Mental models in Galileo’s early mathematization of nature

Abstract

Distinguishing between the mathematical followers of Archimedes, notably Galileo, and the Aristotelians of the late sixteenth century, William R. Shea asserted that ‘[m]athematicians, under the guidance of Euclid and Archimedes, viewed the world in terms of geometric shapes which obeyed mathematically expressible laws’. In my judgement, Shea’s view should be accepted, even though it was not only Euclid and Archimedes who escorted Galileo into new territories such as, for instance, Two New Sciences, or the Discourse on Buoyancy. A more complex picture has gradually emerged thanks to a number of studies that have examined in detail Galileo’s acceptance of the Euclidean theory of proportions (or proportional reasoning) as the language of early mathematized physics. Yet no research has so far been devoted to the cognitive mechanisms underlying Galileo’s mathematization of nature. This paper addresses some questions related to this theme by adopting a cognitive history perspective which relies on the theory of mental models (on mental models, see Sect. 2, Pt. I; on cognitive history, see Sect. 2, Pt. II). Moreover, through a discussion of Galileo’s alleged use of thought experiments the paper suggests how a cognitive history perspective might complement