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An advanced introduction to the philosophical work of Ludwig Wittgenstein. We shall begin by examining the central ideas of Wittgenstein’s Tractatus Logico-Philosophicus against the background of the philosophical work of Frege and Russell. We shall then move on to the Philosophical Investigations, paying special attention to his searching self-criticisms and to the “rule-following” and “private language” problems, as highlighted by Saul Kripke’s pathbreaking but controversial account of Wittgenstein’s argument.