Implication or core function

Grammars of many languages claim that the language in question has a special form for indicating situations that occur in sequence, or for distinguishing sequences of situations from simultaneously occurring in situations. However, in nearly every case, it is impossible to tell from the limited range of examples given whether the interpretation of sequentiality is indeed part of the meaning of the form in question, or whether this is just an implicature following from a basically aspectual distinction. This is one of the major deficiencies of descriptive work in this domain. More generally, the failure to distinguish between meaning and implicature is one of the main problems in working out an adequate characterization of tenses.—Tense, page 28

<idle musing>
Of course, we could say the same thing for more than just tense! The failure to distinguish between what is a core function and just an implication is probably a good percent of our problem in communication in general!

We talk past each other; we don't take the time to ask what someone is—or isn't—implying in a statement. Instead, we interpret it and react. Unfortunately, we are sometimes/often incorrect in our deciphering of what the other person is or isn't really implying...
</idle musing>