Abstract
A new paradox offers the opportunity to recapture the sense of confusion and uncertainty that faced mathematicians in the early part of the twentieth century, including those common initial feelings that the eventual fix is a dishonest legalism which walks around a key question instead of answering it. Also, it provides a new probe with which to explore the relationship between paradox and proof. I stumbled across the Hypergame Paradox when I was teaching a section on games and strategies for a Mathematics for the Liberal Arts Major course occasionally offered at Union College, and an idea for a bonus test question came to me. Let us define a game G to be totally finite if it satisfies the following conditions:
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