Saturday, November 2, 2013

Mathematical Verities are Mind Dependent

What is the number 1? It is a concept, an idea. We don’t find the number 1 in nature apart from our conceptualizations of it. It is therefore mind dependent, unlike the rain, which doesn’t depend on what I think about it!

If this is true about the number 1, it is also true about the numbers 2, 3, 4 …. And it must also be true about higher level mathematical constructs, like the Pythagorean Theorem, which depends on the number 1.

However, clearly, we didn’t create this Theorem; we discovered it! Although distinct from the material world, it seems to understand the material world and tell us so much about it, as if it has intimate knowledge of this world.

Likewise, the angles of every triangle contain exactly and invariably 180 degrees. If you were to add a fourth line or side to the triangle, this four-sided figure would contain angles equaling 180 + 180 = 360 degrees. If you would add a fifth line or side to this four-sided figure, it would contain angles equaling 180 + 360 = 540 degrees, ad infinitum.

How can we explain this uniformity, this elegance? Certainly, this isn’t an elegance that we created, but rather discovered. Besides, this uniformity seems to be immutable and universal – traits that transcend our individual, changing minds. However, if mathematics is conceptual and therefore, mind-dependent, but doesn’t depend on our minds, then there must be a universal and immutable Mind that it does depend upon.

To state this another way:

  1. Mathematical truths are conceptual.
  2. They therefore require minds.
  3. Our human minds are not adequate to account for the uniformity, immutability, and elegance that we find in mathematical realities.

CONCLUSION: Therefore, a greater, immutable Mind must exist.

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