Final answer:
Appiah discusses Wittgenstein's argument about private mental events and the existence of private languages.
Step-by-step explanation:
Appiah discusses the argument put forth by Ludwig Wittgenstein about private mental events and the existence of private languages. The argument states that if we accept the idea of private thoughts, then we must also accept the idea of private 'marks' or names for these thoughts. However, Wittgenstein argues that for these 'marks' to exist, there must be a way to check whether they are being used in accordance with a rule. And Wittgenstein's argument suggests that such checking is impossible, leading to the conclusion that private mental events are impossible.