1. In PI, PPF, section x, Wittgenstein discusses what is known as ‘Moore's paradox’. Wittgenstein heard G. E. Moore present the paradox in a paper he gave to the Cambridge Moral Sciences Club in 1944, and he expresses great excitement at Moore's observations in a letter he wrote to Moore after the meeting. The paradox concerns the first-person present indicative use of the verb ‘to believe’. Moore observes that although it may, for example, be true that it is raining and I do not believe that it is raining, it is absurd for me to say ‘It is raining but I do not believe that it is.’ For Moore, the paradox arises insofar as there may be truths about me which I cannot, without absurdity, assert. How is this to be explained?

Moore's own suggestion for how to resolve the paradox is to recognize that we need to distinguish between what someone asserts and what he implies in asserting it. Someone who asserts ‘It is raining’ does not thereby assert that he believes it is raining, but his asserting it does indeed imply that he believes it. It is, according to Moore, because someone who asserts that it is raining implies that he believes that it is, that it is absurd for him to go on and assert that he does not believe it.

Wittgenstein clearly believes that Moore's paradox reveals something important about the way the concept of belief functions. However, his reflections quickly lead him to formulate what he sees as the real paradox in a different way from Moore. Moore focuses on the fact that there is something which may be true of me – it may be true that p and I don't believe that p – but which cannot, without absurdity, be asserted by me. Wittgenstein's reformulation of the paradox, by contrast, directs our attention to the fact that ‘I believe that this is the case’ appears to be used differently in the language-game of assertion and the language-game of supposing. He writes: