On 7/1/06, Les Schaffer <[EMAIL PROTECTED]> wrote:
Doyle Saylor wrote: > It is obvious to me that math is not a language. It is a different > kind of mental work.
Just because it is obvious to you does not make it true. First "math" is not a languge. Mathematics is an art that includes a variety of languages. Secondly it seems likely that languges we normally think of as languages (English, Arabic, Basque and such) use a particular part of the brain, while mathematics taps another. So it is very diffrent type of mental labor. Don't have time to go further. Look up the difference betwee "natural" and "artificial" languages - "natural" being used even more problematically than usual; but that seems to be the standard term. (In other words "natural" in this sense is a technical term, and does not mean the same as in standard English.) The primary difference between mathematical and natural languages is concision. You can express mathematically in a paragraph something that would require a book in a natural language. This allows in practice solutions that could not be arrived at in natural languages - not because they are impossible in principle, but because we have not world enough and time to solve them without mathematical short cuts. How do we distinguish between artificial and natural languages? Well the languages we think of as "natural" evolve by a certain social process without a great deal of deliberate intent to create a new language on the part of those speaking, while artificial languages are usually invented deliberately and conciously by an individual or small group. That I suspect is the basis of the term. However in practice languages that behave like natural ones have been invented deliberately - for example esperanto. And I dimly seem to remember that Euclid systemized and compiled knowledge that was widely known among the trades people of his day. Carrol, is that right? In modern linguistics the distinction between natural and artificial languages is type of grammar. However the language arises,if it has a certain kind of grammar it is considered a "natural" language otherwise not. Like I said, the use of "natural" in this context is completely problematic. But languages with the meta-grammatical structure labeled "natural" do access a certain part of the brain and are much easier for most people to learn than languages (such as mathematical ones) that don't use that kind of grammar and don't access that part of the brain.
