Geometry, Modern Philosophy, Medieval Theology

Taken on its own, the primary purpose of the Meditations seems to be Theological--the application of Cogito to two Medieval proofs of the existence of God--with renewed confidence in Mathematics one of its immediate consequences, i. e seems to be the work of a Jesuit experiencing an intellectual crisis.  In contrast, as a follow-up to a work called Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences, and one in which is developed Analytical Geometry, against a back-drop of the fate of Galileo at the hands of the Church, the real purpose of the later work can be recognized as a reinforcement of Descartes' innovative concept of Geometry, with the Theological dimension an extrinsic precaution.  Thus lost in the abstraction of the Mediations from its context, common in contemporary academic curricula, is the earlier innovation--from the traditional concept of Geometry as an eternal object of contemplation, e. g. for Plato, to the concept of it as a Technical device.  Now, Spinoza considers one of the implications of this innovation when he proposes the concept of a Circle as operational--the function of Mind as immediately applicable to, not the objects of perception, but to conduct.  In contrast, Kant just misses the implication, when, while examining how one cognizes oneself as one draws a line, he fails to consider the role of Mind in the act of drawing, i. e. how it determines how one is conducting oneself.  He thus misses the implication that Geometry is an a priori Form of cognition only because it is a priori qua Form of conduct that is cognized a posteriori.  In contrast, Bergson recognizes that Space is primarily a field of Action, which Geometry thus guides.  Otherwise, the predominant concept of Geometry in Modern Philosophy stems from one that is subordinated, as a precaution, to the principles of Medieval Theology.