Probability is false. Imagine the following scenario:
You and Dominique Jones are great friends in 2nd grade. Then, twenty years later, Dominique moves to Venezuela and loans a Noam Chomsky book to Hugo Chavez. Then, you become a custodian for a small high school. Then, you win the lottery – without even buying a ticket. Then, you travel to the Congo. In Congo, you run into Dominique. Dominique says, “Oh gosh! What are the chances?”
Most people would respond with something ignorant such as “Yeah I know!” or “Pretty low!” According to my research, however, the proper response is 100%. But why?
Because if this scenario happens, the chances of it happening are of course 100%. The key terms in my analysis are “if,” “happens,” and “of course.” If it didn’t happen, then the chances of it happening were always 0%. Some people would argue that this commits me to hard determinism, but it does not. A la carte Peter van Inwagen free will exists. What it commits me to is the world of facts. If you are pro-fact, then you will abandon all probabilities between 0 and 100%.
This concept kind of shoots itself in the foot, so I don’t need to spend much time on it. Using an imaginary number in an equation is like intentionally using a false premise in an argument, which is of course totally inappropriate in scholarship.
In fact, the man who invented Imaginary Numbers was an ophthalmologist named Renes Descartes. He coined the term. And guess what. It was in a criticism of the idea. Orwell would have a field day.
I don’t think I need to spend much time on infinity. Infinitus est numerus stultorum. It suffices to point out that you cannot show me infinity of anything whatsoever. Since everything is finite, including every number, putting them all together will still not get you to infinity. According to math (and also its feisty sidekick, the English language), the number before infinity would be known as the “penultimate” in the series of all numbers. So in my opinion, the last number in the number line is the penultimate.
There is also a convenient common sense method for refuting infinity. If there were infinite numbers, then the Universe couldn’t fit them all in. But clearly the Universe does fit them all in, by the transitive property. It fits our brains, and our brains fit all the numbers. Please see William Lane Craig on this point, for further discussion.