Hallo, This is Dr. Bin Song at Washington College.    

In 1644, Descartes published his Principles of Philosophy, and intended to promote it as a textbook of philosophy to be adopted by universities of Europe at that time. Descartes knew that this was deliberately to challenge the dominant role of Aristotelianism in the European academia. After all, the replacing of one textbook with another means a great deal. Although whether Descartes succeeded to promote his textbook in the institutional level is another story, he is indeed universally acclaimed by later historians as the father of modern philosophy.

Before Descartes, we discussed Aristotle, Copernicus, and Galileo in this second section of “modern scientific revolution” at the course of “Modern Philosophy.” We find that although Copernicus and Galileo laid out a very robust refutation against key points of Aristotle’s natural philosophy, none of these scientists’ thought is comprehensive enough to address the established Aristotelianism as a whole. As we have discussed, the philosophical system of Aristotle was so comprehensive as to be able to include everything that humans could know in his time. Therefore, to challenge the official status of Aristotelianism, Descartes’s philosophy must also be no less comprehensive. Descartes likened his comprehensive version of philosophy to a tree:

“Thus the whole of philosophy is like a tree. The roots are metaphysics, the trunk is physics, and the branches emerging from the trunk are all the other sciences, which may be reduced to three principal ones, namely medicine, mechanics and morals. By ‘morals’ I understand the highest and most perfect moral system, which presupposes a complete knowledge of the other sciences and is the ultimate level of wisdom.” (Principles, 9B:14)

Put in the background of the entire corpus of Descartes’s works, why Descartes thinks of philosophy as such would be more comprehensible. Metaphysics studies the most generic traits of things in the universe which exist under three major categories: soul, body and God. Physics studies the “body” part of the universe, and furnishes the laws of nature which explain the movement of varying bodies in the world. Medicine and Mechanics are two branches of applied physics, which are about how to cure human diseases and how to design technologies to alleviate human labor, two crucial areas pertaining to the convenience and sustainability of mundane human life. The “morals,” or the ethics is about what humans should do in varying situations, and according to Descartes, this is the highest branch of human knowledge since it needs all sorts of other knowledge in order to deliver the right ethical decisions.

Among all these parts of philosophy, we’ll focus upon “metaphysics” in the following weeks, where we’ll scrutinize Descartes’s famous argument for “I think therefore I am” and how he built his metaphysical system addressing the substances of soul, God and body. However, when Descartes presented his tree of philosophy in an intended textbook, his thought was in a relatively mature stage. The tree didn’t include much information about how he got to the root of his philosophy, viz., that dualistic metaphysics of soul and body, in the first hand. In order to understand how he got there and prepare our study of his metaphysics, we therefore need to trace his philosophical career back to a much earlier stage.

Before Descartes turned into his metaphysical thought in 1628, he was a very successful mathematician and physicist. Seen from the perspective of the on-going scientific revolution, the greatest contribution Descartes made as a scientist is surely his invention of analytic geometry, which unifies algebra and geometry, and hence, paves the way for the birth of calculus in Newton’s and Leibniz’s thought.

There are two major points we need to grasp in the ground-breaking work of the Geometry of Descartes.

Firstly, the unification of algebra and geometry leads to the full digitization of the objective natural world, which is unimaginable before Descartes. The crucial step for Descartes to achieve this is to illustrate that all major algebraic operations in Descartes’s time, including addition, subtraction, multiplication, division, and the square root, can correspond to a certain segment of a line, and hence, there is no reason to limit human imagination of a magnitude within three dimensions. Instead, a simple line segment can express a magnitude of any dimension, and once discovering the way how to express geometrical figures using algebraic means, the capacity of measuring and calculating natural movement in reality will be exponentially increased. If any one wonders where the idea of the digitization of the entire world in the movie of “Matrix” originally comes from, let’s ask Descartes.

Secondly, to resolve complex geometrical problems in his time, Descartes indicates an unusually high awareness towards the underlying “method” for the desired solutions. For instance, to resolve a geometrical problem, Descartes would firstly assign a letter to each of the known and unknown magnitudes. Then, he would write down as many equations as he can find to express the varying relationships between these unknown and known magnitudes. In the following, he would try to reduce the complex level of these equations so as to find a way to express the unknown from the known. Finally, once he found the answer of the unknown, Descartes would furthermore deduce complex relationships among magnitudes from the newly discovered simple ones. In the work of the Geometry, we can find many concrete examples about how Descartes described and applied this “method.” And the application of this method is so successful that Descartes furthermore thought he should use it to resolve all questions humans can ask, including those most abstruse and abstract ones in metaphysics.

Therefore, in 1637, Descartes published his “Discourse on the Method,” and generalized his “method” in four points:

“The first was never to accept anything as true if I didn’t have evident knowledge of its truth: that is, carefully to avoid jumping to conclusions and preserving old opinions, and to include in my judgements only what presented itself to my mind so vividly and so clearly that I had no basis of calling it in question. The second was to divide each of the difficulties I examine into as many parts as possible and as might be required in order to resolve them better. The third was to direct my thoughts in an orderly manner, by starting with the simplest and most easily known objects in order to move up gradually to the knowledge of the most complex, and by stipulating some order even among objects that have no natural order of precedence. The last was to make all my enumerations so complete, and my reviews so comprehensive, that I could be sure that I hadn’t overlooked anything.” (pp. 9, Discourse on the Method, trans. Jonathan Bennett 2017.)

The four rules are quite self-explanatory, and they can all be understood against the practice Descartes conducted in his analytical geometry. In other words, in any pursuit of human knowledge, Descartes believes we should aim for evident knowledge, which should be as vivid and clear as the one of math. Then, we would find all available chunks of information relevant to the solution of puzzles, put them into order, and then, reduce the complex ones to the simple ones, and address the simples ones first with a final synthesis to move from the simple to the complex. Since the aforementioned tree of philosophy is just a result of Descartes’s application of his method which ultimately derives from math, we can safely conclude that although metaphysics is seen as a root of the tree, the real soil to grow the entire tree of philosophy of Descartes is actually his mathematics. So, whoever said that nobody unfamiliar with math cannot learn philosophy? I hope you find some historical predecessor to Descartes’s thought here.

So, how would Descartes employ this “method” so as to create the dualistic metaphysics of “mind” vs “body” as the foundation of modern thought? That will be the question we will tackle for our following learning of modern philosophy. In general, Descartes’s thought is rigorous, methodic, systematic and creative, indeed a rare talent of philosophy, the learning of which can almost be guaranteed to bring a transformation of our own thought.