Discrepancies between truth-functional meaning and utterance meaning
Grice was committed to a truth-conditional or truth-functional view of meaning, which can be described as the view that knowing the meaning of an expression consists in knowing the conditions under which it is true (see 3.2.1 for discussion). It was from this point of view that he was struck by a disparity between the (truth-conditionally conceived) sentence meaning of certain fundamental linguistic expressions and the utterance meanings they seem to have in actual language use. Grice’s main example is provided by logical operators like and. Grice takes the sense of and to be the function it has in logic, where it simply denotes the union of two entities or propositions – apples and oranges, seeing and believing, Toni and Amitavo (see Chapter 6 for explanation). It may not at first sight be obvious why one should take the logical function of and to be primary in natural language. The essential reason is that, for many philosophers, the principles of logic are universal and underlie the operation of all human conceptual activity, including language: to study logic is thus to study the fundamental bases of rational human thought. As a result, words like and, or and not, which have analogues in the ‘language’ of logic, are naturally thought of as basically expressing the same ideas as their strict logical counterparts. In light of this basic function of and, consider (4):

Grice notes the obvious fact that it would not be appropriate to utter (4) about someone who fi rst took off his shoes and then got into bed. One might claim, therefore, that there is an element of temporal succession to the meaning of and which is not reflected in its logical, truth-functional meaning. Grice does not want to say, however, that the meaning of and in (4) is any different from its basic meaning as a logical connective. This is for two reasons. Firstly, he is committed to a truth-functional approach to meaning in which the sense of logical operators like and simply is their role as a logical connector. This means that he needs a way of dealing with instances like (4) which seem to show that ordinary language does not obey truth-functional principles. Second, he believes that most people would say that although (4) is a misleading description of the situation in question, it is nevertheless true: strictly speaking, there is nothing false in (4) as a description of the situation in which someone took off his shoes and then got into bed, although it is an unusual and confusing way to describe this situation.
Another example of a discrepancy between truth-conditional (logical) and conventional meaning would be the meaning of some in the following sentence:

Under normal circumstances, the speaker of (5) would be taken to mean that Tuptim hasn’t finished all her homework. From a strictly logical point of view, however, (5) is just as true if Tuptim has finished all her homework as it is if she has just finished some of it: if she has finished all her homework (say her history, geometry and German homework), it follows logically that she has also finished some of it (say her history and geometry homework). This would, however, be a misleading way of describing the situation, since in real conversation some typically gives rise to the interpretation ‘not all’: if I say that I have read some of the book, I imply that I have not read all of it. (This is called a scalar implicature; see Horn 1984.)
A final example of the same sort is the conjunction but. Strictly, but has exactly the same truth-conditions as and: there is no logical distinction between them (see 6.2). As a result, the following pairs of sentences have identical truth-conditional meanings:

From the truth-conditional point of view, there is no difference between the sentences in (6) and (7): they are true in exactly the same conditions. There is, however, a clear non-truth-conditional difference between (6) and (7): (7) has an implication of contrast entirely missing in (6).