...it is merely, to my knowledge, a method for arriving at the same answer as the person across from you. It is by this that 3 * 4 + 2 = 14, and not 18.
3)where is the philosophy? Science is rooted in methodological philosophy. It has a philosophical root, a foundation. As far as I know, math does not. Granted, Pythagoras used numbers as the thing that the universe was made of, but . . .
I think the first thing to debate here is if you are describing maths or arithmetic. There is a a philosophy of maths - the existence (or lack) of numbers: Do mathematical concepts exist objectively and are discovered by man, or does man create mathematical concepts?
A quick look via google brings up many discussions on the philosophy of mathematics,
the wiki article will probably be a good place to springboard from.
science is tentative. What is known as fact today will not be tomorrow. math is not, to the best of my knowledge, tentative. 2 and 2 will always equal four given the rules we use
The nature of 2, the addition function, the equivalence statement and the nature of the number 4 might be tentative though.
However, I don't think that maths is a science. Though an argument might be made to that effect. Maths might make certain predictions based on certain assumptions and can test them out later, which would lend it the air of science.
Maths works on principles very similar to science (sometimes the same),but I don't think that means they are the same methodology. It just means that we know certain ways of asking questions are better than others. I'd say they are cousins, perhaps brothers - but they are not the same.
Still - I'm willing to hear other opinions on the matter.
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