The inferential and representational techniques in Galileo's models for uniformly accelerated motion

In this essay, I aim to scrutinize several of Galileo’s representational and inferential strategies for dealing with naturally accelerated motion within the context of justification. Galileo’s methodology succeeded in making the process of naturally accelerated motion intelligible via models. The focal point of the study of hand is the Third Day of the Dialogues Concerning Two New Sciences. My aim is, primarily, to provide a detailed historical case-study of the representational and inferential procedures in Galileo’s mechanics. In this essay, I set out to bring these strategies and theoretical suppositions to the fore. I argue that the following inferential strategies were of key importance in Galileo’s Discorsi: abstraction from and idealization of irrelevant factors, geo-infinitesimal representation, substitution of an inferentially recalcitrant type of motion for a less inferentially recalcitrant type of motion, physical interpretation by means of a previously established theorem, transference of geometrical relations to relations on motion, and proportionality as a proxy for otherwise unrelated motions. Furthermore, it will be shown that in Galileo’s proto–mechanics a single unifying theoretical principle was absent. This limitation forced Galileo to use a heterogeneity of inferential strategies and theoretical assumptions. Additionally, Galileo’s models illustrate how theoretical knowledge needs to be concretised by the introduction of specific models in order to obtain the desired inferential steps. In virtue of certain abstract properties pertaining to the models themselves, one is able to obtain novel results which are not derivable from the abstract theory alone. Another way of putting this, is that the information provided by a model helps to constrain and concretize the theoretical knowledge at hand.