The verb ‘to think’ – with its cognates ‘thought’ and ‘thinking’ – covers a wide variety of mental activities, states and conditions. We must begin with some distinctions.

At its simplest and least puzzling, talk about people's thoughts can be a mere stylistic variant for talk about their beliefs. Why did Jack collapse so inelegantly on the floor? – because he thought there was a chair behind him. And why did Jill open the tin marked ‘sugar’? – because she thought it contained sugar. We could equally well have said ‘because he believed …’ or ‘because she took it that …’. In these cases, we may suppose, the thought was not reflectively entertained. Jack didn't deliberate about the position of the chair (maybe that's what got him into trouble). Again, as we might put it, Jill unthinkingly thought that the tin contained sugar. The air of paradox in this description is merely superficial: there is of course no real oddity in the idea that someone's thoughts on a subject, in the sense of her relevant beliefs, may be reached and held without any reflective or deliberative processes.

We have already discussed the nature of belief at length in Chapters X to XII. Our main concern in this chapter is with the contrasting processes of discursive, deliberative thought. More precisely, we want to get a bit clearer about the sort of thing that the mathematician does as he puzzles over his problem, or the amateur carpenter does as she works out how to get her shelves to stay up, or the cook does as he plans the menu.