If the rules of a finite game are the contractual terms by which the players can agree who has won, the rules of an infinite game are the contractual terms by which the players agree to continue playing. For this reason the rules of an infinite game have a different status from those of a finite game. They are like the grammar of a living language, where those of a finite game are like the rules of debate. In the former case we observe rules as a way of continuing discourse with each other; in the latter we observe rules as a way of bringing the speech of another person to an end. The rules,
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