Applying the rules and systems of mathematics and logic to instance ontology, this work argues for the validity and problem-solving capacities of instance ontology, and associates it with a version of the realist position which is named by the author as moderate realism.

It is a common occurence to find Galileo claimed as the father of modern science, particularly as to his method being appropriate for its pursuit. Yet, it is apparent from the literature that little agreement has been reached concerning the specifics of the structure and nature of his method(s). Galileo himself is explicit in little more than describing it as „geometrical“, and as such contrasting its greater demonstrative power with that of the traditional Peripatetic logic. One is then left with (...) examples and glosses in the text as to hints that might place his method in a known context of ancient or medieval science, or metaphysics and logic, or both. (shrink)

It is generally agreed that Galileo’s distinctive place in the history of science is due to the power of his method, and that, in general terms, this consists in an effective combination of mathematics and physical experiment. In attempting to be more specific, some authors have assigned a particular method to Galileo as either new or a unique adaptation of a traditional method, e.g. hypothetico-deduction, the method of analysis, or ex suppositione. William Wallace, for example, has argued that by the (...) time of the «Two New Sciences» (1638) Galileo had fashioned his own version of ex suppositione, combining elements of the Archimedean and Aristotelian traditions into a distinct two-stage mode of reasoning of his own creation. We shall have reason to comment upon this below. (shrink)