 Cognitive science is one area where the difference between models and modelling tends to become blurred. A central question of cognitive science is how we represent facts or possibilities in our minds. If one formalises these mental representations, they become something like ‘models of phenomena’. But it is a serious hypothesis that in fact our mental representations have a good deal in common with simple set-theoretic structures, so that they are ‘models’ in the model-theoretic sense too. In 1983 two influential works of cognitive science were published, both under the title Mental Models. The first, edited by Dedre Gentner and Albert Stevens, was about people’s ‘conceptualizations’ of the elementary facts of physics; it belongs squarely in the world of ‘modelling of phenomena’. The second, by Philip Johnson-Laird, is largely about reasoning, and makes several appeals to ‘model-theoretic semantics’ in our sense. Researchers in the Johnson-Laird tradition tend to refer to their approach as ‘model theory’, and to see it as allied in some sense to what we have called model theory.