Ever since Aristotle and Plato (The Categories; Cratylus), linguists have considered language to be the pairing of form (sounds or gestures or written strings) and meaning. This is true for all meaningful linguistic units from morphemes, through words, phrases and sentences, to discourse. Generally speaking, semantics is the study of how form and meaning are related. However, semantics is more narrowly construed as excluding those meanings that derive from speaker intensions and psychological states, as well as sociocultural features of the context. Furthermore, the boundary between semantics proper and pragmatics is intensely debated and to some researchers constitutes an empirical question. Formal semantics came into being as a system describing formal languages, that is, the mathematical and logical languages of computing machines as opposed to the natural languages of human beings. However, in the late 1960s the philosopher Richard Montague argued that natural languages such as English could be fruitfully described using the same rigorous rules and correspondences utilized in the description of formal languages. Modern formal semantics was born and is currently prospering as a branch of linguistics.

Submitted manuscript version. Published version available at https://doi.org/10.1017/S0261444818000071.