On 09 Feb 2013, at 15:14, Craig Weinberg wrote:
On Saturday, February 9, 2013 8:15:21 AM UTC-5, Bruno Marchal wrote:
On 08 Feb 2013, at 21:38, meekerdb wrote:
On 2/8/2013 12:31 AM, Kim Jones wrote:
Which is a profound problem that we can lay right at the door of
LANGUAGE. Language is indeed a self-serving thing. A description
of something is a dance of language, not a dance of PERCEPTION.
Perception is often throttled by the processes of language. We
need to move beyond words. This is the importance of math and
music (which is audible math IMO.)
That seems contradictory. Mathematics is very restricted language
- declaratory sentences, logically consistent.
Mathematics is not a language at all. You might be confusing
mathematics and the theories used to put some light on some
mathematical reality.
Then Spanish and French and Italian aren't languages either. People
might confuse them with the linguistic theories used to put some
light on some semiotic reality.
Not at all. Spanish and French and Italian are languages. They define
strings of symbols, having meaning, which can be on some subject
matter, but they are different from the subject matter.
Only non-mathematician confuse the mathematical language (that exists
too) and the mathematic subject matter (number, geometrical shapes,
algebras, mathematical structures, etc.).
Also most mathematicians don't care so much about logical
consistency. That notion is studied by logicians, but with few
incidence on the doing of mathematicians. Logic is just another
branch of math, with its own purpose. It can have application in
math, or not.
What branches of math contain no logic?
What branches of anything does not contain logic? Everyday life is
full of logic. But this is different from logic as a branch of math,
which is virtually known only by logicians, and some computer
scientists. It is a pity as it is a useful tool, but things takes
time, and most logicians are not even aware of their ivory tower. They
live in the clouds, we would say in french. I got problems because I
dare to apply what most mathematicians think to belong to pure math.
They don't want people applying their beautiful discoveries. Of course
"pure math" is a myth, provably so with comp.
Bruno
It seems to be an interesting fact that all information can be
encoded in binary numbers, but that is the antithesis of you view
that the form of representation, painting, dance, music matters in
an essential way.
The content of the information is usually not encoded, in any form.
The mathematical study of that content can be done with some tools
in logic, or computare science (with the UM building the meaning),
but again, we have to distinguish the content (usually infinite) and
the syntactical tools to point on it.
Since we can only infer the content through the tools, how can we
assume that it exists independently of them?
Math is as different from language than the physical universe is
different from a book in cosmology.
The referents of math are different from the referents of other
specialized languages, but that doesn't mean that it is different
from other languages. The referents of mathematics are no more
infinite than those of art, literature, poetry, etc.
Craig
Bruno
http://iridia.ulb.ac.be/~marchal/
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