On 20/06/2016 3:34 am, Bruno Marchal wrote:
On 18 Jun 2016, at 02:59, Bruce Kellett wrote:
Smolin's book with someone-or-other is possibly more useful: he
rejects platonism and says that a better way is to seem mathematics
as "evoked" -- i.e., it has properties independent of us, but we
'evoke' it by specifying some axioms. These axioms (and their
consequences) are not pre-existent in any sense.
That expression is misleading.
An axiom is supposed to be true in some structure, not existent. Then
the axiom itself might be existent in some other theories.
Axioms are what we say they are -- they are neither true nor false. They
might be true statements about some model or domain, but that does not
define them as axioms. The Peano axioms might find expression in the
integers, but that does not imply that the integers "exist" in any
meaningful sense.
Now in the case of "rich" (Gödel-Löbian), in fact in the case of all
essentially undecidable theories, (like RA, PA, ZF, ...) the theory
are rich enough so that their axioms and consequences are reflected in
the relation between the objects they talk about. That is why both "2
+ 2 = 4" and "ZF proves "2 + 2 = 4"" are elementary arithmetical
propositions (even provable by the very weak non Löbian RA). In that
sense the axiom are pré-existent, but only in the mind of the
universal numbers. It is like the distribution of primes is well
defined, even before the first mathematician discovered the prime
number and look at its distribution.
Mathematicians are not universal numbers! The axioms exist only in the
minds of mathematicians, not in "universal numbers", whatever they might
be. The distribution of primes is determined by the existence of
integers and the definition of prime numbers -- and both are the
inventions of mathematicians.
May be you could try to formalize your physicalist theory to see if it
assumes or not the numbers or any universal system at the start.
To use numbers, or mathematics in general, in physics does not require
that these things exist at the start. They are simply descriptions of
objects in the universe we observe -- mind-dependent, like colours,
emotions, or sensations. Take a Humean stance -- the "laws of physics"
are not handed down from on high; they are not pre-existent in any sense
-- they are the mechanisms we construct to formalize the regularities we
observe around us. That is why the "laws of physics" are only ever
provisional, subject to revision in the light of new and better data.
Bruce
Then all what UDA shows, is that if you do assume it, adding Matter
just does not work for the mind-body problem.
Physicalism/computationalism is just testable. And then QM (without
the dualist collapse) adds evidence to digital mechanism.
Bruno
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