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| Authored by: PolR on Wednesday, October 17 2012 @ 03:17 PM EDT |
When PoiR says "Mathematics is a language" he/she is in the same
boat. It seem intellectually dishonest not to highlight that math can mean many
things. It also points to gaps in knowledge not to be aware of how one
structures an argument.
Then you should be reading again the
section of the article titled "Mathematics Is a Language". It contains this
paragraph:
Some people, I am sure, will wonder what I mean when I
say mathematics is a language. For them mathematics is about mathematical
subject matter like numbers, geometric figures or abstract set theory. This view
is correct but mathematics is more than this. Serious mathematical work requires
to write symbols on paper or bits in a computer. The linguistic aspect is
unavoidable. On the other hand these symbols are pointless without their
mathematical meanings. This is really like the two sides of the same coin. One
cannot exist without the other. In this sense mathematics is a language even
though mathematics is also the study of mathematical subject
matter.
There is no intellectual dishonesty. I have pointed out
that mathematics is more than the language. See also footnote 5.
Mentions of
formal system are found in textbooks of mathematical logic where the foundations
of mathematics are defined. This is the branch of mathematics where the syntax
and semantics of the language is defined. The argument is not about what is math
in a broad sense. It is about a particular aspect of math as I have
indicated.
You have said:
This is why this whole topic is
closer to metaphysics than being anything useful. To suggest "Eliza (being
software) is Math" is just plain silly. It goes beyond the common meaning of
math, and what is commonly associated with math.
Whether or not
software is manipulation of symbols is not an issue of metaphysics. The symbols
are actually present and the computation is a manipulation of symbols in a real
technical and mathematical sense.
You should also take note of this sentence
from the article.
We say software is mathematics because the
execution of all computer programs is the execution of a universal mathematical
algorithm. In this sense software is making utterances in the language of
mathematics.
Here is footnote 4:
There is more to
software than program execution. But according to patent law, the aspect of
software which is patented is the program execution. We say "software is
mathematics" as a slogan to remind people that the aspect of software which is
patented is entirely a mathematical computation.
The footnote is
appended to this text:
We may use a digital device such as a pocket
calculator or a computer to carry out the calculation. Then the symbols are no
longer marks of pencil on paper. They are bits in some digital electronics
circuit. This too is utterances in mathematical language, but now the machine
and not the human is making the utterances. According to the mathematical
principles underlying the stored program architecture the execution of all
computer programs is the execution of a mathematical algorithm, therefore this
execution is a mathematical computation. This is what "software is mathematics"
means.4
There is no shortage of explanations of the meaning I have
given the the sentence "software is mathematics". The Eliza program is a
manipulation of symbols in the sense just given. You are arguing against a
strawman.
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