Jean De Groot

This paper examines geometrical arguments from Galileo's Mechanics and Two New Sciences to discern the influence of the Aristotelian Mechanical Problems on Galileo's dynamics. A common scientific procedure is found in the Aristotelian author's treatment of the balance and lever and in Galileo's rules concerning motion along inclined planes. This scientific procedure is understood as a development of Eudoxan proportional reasoning, as it was used in Eudoxan astronomy rather than simply as it appears in Euclid's Elements. Topics treated include the significance of the circle in Galileo's demonstrations, the substitution of rectilinear elements for heterogeneous factors like weight and curvilinear distance, and the way in which elements of a motion are used to measure other elements of the same motion. The indirectness of Galileo's proofs, his conception of speed as relative and comparative, and the meaning of his concept of moment all come into clearer focus. Conclusions are drawn about Galilean idealization, and also about the contrast of literal versus figural modes of explanation in Galileo's science.

Examples are presented of Aristotle’s use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empiricalmathematics, which include the non-persistence of mathematical aspects of things and the selective application of mathematical traits and proper accidents. In antiquity, non-abstracted mathematics was involved with practical sciences that treat motion. The suggestion is made that these sciences were incorporated by Aristotle into natural philosophy without first being abstracted as pure mathematics—a state of affairs not envisioned by Husserl, for whom science recast natural ontology by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered.

"This book collects essays by leading scholars, both American and European, on the American understanding of nature from Emerson to Dewey and beyond. The volume features essays on Emerson and Thoreau, Royce, Peirce, Wright, James, Holmes, Tocqueville, and Dewey. Topics include the role of nature in American idealism, the influence of Darwin, naturalism in psychology, and human nature in political thought. The final essay presents a comprehensive taxonomy of views of nature in relation to expressions of nature in American art." "With its focus on philosophy of nature, this book fills a gap in the ongoing reassessment of nineteenth-century American philosophy, and it opens the way to further study of the role played by reflection on nature in the emergence of the American mind."--Jacket.