I believe the traditional Gricean view is that anything that can't be expressed in truth-conditions is pragmatics rather than semantics. I also know that there's the view excluding conventional implicature from pragmatics and grouping it with semantics, since conventional implicature and semantic meaning can't be distinguished except by the fact that conventional implicature can't be expressed truth conditionally.
What are other views on implicatures specifically? Both in how they are subdivided and how they are split between semantics and pragmatics and are there any good citations for this (I'm preparing for a semantics pragmatics exam on Monday and wanted to flesh out my arguments on the distinction a bit more).

  • @curiousdannii is the edit sufficiently separate? I believe it is a more specific and generally different question.
    – Wujagoodoo
    May 28 '16 at 14:02

Semantic entailments cannot be cancelled when you add more premises/information to an argument (i.e. a set of statements from which the conclusion is supposedly derived using the rules of deduction or proof admitted in the underlying logic). Pragmatic implicatures can be cancelled when you add more information to the premises. For instance, if it is the case that Jane has three children, then it is a semantic entailment that she also has two children, for it is impossible for her to have three children and not have two (or one). But saying that Jane has two children in a situation where you know that she has three, is somewhat misleading, for you violate the maxim (pragmatic 'rule' of inference) that you should give as much information as you know to be true in the situation (the truth, the whole truth and nothing but the truth). You can continue later by saying that in fact you think she has three children, after you claimed that she had two, without contradicting yourself, but pragmatically speaking you are 'correcting' yourself, i.e. adhering better to the maxim of maximally true information. Of course, self-correction is a very human and perhaps even 'normal' thing to do, self-contradiction is a pretty bad thing in the morals of logic, as a theory of valid reasoning. In a dynamic theory of reasoning such correction is never contradictory, but a theory of correction is far from clear and our notion of consistency is static.

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