Fooling with infinities

Does infinity exist?

The undergraduate math major might have a minute or two of fun tossing the question around with his buddies at the campus pub. He might point out that, for example, the list of all possible integers is infinite, but so is the list of all even integers.

The philosophy major would take that factoid and spin it into an evening-long discussion of the nature of logical contradictions, or of the ways that language constrains our understanding of reality.

Undergrad philosophers love this sort of thing. That’s why you always find them off in a corner of the pub, talking to each other. No one else will bother with them.

The problem with philosophy is that in its secret heart of hearts it’s essentially a game — a logic game, a word game, or a number game. Internal consistency is the sole criterion for correctness. Continue reading