On 12 Jun 2015, at 07:40, Bruce Kellett wrote:
LizR wrote:
You also say that 1p phenomena - in a physical theory - have to be
eliminated (as per Dennett) or elevated to something we could call
"supernatural" (for the sake of argument - in any case, something
not covered by the underlying physics). But the alternative is
apparently that subjective phenomena exist inside assumed-to-be-
real arithmetic, and the (appearance of a) physical world somehow
emerges from that. Both of these are problematic. The first seems
plausible to me (in the elimiativist mode), but implausible in that
it reifies matter and doesn't have an ontological status that could
be called "final", but merely one that is "contingent" (i.e. "we're
here because we're here because...") while arithmetical truth, if
there is such a thing, does.
This is a false distinction. Arithmetical 'truth' is no more
fundamental or final than physical truth. Arithmetic is, after all,
only an axiomatic system.
Sorry, but here you show that you have no knowledge of modern
mathematical logic.
Arithmetical truth, or reality, is subsumed in the usual structure (N,
0, +, *). Since Gödel we know that this is not a computable reality,
and indeed that it escapes *all* effective theories.
An axiomatic system, like RA, or PA, or ZF, can only scratch on the
surface of the arithmetical reality.
What is true, is that with comp, everything is determined by the much
more tiny sigma_1 arithmetical truth, which is the arithmetical UD.
From inside, the phenomenological is richer, and cannot be bounded in
non computable complexity. Most machine's predicate are not computable.
We can make up an indefinite number of axiomatic systems whose
theorems are every bit as 'independent of us' as those of arithmetic.
Once you assume one universal system, you get all the other for free.
from now one I assume only the combinators K and S, and their
combinations. That will help for the physical derivation.
Are these also to be accepted as 'really real!'?
Once one is real, all the other are real too. The robinson
arithmetical axioms becomes theorem in combinatory algebra.
Standard arithmetic is only important to us because it is useful in
the physical world. It is invented, not fundamental.
Amen.
Bruno
Bruce
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