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MoeBlee wrote:
Tony Orlow wrote:
I am beginning to realize just how much trouble the axiom of
extensionality is causing here.
Oh, now the axiom of extensionality.
When you buy into Robinson's non-standard analysis you buy into the
axiom of extensionality, and all the other axioms of set theory, and
mathematical logic - the whole kit and kaboodle - including the axiom
of choice, ordinals, and uncountable cardinals, and all the
"transfinitology" (even if not with platonistic committments) you so
strenuously disclaim.
MoeBlee
Dear Moe -
When I say there are problems with the axiom of extensionality, I refer
to the application of the fact that two sets, when viewed statically,
contain the same elements. Yes, that means that, without regard to time
or order or anything else, the sets are, theoretically, the same. I
don't dispute that. But, I do dispute the application of that fact to
the exclusion of specifically stated time constraints and their
resulting definition of iterations. I am not saying that the axiom
itself is wrong, as a definition. It just doesn't capture the essence of
what's going on. Static sets are not sequences of arithmetical events.
Do you disagree?
TOE
knee
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