On 16 May 2017, at 04:17, John Clark wrote:
On Mon, May 15, 2017 at 7:06 PM, David Nyman <da...@davidnyman.com>
wrote:
>> Physics prevents the above paradoxes because all of these
thought experiments assume that space or time or both are
infinitely divisible, but quantum physics says there is a smallest
length (1.6*10^-35 meter) and a smallest time (5.4*10^-43 seconds).
> Yes indeed. But why in your view wouldn't this merely
imply that whatever mathematics we invoke in explicating physics
cannot thereby in the limit be continuous?
Because there is no mathematical reason time or space or anything
else can't be continuous, nor can mathematics find anything
special about the numbers 1.6*10^-35 or 5.4*10^-43 , but
physics can. And mathematics can produce paradoxes but physics
never can.
You confuse a mathematical reality, like the standard model of
arithmetic, or a group, with the theory about such object. You cannot
produce a contradictory mathematical reality, only a false theory, and
the same is true for physics or any theory. Mathematics is not a
language. It uses some language, but that is no more mathematics than
soccer journalism is soccer.
> I know you take the view, which you reiterate above, that
mathematics should be conceived exclusively in terms of the
formalised mathematical intuitions we derive from observation of a
physical externality. And if you find you cannot in the last
analysis accept a viable distinction between mathematics defined in
this way and its more abstract generalisation then of course
computationalism in the sense I'm discussing it here can make no
sense to you.
It makes sense to me that Information is physical because
non-reversible computation uses energy and increases entropy.
Computationalism says the human mind is a information
processing system and thinking is a form of computation, and
that makes sense to me too.
We can build reversible computer, so we can implement all computation
without erasing memories and without using energy. Information would
be physical if Everett was false, and von Neumann correct, like with a
reduction of the wave packet by consciousness. But then we get 3p
indeterminacy and 3p non locality, and a lot of magical stuff
incompatible with Mechanism.
>Roger Penrose, for example, has defended very robustly the
view of the "discovery" rather than the invention of mathematical
truths.
In mathematics you start with certain axioms
Hoping they are true on the reality we intend to reason about.
and agree to follow certain rules on how to manipulate those axioms,
and if you follow those rules without error then we say the result
is mathematically true,
No. Not only we don't do that, but we cannot do that. G does not prove
[]p -> p.
You confuse formal mathematics, which is like asking a machine, and
doing mathematics oneself, which is an informal task.
but all we're really saying is that in the language of mathematics
the result is grammatically correct.
Not that is plain false. Read any book in logic. The grammar belongs
to a different chapter than both the proof theory and the semantic of
the theory.
You defend conventionalism in mathematics. It is simply refuted by the
incompleteness theorems, or other non go theorem. Physicists often
defend that conventionalist idea. Even Einstein did, but according to
Jammer, he changed his mind on this at the end of his life, thanks to
Gödel, in Princeton.
Bruno
Noam Chomsky famously gave an example of a sentence in another
language, the English language, that was correct grammatically but
meant nothing:
"The colorless green ideas sleep furiously"
John K Clark
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