English Semantics

We communicate with utterances, and each utterance is an instance of a sentence. But how can we explain what ‘sentence meaning’ is?
Two points are obvious. First, the meaning of a sentence derives from the meanings of its constituent lexemes and from the grammatical meanings it contains. So if you know all the lexical and grammatical meanings expressed in a sentence, you know the meaning of the sentence, and vice versa. Second, at least if the sentence is a statement, if you know the meaning of the sentence, you know what conditions are necessary in the world for that sentence to be true.

Albert Thompson opened the first flour mill in Waterton.

You don’t know whether this sentence is true or not, but you know that if it is true, there must exist (at some time) a person named Albert Thompson and a place called Waterton (presuppositions), that Albert Thompson opened a flour mill, and that there was no flour mill in Waterton before Albert Thompson opened his mill (entailments). You know that if this sentence is true, the sentence Albert Thompson did not open the first flour mill in Waterton is false (a contradiction).