Re: Another Reason Why Collatz is Unprovable


T.H. Ray wrote:

T.H. Ray wrote:

T.H. Ray wrote:


Craig Feinstein wrote:

In my opinion, Satan created Math Analysis.<<

Possibly!

There are
three branches of
math: Applied, pure, and impure. Mathematical
Analysis is an example of
impure math :-)<<

Forget it. After Godel, it's all impure.
Truth,
even in the context of your own demonstration,
is
approachable but not graspable.

That's what make it so pure. The incompleteness
results of the last 80
years, especially Chaitin's work, show that most
of
mathematics is so
pure that it is not even graspable by a mortal
human
being! Chaitin
showed that Godel discovered the tip of a huge
iceberg.

Ray:
I'm not a believer, and yet I don't disagree.
(Except that we do have different philosophical
takes on what is pure and impure.) OTOH, I
have too much of the Hilbert left in me to admit
that there are mathematical properties that we
can't know, even when terms are incalculable.

Feinstein:

Hilbert's ideas have had a great influence on modern
mathematics, even
though they are wrong.<<

Wrong? I can only assume you mean the formalist
program that Hilbert (and Frege, Russell and Whitehead
among others) meant to pursue before Godel published
his proof.

Yes, that is what I was talking about. Hilbert's formalist program only
produces facts which are "trivial", i.e., follow logically from
well-accepted axioms. Because of this, modern mathematics research has
become dull, like some kind of sophisticated logic puzzle. It's never
going to produce anything surprising, as nothing surprising ever comes
from logic. When one takes mathematics to a higher level, trying to
understand numbers as they are from computational experiments, one
finds that mathematics is interesting and one sees things which are
surprising. (In other words, math is interesting; logic is
uninteresting.) Wolfram's way of doing it in his book NKS is ultimately
how mathematics should be done in the computer age, in my humble
opinion. Another person who also has some interesting writing on this
subject is Rudy Rucker.

"Wrong" is not a particularly good choice of
words, I think. One can be wrong in the proof strategy
one chooses, to the extent that the strategy is shown
ineffective. Hilbert is influential, however, because
he was right, in principle, about what mathematics is
and what it can do. He saw far past the obvious -- I
find the Hilbert space much more of a "heaven" than
Hilbert claimed that Cantor created.


My own path leads to the independence of language
and meaning. As Popper said, "I do not believe
in belief." I think, as did he, that what will be
left when belief has been rendered entirely
irrelevant to a mathematical result, is something
like Tarski's correspondence theory of truth.
Something
very naturally graspable ...

Can you give any references to this idea?<<


The Stanford Encyclopedia does a good job of putting it
in negative terms:

http://www.seop.leeds.ac.uk/archives/spr2004/entries/truth-correspondence/#1

When I speak of the correspondence theory of truth,
however, I mean as it was rehabilitated by Karl Popper
(in Objective Knowledge: an evolutionary approach) for
scientific application, sans philosophical baggage. This
view goes by the broad name of metaphysical realism, in
which verisimilitude ("truth-likeness") takes the place
of the Platonic idea of truth.

Tom

Thank you Tom, I'll check out that link.

Craig

.

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