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| Authored by: Tolerance on Monday, February 11 2013 @ 01:25 AM EST |
Oh dear. I really do have to dispute the assertion that 2 is
"... a symbol that represents the set of all sets that
contain 2 members ..."
Set theory isn't the only axiomatic basis for the
integers, and number theory; the Peano axiomatization was
earlier. Its set-theoretic axiomatization sprang from the
mind of Johnny von Neumann, who I would cautiously accept as
human. That set-theoretic basis for numbers bears no
resemblance to your description.
The von Neumann axiomatization starts with 0 (zero) being
equivalent to the Null set, and continues using von
Neumann's successor operator "s" to generate succeeding sets
which behave just like integers under the Peano axioms. In
particular,
2 = s(1) = {0,1}
Obviously, this is not "the set of all sets that contain 2
members". Nor does that appear in other axiomatizations of
the integers that I'm familiar. There are ... heh ... a
number of them, culminating in Zermelo-Frankel theory which
still uses recursive identities like the above von Neumann
ordinals.
Let's see now ... given Math and Logic predate the Big Bang,
you're surely not of the opinion they are laws of nature.
Unless nature predates the Big Bang ... which is actually
consistent with M-theory which ascribes the energy of the
Big Bang do a collision between two M-branes.
But that's Physics, not Math. Tell me, do you think that
Math and Logic predate the Bulk space that M-brane
structures might move in?
Then again, you assert that no-one created them ("NO ONE
invented MATH or LOGIC"), so in particular they are not an
art of the human mind.
And for you it doesn't matter whether anyone is around to
appreciate them. That reminds me a little of the Bertrand
Russell's duelling limericks, which end with "Dear Sir, I
find your astonishment odd, I am always about in the quad,
and that's why the tree, will continue to be, since observed
by, Yours faithfully, God".
But I gather you don't believe Math and Logic were created
by God, either. I guess we need a new category for this
theory of the origins of Math and Logic, because I haven't
met a position with quite such strong ramifications
before.
---
Grumpy old man[ Reply to This | Parent | # ]
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| Authored by: cjk fossman on Monday, February 11 2013 @ 09:50 PM EST |
Are you sure math and logic "just exist" outside of our frame
of reference?
How can you prove it?[ Reply to This | Parent | # ]
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