There is a long list of titles of the form ‘Wittgenstein on X’. There is a somewhat shorter list of cases in which the X is replaced by an unexpected noun. My title falls into that second category, though not squarely. I shall explain why in the first section, where I expound the exegetical importance of my topic and list claims about concepts that can be found in Wittgenstein's later work. Section 2 indicates why the topic is also significant from a substantive perspective. It distinguishes five urgent philosophical questions about concepts – the definition question, the possession question, the priority question, the individuation question and the function question – and introduces Wittgenstein's answers. The next two sections approvingly discuss two of these answers – namely that a philosophical account of what concepts are ought to start with an exploration of concept-possession (Section 3) and that the latter is a special kind of ability (Section 4). Section 5 rejects the Wittgensteinian proposal that concepts can be equated with abilities, and Section 6 does the same with Wittgenstein's own suggestion that they can be equated with techniques or rules. The final section turns to the individuation question. While concepts cannot be equated with word-meanings, they are individuated along the same lines. An adequate criterion for the identity of concepts emerges through combining Frege's idea of cognitive equivalence with Wittgenstein's idea that meaning is determined by explanation. All in all, Wittgenstein has made an important – though not definitive – contribution to our understanding of concepts, especially through delineating connections between concepts and concept-possession on the one hand, and linguistic meaning, understanding and explanation on the other.

The Exegetical Importance of the Topic

Prima facie, linking Wittgenstein to the topic of concepts is hardly sensational. For one thing, Wittgenstein is widely associated with the historical movement of conceptual analysis, and for good reasons. The Tractatus was a major starting point for the Cambridge analysts of the 1920s and 1930s. Furthermore, following his return to Britain in 1929 Wittgenstein became the major inspiration behind a movement which is often misleadingly referred to as ‘ordinary language’ or ‘Oxford philosophy’. The philosophers concerned rightly preferred labels such as ‘linguistic philosophy’ or ‘conceptual analysis’. For, like Wittgenstein, they regarded philosophical problems as conceptual and concepts as embodied in language.