Moore's paradox

G. E. Moore remarked once in a lecture on the absurdity involved in saying something like "It's raining outside but I don't believe that it is." This paradox, sometimes known as Moore's paradox, might well have been forgotten if not for the fact that Ludwig Wittgenstein reportedly considered it Moore's most important contribution to philosophy. Wittgenstein himself devotes numerous remarks to it throughout his later writings.

Moore's Paradox forces us to think about such diverse topics as, among other things, the relation between assertion and belief, content and expression, the nature of belief, knowledge and rationality. There is, as yet however, no generally accepted explanation to Moore's Paradox in the philosophical literature.

Moore himself presented the paradox in two ways. The first more fundamental way of setting the problem up starts from the following three premises:

1. It can be true at a particular time both that p, and that I do not believe that p.
2. I can assert or believe one of the two at a particular time.
3. I cannot without absurdity assert or believe both of them at the same time.

So I can say that it is raining, or instead, I can say that I do not believe that it is raining. If I say both, I am contradicting myself. But, it is perfectly possible for it to rain, and for me not to believe it. So it appears we have a peculiar situation: I can contradict myself by saying something which, in itself, is not contradictory (i.e. a possible state of affairs). Put another way, the following two conditions could easily be met: (1) It is raining outside and (2) I fail to believe it (because I haven't looked out the window, perhaps) yet if I ever tried to express this situation, I would be caught in a contradiction ("It is raining outside, but I don't believe it"). How can this be so?

Moore presented the problem in a second way: first, there is nothing absurd — i.e. nothing wrong — with the past-tense counterparts to Moore's sentences, e.g. Someone asserting:

• It was raining but I did not believe that it was.

Second, there is nothing absurd with the second- or third-person counterparts to Moore's sentences. For example, someone asserting:

• It is raining but you do not believe that it is, or
• Elvis is dead but they do not believe he is.

An alternate form results by moving the negation, for instance, "Elvis is dead, but I believe that he's not." Roy Sorensen popularised the terms omissive for sentences of the form p, but I don't believe p, and commissive for sentences of the form p, but I believe not-p^[2]; the terms relate to whether the sentence involves an error of omission or of commission with respect to one's beliefs.

In addition, many commentators hold that Moore's Paradox arises not only at the level of assertion but also at the level of belief; it is not only absurd to assert "It is raining but I don't believe it is" but also to believe it.

Most commentators, following Moore, take it as a condition on a satisfactory explanation of the peculiar absurdity involved in asserting or believing Moore's sentences that it explains the contradictory-like quality of using tokens of the omissive and commissive sentence-types.

It is important to emphasize that what is absurd is not, prima facie, the sentence-types themselves (i.e. 'p & X believes that not-p' and 'p and X does not believe that p') but using them where X is replaced by the first-person pronoun 'I'.

While in more traditional philosophical circles, Moore's Paradox has perhaps been seen as a philosophical curiosity, Moore's sentences have been used by logicians, computer scientists, and those working in the artificial intelligence community, as examples of cases in which a knowledge, belief or information system is unsuccessful in updating its knowledge/belief/information store in the light of new or novel information. Philosophical interest in Moore's Paradox has undergone a resurgence, starting with Jaakko Hintikka, continuing with Roy Sorensen,David Rosenthal and the first publication of a collection of articles devoted to the problem.