The most famous one is:
i. It is raining but I don't believe it.
Grice overreacted, shall we say, when his notion of 'implicature' was used to explain the Mooreian paradox.
For Grice, rather, the Mooreian paradox is a refutation of the conceptual analysis of the 'indicative mode'.
For years, Grice used 'mood', instead of 'mode', until Moravcsik taugh him right (at Stanford).
The indicative mode, as per conceptual analysis, is the mode by which the utterer
An implicature, rather, is connected to some flout (or other) to a conversational maxim -- or 'desiderata' and 'principle' as he would prefer in his earlier "Logic and Conversation" lectures that Grice gave at Oxford (prior to the more famous Harvard ones) and that Grice preferred to the latter version.