If you hear your friend Moore say, “It is raining, but I don’t believe it,” you might say that it is absurd, ridiculous or sounds illogical. It would also be absurd if he stated, “The stock market is down, but I don’t believe it.” He would seem to assert that the market is down, but he is not convinced. It would equally sound illogical if he stated, “The market is down, but I believe it is not.” Here, Moore seems to say that the market is down, but he is convinced otherwise, e.g., that it is up. These sentences are called Moorean sentences, and they come in two forms: (O) “X but I don’t believe it” and (C) “X but I believe not-X”. O sentences are called omissive, while C sentences are commissive.

Even though asserting Moorean sentences sound illogical, there is no clear logical contradiction. If Moore only stated that “the stock market is down” (D), there would be no problem, nor if he only stated “I don’t believe that the stock market is down” (~B(D)). In logic a proposition of the form D & ~B(D) is not a contradiction either. Yet, when Moore asserts D & ~B(D), it sounds illogical. This might seem paradoxical, and it is, hence the name Moore’s paradox.

Moorean sentences are problematic in the future tense too, e.g., “The stock market will go down, but I won’t believe it.” However, the past tense is fine: “The stock market was down, but I didn’t believe it.”

However, not all present-tense cases are problematic. For example: ‘He’s coming, but I can’t believe it!’¹ is acceptable, since ‘I can’t believe it’ expresses surprise. Similarly, ‘The disaster is contained, but I don’t believe it’ may be reasonable if the speaker is referring to a propaganda announcement over the radio. Or consider: ‘Train No. … will arrive at … o’clock. Personally, I don’t believe it,’² said by an announcer at the station.

We can turn both the omissive and commissive versions of Moorean sentences into a clear contradiction by adding “I believe” in front of X. For example:

• “I believe it is raining, but I don’t believe it” or
• “I believe it is raining, but I believe it is not raining” or ³

By contrast, by providing a source of assertion that is not a personal belief, we can defuse the absurdity. For instance:

• “My eyes say it is raining, but I don’t believe it” (skepticism of one’s sensory impulses is not absurd)
• “Science says that the universe started with the Big Bang, but I don’t believe it”
• “The government says that unemployment is down, but I believe it is not”

In general, Moorean sentences appear incomplete, as they leave unspecified who is asserting X. This missing part is left for us, the interpreters, to fill in. If we choose personal belief as the source of assertion, we get a contradiction. If we choose something else, we get a coherent sentence. 

We can analyze the situation by mapping all the different languages that are used when talking about the Moorean sentences. First, there are Moorean sentences which belong to the subset of English, this is level 0, the object-language. These are then talked about in a bigger language (the meta-language) which embeds the object-language and also has propositional logic, this is level 1. Level 1 only talks about the logical form. Finally, we extend the analysis in an even bigger language (the meta-meta-language) which is complete English. This is level 2. The meta-meta-language allows exploring what stating a proposition X might actually mean. What are problematic and non-problematic cases? Is it equivalent to believing it or not? What if the source of assertion is not one’s personal belief?

Level 1 shows no contradiction. However, level 2 provides two contradictory interpretations of what it means to state X: illogical and logical. The illogical interpretation comes from interpreting X as equivalent to B(X), and not-X as equivalent to B(not-X). The logical interpretation comes from interpreting X as equivalent to A(X), and not-X as equivalent to A(not-X), where A is some source of assertion that is not a belief. We can visualize this as follows:

The classical Moore’s paradox arises if one ignores the logical interpretation (green box) in level 2. This creates a situation where the logical interpretation in level 1 (blue box) sounds illogical, because of the highly likely illogical interpretation (red box) in level 2. However, the actual paradox is due to the contradiction in level 2, where a problematic Moorean sentence is both logical and illogical.

1. Ludwig Wittgenstein, Remarks on the Philosophy of Psychology, Volume 1 (ed. G. E. M. Anscombe & G. H. von Wright, trans. G. E. M. Anscombe, 1980), §485. ↩︎
2. Ludwig Wittgenstein, Remarks on the Philosophy of Psychology, Volume 1 (ed. G. E. M. Anscombe & G. H. von Wright, trans. G. E. M. Anscombe, 1980), §486. ↩︎
3. Wikipedia, Doxastic logic – Consistent reasoner: https://en.wikipedia.org/wiki/Doxastic_logic#Types_of_reasoners ↩︎