Difference between Maths and Science
Joined: Jul 17, 2011
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Total Posts: 59
Posted Jul 17, 2011 - 8:21 AM:
Math is a study of language. Science is a study of natural systems.
I'm not so sure. What do you mean by "a study of"
Do you mean that the object of math is language. For that kind of statement, I think you will need a convincing argument, as it's somewhat counterintuitive. At least to me.
Math obviously needs language. The natural languages work out pretty well, but sometimes, it needs a formal language too. But should we actually say that math is to language as science is to natural systems?
I think science looks at how nature works and then makes assumptions about fundamental principles. (After being hit by a truck a certain number of times, anyone will believe that force equals mass times acceleration). So the object of science is natural events, right? Not the laws or principles themselves. They remain hypotheses. I mean it's one thing to say 'from all we observe nature works this way' but it's another to say 'nature works this way--we know that for a fact'
Now, if natural events are the object of science and natural laws are the axioms of this disicpline what takes these roles when we are talking about math? Well, as for for the axoims that is pretty clear. Some of the fundamental axioms would be Peano's. And there are others. Taken together, there seems to be a set of axioms from which all mathematical statements can be deduced. Is that not so?
But what takes the role of the object. So what is for math what natural events (e.g. something falling to the ground, something blowing up in a fireball, a tree growing, etc.) are for science. Well, we could say numbers. Okay, but is that all there's to it? Aren't there also sets, functions, vectors, matrices, and all sorts of things? And are they really the object of math in the same way as natural events (or phenomena) are the objects of science.
I don't think that these mathematical things are really the object of math. I think that they are for a mathematician what substances, bodies, species are for a scientist. But the object of math is what a mathematician studies. And what a mathemtatician studies is what happens to those things when we do certain things with them. So we actually kind of experiment with things too in math. We do things with numbers and sets and functions and so on and see what happens. Right, I mean what math is about is not to say that *there are* numbers, or *there are* sets, etc, etc. We try to make statements about how these things combine.
Part of the difference is, then, that science looks at things which are visible. And math looks at things which are thinkable (this is actually a Platonic difference). The object of science is natural phenomena. The object of math is ... well, mathematical events, i.e. what happens to sets, numbers, etc. when we try certain things.
The things (as opposed to objects) that science looks at are material. The things that math looks at are immaterial. They are actually metaphysical while science things are physical.
It's interesting to see what this means for statements that try to express natural facts by method mathematical language.
'force equals mass times accelarion' should actually be:
if you do to mass (in Kg) and acceleration (in m/s^2) what a mathematician does when he multiplies two numbers, you get force (in N). Because actually, only a mathematician knows what multiplication really is and only he knows how to handle the '25' in 25N. It is the scientist who can handle the 'N'.
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