence of a
bigger prime, or the statement that some digital machine will stop,
or any Boolean formula bearing on numbers, are true independently of
me, you, humanity, the physical universe (if that exists), etc."
As above, I'd say this is possible, but show me where these
arithmetical propositions are that are independent of everything
else. As you say, it's just another assumption.
Overall, I don't think it really matters if it's physical stuff
or mind, machine psychology, or arithmetical propositions that are
the basis of our existence. Whatever it is that's the basis, it
exists, and the whole point of this thread was about trying to
figure out why it exists instead of not existing.
~~~~~~~~~~~~~~~~~~
>Thanks.
>You are welcome,
Roger: Real nice there, dude.
~~~~~~~~~~~~~~~~~~~
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