On "Meaning" (1957), "Utterer’s Meaning and Intentions" (1969), and "Logic and Conversation" (1975), featuring Mark, Seth, Dylan, and guest prof. Steve Gimbell of Gettysburg College.
Someone who utters something typically means something in particular, but is that meaning determined just by the definitions of the words uttered? Clearly not, as words can be used in non-standard ways, and an "utterance," taking that word broadly, might not even include words at all, but gestures or noises, which can still be exhibited with intent. Grice was reacting to behaviorists and logical positivists who wanted to define meanings purely in terms of public properties of language, and he wanted to give a philosophically respectable account of meaning that acknowledges the psychology involved: That the speaker has some intention to communicate, which is some belief that the speaker wants to impart to the listener. Grice refers to this as "non-natural" meaning, as opposed to "natural" cases like "spots mean measels." Non-natural meanings are consciously held in people's minds as something they intend to communicate.
Grice considers numerous possible counter-examples to the theory as I've just stated it. For instance, if I leave a false clue at a murder scene, I may want a detective to have some belief (that someone in particular committed the murder), but that doesn't mean that the clue was a communication that had the intended meaning "X committed this murder." For something to be a communication, the hearer can't just receive the information, but has to understand that it was a communication, that I as the communicator had the intention to communicate that message.
Our second article, "Utterer's Meaning and Intentions," considered many more potential counter-examples to defend the theory. For instance, if I yell at you in a language that you don't speak as you're walking on my lawn, but the literal words I'm saying mean "I love you," I clearly haven't communicated the sentiment that I love you despite my use of those words, but I may have successfully communicated that I want you to get off of my lawn. Grice considers highly layered examples: For instance, a man is playing poker against his boss. He wans to let his boss win, and he wants the boss to know that he's letting him win, but he doesn't want the boss to think that he (the first man) knows that the boss knows that he is letting the boss win. According to the theory, the man has the intention of both letting the boss win and letting the boss know that there's an effort to let him win, but this is still not a communication, as the boss is not supposed to think that his employee is trying to communicate the sentiment, "I'm letting you win." Yes, these examples can get confusing in their complexity.
The third article goes into "conversational implicature," i.e. ways in which meanings are implied in idiosyncratic conversational gambits. Wes and Mark will actually read this paper in part three of this episode, continuing through two further parts as Closereads to finish the whole article.
Steve's book that features some talk about Grice is actually about humor: Isn't that Clever: A Philosophical Account of Humor and Comedy.