Plato's Monstrous Mistake

The Platonic view is that mathematics is a landscape, a world that is “out there,” pre-existing, and that mathematicians are discoverers, not inventors. That’s the view held by every mathematician I have heard who has an opinion on the topic, and they are all, of course, wrong, and I am (Surprise!) correct in saying that the ideal world is entirely of human construction.

The Platonic view is strangely seductive and reassuring, and Platonism accordingly drove early Christian philosophy (Plotinus, St. Augustine, St. Thomas Aquinus, Duns Scotus, etc.). However, consider this little anomaly at the center of the mathematical structure, the number zero to the power zero. How is it evaluated? Here’s where mathematicians fall back on contrived convention. Zero and every other number to the zeroeth power is defined as one. For non-zero numbers, this makes perfect sense. However, zero raised to any power but zero evaluates to zero! If you graph zero to the power x as a function of x, you will see a constant line of zero except at zero where it jumps up to one and then back to zero. The convention that zero to the zeroeth power equals one minimizes other impacts to the mathematical edifice.

Need more evidence? Consider that the Pythagorean theorem makes no sense to a student until (s)he constructs an understanding in his/her own mind. Everyone who understands that in a right triangle, a2 + b2 = c2, has constructed that understanding for him or herself. Math’s a building project (artifact), not a mountain to be taken as given.

This would all be obscure philosophizing if it were not for the historical impacts of Plato's Mistake. Platonist and Neo-Platonist philosophers had strong influence on the theology of the Christian Church in the middle ages, reinforcing the view that life and the moment are unimportant in the grand scheme of Heaven, emphasizing instead the nonexistent "afterlife." This kind of slipshod thinking led directly to Calvin's Colossal Blunder.

This hand-crafted, human readable, HTML file was created August 17, 2009, by Rick Wagner, and last updated August 19, 2010 by Rick Wagner.
Copyright © 2002-2010 by Rick Wagner, all rights reserved.