Moore's paradox concerns the apparent absurdity involved in asserting a first-person present-tense sentence such as "It is raining, but I do not believe that it is raining" or "It is raining, but I believe that it is not raining." The first author to note this apparent absurdity was G. E. Moore. These 'Moorean' sentences, as they have become known, are paradoxical in that while they appear absurd, they nevertheless Can be true; Are (logically) consistent; and Are not (obviously) contradictions. The term 'Moore's paradox' is attributed to Ludwig Wittgenstein, who considered the paradox Moore's most important contribution to philosophy. Wittgenstein wrote about the paradox extensively in his later writings, which brought Moore's paradox the attention it would not have otherwise received.
Moore's paradox has been associated with many other well-known logical paradoxes, including, though not limited to, the liar paradox, the knower paradox, the unexpected hanging paradox, and the preface paradox.
There is currently not any generally accepted explanation of Moore's paradox in the philosophical literature. However, while Moore's paradox remains a philosophical curiosity, Moorean-type sentences are used by logicians, computer scientists, and those working with artificial intelligence as examples of cases in which a knowledge, belief, or information system is not modified in response to new data.
The problem
Since Jaakko Hintikka's seminal treatment of the problem, it has become standard to present Moore's paradox by explaining why it is absurd to assert sentences that have the logical form: "P and NOT(I believe that P)" or "P and I believe that NOT-P." Philosophers refer to these, respectively, as the omissive and commissive versions of Moore's paradox.
Moore himself presented the problem in two versions.
The more fundamental manner of stating the problem starts from the three premises following: It can be true at a particular time both that P, and that I do not believe that P. I can assert or believe one of the two at a particular time. It is absurd to assert or believe both of them at the same time.
I can assert that it is raining at a particular time. I can assert that I don't believe that it is raining at a particular time. If I say both at the same time, I am saying or doing something absurd. But the content of what I say—the proposition the sentence expresses—is perfectly consistent: it may well be raining, and I may not believe it. So why can I not assert that it is so?
Moore presents the problem in a second, distinct, way: It is not absurd to assert the past-tense counterpart; e.g., "It was raining, but I did not believe that it was raining." It is not absurd to assert the second- or third-person counterparts to Moore's sentences; e.g., "It is raining, but you do not believe that it is raining," or "Michael is dead, but they do not believe that he is." It is absurd to assert the present-tense "It is raining, and I don't believe that it is raining."
I can assert that I was a certain way—e.g., believing it was raining when it wasn't—and that you, he, or they are that way but not that I am that way.
Subsequent philosophers have said that there is an apparent absurdity in asserting a first-person future-tense sentence such as "It will be raining, and I will believe that it is not raining." However, when it does not specify an exact time for when the belief is mistaken, the proposition will tend to be true at some time in the future; its negation would imply that "Every time I believe it's not raining, it will not be raining", which is unlikely since human beliefs are often mistaken.
Many philosophers claim that Moore's paradox exists not only at the level of assertion, but also at the level of belief. One who believes an instance of a Moorean sentence is tantamount to one who is subject to or engaging in self-deception, at least on one standard way of describing it.
Proposed explanations
Philosophical interest in Moore's paradox, since Moore and Wittgenstein, has experienced a resurgence, starting with, though not limited to, Jaakko Hintikka, continuing with Roy Sorensen, David Rosenthal, Sydney Shoemaker and the first publication, in 2007, of a collection of articles devoted to the problem.