In his recent address to the Aristotelian Society, Aurel Kolnai suggests that games exhibit what he calls a “genuine paradoxy.” I do not believe that he has shown this to be the case, even on the most permissive interpretation of what it means to be a paradox. Kolnai has, however, called attention to an aspect of games which invites further investigation, and I should like to advance the following considerations not so much as a criticism of Kolnai as an attempt to take the investigation along a path which Kolnai has indicated, but which he has not himself, in my opinion, followed. It is not that Kolnai does not say many interesting, indeed penetrating, things about games, for he does. That Kolnai's inquiry is an important contribution to the philosophy of games is not in question. What is questionable is whether paradox has very much to do with that contribution.