On Mathematics

[jackofallgeeks]

So here's a semi-interesting article on whether mathematics are discovered
or invented. Now, at first blush I think it's kind of an absurd
question, because no one invented 2 + 2 = 4, it just is.
That's the way the world operates, so if we find something 'new,' it's just
that we never saw it before, not that we made it up. Given a little time to
thinjk about it, though, I think it becomes a more interesting question.

Now I expect no more than three of you to care in the slightest -- most of
my friends, it seems, hate math -- and I didn't read the whole article (even
I can't take math before 9am), but just a few thoughts. Someone made a
point of how they were trying to compare math and physics; I'm not sure what
his point was in making the remark, but it got me thinking about the
similarities and differences between math and physics. They both describe
the way the world works, although physics are a bit more concrete than pure
math. But a lot of times, physics is just a "best guess," and theories are
constantly being concocted, accepted, and refuted. Newton's laws were true
until Einstein proved them false (though, for the layman Newton is usually
good enough). Math, typically, doesn't have this problem; it's abstract.
If the numbers work out, you can't disprove a formula. Physics is
the application of mathematics to the world around us; the application can
be wrong, but the math simply is. You invent theories, you discover
laws when those theories prove true. Perhaps you can invent formula, but
you don't invent math.

I had a philosophy class on what knowledge is; it was really more of s
survey course because, as should be obvious, 'knowledge' is a pretty broad
topic. At one point the professor got onto the topic of the interesting
nature of mathematics. It's abstract, only in our hears, in that you can't
go into the world and find a 2, or point to a formula. But it's different
from other abstract subjects, his example being hobbits. Someone can know A
LOT about hobbits, but that knowledge can never have any read bearing on our
undetstanding of the world. If someone knows a lot about math, though, that
can actually be applied to describe, rather acurately, the world around us.

Comments

[dikaiosunh.livejournal.com]

Interestingly, even the most "mathy" parts of physics are generally not treated as set in stone: Newton defined momentum as mass*velocity. That didn't stop relativistic mechanics from adding a Lorentz factor to it (which, according to most classical conceptions of definitional truths, should be like finding out that "bachelor" != "unmarried man").

Also, I'd be a bit skeptical of the status of some of these discussions - arithmetic is a formal system; nothing stops us from using a different formal system (Kripke's "qus" rather than "plus") except that this one works pretty well.

You should take a look at W.V.O. Quine's Two Dogmas of Empiricism...

[jackofallgeeks.livejournal.com]

There's a difference, though, in the problem with Newton and the problem with bachelor. That is, newton was trying to explain a phenomenon. He called this phenomenon 'inertia', and then defined 'inertia' to be mass*velocity. But that this phenomenon was mass*velocity was really just a guess, and the addition of the Lorentz factor just proof that the guess was wrong. Inertia as a phenomenon didn't change, we were just wrong about it. It would be more akin to saying that Daniel is a bachelor and then defining bachelor to be an unmarried man. That we label a thing and then attach meaning to the label doesn't change the thing itself.

[bsgnome.livejournal.com]

So the article was fairly short, and didn't add anything substantial to what you had posted ... I'm disappointed. I was oddly looking forward to an article on the nitty-gritties of mathematics.

That said, I'd argue that math is neither discovered nor invented, and that it's a false conundrum.