by riemannman

A recurring idea on r/debateanatheist and r/debatereligion is to use mathematics and logic as examples of a priori reasoning to support the idea that the existence of God can be proven without reference to observable evidence. In response, many atheists deny outright that there can be any truth without repeated experiment. Thus to them, the only mathematical statements that can be considered true are those that accurately depict some facet of our universe.

I find this to be patently absurd. It is as if these atheists are defining truth in this manner in order to never have to consider a priori arguments for God’s existence. But the fact remains that math in particular is an extremely good example of a priori reasoning that is undeniably true. All one must do is look at some history.

Although they do not depict anything concrete in the observable realm, complex numbers are extremely important for the inner workings of our universe. I have once heard a mathematician joke, “If God exists, he prefers complex numbers over the reals, and the L2 norm over the L1”. The deeper you go into physics, the more prominent a role these “imaginary” numbers play. If the aforementioned atheists were correct, mathematicians should have discovered complex numbers only in response to advances made in physics. But nothing could be farther from the truth.

During the 15th and 16th century, finding methods to solve polynomial equations was all the rage. Italian mathematicians soon discovered that in order to find all the solutions to certain equations, you must first manipulate square roots of negative numbers. It soon became clear that these “imaginary” numbers, as Descartes called them, had properties all on their own. They were worthy of study in their own right. Tell me, oh evidentialist atheist, how did we get from the abstract practice of using square roots of negative numbers to find roots of polynomial equations, to the countless applications of complex analysis to applied and theoretical physics? To me, the story of complex analysis provides an excellent example of a priori reasoning.

There are even better examples of how mathematics has been developed before the truths they state about our universe were realized, but these examples involve deeper, more abstract math. Lie theory is a great example – its rise to importance in mathematics is due to its power in explaining relativity.

I’m hesitant to say this, as to not come off arrogant, but I believe that atheists who argue in this way just don’t fully understand the depth of theoretical mathematics. Many atheists, with their leanings towards science, view math through a physics perspective. It is only when you view physics through a math perspective do you realize, as physicist Eugene Wigner described, “the unreasonable effectiveness of mathematics in the natural sciences.”

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html