Re: Universal grammar

In article <1161673313.875193.274180@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Franz
Gnaedinger" <frgn@xxxxxxxxxxx> wrote:

Hans Aberg wrote:

One important (meta-)scientific development coming after Goethe, was
moving away from positivism, where one believed one would develop theories
identified with reality, towards merely describing theories. Developments
in physics such as QM, GR, etc., forced that development.

I think Goethe's formula "all is equal, all unequal" holds truth,
as the "panta rhei" (everything flows) by Heraclitus, considered
the wisest insight ever by Eric J. Chaisson (Cosmic Evolution,
The Rise of Complexity in Nature, Harvard University Press
2001). Earlier on, physicists believed they will soon have
completed their "zoo" of elementary particles. By the end of
the 1970s I contradicted: Sorry, this won't happen, elementary
particles are but a useful fiction, they satisfy the formula p
equals p equals p equals p ..., while ignoring the other half
of the truth: p unequal p. Now I must tell you the same:
you can't possibly conceive of a universal mathematical
grammar, for mathematics, while being entangled with every
part of the world, covers but half of the truth. There might be
an equivalent of Heisenberg's uncertainty principle in the
relation of mathematics and language: the more mathematical
the grammar one uses, the drier the language one can define.
Heisenberg's formula was a blow for classical physics, yet
allows a plethora of exotic phenomena and effects that boost
modern physics. The second law of thermodynamics is another
severe constriction, yet Eric Chaisson makes it bloom ...
A categorical No, when accepted, can turn into a surprising Yes.

I can't help you wit the Goethe idea, not knowing much about the context.

But the point is very much that there is no universal mathematical
grammar. Real working mathematics in reality passes between several formal
theories, each having its own formal language.

--
Hans Aberg
.