On 23 Jun 2016, at 22:09, John Clark wrote:
On Thu, Jun 23, 2016 at 11:16 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
>> you've got to give those symbols a meaning, otherwise
you're just talking about squiggles. And by the way, "=" is just
another squiggle. The way we get around this problem and the reason
mathematics and other languages are not just silly squiggle games is
that we can point to a squiggle and then point to something in the
real PHYSICAL world and people get the connection.
> The theory of model is a branch of pure mathematics. Model =
semantic,
As I said, without examples from the physical world "=" is
just another squiggle.
> To prove that the euclid axiom on parallel is not derivable
from euclid geometry, mathematicians discovered this with the non
riemannian geometry,
Without space and physical things in it mathematicians would
have discovered neither euclidean geometry nor riemannian geometry
and "parallel" would just be another squiggle standing for nothing.
Without the DNA polymerase enzyme, bacteria nor physicist would have
discovered anything, but that does not made physics into a branch of
molecular biology.
> Physicalism might be true, but my point is that it is
incompatible with the assumption that the brain is Turing emulable.
The brain is NOT Turing emulable,
The material brain is not, indeed, but it probably does not exist per
se. It is an idea, all in our head :)
in fact nothing is Turing emulable, not even arithmetic, UNLESS
the Turing Machine in question is physical.
The sigma_1 part of arithmetic is Turing emulable, and actually Turing
universal. The rest of the arithmetical hierarchy is not Turing
emulable.
Read the definition in the literature, it does not involve physical
assumption.
> Arithmetic is about numbers. We develop intuition (and thus
informal semantics) well before developing theories.
If there was only one thing in the physical world mathematicians
wouldn't have the slightest intuition about what numbers mean,
they'd just be playing with squiggles. Of course if there was only
one thing in the physical world mathematicians couldn't even exist,
but never mind.
You confuse the mathematics developed by the humans, which are very
plausibly inspired by the observation of nature, and the reality of
some mathematical facts.
You just repeat your commitment in physicalism, but science begins by
doubting.
Bruno
> That would contradict the UDA conclusion.
And that would contradict the IHHA axiom.
John K Clark
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