Conversational implicatures and cancellability
You might be a bit worried about the possible gap between what’s said (explicitly, by the sentence used) and what’s merely suggested. It might seem like we can never be sure about sentence- and word-meanings, because we can’t draw the line clearly between them and occasion-meaning.
Fortunately, there’s a way to address this worry. Conversational implicatures are cancellable; word- and sentence-meaning are not. The idea here is simple: where a message is just suggested by a conversational implicature, we can cancel it with an explicit rider. Where something is part of word- and sentence-meaning, we can’t cancel it: attempts to do so just result in self-contradiction.
Take the Obama/Trump example. Someone talking about the dinner could say ‘Obama made fun of Trump and Trump decided to run for President, but there’s no causal connection between those two facts’ and that would be perfectly coherent (so the idea that there is a connection can’t be part of the content of the original sentence or the meaning of ‘and’). But an attempt to ‘cancel’ parts of the sentence-meaning of the original will just result in incoherence and self-contradiction. If someone said, for instance, ‘Obama made fun of Trump and Trump decided to run for President, but I’m not saying it’s true that Trump decided to run for President’, they would just have contradicted themselves. (And that’s not fake news.)
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