Re: Are there things that don't evolve?

In a message dated 3/26/2006 12:00:55 AM Eastern Standard Time,
dfsiemensjr@juno.com writes:
You have just dogmatically disenfranchised a group of mathematicians, the
strict constructionists. Also, the three Aristotelian calculi do not match the
logics that have developed from Frege's work. I recall a remark that C. L.
Dodgson had come up with a calculus that differed from both Aristotle and PM, which
remained undeveloped. I have not dug into that.

I note that there are various conjectures floating around mathematics. Are
these discovered axioms, invented assumptions, wicked perversions, or something
else?

I think we can safely say that nothing that is a constant evolves. This must
apply as surely to pi as to G. If they change, they can hardly be constants.
Dave

Hi Dave,

I think you're reading too much into what I said, or maybe not enough. Let
me just take the issue you raised about conjectures as illustrative of the
whole:

it is conjectured that if Zermello's set theory is consistent, then this
implies that Quine's set theory is also consistent.

Well, if mathematical logic were evolving, then it would be impossible even
to meaningfully raise such a conjecture, much less hope to prove it. If it
were proven today using today's logic, but then logic evolved, then tomorrow it
would be unproven again. If this could actually happen then mathematics would
cease to exist as a discipline and everyone would stop making conjectures.
but it doesn't, and we don't, because of our deep-seated, universal belief that
there really is essence to logic and that it does not evolve.

I hope that clarifies what I intended. Of course folks can build different
axiomatic systems or calculi or logics and then discuss consistencies using the
different rules, but the ability to even engage one another in these
discussions implies that there is something that doesn't evolve, and that is what I'm
talking about.

God bless!
Phil Metzger
Received on Sun Mar 26 01:48:26 2006