On 25 Sep 2011, at 09:05, Roger Granet wrote:
Bruno,
Hi.
>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).
Roger: I agree that this is an assumption; although, I'd say it's
also an assumption that mathematical truths exist somewhere outside
of all other physically existent things.
When a mathematician assume something, like (x ≠ y -> s(x) ≠ s(y),
say. He is neutral on the interpretation of x, s(x), etc. So it is not
part of the assumption made by the mathematician, that mathematical
truth is in or outside some other object assumed, or not, by some
other people.
In cognitive science, or in theology, we don't have to postulate that
a mathematical truth, like "17 is prime" is outside of physical
things. We might just NOT postulate physically existent thing. And
remains agnostic on that question until further clarifications appear.
I realize now from later in your email that you also don't think
these truths exist separate from all other physically existent
things (?), but it seems like many physicists and mathematicians do
think they exist outside of all other physical things.
~~~~~~~~~~~~~~~~
>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.
Roger: While I admit explaining the numbers isn't the area I think
about the most, it seems like if you have a set of existent states
in which some intelligence developed, this intelligence would see
the presence of a single existent state and could equate that to the
number 1, the existence of another one next to it to a total of two,
etc.?
~~~~~~~~~~~~~~~~~~
All right. But set of existent state already exists in many
mathematical structures. You explain well how intelligence might
develop from such state and BET on the presence of a single state, and
conceptualize through it the idea of number 1. I don't see anything
physical here.
You are using Aristotle idea that seeing is sort of proof of
existence, a bit like animals are programmed to do (it pays in the
short run). Platonist took distance with that idea. They better
remember their dreams, I guess, so that they stop to consider that
seeing, or measuring, observing, is a proof of existence. They take
"seeing" as an opportunity to bet on something which would explain the
seeing, and which is not necessarily made of what is seen.
>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.
Roger: But, many question whether or not quantum mechanics is the
one theory that can explain all of reality, so I'm not convinced
that all biochemical activity is explained by quantum mechanics.
~~~~~~~~~~~~~~
I mentioned QM only to mentioned a computer emulable theory of
molecules.
I find quite possible that QM explains biochemistry, given the
incredible theory of chemistry the SWE equation allow (molecules and
the electronic shape of atoms is really what QM explains the most
elegantly and successfully, but this is besides my point).
But you are coherent: if you want materialism, you will need a non
turing emulable theory of matter, and of mind.
Good luck, because it needs already some amount of work to conceive
something not Turing emulable in math, and in physics, it is even more
difficult. But it is logically possible, and the study of computer
science is the must, for those who hope to succeed in going beyond.
But the universal machine is good in defeating such arguments, already.
>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.
Roger: I'm not clear how the existence of a single physical object/
existent state can't be described by an intelligence as the number 1.
I' not clear how the existence of a single biological organism/
existent state can't be described by an intelligence as the number 1.
Would you infer from that 1 is biological? A single physical object
can only be an example of an instanciation of the idea of one.
Actually you already need the notion of 1 to single out that single
physical object.
Then the existence of another object next to it, and that
intelligence can get 1+1=2. But, I'd agree that you need the
intelligence to make up this addition system. I guess where we
disagree is in that I think intelligence/mind is entirely made of
these physical objects, and you don't?
Not really. I am a logician, and I try to hide what I think. (I
confess I can change my mind easily on so deep question, and that is
why I focus on what follows from assumptions).
I am just trying to explain (prove) that IF some rational agent
believes that he can survive with an artificial digital body/brain/
universe, THEN, if he can be 100% honest with itself (ideally
correct), he will soon or later understand that, as far as he is
correct in its mechanist beliefs, the laws of physics arise from a
self-reference ability of the numbers.
And this leads to a way to derive physics from number theory
(intensional number theory, for the detail), making the mechanist
thesis refutable by observation. In fact my point is that mechanism
leads to sort of theology which is scientific in the sense of being
refutable.
In my youth I tended to believe in mechanism by looking at amoebas and
tiny animals and plants. That feeling in favor of mechanism has been
multiplied by a lot, when I read James Watson's book "Molecular
biology of the gene", and I like very much biochemistry.
But then I studied QM, to see how macro and micro molecules "really
work", and I got permanently (like many) stumbling on the "nonsense"
of it, and I begun to doubt seriously about mechanism, despite my
theoretical interest continue to grew (especially through the study of
Turing, Gödel, Post, Church, etc.)
Then I read Everett, and now I consider that Everett *formulation* of
QM (= the usual one without collapse); might be, like Gödel's theorem,
an incredibly strong evidence for mechanism. My work goes in that
direction by showing the hardness to refute mechanism.
But who knows? If we are machine, then it is a theorem that we will
never know that mechanism is true for sure.
Overall, thanks for all the interesting things to think about in
my physical brain! :-)
In your dreams :)
Thanks for sharing the pleasure to muse and dig on deep questions.
Bruno
http://iridia.ulb.ac.be/~marchal/
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