On 09 Nov 2014, at 07:01, meekerdb wrote:
On 11/8/2014 5:09 AM, David Nyman wrote:
On 8 November 2014 07:54, LizR <[email protected]> wrote:
Are not the relations between the subsystems part of the ontology?
Explicitly so in arithmetical realism, I would say.
Not really. Perhaps I could respond both to you and Brent in one
here. I'm trying to make an explicit distinction between an assumed
ontology and its (possible) epistemological consequences. In comp,
the assumed ontology is restricted to basic arithmetical relations;
physics likewise is a search for a fundamental level of
explanation in terms of which everything else can explicitly (at
least in principle) be rendered. Of course, one can speak in terms
of systems and sub-systems composed of such basic entities and
relations. But it is surely a guiding principle of reductive
explanation that such composites, and the relations between them,
must ultimately be exhaustively accountable in terms of the
fundamental ontological assumptions.
So is the value of the fine structure constant and its role in
coupling photons and electrons part of the ontology? Is s() in
arithmetic fundamental? I'm not clear on what it means to account
for relations in terms of the fundamental ontology.
Take elementary arithmetic. What exists are the number, but you can
prove that a number having some property exist. You can prove the
existence of a prime number by proving ExAy (y divides x -> (y = 1 V y
= x)), you can prove that there is an infinity of primes, and you can
prove that some numbers entertain a computational relationships, or
prove, for all terminating computations that they exist.
Are you saying relations can't be in the fundamental ontology?
Some relations can be proved to exist in the sense that you can define
the relation in the arithmetical language, and you can prove the
existence of the numbers which verifies such relation. For each finite
piece of computation, RA can prove its existence, but PA can prove
much more existence of that kind, and PA + consistent(PA) even more.
Usual math is *much* more rich than RA, but not so much rich than PA,
unless you do category theory with large categories, or unless you do
mathematical logic.
It is a matter of convention how much you put in the ontology, but if
we are machine, it is absolutely undecidable if the "universe" has
cardinality above aleph_zero.
So, with Occam, the motto would be to put as less as possible in the
ontology. All the extensions of PA appears in the mind of the machines
which exist in RA (in a way provable by RA).
The physics, probably a multiverse, is an appearance from inside, and
analysis (real, complex) is just a simplification tools for number to
grasp themselves, especially from their internal povs. They are
projections. s() is fundamental, as they are defined directly by the
first axioms, but the electrons and spins must be derived, a priori.
Bruno
And I don't see that subsystems are necessarily composite.
Brent
If that were not the case, the attempted "reduction" would merely
have been unsuccessful.
Indeed it is only in terms of some explicit point of view that we
are ever forced to contemplate a strong form of emergence, or
"realism", about any level of composition over and above the
reductive base.
?? Can you give an example? What does "forced to contemplate" mean?
Strictly speaking, composite systems and relations are
*epistemologically* real, rather than ontologically so, in any
strong sense.
That again seems to deny reality to relations. Yet some
philosophers and physics think things can be entirely defined in
terms of their relations.
In fact so-called "weak emergence" isn't really emergence at all
as, objectively speaking, nothing is to be conceived as being
"there" over and above the basic entities and their relations.
So the relations are back into the fundamentals.
So my point is that it is simply self-defeating to deny that there
is in fact any such thing as epistemological realism,
Epistemological realism would be a theory that says knowledge is real?
Brent
as Graziano explicitly does. In attempting to do so, he simply cuts
the ground from under his own claim.
David
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