Monday, February 27, 2006

In class, Professor Tillman said that while Euclidean geometry is mathematically consistent, it does not describe the way that the world really works. However, I think there is still a problem with the idea that mathematics does not necessarily describe the universe (or describe "the way things really are", which is actually an identical statement.) Namely, that another mathematically consistent set of ideas - non-Euclidean geometry (which in no way contradicts Euclidean geometry) - actually does describe the universe.

For any situation what so ever, one is able to find a particular mathematical reason for what is to be the way that it is - in fact, logic itself is a form of mathematics. Stating that there are certain branches of mathematics which do not actually describes the universe is equivalent to stating that there are certain logical systems which do not describe the universe; i.e. there are arguments which are valid but unsound.

I would view any mathematical theorem whatsoever as being merely a logical argument. In fact, the "proof" construct which is used in mathematics to provide theorems is identical to the "proof" construct used in logical philosophy to construct arguments. By all of this, I mean merely to say that if mathematics does not describe the universe, then it is necessary that logic does not either (since for any system of logic there can be constructed a corresponding system of mathematics.)

I hope my rant wasn't too lengthy; sorry for not formulating this post in the form of a formal argument.

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