On 19 Jun 2016, at 20:15, Brent Meeker wrote:
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.
In which theory?
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.
In which theory?
Well, any theory like that is refuted by digital mechanism.
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
Not at all. You confuse some mathematical reality with the language
and theories used to shed some light on such reality.
so that it's "truth" preserving. So it assumes the truth of some
mathematics, but not existence.
Existence is just truth of existential proposition.
Primary existence is truth of existential propositions taken from the
base theory, or the "ontological" theory.
Here the problem is that with comp we can easily formalize the base
theory, but physics is not really as much sophisticated as such.
But we don't do physics. We try to solve the mind-body problem and the
search of TOE problem.
Some people here seems to decide of the solution, and ignore the
problem ...
Bruno
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.
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