On 24 Sep 2011, at 08:12, Roger Granet 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,
This is something you assume. It is not obvious, and provably false if
we assume that brains are Turing emulable at some level such that we
would survived through such an emulation. (this is not entirely
obvious, and I explain this from times to times on the list, but you
can also take a look on the papers in my url).
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.
But why do you want that if something exists implies it exists
somewhere? This is assuming physicalism, which has been shown
incompatible with mechanism.
I'm not sure where you're getting that I don't accept truths like
"17 is prime".
Where did I say that. On the contrary I was just asking you the
question.
I didn't say that.
I didn't say that you did it.
All I'm saying is that these truths don't have independent existence
outside of everything else that exists.
I agree with that statement also, but I guess for a diametrical
reason. Mechanism makes not just physicalism false, it makes this in a
constructive way: it explains where the appearance of the physical
reality comes from. So by assuming things easy things like the laws of
addition and multiplication of the natural numbers, we can explain
where both the quanta and the qualia arise. To explain the numbers
from physics does not work, if only because all physical theory has to
assume the numbers (which of course is almost never made explicit by
the physicists).
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.
~~~~~~~~~~~~~~~~~
I don't see how you answered this above. I do see that you assume a
physical reality. But I don't see how you explain the numbers from
that, still less the mind.
>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.
~~~~~~~~~~~~~~~~~
I know. We agree on that. But then you seem to derive from this that a
physical reality exist *primitively*, and that we have to assume time
and space, etc. Then what I say, is that for such a physicalism/
materialism to be true, you need to make brain and mind both
substantial and infinite.
>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.
~~~~~~~~~~~~~~~
But biochemical activity is explained by quantum mechanics, which is
Turing emulable, and so this, by the UDA result, makes phsyicalism
wrong.
In fact QM can be (and, assuming we are machine, has to be) explained
by addition and multiplication. That has been partially done.
Contrariwise, nobody has been able to explain how consciousness can be
the product of anything described by third person notions.
> Again, if it's something else, I'd say: Show me where this
consciousness/mind is that's not in the brain.
It leaves on the border of the arithmetical truth, or on the frontier
between the computable and the non computable.
The notion of "where" is an indexical based on the notion of "here",
which is also an indexical.
>It belongs, assuming mechanism, to the infinite number relations
that you can derive from addition and >multiplication alone.
Roger: Hmm
~~~~~~~~~~~~~~~~
This is a logical consequence of the assumption that "my" brain can be
approximated at a digital level, so that I would not feel any
difference if a digital device is substituted fro my brain at that
level. To assume this false, you have to make the brain infinite, or
to assume consciousness in the components of the brain.
>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.
But that assumption is used commonly in physics. If "1+1=2" can be
derived from physics, without assuming it, then please show this to
me. You might begin to give me a physical definition of what is 1,
without assuming the usual arithmetical meaning of 1.
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.
~~~~~~~~~~~~~~~~~~
I can answer this. We don't know, and if we are machine, we will never
know. The reason to start from arithmetic, is that it can be proved
that there is no theory capable of explaining where arithmetic come
from. We can only assume it. If you assume any theory in which you can
derive the laws of addition and multiplication of the natural numbers,
then it can be proved you assume a logically equivalent or stronger
theory. So, the natural numbers is the only mystery which remains, but
assuming them, we can explain why we cannot explain them. This is
"well known" by logicians. In a sense, arithmetic is the simplest
(turing universal) theory. From it you can explain why the numbers
develop stable belief in consciousness and physical realities, and
that the first one is fundamental, and the second one derived from the
first one. It is big, in the sense that it shows that the platonist
theologians are more rational than the aristotelian theologians
(atheists and christians, notably). We might have to backtrack 1500
years, in the fundamental matter.
Bruno
http://iridia.ulb.ac.be/~marchal/
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