Model theory - Routledge Encyclopedia of Philosophy (2024)

• By
• Hodges, Wilfrid

DOI: 10.4324/9780415249126-Y017-1
Version: v1,Published online: 1998
Retrieved September 17, 2024, from https://www.rep.routledge.com/articles/thematic/model-theory/v-1

Model theory studies the relations between sentences of a formal language and the interpretations (or ‘structures’) which make these sentences true or false. It offers precise definitions of truth, logical truth and consequence, meanings and modalities. These definitions and their consequences have revolutionized the teaching of elementary logic.

Model theory also forms a branch of mathematics concerned with the ways in which mathematical structures can be classified. This technical work has led to philosophically interesting results in at least two areas: it has thrown light on the nature of the set-theoretic universe, and in nonstandard analysis it has suggested new forms of argument (where we prove something different from what we intended, but then use a general model-theoretic argument to change the result into what we wanted).

The word ‘model’ has many other uses. For example, model theory is not about scientific theories as models of the world. It is also a controversial question – not considered here – how model theory is connected with the ‘mental models’ which appear in the psychology of reasoning.