I am currently reading "Meaning" and "Logic and Conversation" by Paul Grice.
I find it a little difficult to differentiate clearly between his concepts "natural meaning", "non-natural meaning", "conventional implicature" and "generalized conversational implicature".
So far this is what I gathered:
Natural meaning: Literal meaning. For something q to have the natural meaning p, q must entail that p. If q then p. E.g. "those spots mean measles".
Non-natural meaning: Communicative meaning. If q meansNN p this does not convey entailment. For naturalNN meaning it is necessary that the utterer intends to induce the belief p in their audience. Further it is necessary that the audience recognizes that intention. Lastly, the audience needs to come to the belief that p by recognizing the intention.
Implicatures are kinds of meaningNN.
Conventional implicature: Cannot be explained argumentatively. Representing the literal meaning logically and representing the implicature leads to the same output. However, something else is implicated that cannot be grasped by propositional logic. Example: "Tim is 5 years old but he is smart." This sentence is true if Tim is 5 years old AND he is smart. However, the conventional implicature caused by the word "but" also conveys a contrast between his age and his intelligence.
Generalized conversational implicature: This is an implicature that is generally tied to the language. As opposed to the conventional implicature, we get a different logical output from representing the literal meaning and representing the implicature. E.g. "some students passed the exam". Logically this is true if there exist some students who passed the exam. Representing the implicature logically it is true if there exist some students who passed the exam AND there exist some students that did not pass the exam. Looking at the literal meaning the sentence could convey that "all students passed the exam" however thinking of the maxim of quality you could have just said that instead of omitting Information therefore some students did probably not pass.
My questions are: did I Interpret this correctly or did I miss something? In both my example for conventional implicature and generalized conversational implicature, the implicature is tied to the language- "but" usually evokes a contrast and "some" usually means "not all" (or that someone is lacking Information). Therefore I would argue that the conventional implicature I gave as an example can be explained argumentatively. Yet I have seen several similar examples for conventional implicature. Are they wrong? Is there a better example? Is the difference just in the propositional logical representation? And further: for something to have natural meaning, it must be true, right? If "those spots" do not entail measles, this would thus make the sentence "those spots mean measles" devoid of natural meaning? If the audience does not come to belief that p although that was the speakers intention, e.g. because they do not trust them- is there no meaningNN?
Thanks a lot and all the best, Anna