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.

Elaboration

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? This is especially strange considering that others could easily explain my unfortunate situation without contradiction ("It is raining outside, but he doesn't believe it").

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; 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'.

Commentary

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.

Proposed explanations

There have been several proposed constraints on a satisfactory explanation in the literature, including (though not limited to):

• It should explain the absurdity of both the omissive and the commissive versions.
• It should explain the absurdity of both asserting and believing Moore's sentences.
• It should preserve, and reveal the roots of, the intuition that contradiction (or something contradiction-like) is at the root of the absurdity.

The first two conditions have generally been the most challenged, while the third appears to be the least controversial. Some philosophers have claimed that there is, in fact, no problem in believing the content of Moore's sentences (e.g. David Rosenthal), while others (e.g. Sydney Shoemaker) hold that an explanation of the problem at the level of belief will automatically provide us with an explanation of the absurdity at the level of assertion. Some have also denied that a satisfactory explanation to the problem need be uniform in explaining both the omissive AND commissive versions.

Most of the explanations offered of Moore's Paradox are united in holding that contradiction is at the heart of the absurdity. One type of explanation at the level of assertion exploits the view that assertion implies or expresses belief in some way so that if someone asserts that p they imply or express the belief that p. Several versions of this view exploit elements of speech act theory, which can be distinguished according to the particular explanation given of the link between assertion and belief. Whatever version of this view is preferred, whether cast in terms of the Gricean intentions (see Paul Grice) or in terms of the structure of Searlean illocutionary acts (see speech act), it does not obviously apply to explaining the absurdity of the commissive version of Moore's Paradox. To take one version of this type of explanation, if someone asserts p and conjoins it with the assertion (or denial) that he does not believe that p, then he has in that very act contradicted himself, for in effect what the speaker says is: I believe that p and I do not believe that p. The absurdity of asserting p & I do not believe that p is thus revealed as being of a more familiar kind. Depending on one's view of the nature of contradiction, one might thus interpret a speaker of the omissive Moorean sentence as asserting everything (that is, asserting too much) or asserting nothing (that is, not asserting enough).

An alternative view, often controversially attributed to Wittgenstein, is that the assertion "I believe that p" often (though not always) functions as an alternative way of asserting "p", so that the semantic content of the assertion "I believe that p" is just p: it functions as a statement about the world and not about anyone's state of mind. Accordingly what someone asserts when they assert "p and I believe that not-p" is just "p and not-p" Asserting the commissive version of Moore's sentences is again assimilated to the more familiar (putative) impropriety of asserting a contradiction.

None of the explanations offered, at the time of writing, at the level of assertion convincingly explain both the omissive and commissive versions, nor the belief version of the problem.

At the level of belief, there are two main kinds of explanation. However, obviously enough, they all make some assumption about our ability to know our own minds, otherwise known as self-knowledge. The first, much more popular one, agrees with those at the level of assertion that contradiction is at the heart of the absurdity. The contradiction is revealed in various ways, some using the resources of doxastic logic (e.g. Hintikka), others (e.g. Sorensen) principles of rational belief maintenance and formation, others relating the problem to our capacity for self-knowledge. Sorensen's proposed explanation should be lauded for connecting Moore's paradox up with many other well-known logical problems (including, though not limited to: the liar paradox, knower paradox, prisoner's dilemma).

Another alternative view, due to Richard Moran , views the existence of Moore's Paradox as symptomatic of creatures who are capable of self-knowledge, capable of thinking for themselves from a deliberative point of view, as well as about themselves from a theoretical point of view. On this view, anyone who asserted or believed one of Moore's sentences would be subject to a loss of self-knowledge - in particular, would be one who, with respect to a particular 'object', broadly construed, e.g. person, apple, the way of the world, would be in a situation which violates, what Moran calls, the Transparency Condition: if I want to know what I think about X, then I consider/think about nothing but X itself.

Moran's view seems to be that what makes Moore's Paradox so distinctive is not some contradictory-like phenomenon (or at least not in the sense that most commentators on the problem have construed it), whether it be located at the level of belief or that of assertion. Rather, that the very possibility of Moore's Paradox is a consequence of our status as agents (albeit finite and resource-limited ones) who are capable of knowing (and changing) their own minds.

Modal logic

In modal logic, a subfield of mathematical logic, the paradox corresponds to a violation of axiom 4.

See also

• Faith and rationality
• Irrationality
• self-deception
• Epistemology
• Philosophical skepticism
• belief
• Rationality

External links

• "Epistemic Paradoxes" (including Moore's) at the Stanford Encyclopedia of Philosophy