Wittgenstein on the primacy of games

The later Wittgenstein compared language and mathematics to games. In this paper I explore why he did this and whether he was justified in doing so. I begin with Wittgenstein's philosophical development in his middle period, arguing that he was already at this point grappling with the problem of rule-following skepticism. In response to this problem, he began appealing to possible activities involving language or calculation, which he famously called 'language games'. Here, I suggest that he was not simply emphasizing the rule-bound nature of language or mathematics. Rather, his motivation came from seeing games as anthropological phenomena which frame and contextualize the behavior of their participants. Rule-following behavior stands out distinctly in the context of a game. From this, Wittgenstein inferred that language and mathematics require possible activities of application. I contrast this account to some prominent commentaries on Wittgenstein's philosophy and conclude by highlighting some limits of the comparison of language and mathematics to games.