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| Authored by: PolR on Sunday, October 14 2012 @ 04:30 PM EDT |
You should have kept reading. The issue you are raising are being addressed.
Here is an example:
First, if mathematics is a language, then what
does language mean? As languages may be described via mathematical notation, and
we know as an absolute that natural languages cannot be described formally, and
mathematics require formal definitions, mathematics is a formal language
described mathematically. That seems to be a loop. Or, looking at it another
way, if mathematics is a language, what is the grammar? What are the words and
sentences that are provably in and out of syntax?
This information
is found in textbooks of mathematical logic. [Kleene 1967] mentioned in the
reference section of the article is a good one. Had you kept reading you would
have read this paragraph:
There is also the issue of foundations.
There is a branch of mathematics called mathematical logic. This is where
mathematicians define the foundations of their discipline. What is a
mathematical formula? What is a theorem? What are the criteria of logic that
must be met for a mathematical proof to be valid? These are some of the
foundational questions answered by mathematical logic. There is also a branch of
mathematics called the theory of computation. This is actually a subbranch of
mathematical logic. This is where mathematicians define what is an algorithm and
what is a computation according to an algorithm. If you go read these
definitions in textbooks from competent authors you will find they are all
elements of the language of mathematics. The definitions expressly refer to the
symbols, their arrangement in syntax and their semantics. All of mathematics
ultimately rely on these foundations. In this sense, mathematics is indeed a
language.
All the other issues you mention are being addressed in
a way or another. So please keep reading.[ Reply to This | Parent | # ]
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| Authored by: Wol on Sunday, October 14 2012 @ 06:37 PM EDT |
It'll answer your question.
For the record, the answer lies in the distinction between reality and
imagination. I know some people can't tell the difference, but maths and
software lie on the imaginary side of the line, patents lie on the reality
side.
Cheers,
Wol[ Reply to This | Parent | # ]
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