Mathematical Knowledge

I consider mathematics to be an invention. Axioms, the definitions of mathematics, are arbitrary. Take Euclidean geometry, for instance. According to Euclid, two parallel lines never intersect. That's how we naturally assume space works. However, on a map, the perfectly parallel lines of longitude all converge at both poles. From the north pole, you can move one mile due south, one mile due east, and one mile due north, and thereby return to the starting position, forming a triangle with interior angles adding up to 270 degrees.

The rules that follow from axioms may as well be the rules of soccer for how necessary they are. Even the logical values of "true" and "false" represent nothing more than a decision to work with two values. I'd like to say that truth has something more to it than that, but really, a "truthful" operation is an a operation that we approve, which has nothing to do with logic. When we try to make truth metaphysically meaningful, all we end up doing is expressing our agreement.

Another example. With a bit of thought, most people will agree that a thing is the same as itself, mathematically represented by the formula A=A. I can't imagine any logical fact that is closer to the ideal of Truth. It is the definition of a tautology. However, it is still just something people tend to agree with: I can't find any reason to think that a tautology cannot possibly be otherwise. Logic is still only human.

But, am I mistaken? Is mathematics, instead of being an ingenious invention, a profound discovery? Can we know?

As Galileo said: "Philosophy is written in that great book which ever lies before our eyes ? I mean the universe ? but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth."

Is mathematics the language of God, or a language of us mortals?

Source: http://feedproxy.google.com/~r/RolePlayGateway/~3/r591Kt59udc/viewtopic.php

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