The aim of Descartes' philosophy is to use his method to reach the truth. Descartes' goal is not to discover a multiplicity of isolated truths, but rather a system of true propositions in which nothing is presupposed that is not self-evident. Thus, he insists on strong connections between all the parts of the system of knowledge he constructs. The system is thus impervious to the dangers of skepticism.
Descartes understood philosophy to mean the study of wisdom. And this wisdom meant to him a perfect knowledge of all things that human beings can know or understand. Descartes therefore included in his philosophy also metaphysics and physics and natural science. He even included in his philosophy anatomy, medicine, and morals. Descartes stressed the practical aspects of philosophy, saying that a state can have no greater good than the possession of true philosophy. Descartes deliberately broke away from the past, and was determined to start his search for truth at the beginning of all knowledge, never accepting the authority of any previous philosophy. According to Descartes, all the sciences are interconnected and must be studied as a single entity using one process designed to elicit truth. As such, his thought was at odds with the established medieval Christian philosophy, called scholasticism, which embraced Aristotelian principles and held that the various areas of knowledge are distinct from one another.
The Discourse was Descartes' first published book (other than the thesis he had written for his law degree in 1616). Descartes was forty-one years old when the Discourse appeared and became the most important, most widely read, and most controversial book of the time. People soon learned the identity of the author of this seminal work. While he had not published anything until he reached this relatively advanced age, Descartes had already written much. He had written the withdrawn Le Monde (whose full title was Le Monde cm Traite de la lumiere) and had authored his Rules (Regies pour la direction de ?esprit en la recherche de la verite), which is generally believed to have been written as early as 1628. Descartes had refused to publish this work as well. The reasons for the late publication of the Discourse, and the withholding from publication of the Rules, have remained a mystery extensively debated by scholars. Here was a very private, “masked” man, reluctant to reveal to the world his deepest thoughts and theories. We know that the trial of Galileo in 1633 caused the withdrawal of Le Monde—but why the refusal to publish earlier, five or more years before that trial? Was fear of the Inquisition affecting Descartes even at that early period? Or were there other reasons for Descartes' behavior?
Galileo was first condemned by the church in 1616 for his support of Copernicus. And in an edict issued that same year, the Inquisition forbade the publication of any book supporting the Copernican theory in all the countries under the influence of the Catholic Church. Descartes had been aware of these developments and may already have been wary of the church and its potential response to his own work should it be published. He therefore may have decided well before Galileo's trial to refrain from letting his work become public. The news of Galileo's trial, however, greatly intensified Descartes' feeling that he had made the right decision.
The Discourse on the Method and its scientific appendixes reflect Descartes' painful dilemma. On the one hand, he could not allow himself to publish freely about physics, since the concepts behind his theories were all in line with those of Galileo and Copernicus, and Descartes had vowed not to contradict the views of the church. On the other hand, by 1637, Descartes felt a strong internal need to publish, and had already been under pressure from many friends and correspondents asking to read his philosophy and his views of nature.
The book and its appendixes were thus a compendium of Descartes' ideas, but one in which essential parts of physics were suppressed in order to keep the text from professing the forbidden heliocentric view. Descartes' universe, as implied by his published writings, is one that has no center and whose dimensions are infinite. These assumptions allowed Descartes to hide his true opinions and deductions about the universe and to avoid altogether the Copernican controversy. These views, however, were contrary to the scholastic tradition, according to which the universe is finite and infinity belongs to God alone.
According to recent research on Descartes' writing chronology and development of ideas, the three appendixes, the Dioptrique, the Meteor es, and the Geometrie, were formulated within the withdrawn Le Monde. They had thus been written some years earlier. What Descartes had done in the intervening years was to carefully reformat his work, discarding Le Monde and rewriting his science in such a way that it contained no traces of the forbidden physics. He then wrote a preface to the three appendixes containing his sanitized scientific writings, and published them. In fact, as evidenced from the sixth part of the Discourse, as well as from various letters Descartes wrote in 1633 and 1634, Le Monde itself was simply an extension of an earlier work titled Les Meteores, dealing with a wide variety of issues in natural science, which was ready for publication in 1633. Furthermore, a treatise titled La Dioptrique was ready to be shipped to the printers as early as 1629, when it was withdrawn from publication. These early writings were painstakingly revised and appeared with the now-famous preface, titled the Discourse on the Method. Descartes' complex publishing history demonstrates the lengths to which he was ready to go in order to protect himself. His was probably the most complicated attempt to edit out controversial material in publishing history.
The Discourse on the Method, intended as a preface, became the main piece of writing, for it contained the principles of Descartes' philosophy. And thus this book is often published as a stand-alone treatise. The Discourse is unique in its format as well, as it constitutes a biographical account of the development of a philosophy—the story of the philosopher's journey of discovery.
Descartes' Discourse on the Method is composed of six parts. In the first part of the book, Descartes introduces his thoughts and explains how they developed. He writes about his education at the College of La Fleche and describes the ideas to which he had been exposed. “What pleased me most was mathematics, because of its certitude and its reasoning,” he writes. Descartes explains how he came to believe that he could use the idea of mathematical proof in philosophy. This led him to the concept of doubt and the decision to doubt everything that he could not ascertain as true. Here the nascent Cartesian thought diverges from the accepted medieval scholastic philosophy, which held that there were three possible levels for all propositions: false, probable, and true.
In embracing purely mathematical methods of obtaining knowledge, Descartes does away with the probable and assumes the falsity of everything that he cannot prove with logical power analogous to that used in the demonstration of a theorem in geometry. He writes: “I have always had an extreme desire to learn how to distinguish the true from the false, in order to see clearly in everything that I do, and to march forward with confidence in this life.” Descartes mentions his years of travel that followed his education, “thus studying from the book of the world,” and concludes by stating his resolution to continue his search for truth through introspective study, never straying too far away from his books.
Descartes begins the second part of his Discourse by telling us that after witnessing the coronation of the new Holy Roman Emperor and joining the army in Germany, he spent the winter in an “oven,” devoting his time to thinking. Among his first ideas was the notion that works by a single master are more attractive, and in a way more true to reality, than those that had been constructed by several people. From this view, he concludes that his first duty is to renounce all knowledge that had been obtained as a result of the work of many different people, that is, he wants to reject the prevailing philosophy—surely the work of many minds over generations—and to start the construction of a system of knowledge that is the work of one man alone: namely Descartes himself. All he would retain from previous knowledge would be logic, geometry, and algebra. He then states four principles that would guide him in this endeavor:
To accept as true only th
at which cannot be doubted.
To divide every problem into as many parts as would be necessary in order to solve it correctly.
To order his thoughts from the simplest to the most complicated.
To enumerate all concepts so that nothing pertinent is omitted.
Descartes then discusses how problems of mathematics are solved using his system, which is an extension of the ancient Greek method of proving theorems by means of first principles and logical concepts. He states his desire to be able to derive philosophical knowledge by way of the same mathematical methodology used in geometry.
The third part of the Discourse on the Method is devoted to questions of morality. Descartes tells us that he had resolved to follow the laws and customs of the land in which he lives. He wants to be firm and resolute in all his actions; and he wants to devote his life to cultivating his reason and rationality and to apply them in all his actions. Descartes tells us how he returned to his travels and spent the following nine years “rolling here and there in the world.” He describes his move to Holland, away from the places where he was known.
In the fourth part of the Discourse, Descartes returns to the main thrust of his development of a philosophy. He starts with his methodical doubt: I doubt, or negate, everything that cannot be proven in a mathematical way, he says. So what can Descartes prove ? Everything is taken to be false. But Descartes, the person, is doing this doubting. So one thing can be deduced as true: Descartes exists. Otherwise, he could not doubt. Thus, from the negation of everything, a proof is derived of the existence of the person doing the doubting. This is the most brilliant deduction in the history of Western thought. The proof is absolutely beautiful, and it follows mathematical principles of proof. One could even look at this deduction as a proof by contradiction—a favorite method of mathematical proof: Assume that I do not exist. But if I don't exist, then I could not doubt, or assume the falsity of everything in the universe. Thus I must exist. From this deduction comes Descartes' famous “Cogito, ergo sum”: I think, therefore I am.
The thought that I have is the primal doubt that begins the chain of deduction. I doubt everything; but this doubt is a thought; and the thought proves that I exist. I cannot doubt the fact that I am doubting; thus I, at least, must exist.
Descartes continues his logical process of deriving truth. Doubt implies uncertainty. And uncertainty implies imperfection. Human beings and everything in their environment are imperfect. But the idea of the imperfect implies the existence of something that is not imperfect. That which is not imperfect is, by definition, perfect. And perfection belongs to God. Thus Descartes deduces the existence of God from the fact that the perfect must exist. Perfect triangles and circles are geometrical figures that do not exist in our imperfect everyday world—but they do exist as ideas, as models that imperfect triangles and circles of the real world approximate. The ideal perfection implies a perfect being, God. Descartes then proceeds to the concept of a geometric space. According to Descartes, space is infinite: it extends indefinitely in all directions. Descartes' idea of a space that is unlimited in its extent leads him to the idea of infinity, and the conclusion that the infinite is God. Hence the notion that space is infinite gives Descartes another confirmation of the existence of God.
In the fifth part of the Discourse, Descartes turns to problems of physics and natural philosophy. He states that he cannot divulge all his beliefs about the physical world, a hint about the withdrawal of Le Monde. He writes about gravity, about the moon, and about the tides. His writing shows that he understands a great deal about physics. Then Descartes turns to biology and anatomy, as another example of the application of his method of reasoning. He describes the function of the heart, but incorrectly. Descartes assumes that the heart's temperature is higher than that of the rest of the body, and that the difference in temperature makes the blood flow in and out of the heart. A discussion of the function of other body parts, again flawed (he does not understand the function of the lungs, thinking their purpose is to cool the blood), leads him to the difference between animals and people. Descartes believes that language implies the existence of reason and intelligence, and hence that animals possess neither. Animals are automata, he concludes, and lack intelligence and a soul. Body and soul are separate, according to Descartes, and here again, his philosophy is at odds with scholasticism, according to which the soul is part of the body.
In the sixth and final part of the Discourse on the Method, Descartes states the reasons why he wrote his book. His main purpose was to contribute to the general good: he became an author in order to improve the conditions of human existence. He again returns to the dangers inherent in writing, and the fact that he could not tell us everything about his thinking and deductions about the physical world. He would accept no patronage or state pension for his work, he tells us. He wants to apply his method to the search for a deep understanding of nature with the goal of finding a way to prolong life. This aim was in keeping with the spirit of the time, the seventeenth century, when people hoped to live to the ages of the patriarchs. Finally, Descartes explains why he wrote in French rather than Latin.
But Descartes realizes that his philosophy is controversial. He is well aware of the fact that it contradicts the prevailing thought of his time. Perceptively, Descartes predicts that he would face staunch opposition for his views—but as a soldier, he is ready to defend his philosophy. He would indeed be forced to do so.
The publication of the Discourse on the Method made Descartes immensely famous. The book quickly elicited both positive and negative reviews by scholars, and Descartes would spend much time over the following years answering letters by many scholars about his work. His treatise became a best seller all over Europe, but the controversy result ing from this work made Descartes withdraw from people even more, interacting with the outside world mostly through letters.
In their Fama fraternitatis (1614), the Rosicrucians advocated “correcting the deficiencies of the church and improving moral philosophy.” Descartes, who in 1637 was still unhappy about the rumors that he was a member of the Brotherhood of the Rosy Cross, continued to counter them. He wrote in his Discourse: “There have been as many reformers as heads,” implicitly arguing against reform, to further distance himself from the Rosicrucians. He also made statements about being “suspected of this folly,” elliptically alluding to the association with the brotherhood. And toward the end of the first part of his Discourse, Descartes puts it quite clearly:
And finally, about bad doctrines, I thought I already knew well what they are worth, so as not to fall prey to deception, neither by the promises of an alchemist, nor by the predictions of an astrologer, nor by the impostures of a magician, nor by the device of praise by those who make a profession of knowing more than they know.
Thus, almost two decades after he left Germany, Descartes was still concerned about the rumors connecting him with the Rosicrucians. Yet some doubts linger as one reads his writings. Earlier in the Discourse, Descartes writes: “I had browsed through all the books treating the topics one would consider the most curious” (emphasis added). According to a number of scholars, the French word curieuses had a particular meaning in the seventeenth century, and “curious” sciences were those dealing with special knowledge: magic, astrology, and alchemy. The words “curious science” and “curious books” appear often in the Discourse.
In his Discourse, Descartes placed hints about his secret notebook. In the second part, Descartes writes about the “analysis of the ancients and the algebra of the moderns.” He alludes to the use of symbolic secret characters that are part of a “confusing and obscure art.” Three pages later, he refers to an important “solution” to a problem he had found after an intense period of work. Descartes writes about a method that, applied to “arithmetic,” gave him the solution, the proof, to his problem. It has been conjectured that Descartes refers here to the problem solved in his secret notebook.
Descartes' geometrical work w
as described in his Geometric This treatise is the most important appendix in history, for it encompassed Descartes' groundbreaking work in geometry and his wedding together of geometry and algebra—his greatest legacy in mathematics. His Geometrie was the “sum of all the science of pure mathematics.” It would play a crucial role in the development of modern mathematics. Descartes knew that this appendix was, by far, the hardest to understand, and noted so in his text, warning the reader that an advanced level of knowledge in geometry might be required. The Geometrie contained extensive discussions of equations and graphs. The graphs representing the equations could not have been created without the idea of the Cartesian coordinate system, which allowed each equation to be represented with perfect precision as a curve drawn on paper. This invention was an extension of ancient Greek ideas. The Cartesian coordinate system in two dimensions is shown below.
The Cartesian Coordinates
Chapter 15
Descartes Understands the Ancient Delian Mystery
DESCARTES WAS ENGROSSED IN THE problem of the doubling of the cube—the Delian puzzle that had eluded the ancient Greeks. In order to attack it, however, he needed to make more progress on understanding exactly how constructions with straightedge and compass work. He needed a tool to allow him to study these constructions, and his coordinate system constituted the required tool. Using the Cartesian coordinate system, Descartes constructed a connection between numbers and shapes—between geometry and arithmetic. The ancient Greeks had come close. For example, the Pythagoreans were able to see that the sides of a square or rectangle could be represented by numbers. This is how the Pythagorean theorem worked. If you defined the dimensions of a square as 1 unit by 1 unit, then by the Pythagorean theorem, the hypotenuse was the square root of 2. This is seen as follows.
Descartes's Secret Notebook Page 14