Conceptual and Historiographical Foundations—Natural Philosophy, Mixed Mathematics, Physico-mathematics, Method

Abstract

This chapter examines a number of conceptual and historiographical issues which frame the entire project. First of all, a model is constructed for how the increasingly competitive and turbulent culture of natural philosophizing worked in the era of Descartes. This model also addresses the question of the place of the subordinate mixed mathematical sciences, and the meaning Descartes, and others, attached to the idea of a physico-mathematics, that would render those mixed sciences more properly ‘natural philosophical’. Also presented are the generic rules of construction and contestation which governed natural philosophizing; a model for dealing with the problem of ‘external or contextual’ drivers of natural philosophical utterance; an heuristic model for assessing the nature and degree of ‘systematicity’ of a natural philosophy; and an outline of the main phases in the trajectory of natural philosophizing in the period of the Scientific Revolution, so that Descartes’ location and role can be better identified. Additionally, the basis is set down for the deconstruction of Descartes’ method, which takes place in Chap. 6.