Descartes is often referred to as the “father” of modern philosophy and for good reasons. In several of his works, Descartes speaks openly of his frustrations with his philosophical predecessors, highlighting the various ways that they contradict themselves and leave one in a state of skepticism and despair. Although embracing fervently the scientific revolution of his day and hoping to clear away the clutter of the philosophic past, Descartes, despite his own intentions, retains much of the previous tradition. Like Beethoven, who mediates the Classical and Romantic eras of music history, Descartes functions as a transitional figure mediating the medieval and modern periods. Many scholars have noted that his Meditations are modeled after the spiritual exercises of St. Ignatius. (Cf. Amelie Oksenberg Rorty, “Experiments in Philosophic Genre: Descartes’ ‘Meditations’. Rorty discusses the various meditational traditions that Descartes brings together in the Meditations). Although literary analyses of the Meditations vary and suggest complex, multiple levels at work in the Meditations, it seems safe to say that Descartes’ concern in that work is with certainty (a common quest of the modern period) rather than spiritual growth. In light of the new scientific discoveries of the 17th century, Descartes is convinced that he must make a break with the past (Aristotelian/medieval) tradition and build a new, more secure philosophical system on the model of geometry and compatible with modern science. One of the components of his razing project involves the use of methodological doubt. (As Gadamer highlights in Truth and Method, the search for the “right method” is a common quest of the modern philosophers). Having shown that the various possible avenues of knowledge can be deceptive or called into question (senses, mathematical knowledge [cf. the evil demon exercise], various authorities etc.), Descartes finally arrives at his indubitable truth, viz., that he cannot doubt his own existence, as doubting presupposes thought and thought presupposes existence. From this supposed Archimedean point, Descartes attempts to construct a philosophical system that will yield the certainty lacking in views of his predecessors.
Ironically, Descartes, though criticizing past thinkers, continues to rely on ancient and medieval theological and philosophical insights. We see this especially in Descartes’ various arguments for the existence of God, one of which is a version of St. Anselm’s ontological argument. In the other arguments for God’s existence, Descartes takes the causal principle as self-evident, viz. there must be at least as much formal reality in the cause of an idea as there is objective reality in the idea itself, where the objective reality of the idea is something like the intentional or representational complexity of the idea. For example, the idea of a computer contains more objective reality than the idea of a plastic screw. In addition, Descartes even engages in a defense of God’s goodness—a kind of theodicy—by appealing to an Augustinian, Neoplatonic understanding of evil as a privation. In meditation IV the question arises, if God a non-deceiving God and is all-powerful, why did he create us as beings capable of going astray? In other words, why not make us incapable of erring? How does Descartes respond to these questions? He appeals to a traditional Neoplatonic-Augustinian answer! First, he says that evil is a privation; it is not a thing but is rather the absence of good. Thus, God does not create evil, as evil is a form of non-being. Second, God created a diverse universe, which contains beings of various sorts and of varying degrees of perfection depending upon how “close” or “far” they are (ontologically speaking) from God who is all-perfect.
In short, though Descartes wants in many ways to “throw off” tradition, both the form and content of the Meditations show how indebted he was to the past,
 Descartes does in fact separate himself from the ancient and medieval past when he replaces Aristotelian empiricism with his own version of rationalism. That is, in Aristotelian empiricism one knows an external object by the process of abstracting a form from it. In Descartes’ rationalism, one knows an external object by grasping it directly through intellectual intuition—as e.g., the way in which I know myself directly as an immaterial substance, a res cogitans. With regard to external objects, we grasp these directly as well; however, we know them as something extended, a res extensa. For Descartes, material substance just is extension. Given this identity, Descartes can then explain why mathematics applies to external reality: as a quantity, extension is describable in purely mathematical terms. Since external objects just are quantities of extension, they are also mathematically describable.