Re: math development curiosity question

Han de Bruijn wrote:
Robert Low wrote:

In fact, HdB didn't speak at all there. (Though I tend to agree
with the general sentiment that David is well out on a limb
with this.)

HdB has spoken elsewhere. I kept my promise about the _infinitesimals_
in physics. Not Richard Feynman though, but Max Planck. Would you like
to join in? It's in the "Calculus XOR Probability" thread where I have
a debate with Randy Poe about this:

http://groups.google.nl/group/sci.math/msg/6dd5232666f1bc46?hl=en&;

Han de Bruijn

The cow is its complement in the universe.

It's defined by everything it's not.

People like Ernst Zermelo called AC the well-ordering principle and
accept it as fact, Zorn found it a lemma. Where infinite sets are
equivalent, AC is redundant, and where it would overconstrain a
theoretical system leading to incompleteness and thus eventual
inconsistency of a backing theory, where its implication is obvious,
it's useless, except in a countable universe as a trivial theorem,
where it's quite useful.

"A good partial differentialist outranks most set theorists." Ah, the
memories. I'm how you say pleased that's quite correct, still is, and
always will be.

There's no universe in ZF. ZF is, incomplete, there is no set of true
statements in ZF, unconditionally true statements.

I borrowed a copy of Graham Priest's "Beyond the Limits of Thought"
today. Priest discusses "paraconsistency", where I am more interested
in the "intraconsistency."

http://www.oup.co.uk/isbn/0-19-925405-2

Check it out.

About Hegel, and Kant, there is much discussion, although I tend to
focus on the Thing-in-Itself moreso than the noumena, and Hegel's Being
and Nothing as the important elements instead of his rephrasal of
potential versus actual. Graham closes with:

Certainly there is no going back to how things were before htis. But
maybe this century will see a return to the mainstreaming of a more
traditional philosophical issue, the nature of reality -- and if I am
right, a nature that is contradictory.

I think that instead there can be found a nature that is
uncontradictory because everything is natural, in terms of its
existence or being. While it would be contradictory to nature for
nature to be contradictory to itself, that resolves to the liar paradox
which with these notions of, say, true axioms, or ever the possibility
of calling anything true, ever, that has it being quite uncontradictory
for nature to be. A paradox would be paradoxical, anathema to reason.
Beyond _limits_ of thought is an axiomless system, of natural
deduction.

That's not to be taken that I don't agree with many or most of Graham's
statements and descriptions of the historical evolution of
paraconsistency in dialethism, I do. Priest is generally considered to
be "heretical", AND state-of-the-art. Non-heretical art is craft.

Recently I read "The Infinite Book", that's another nicely bound
volume, if you're interested in infinity and care it wouldn't take too
much space on the shelf, nor is it particularly an involving read.

Next, about infinity, I hope to read Yaroslav's volume, it appears to
be in somewhat more limited circulation.

Han, I'm still looking for a management summary of differential
equations, the Handbook, of Differential Equations, and one of these
"An Atlas of Functions" seems to be a helpful start, along with say the
H.M.F., "Handbook of Mathematical Functions", that is quite an amount
of information.

Regards,

Ross F.

.

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