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Gricean is a reference to the maxims of conversational implicature proposed by the philosopher H.P. Grice. These maxims help us construe meanings based on sometimes incomplete input; when something we hear is ambiguous, they help us pick out the most plausible interpretation, although this construal is conventional, and not logical. If the maxims are being violated, your interlocutor is being either clever/poetical ('flouting', and you have to work out what the joke is - what the underlying motivation of the violation is, what they are 'really' trying to say), or just plain uncooperative.
The four maxims are:
- Maxim of Quality: Do not say what you believe is false.
- Why this maxim is a good default assumption should be obvious.
- Maxim of Quantity: Make your contribution as informative as possible.
- E.g. don't say a goat has two legs when it has four legs, even if logically four legs implies [at least] two legs.
- Maxim of Relevance: Be relevant.
- E.g. if you say something which doesn't appear immediately relevant to what you've been saying, I'm going to assume it is relevant on some deeper level. That's what makes a lot of allusive talk work.
- Maxim of Manner: Be orderly.
- E.g. if you say A, and then say B, I can assume B happened after A.
These assumptions are frequently encoded into Lojban as interpretive conventions; e.g. story time, goat's legs quantification, etc. Wilson & Sperber, in their Relevance theory, reduce these maxims to just one: "Be relevant".
The unoffical fifth maxim: