Monday, August 8, 2011

Math: Discovered or Invented?

In my previous post, I offered up two classes of truths: Discovered Truths (The Earth is round) and Created Truths (Darth Vader is Luke Skywalker's Dad). Then I asked what class mathematical truths (2+2=4) belong to. Here are some possible answers:

Math is Discovered

Math, like science, is something we discover. Before there was anyone to count them, one dinosaur and one dinosaur made two dinosaurs. Before we had a word for 50, it was still the sum of two squares in two different ways (7²+1² = 5²+5² = 50).

Math is Created

Math is an art and, like the arts, is a creation. We create the truths in math. Mathematical objects like triangles and the number 17 are created by mathematicians, thus any truths about them are constructed.

Math is A Priori

Unlike the arts, which are dependent on our imaginations, or the sciences, which are dependent on the physical universe, math is A Priori, independent of everything. If there were no physical universe, 1+1 would still equal 2 (though there would be no way to express it). Math does not fit into the categories of "Discovered Truths" and "Invented Truths," Rather, they get their own category: A Priori Truths.

There is No Truth

Truth is a convenient fiction. Language is just a series of meaningless sounds (or symbols) that are used to invoke specific behaviors in others (or oneself). But just because those sounds/symbols succeed in creating reactions in others, doesn't mean they actually mean anything. There is no meaning therefore, there is no truth [footnote 1].

All Truths Are Created

We create our language(s), we express all of our truths with language, therefore we create all of our truths. Any "truth" of science (or math) is a construct of our minds and hence a created truth.

All Truths Are Discovered

Every possible linguistic expression is essentially a number (See Jorge Borges, Library of Babel), all numbers exist independently of us, so any truth expressible in language exists independently of us. More on this soon.

[1] I am very much aware of the irony of using language to express the meaninglessness of language.