On 6/19/2016 10:34 AM, Bruno Marchal wrote:
An axiom is supposed to be true in some structure, not existent. Then
the axiom itself might be existent in some other theories.
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,
It just means there is a structure to counting, a natural invention of
evolution.
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.
You casually use words like "universal number" and "discovered"; but
these concepts were "discovered" only relative to axiom systems that
were invented.
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.
Physical theories are expressed in mathematics, because mathematics is
just language made precise so that it's "truth" preserving. So it
assumes the truth of some mathematics, but not existence.
Brent
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.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
