Re: the need for relevance
- From: Gonçalo Rodrigues <nospam@xxxxxxxxxxxx>
- Date: Tue, 15 Jan 2008 12:39:16 +0000
On Tue, 15 Jan 2008 09:22:42 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> fed this fish to the penguins:
The point I'm trying to make is that Math does care about reality, but
readily allows further abstraction in order to get a handle on it.
Still, for any new theory, there is a sense of obligation to reveal,
however indirectly, something new about existing theories. In other
words, if some theory A sheds some new light on existing theories, and
if those existing theories lead, in some chain, down to the core
theories, then that provides some justification for A.
This has clearly happened to e.g. Set Theory. The _ZFC_ system contanins
many axioms which are nearly trivial (perhaps better: may be considered
instead as _theorems_) for _finite_ sets. What has happened next is that
infinite sets have be endowed with finite set like properties, in order
to make them look a great deal like the already well known finite sets.
So _theorems_ for finite sets have been adopted as _axioms_ for infinite
sets, for the simple reason that, otherwise, we would have no starting
point, at all, for the latter. But these choices seem rather arbitrary.
And consequently, there is more than _one_ set theory for infinite sets.
But the problem could have been solved otherwise, by simply not allowing
other than finite sets, together with a limit concept of some sort, for
the purpose of approaching infinite sets in "the calculus way".
I see that you acknowledge that the problem *was solved*. Could be
solved in any other way? And doesn't the very question tell you
anything? I mean, besides wishful thinking on your part, what sort of
evidence do you have that the problem *can* be solved by "simply not
allowing other than finite sets, together with a limit concept of some
sort, for the purpose of approaching infinite sets in "the calculus
way""?
Hint: half-ass half-baked set-theory like axiom systems with funny
names like "Implementable Set Theory" or something like it, do not
count as solutions.
Neither does half-ass half-baked set-theory like the one in Halmos with
funny names like "Aleph_0", "Continuum Hypothesis" or something like it
count as solutions. But anyway (to be upgraded soon):
http://hdebruijn.soo.dto.tudelft.nl/jaar2007/set_theory.pdf
huh... you yourself said above that "But the problem could have been
solved otherwise", etc. So you acknowledged that the problem was
*solved* by ZFC. Changed your mid?
And I do not need to see your pdf to know that you do *not* have a
solution. When you have something to replace ZFC with, presumably some
axiomatics of finite sets only, when you have a "limit concept a la
calculus" that can effectively replace what *theoretical physicists*
daily use (mind my words, not mathematicians, theoretical physicists),
come back. Until then you are not only a crank, and a very
intellectually dishonest man as the quote
Neither does half-ass half-baked set-theory like the one in Halmos with
funny names like "Aleph_0", "Continuum Hypothesis" or something like it
count as solutions
shows.
Regards,
G. Rodrigues
.
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