DESCARTES, RENÉ
(1596–1650)

In Discourse on Method (1637), his first published work, French philosopher and scientist René Descartes combined an intellectual autobiography with a popular presentation of the system he was to develop more rigorously in his Meditations (1641) and Principles of Philosophy (1644). Meditations begins with a radical attempt to doubt all past beliefs, but finds a proposition that resists doubt in the existence of the self as a thinking thing. It then uses this initial certainty as a basis for arguing that God exists, that mind and body are distinct, and that we can achieve certainty in the sciences if we assent only to clear and distinct ideas, provided we have first shown that God would not deceive us about those ideas. The Principles uses the metaphysics and epistemology laid out in the Meditations as the foundation for an ambitious attempt to provide a scientific account of the entire world.

Childhood and Formal Education (1596–1618)

Descartes was born on March 31, 1596, in the village of La Haye, in Touraine, at the home of his maternal grandmother, with whom he lived after his mother's death in 1597. His father, Joachim Descartes, was a member of the gentry and a councilor in the parliament of Brittany whose duties required him to spend several months each year in Rennes. When René was four, his father remarried and moved to Rennes; René and two older siblings remained with his grandmother. We do not know much about his earliest years, but it appears that he was never close to his father, either as a child or as an adult. His grandmother died when he was about fourteen.

At ten, Descartes entered the Royal College at La Flèche, founded two years earlier by Henry IV and run by the Jesuit order. The first five years of the program were guided by the ideals of Renaissance humanism, and thus were devoted to studying Latin, Greek, and classical literature (especially Latin and the works of Cicero). The last three years were dedicated to instruction in numerous subjects, including:

• Thomistic-Aristotelian philosophy, including dialectic (Aristotle's Organon ), natural philosophy (Aristotle's Physics ; On the Heavens [De caelo ]; and On Generation and Corruption [De generatione et corruptione ], book I);
• Mathematics (arithmetic, geometry, and topics in applied mathematics, such as astronomy);
• Metaphysics (Aristotle's On Generation and Corruption, book II; On the Soul [De anima ]; and Metaphysics );
• Moral philosophy (Aristotle's Nicomachean Ethics and the work of Jesuit casuists).

Study of Aristotle and Aquinas made extensive use of late-sixteenth- and early-seventeenth-century commentaries, especially those by the Jesuits at the University of Coimbra. Sometimes the curriculum ignored aspects of Aristotle's thought difficult to reconcile with Christian doctrine. Instead of reading the theological portions of Aristotle's Metaphysics, whose remote God is not the creator of the universe, students read a creationist treatise from the first century CE, On the World (De mundo ), which was mistakenly ascribed to Aristotle. In other cases the problems were faced. Thomas Aquinas had interpreted Aristotle's teaching about the soul as consistent with the Christian doctrine of personal immortality. In the sixteenth century Pietro Pomponazzi had argued persuasively that Aquinas misread Aristotle and that Aristotle in fact held the soul to be mortal. Pomponazzi himself did not deny immortality; his official position was that philosophy could neither prove nor disprove the immortality of the soul, but that revelation made it certain. However, since he tended to identify Aristotle's views with those views that human reason would naturally reach unaided by revelation, he came perilously close to the doctrine of double truth associated with the Averroist tradition—the idea that philosophical truth and theological truth may conflict irreconcilably. The Jesuit curriculum called for the teachers in its colleges to attack the authority of such commentators.

Descartes may have drawn an unintended conclusion from these disputes. When he first began to work out his own theory of knowledge, he wrote, "Whenever two people make contrary judgments about the same thing, it is certain that at least one of them is wrong, and it seems that neither of them has knowledge. For if one had a certain and evident argument, he would be able to propose it to the other in a way which would in the end convince his intellect" (Adam and Tannery X, p. 363). The persistence of the dispute about whether immortality was consistent with an Aristotelian theory of the soul probably encouraged Descartes to develop his own anti-Aristotelian theory. His studies in mathematics may also have encouraged skepticism about Aristotelian natural philosophy. At La Flèche the teachers used the texts of the Jesuit mathematician Christopher Clavius (1538–1612), who argued that mathematics was superior to the other supposed sciences, because it succeeded in eliminating all doubt, and that the other so-called sciences demonstrated their uncertainty by their inability to elicit consensus.

At the time, the Jesuit colleges dominated secondary education in France and had an immense influence on the formation of a generation of leaders in politics, philosophy, and religion. Their primary mission was to combat the Protestant heresy, but they also reciprocated the King's support, defending his claims to absolute power. The colleges required total immersion in the Jesuit educational program, permitting little contact with the outside world (parents included). Descartes had mixed feelings about this education. In his Discourse on Method he was quite critical of it, claiming it had not provided him with what he had hoped for—clear and certain knowledge of everything useful in life—but had instead left him embarrassed by many doubts and errors. It seemed to him that he gained nothing from his studies but an increasing awareness of his own ignorance. Still, he was careful to say he thought his school had given him as good an education as was then available, and he later recommended it to friends for their children.

Descartes completed the program at La Flèche in 1614. In Discourse he wrote that as soon as he was old enough to leave the control of his teachers, he completely quit the study of letters and sought what knowledge he could find either in himself or in the great book of the world. This is not entirely true. We do not know much about what he did in the years between 1614 and 1618, but we do know that he completed a degree in law at the University of Poitiers in 1616. His earliest biographer, Adrien Baillet, reports that Descartes spent the first year after leaving La Flèche in St. Germain-en-Lay, a village outside Paris. The Royal Gardens there contained remarkable statues, designed to move, play music, and even speak. Seeing these machines mimic the behavior of living, intelligent creatures may have helped make plausible to Descartes his later doctrine that animals are nothing but machines.

Informal Education: Encountering Beeckman (1618–1619)

In the summer of 1618 Descartes left France to join the army of Maurice of Nassau in the Netherlands. His legal studies would more naturally have led to a career in the law or government, possibilities he considered at various times in the next several years. But in 1618 military life was more enticing, with its opportunities to travel and to learn about the practical application of scientific theories. Maurice encouraged scientific research and employed one of the leading scientists in the Netherlands, Simon Stevin, to oversee his army's education in military technology. Among Stevin's scientific accomplishments were an experimental refutation (anticipating Galileo Galilei) of the Aristotelian theory that heavy bodies fall faster than light ones and his discovery of the "hydrostatic paradox": that the downward pressure of a liquid depends only on the height and base of its vessel and is independent of its shape. As a military engineer, Stevin developed a system of sluices to flood the fields, giving the Dutch a critical (if Pyrrhic) means of defense against invading armies. In 1618 the Dutch were still enjoying an extended truce in their war for independence from Spain, so Descartes saw no combat. In a letter from this period he wrote that he spent his time learning drawing, military architecture, and Dutch. But he also mentioned plans to write books.

The stimulus for this last ambition was his encounter with Isaac Beeckman, a Dutch scientist, several years his elder, whom he met in November 1618. In a letter to Beeckman, Descartes credits Beeckman with having roused him from his laziness, recalled to his mind the learning he had almost forgotten, and brought him back to serious pursuits. By the spring of 1619 Descartes was contemplating two works, one in mechanics, the other in geometry. In his enthusiasm, Descartes wrote to Beeckman and promised to embrace him as "the promoter and first author of my studies" (Adam and Tannery X, p. 162). Their later relations were not so cordial. In 1630 Descartes was to write Beeckman complaining that the older man was claiming too much credit for having been Descartes's teacher. Though they later reconciled, Descartes makes no mention of Beeckman in the Discourse.

Why was Descartes's encounter with Beeckman so important? First, as Beeckman put it, they shared a desire to "combine physics with mathematics in an exact way" (Gaukroger 1995, p. 69). Beeckman had been working on problems in this manner for some years and was delighted to find a like-minded colleague. One result was a short treatise that Descartes wrote on music, attempting to work out a mathematical relationship between the various sounds that appear pleasing to us in combination. He may have begun this treatise before he met Beeckman, but he finished it in December and presented it to Beeckman as a gift on New Year's Day, 1619.

Their more normal pattern of interaction was that Beeckman would set up Descartes with a problem in mechanics or some related area, and invite him to solve it. For example, Beeckman recognized that bodies falling freely in a void would accelerate uniformly. So he posed the following problem: Suppose that a body moving in a void will move eternally (in opposition to Aristotelian physics, Beeckman assumed a version of the principle of inertia). Suppose further (again in opposition to Aristotle) that there is a void between a falling stone and the Earth, and that the stone covers a given distance in a given time. How far will it fall in half that time? As early as 1604 Galileo had worked out the correct law governing the free fall of bodies, which implied that the velocity of the falling body is proportional to the duration of time that it falls, but he did not publish this result until 1638. Descartes concluded that the velocity was proportional to the distance covered, a mistake that Galileo had also made in his first attempt to solve the problem. What is important here is that Beeckman was encouraging Descartes to engage in the Galilean project of discovering laws governing the motion of bodies, expressible in mathematical formulas.

Another area where Beeckman influenced Descartes involved his program of explaining macroscopic physical phenomena in terms of the mechanical properties of the microscopic particles composing them. This program—generally now called "the corpuscularian hypothesis" or "the mechanical philosophy"—had connections with ancient atomism, but differed from atomism in important respects. It did not assume that the component particles were indivisible, and as Descartes was to develop it, it did not assume the existence of a void. Moreover, whereas ancient atomism had regarded the size and shape of the atoms as the primary explanatory factors, the corpuscularians emphasized the speed of the particles and direction of motion.

One problem that Beeckman set for Descartes was to explain in corpuscular terms Stevin's hydrostatic paradox. Descartes postulated that the weight of the column of water can be reduced to the force exerted by its particles in their tendency to downward motion and that each particle of water on the bottom of the container is connected with a particle on the surface by a unique line of particles along which the force (tendency to motion) is transmitted. It is surprising that Descartes thought this explanation worked. It seems plausible where the area at the surface and the area at the base are equal in size, but not in the cases that most require explanation, cases where the area at the surface is smaller (or larger) than the area at the base.

These examples give us an idea of the sort of study that Descartes might have included in the work on mechanics he was contemplating. His work in mathematics seems to foreshadow his discovery of analytic geometry, his most enduring contribution to the sciences. In a letter to Beeckman in March 1619, Descartes excitedly wrote that he hoped to discover "a completely new science," one that would "provide a general solution of all possible equations, involving any sort of quantity, whether continuous or discrete" (Adam and Tannery X, pp. 156–157). The path to solving these geometric or arithmetic problems seems to have involved using complex instruments, "proportional compasses." Descartes devised compasses that not only solved the problem of dividing an angle into any number of equal smaller angles, but also solved cubic equations of varying degrees of complexity. He had not yet formulated the program, which he was to develop in his Geometry, of using algebraic means to solve geometric problems. But he had taken a step toward unifying arithmetic and geometry.

Finding a Vocation in Germany (1619–1620)

In the spring of 1619, as the Thirty Years War was just beginning, Descartes set out for Germany to join the army of Maximilian of Bavaria, the leader of the Catholic League. In the Discourse he tells us he attended the coronation of Ferdinand II as Holy Roman Emperor. As he was returning to the army, the onset of winter detained him in a place where he had no one to talk to and no cares to trouble him. Shut up all day in a stove-heated room, he was alone with his thoughts. This isolation produced the first of two major turning points in his life. In a document now lost that Baillet saw and preserved (apparently in a mixture of paraphrase and quotation), Descartes wrote that on November 10, 1619, while "full of enthusiasm," he discovered "the foundations of a wonderful science." Descartes left behind conflicting indications of what this discovery was.

The account in the Discourse, written seventeen years later, implies that Descartes's discovery involved a decision that to make firm judgments in the sciences, he would have to rid himself of all his previous opinions and reconstruct his system of beliefs on new foundations, accepting nothing he had previously believed until he had squared it with reason. Too much of what he believed was based on uncritical acceptance in his youth of the opinions of others. The document Baillet saw—an account of three dreams that Descartes reported having had on the night of November 10, probably written not long after the event—doesn't suggest a project of ridding himself of all his past opinions. Nor does Descartes's earliest methodological work, Rules for the Direction of the Mind, which he apparently began around this time.

Of the three dreams, the most important was the last. In that dream Descartes found two books on a table. One he describes as a dictionary; the other was an anthology of poetry. When he opened the anthology, he found a poem by Decimus Magnus Ausonius (c. 310–395) that opens with the sentence Quod vitae sectabor iter? ("What path shall I follow in life?") Descartes said that while he was still asleep, he recognized he had been dreaming and began to interpret his dreams. He construed his discovery of the poem by Ausonius as indicating that he must choose the proper direction for his life. And the dictionary, which we should probably think of as more like an encyclopedia, he interpreted as representing a collection of all the sciences. The dream as a whole he took to indicate that the path he should choose in life was to pursue the sciences and demonstrate their fundamental unity. A fragment preserved from this period expresses that idea vividly: "The sciences now are masked, but if the masks were taken off, they would appear most beautiful. Someone who sees how the sciences are linked together will find them no harder to retain in his mind than the series of numbers" (Adam and Tannery X, p. 215). Descartes's vocation was to unmask the sciences. The ambition to construct a unified system of all scientific knowledge was to guide him for the rest of his life.

Rules for the Direction of the Mind (Earliest Stages, 1619–1620)

Among the unfinished works Descartes left behind at his death was a treatise on methodology, which he apparently worked at, off and on, between 1619 and 1628: Rules for the Direction of the Mind (Regulae, for short). He intended the Regulae to be a three part work, each part of which would consist of twelve rules. Although he completed only the first part and about half of the second part, this is the most substantial work we have from the period before 1629. Its parts often seem inconsistent with one another, apparently reflecting different stages of the work's composition and the lack of any unifying revision. Nevertheless, the work sheds light on Descartes's development and later thought. Our best current theory of its composition—resulting from the analyses of Jean-Paul Weber (1964) and John Schuster (1980)—holds that Descartes wrote a part of Rule Four first, perhaps before the night of the three dreams, that he completed most of Part One sometime during the period from 1619 to 1620, and that he then set the work aside for several years, returning to it in the period between 1626 and 1628, when he added Rules Twelve through Twenty-One. After that, he abandoned the work, for reasons we can only guess.

The second half of Rule Four ("Rule IV-B," as it is now called, beginning at the bottom of Adam and Tannery X, p. 374) recounts Descartes's first investigations of mathematics and his disappointment with the ancient mathematicians. He found in them many propositions about numbers that he recognized as true after doing his own calculations and many conclusions about figures that his authors reached by logical arguments. But they did not explain why these things should be true or how they had discovered them. Descartes conjectured that the ancient mathematicians possessed an algebraic method of discovery they concealed because it made the discovery of mathematical truths too easy. They feared that revealing their method would diminish people's respect for their accomplishments. Rule IV-B is entirely concerned with the project of developing a general method for discovering mathematical truth.

The second stage of the Regulae is more ambitious, aiming to formulate a methodology that applies to all the sciences. They are all, he says, "nothing but human wisdom, which always remains one and the same, however much its objects may differ" (Adam and Tannery X, p. 360). The sciences are so interconnected and interdependent that it is easier to learn them together than separately. What someone seeking truth in the sciences must first do is to consider how to increase his "natural light of reason," the cognitive abilities he is naturally endowed with. ("Ingenium," the term traditionally translated as "mind" in the title, Regulae ad directionem ingenii, might more happily be translated as "native cognitive powers.") Negatively, this means that we should rely only on intuition and deduction—that is, on propositions whose truth we can see distinctly, with certainty, when we attend to them carefully, without being confused by what our senses and imagination tell us, and on propositions that can be inferred from propositions of the first kind by a process of inference equally clear and certain.

Descartes claimed that the only genuine sciences discovered thus far were arithmetic and geometry. But he denied that these were the only areas where we could achieve absolute certainty by intuition and deduction. There are more intuitively certain truths than most people suspect. He gave as examples the propositions that he exists, that he thinks, and that a triangle is bounded by just three lines, among others. If we make proper use of such truths, not mixing them up with probable assumptions, we will be able to extend the certainty of mathematics to other areas. This was an attack, not only on reliance on the senses or imagination, but also on the scholastic use of "probable syllogisms," whose premises needed only the support of a majority of the wise to be acceptable. Descartes thought that in difficult matters the minority is more likely to be right than the majority.

Positively, Descartes's central message is that we must conduct our investigations in an orderly way, gradually reducing complex and obscure propositions to simpler ones, until we reach propositions simple enough that we can know them intuitively, that we can see their truth without the aid of other propositions. Once we have completed that reduction, we can work our way back, step by step, to the proposition whose truth or falsity we originally wished to determine. Suppose that the problem is to find the three mean proportionals between 3 and 48. We might not have any intuitions about the answer. But if we look for the single mean proportional between those numbers, 12, then we will have reduced the original problem to something more manageable, finding the mean proportionals between 3 and 12 and between 12 and 48. We can see easily enough that 3 is to 6 as 6 is to 12, and that 12 is to 24 as 24 is to 48. Seeing this enables us to see that 6, 12, and 24 are the numbers sought.

The visual metaphor here is deliberate. "Intuitus," the Latin noun translated as "intuition" is derived from a verb, "intueri," whose basic reference was to visual perception, though it was commonly extended to mental acts of consideration and contemplation in classical Latin. Descartes thought that we can learn how to better use our mental power of intuition by comparing it to vision. If we try to look at many physical objects at once, we see none of them distinctly. Likewise if we try to attend to many propositions in a single act of thought. We can improve our vision, both physical and mental, by focusing our attention on one simple object at a time.

Descartes emphasized that intuition is required not only for our knowledge of the premises of our inferences, but also in the inferential process itself. To have scientific knowledge of the conclusion of an inference, we must intuit not only the premises of the inference, but also the connection between the premises and the conclusion. To know by deduction that 2 + 2 = 3 + 1, we must see not only that 2 + 2 = 4 and that 3 + 1 = 4, but also that our conclusion follows necessarily from these premises. We cannot avoid relying on intuition by insisting, with the Scholastics, that our arguments possess formal validity. Descartes accepted the classical skeptical critique of syllogistic reasoning: that it is useless as a means of acquiring knowledge, because the formalization of the argument—the addition of a suppressed conditional or universal premise to transform an enthymeme into a formally valid syllogism—accomplishes nothing. If the suppressed premise is evident, it is unnecessary for the argument's validity. If the suppressed premise is not evident, then all that the formalization of the inference accomplishes is to increase the number of assumptions requiring proof.

Wanderer Years (1621–1625)

After the initial burst of energy that produced the earliest stages of the Regulae, Descartes appears to have set the project aside for a while and to have produced no significant work. He traveled here and there, returning to France, visiting Italy (perhaps more than once), and finally returning to France for an extended stay in Paris. He sold the property that he had inherited from his mother, using the proceeds to secure a modest but regular income. This freed him from the need to earn a living. He probably made a pilgrimage to Loreto, Italy, fulfilling a promise made after the night of the three dreams. Apparently, he did not visit Galileo when he passed through Florence. But during this period he seems to have made the acquaintance of Marin Mersenne (a member of the Order of Minims, residing at a convent in Paris), who shared his interest in mathematics and the new mechanical philosophy.

In these years Mersenne was preoccupied with arguing against the radical, Pyrrhonian skepticism that Michel de Montaigne had popularized, which he regarded as a serious threat to religion and society. His "refutation," summed up in La vérité des sciences contre les sceptiques ou pyrrhoniens (The Truth of the Sciences ; [1625]), conceded to the skeptic that we cannot have certain knowledge of the essences of physical things, but insisted that we can have certain knowledge in mathematics (including such applied mathematical disciplines as geometrical optics). He also argued that sense experience provided the basis for knowledge of the physical world, so long as it claimed to be no more than knowledge of appearances, not of the essences of things. If Descartes was not familiar with the Pyrrhonian skeptical challenge before his association with Mersenne in the 1620s, he must have been aware of it by then.

Life in Libertine Paris (1625–1628)

When Descartes returned to Paris in 1625, he encountered a contentious intellectual scene. Not only were men like Mersenne concerned about the threat of Pyrrhonism, but Paris had just seen the trial of Théophile de Viau, a protestant poet whose writings contained suggestions of Lucretian atomism, a celebration of sensuality, and an advocacy of free thought. Only a few years earlier Giulio Cesare Vanini had been burned in Toulouse for spreading doctrines alleged to be materialistic. The "libertines," as these and other freethinkers were called, were accused of holding scandalous religious opinions and of leading a debauched, hedonistic way of life—the natural consequence of their denial of (or skepticism about) the afterlife. One of Mersenne's projects in this period was a lengthy attack on religious unorthodoxy, L'impiété des déistes, athées et libertins de ce temps (The Impiety of the Deists, Atheists, and Libertines of Our Time [1624]). Using, no doubt, a very generous criterion for atheism, Mersenne estimated that in Paris alone there were then at least 50,000 atheists (the population of the whole city at the time was only about 300,000).

Whether or not the threat was as grave as Mersenne claimed, it provoked a response that sought to repress any kind of unorthodoxy. In 1624 three men attempted to hold a public debate in which they would have challenged various theses in Aristotelian natural philosophy. There was apparently considerable public interest in the proposed debate, for it is said to have attracted a crowd of eight or nine hundred people. But the Theology Faculty at the Sorbonne prevented it from occurring. The men were banished from Paris on pain of death; the parliament prohibited anyone from holding or teaching theses "contrary to the ancient approved authors, and from holding any public debate other than those approved by the doctors of the Theology Faculty" (Gaukroger 1995, p. 136). The penalty for violating this edict would be death.

Descartes does not seem, at this stage of his life, to have engaged in these culture wars. His main preoccupations, apparently, were with solving problems in geometrical optics and resuming work on the Regulae. Sometime during these Paris years he evidently discovered the law of refraction known as Snell's law: When light passes from one medium to another, the sine of the angle of incidence is proportional to the sine of the angle of refraction. (Though Willebrord Snell discovered this law before Descartes, Descartes's discovery was independent of Snell's.) Knowledge of this law is required to solve a practical problem in optics, that of finding the anaclastic curve, the shape that the surface of a lens must have to collect parallel rays of light into a single focus. This knowledge was necessary to design a telescope that would provide a clearer image than existing telescopes did. When Descartes was doing this work, the telescope was a recent invention, dating back only to his years at La Flèche. Descartes was quite excited about the potential of the new scientific instrument for extending our knowledge of nature.

In his treatise on Optics, published in 1637 with Discourse on Method, Descartes tried to explain Snell's law micromechanically, in terms of the tendencies to motion of the particles involved in the transmission of light rays and the laws of motion, which he held applied to tendencies to motion as well as to motions. He also proposed a solution to the problem of the anaclastic curve: that the lenses should have a hyperbolic shape. His new studies in optics also had an impact on his revision of the Regulae, providing him with an example of the use of the method that extended its range from mathematics to physics.

The Later Regulae (1626–1628)

According to our best current theory of the composition of the Regulae, one change that Descartes made when he returned to this work was to add two examples of the method to Rule Eight in a passage now generally designated as "Rule Eight-C" (Adam and Tannery X, p. 393–396).

The first example deals with the problem of determining the anaclastic curve. Earlier rules prescribed that we gradually reduce complex and obscure propositions to simpler ones, till we reach an intuition of the simplest propositions, from which we can then retrace our steps till we achieve intuitive knowledge of the proposition we originally wished to know. Someone who follows this advice is supposed to see, first, that determining the anaclastic line depends on determining the relation between the angles of refraction and the angles of incidence. He will not be able to determine that relation by conjecture or by appeal to experience or by learning it from the philosophers. But he will make progress if he realizes that the relation depends on the change made in the angles by the difference of the media, and that this change depends on how a ray of light penetrates a transparent medium. Knowing how it penetrates that medium requires knowing the nature of light. Understanding light requires, finally, knowledge of what a natural power is in general.

In this passage Descartes did not say what a natural power is. Here he limited himself to claiming that because this is "the most absolute thing in the whole series," the most basic item in the investigation, which does not depend on anything more fundamental, it is something we will be able to grasp intuitively. Once we have done that, we will be able to retrace our steps—using our understanding of natural powers to understand the nature of light, our understanding of light to understand how it penetrates transparent media, and our understanding of light penetration to understand how a change in the medium changes the path of a light ray—until we are finally able to answer the question about the anaclastic curve. Elsewhere in the Regulae (Adam and Tannery X, p. 402), Descartes suggests that understanding the concept of a natural power requires reflection on the local motion of bodies—the idea apparently being that bodies always act on one another by transmitting motion from one body to another through contact.

The frequent talk of intuition and deduction in the Regulae is apt to suggest—what many people are inclined to believe on other grounds anyway—that Descartes's scientific methodology is wholly a priori. But this is not true, even in the Regulae. Although Descartes says in Rule Eight-C that we cannot determine by experience the relation of the angle of refraction to the angle of incidence, the reason seems to have been that the question is too complex to be resolved by an appeal to experience. "We can have certain experiential knowledge," he said, "only of things completely simple and absolute." We might infer that we derive from experience our intuition of what in this case is most simple—of what a natural power is, of how bodies naturally act on one another in cases where this action is immediately intelligible.

When Descartes was developing his theory of light in the Optics, he frequently used analogies from experience. The transmission of light from a luminous body to the object of illumination is like the transmission of resistance through a blind man's cane from the object in his path to his hand. The reflection of light from a shiny surface is like the motion of a tennis ball when it bounces off an impermeable surface. Refraction is like the motion of a tennis ball when it encounters a permeable surface. Not everything we observe is as immediately intelligible as these analogical cases are. The movement of iron filings subjected to the power of a magnet is mysterious. But it's part of Descartes's scientific program to try to understand such phenomena by reducing them to others that are readily intelligible. Insofar as Descartes appeals to common experience in support of these intuitions, his method in the sciences is not wholly a priori.

The other example that Descartes added when he returned to Rule Eight he describes as "the most notable of all." Everyone who loves truth in the slightest degree, he said, should, set himself, once in his life (semel in vita ), the task of determining what truths human reason is capable of knowing and what questions are beyond our cognitive powers. This will prevent him from always being uncertain about what the mind can do and save him from wasting time on matters our faculties are not capable of dealing with. Someone who undertakes this task will discover that nothing can be known prior to the intellect, since knowledge of all other things depends on it, and it does not depend on knowledge of them. But though Descartes asserted the priority of the pure intellect, he also acknowledged that we have other instruments of knowledge in addition to the intellect. In Rule Eight-C Descartes said that there are two such instruments: the imagination and the senses. In the text that follows (from Adam and Tannery X, p. 396, 26, to the end of Rule Eight, commonly dubbed "Rule Eight-D" and apparently a rewrite of Eight-C), he added a third instrument: memory.

What is most striking about this passage is its difference from well-known later texts to which it is in other respects quite similar. Three times in Rule Eight (once in Eight-C, twice in Eight-D) Descartes used the phrase "semel in vita" to refer to a project that everyone who wants to use his cognitive powers well should undertake once in his life. Each time he describes the project, with minor variations, in Lockean terms, as one which requires us to determine the limits of the human understanding. Descartes used the same phrase, "semel in vita," in the opening sentence of the First Meditation, also to refer to a project one should undertake once in one's life. But in the Meditations the project involves, not determining the limits of the human understanding, but overthrowing all the opinions he has haphazardly acquired over the years, so he can start anew, from firm foundations. Three years later, in Principles of Philosophy, he used the same phrase, "semel in vita," to again call all seekers after truth to the same overthrow of any past opinion in which they find even the smallest suspicion of uncertainty. As Descartes develops this project in the Meditations, it becomes clear that among the opinions to be rejected, at least provisionally, are those involving even the simplest truths of mathematics, which in the Regulae were paradigms of certainty. The call to radical doubt, undertaken in the hope of achieving absolute certainty—the most characteristic feature of Descartes's published works—is nowhere present in the Regulae.

Seeking Solitude in the Netherlands (1629–1633)

Toward the end of the Paris years Descartes attended a meeting that was to become the second major turning point in his life. The meeting, attended by many of Paris's leading intellectuals, occurred at the palace of the papal nuncio. The speaker was a chemist/alchemist named Chandoux, who attacked Aristotelian natural philosophy as an inadequate basis for chemistry and apparently proposed a mechanistic approach in its place. Contrary to what we might have expected from the ban on criticisms of Aristotle in 1624, most of those present, who included Mersenne and Cardinal Pierre de Bérulle, received Chandoux's speech well. Descartes did not.

Bérulle noticed that Descartes did not share the group's enthusiasm and asked why. After politely trying to excuse himself from saying what he thought, Descartes gave an extended critique of Chandoux, praising his desire to rescue philosophy from "the perplexity of the schoolmen" (Baillet, p. 69), but faulting him for replacing it with something merely probable. If merely probable arguments are allowed, he contended, it is easy to make the false appear true and the true false. He then challenged the company to give him an example of an incontestable truth. When they did, he produced a dozen probable arguments designed to prove its falsity. Then he asked them for an example of an evident falsehood. When they provided one, he showed the falsehood to be credible by another dozen probable arguments. The group then asked him whether there was any infallible way of avoiding sophisms. He replied that he knew of no more certain way than to use the method he commonly followed, which was derived from mathematics, and which he thought sufficient to provide a clear demonstration of all truths.

Descartes's dialectical ingenuity made a deep impression on his audience, especially Cardinal Bérulle, who asked to see him privately. When they met later, Descartes claimed that if he continued his inquiries, the benefits to the public would be considerable. He could achieve results in medicine that would greatly improve people's health and results in mechanics that would greatly lessen people's labor. Bérulle replied that since God had given Descartes this extraordinary talent, he owed it to God and his fellow men to make full use of it. Descartes had been thinking about leaving Paris for some time. This conversation tipped the balance. He resolved to take up residence in the Netherlands, where he would find a more congenial climate and, more important, the solitude that would allow him to meditate without constant interruptions by his friends.

There is nothing up to this point to indicate that Descartes had entertained radical skepticism as a serious possibility. He must have been aware of the debates about Pyrrhonism and of some of the Pyrrhonist literature. But Baillet's account of the Chandoux episode and Descartes's own description of the event in 1631 both suggest a Descartes whose epistemology is very like that of the Regulae : dismissive of scholastic philosophy and of any reliance on probable arguments, confident of the certainty of mathematics and of the method he had modeled on his discoveries in mathematics. In his first years in the Netherlands, Descartes's attitude on these issues changed, it seems.

We know from a letter to Mersenne in November 1630 that soon after Descartes moved there (probably during the winter of 1628–1629), he began what he described as "a little treatise on metaphysics," in which he set out to prove "the existence of God and of our souls when they are separate from the body, from which their immortality follows" (Adam and Tannery I, p. 182). This "little treatise" sounds like an early version of the Meditations. It was evidently not complete at that point, and we do not know much about its specific content, but from an earlier letter to Mersenne (April 15, 1630) it appears that Descartes worked on this treatise for the first nine months that he was in the Netherlands.

In that letter of April 15, Descartes also described what seems to be a different "little treatise," begun more recently. To provide himself with an extra incentive to finish it as soon as possible, he promises to send it to Mersenne by the beginning of 1633. Mersenne will be amazed, he says, that he is taking such a long time to write a treatise so short that it requires only an afternoon to read. This treatise was apparently focused on physics. But Descartes said that he would not have been able to discover the foundations of his physics if he had not approached them by first trying to know God and himself, and that he had discovered how to prove metaphysical truths in a way more evident than the proofs of geometry. This suggests, for the first time, that Descartes was trying to ground physics on metaphysics, specifically on a metaphysics that focuses on a knowledge of God and the self. It also suggests, for the first time, that there may be something defective about geometrical proofs, that considered apart from a metaphysical foundation, they may be less certain than the metaphysical proofs Descartes discovered.

Why did Descartes then think geometrical proofs might need a metaphysical foundation? The letter of April 15 contains a possible clue. For the first time Descartes stated a doctrine for which he was to become notorious: the creation of the eternal truths. He wrote to Mersenne that in his treatise on physics he would discuss several metaphysical topics; in particular, he would defend the view that the eternal truths of mathematics have been established by God just as a king establishes laws in his kingdom, that they depend entirely on him, no less than does the rest of his creation.

There has been much debate about what this doctrine means and why Descartes held it. But our present concern is its relation to the certainty of mathematics. When Descartes argued, in the First Meditation, that even mathematical truths are subject to doubt, he did not invoke this doctrine that God created them. He simply appealed to the idea of God as an omnipotent being who created him, and who could, if God had chosen, have created him so imperfectly that his cognitive apparatus might lead him astray, even in the things that seem most evident to him. In the correspondence and elsewhere, we can see that Descartes thinks a proper understanding of omnipotence would conclude that it requires the ability to determine what the eternal truths are. But Descartes knows this was an unusual, controversial conception of omnipotence, and he did not deploy it in the First Meditation. In the Discourse, as he was about to justify his skepticism about mathematics, Descartes would write, "I don't know whether I should tell you of the first meditations that I had [in the Netherlands], for they are perhaps too metaphysical and uncommon for everyone's taste."

Since Aquinas, the dominant view among Scholastics was that God has the power to determine, by his will, what contingent truths are true, but that his will does not determine what necessary truths are true. Those truths were supposed to be grounded in God's intellect, in the ideas he has, not in his will. The meditator of the First Meditation approaches the question of what things are subject to doubt from the perspective of someone just beginning to philosophize, who presumably holds conventional views about what God's omnipotence implies. Moreover, the ability to interfere with his creatures' cognitive faculties would not seem to require God to have the power to create eternal truths. Surely, anyone with enough power to create the world of contingent beings must have the power to make one species of contingent being defective in its perception of necessary truths.

Skeptics nevertheless suggested that God's power might extend to eternal truths and used that thought to ground a doubt about mathematics and any other truths we might think necessary. In his Apology for Raymond Sebond, one of Montaigne's arguments for Pyrrhonian skepticism involves the claim that because God's power is incomprehensibly great, we speak irreverently if we say that there is something he cannot do. Among the things that Montaigne suggested it would be impious to say God cannot do are to make two times ten not equal twenty, to go back on his word, to cause a man who has lived not to have lived. Montaigne did not say that God created the eternal truths. But he did say it is arrogance on man's part to claim that God cannot render false the truths commonly classed as eternal. This category includes not only simple mathematical truths, but also metaphysical truths (such as "The past is immutable" and "Nothing is made of nothing") and moral truths (such as "A perfect being would not go back on his word"). And he uses these accusations of irreverence and arrogance to justify his claim that we ought to suspend judgment about everything, including these supposedly incontestable truths.

Descartes agreed with Montaigne that we do not do justice to God's power if we say that there is something God cannot do. "We can assert that God can do everything within our grasp, but not that he cannot do what is beyond our grasp" (Adam and Tannery I, p. 146). To say that God's power is limited to what we can comprehend would be rash and disrespectful. Descartes did not want to say that God can render the eternal truths false. They are immutable. But they are immutable because God's will is immutable. So by the spring of 1630 Descartes thought there was a need to ground physics (including the truths of mathematics) in metaphysics, and his perception of this need was connected with his view that God's power is incomprehensibly great. He thought that he had a way to accomplish this grounding, and he began, but did not complete, a draft of a treatise on metaphysics like the Meditations that would accomplish that.

The World (1629–1633)

Descartes never did publish the treatise on physics he referred to in his correspondence as "The World " (or "my World "), but he used material from it in his Optics (1637) and Meteorology (1637) and Principles of Philosophy (1644). And portions of the work appeared after his death: one under the title Le monde, ou Traité de la lumière (The World, or Treatise on Light [1664/1979]), which reproduced the beginning of the treatise, another titled Traité de Homme (Treatise of Man [1662/1972]), which reproduced a later part of it. Here the entire physical treatise, as projected in the early 1630s, will be referred to as The World, and the title Treatise on Light will refer to the opening portion published in 1664.

The World originated in Descartes's concern with the problem of explaining parhelia, the bright spots that sometimes appear in a solar halo, caused by the refraction of sunlight through ice crystals in the atmosphere. In the summer of 1629 a friend had shown him a description of this phenomenon and asked him what he thought of it. Descartes set aside work on his treatise on metaphysics to see what he could make of it:

My mind is not so strong that I can devote it to many tasks at once, and as I never make any discoveries except through a long train of diverse considerations, I must devote myself wholly to a subject when I wish to investigate some particular aspect of it" (Adam and Tannery I, p. 22–23).

His curiosity about parhelia led him first to inquire into meteorological phenomena in general (including the rainbow, another effect of refraction in the atmosphere) and then to the incredibly ambitious project of explaining "all the phenomena of nature, that is, the whole of physics."

The Treatise on Light begins by arguing that there can be a difference between the visual sensation we have of something and what there is in the object that produces this sensation. The common view, he claimed, is that our ideas are completely like the objects from which they proceed. But there are many experiences which should cast doubt on this. For example, in the case of sound, most philosophers think that the cause of our auditory sensations is a vibration in the air, which does not resemble those auditory sensations at all. Descartes proposed that something similar is true of light.

The first step in discovering the nature of light is to identify the bodies that we know produce light. These seem to be the stars and fire. Because the stars are too remote to be easily observable, Descartes concentrated on fire. When we watch fire burning a piece of wood, we observe that it sets the minute parts of the wood in motion and separates them from one another. It transforms the smallest particles into fire, air, and smoke, and leaves the grosser particles as ash. Scholastic philosophers might have supposed that in addition to these mechanical processes, there is a form of fire or a quality of heat involved. But Descartes (applying Ockham's razor) limited himself to what he saw as necessarily part of the process and did not postulate anything unnecessary to explain the phenomena. Since it is inconceivable that one body should move another except through its own motion, Descartes inferred that the body of the flame is composed of particles so small as not to be observable but moving so rapidly that, in spite of their small size, the force with which they act on the wood is great enough to disperse its particles. The motions of the flame particles cause both the light the flame produces and its heat, depending on which sense organs they encounter. But in neither case is there any resemblance between the cause and the idea.

Descartes observed that there is nothing anywhere in nature that is not changing. He suggested that the changes involved in combustion are not unusual: In many cases the cause of observable changes will lie in the motions of unobservable particles. The principle at the core of the mechanical philosophy is that all physical change is reducible to change of place in bodies, if not in bodies large enough to be observable, then in bodies so small as to be unobservable. The fundamental differences among bodies are in the size, shape, and motion of their constituent particles.

Descartes distinguished three elements, which he called "fire," "air," and "earth." These are not to be identified with the elements traditionally so-called or with the familiar substances commonly so called. Fire is a very subtle liquid, made up of the smallest, fastest moving particles, which have no determinate size or shape. This permits them to fill the gaps between the particles of the other elements and makes it unnecessary to allow for the existence of a void. Air too is a subtle liquid. Its particles are small and fast-moving compared with those of earth, but large and slow-moving compared with those of fire. They have a determinate size and shape; almost all of them are round. The particles of earth are the largest and have little or no movement. Descartes emphasized that he did not attribute the traditional qualities of heat and cold, moisture and dryness, to his elements. He took those qualities to require explanation themselves, by appeal to the size, shape, and motion of bodies or their constituent particles.

Having explained the basic elements of his physics, Descartes then asked us to imagine that God has created, somewhere in space, a new world, made only of such matter, and has distinguished the different bodies in this world from one another only by the different motions he has given to the different parts of its matter. There is no order in the initial state of this imaginary world. Descartes's project was to show how a world like ours could emerge from this chaos, given only the laws of nature that God established when he created this world. (Genesis, of course, tells us how the world we are familiar with was created. Descartes professed to be interested only in exploring other ways God could have done it.)

The language Descartes used here—that God established the laws of nature—is reminiscent of the language he used in his letter to Mersenne, where he said that God established the eternal truths (referred to as "laws in nature") as a king establishes laws in his kingdom. The comparison to a king suggests that there is something arbitrary about this act and may also suggest that the laws are subject to change. Descartes wanted the suggestion of arbitrariness, but he did not want the suggestion of mutability. Writing to Mersenne in 1630, he anticipated an objection that Mersenne might encounter when he publicized Descartes's view (as Descartes encouraged him to do):

They will tell you that if God had established these truths, he could change them, as a king makes his laws. To which one must reply: Yes, if his will can change.—'But I understand them as eternal and immutable.'—And I make the same judgment about God" (Adam and Tannery I, p. 145–146).

In the correspondence of 1630, Descartes invoked the immutability of God's will to explain the immutability of the eternal truths. In The World he used it to give content to the laws of nature.

God, "as everyone must know," is immutable. (Presumably, this could have been established by an argument from God's perfection in the 1629 treatise on metaphysics.) This entails that he always acts in the same way. This, in turn, entails that he continues to preserve the objects he created in the same way he created them. That does not mean that things do not change. On the contrary, since God endowed some of these things with motion when he created them, it means that he preserves that motion. This fact, combined with the absence of a void, entails that when beginning to move, bodies also begin to change and diversify their movements through their encounters with other bodies.

Descartes claimed to derive three principal laws of nature from God's immutability: (1) Each part of matter always continues to exist in the same state, so long as encounters with other bodies do not cause it to change. (2) When bodies push against one another, the total quantity of motion is preserved (one body cannot increase the motion of another body without losing as much of its own motion as it transfers to the other body). (3) Although the motion of a body is usually in a curved line, it always tends to move in a straight line. Because Descartes denied the existence of a void, he insisted that all motion must be "in some way circular." Since there is no empty space for a body to move into, it can move only by displacing other bodies. Ultimately, each moving body must be part of a chain of moving bodies that forms a closed curve of some sort. Though Descartes deduced these laws from God's immutability, which he presumably knew a priori, he also insisted that they agree well with what we find in experience. Aristotelian physics, he pointed out, assumes that motion will continue only as long as force continues to be applied to the moving object; so it has difficulty accounting for projectile motion.

From these assumptions about the nature of matter and the laws according to which matter moves, Descartes developed a theory about how a world like ours might have evolved from the chaos that he supposed God originally created in the hypothetical new world. Since that world is a plenum, whose parts must displace other parts to move at all, and all motion must be in a closed curve, matter will naturally organize itself into vortices, masses of matter swirling, whirlpool-like, around a center. The element of fire will tend to concentrate at the centers of the vortices, composing the Sun and the stars; the element of earth will tend to form into large clusters, rotating around the centers of their vortices and carried along by particles of the second element. The planets are formed from such clusters, as are the comets. But the planets remain in one vortex, whereas the comets have motions that carry them from one vortex to another. This clearly heliocentric system implies not only that Earth rotates around the Sun, but also that our solar system is only one of many in the universe, each forming around the various stars, which are no longer embedded in a single sphere, as in the Aristotelian-Ptolemaic cosmology.

Descartes went on to offer explanations for the planets' rotations around their axes, the motions of satellites (moons) around their planets, the movement of the tides, weight, and light. The last he interpreted as resulting from the rotation of the Sun and the matter around it. This generates a radial pressure, which spreads outward from the Sun along straight lines from its center. He enumerated a dozen properties of light that he claimed this theory can account for: that it is propagated from all sides of the luminous body, to any distance, instantaneously, normally in a straight line, but subject to reflection when it encounters a body it cannot penetrate, and subject to refraction when it encounters a medium it can penetrate, and so on. The treatise as it has come down to us does not explain reflection and refraction but instead refers us to his Optics, published in 1637. In another work, Meteorology (1637), Descartes offered explanations of rainbows and of parhelia.

The work commonly known as the Treatise of Man was to have been part of The World, though it appears that it would not have come immediately after the Treatise on Light. We do not know how many intervening chapters are missing, but we can have a fair idea of their intended contents from the description of The World in Part Five of the Discourse. Among the topics covered would have been the formation of mountains, seas, springs, and rivers on Earth; the formation of metals in the earth and plants in the fields; and the nature of fire and its various properties, such as its ability to form glass from the ashes of the material it has burned.

The Treatise of Man was to have included accounts of both the body and the soul, though only the chapters dealing with the body survive. These chapters begin by asking us to imagine that God created a statue or machine made of earth (the element), which he intended to make as much as possible like us. Just as the Treatise on Light tries to show that God could have produced a world that would look just like ours, using only the materials and mechanisms Descartes described, so the Treatise of Man tries to show that God could have produced machines that would have looked and behaved just like the human body, using only such means. Though an exception would be the functions that Descartes thinks need to be attributed to the rational soul, notably the intelligent use of language, he claimed to give a mechanistic explanation of all the animal functions that Aristotelian philosophy attributed to vegetative and sensitive souls: the digestion of food; the beating of the heart; the nourishment and growth of members; waking and sleeping; the reception of light, sounds, smells, heat, and so on, by the sense organs; the transmission of ideas of these qualities to the brain; the retention of these ideas in memory; the internal movements of the appetites and passions; and the external movements of the limbs (insofar as their explanation does not depend on the actions of the soul).

We cannot go into these explanations here, but two points about them deserve notice. First, we know from his correspondence that Descartes spent a lot of time during these years dissecting animals to learn anatomy. However much works like the Regulae encourage the picture of Descartes as a purely a priori scientist, and however much justice there may be in that picture, it is clear that in practice Descartes believed it was necessary for scientists to do a great deal of data collection. When Mersenne wrote saying that he knew people so dedicated to advancing the sciences that they were willing to make all kinds of experiments at their own expense, Descartes replied,

It would be very useful if some such person were to write the history of celestial phenomena, according to the Baconian method, describing exactly for us the present appearance of the heavens, without any explanations or hypotheses, reporting the positions of each fixed star in relation to its neighbors, and their differences in size, color, visibility, brilliance, and so on. He should tell us how far this accords with what ancient astronomers have written about it and what differences there are; for I have no doubt that the stars are constantly changing their relative position somewhat, in spite of being called fixed. (Adam and Tannery I, p. 251–252)

Descartes himself regularly offered hypotheses to explain phenomena. But he knew that a satisfactory explanation of phenomena required good descriptions of the phenomena to be explained and that such descriptions required empirical inquiry. He might also have acknowledged that the necessary empirical inquiries would be guided by intuitions about what the ultimate explanation of the phenomena was likely to be. In this case, his call for a Baconian history seems to be guided by his conviction that the so-called fixed stars are not really fixed.

Second, although it may not be obvious that Descartes's scientific procedure in The World exemplifies his method, we can regard it as an extension of the method described in Rule Eight-C of the Regulae. Reflection on the problem of determining the anaclastic curve had persuaded Descartes that solving that problem would require understanding refraction, which would require understanding the nature of light and its transmission, and ultimately, understanding what a natural power is. In the Regulae Descartes was vague about what a natural power might be, suggesting only that it had something to do with local motion. When he began to write The World, his starting point was a similar problem in optics, explaining parhelia, which he must have realized would also involve understanding refraction. He already believed that understanding refraction required understanding the nature of light, and that understanding light required understanding what a natural power is. He then saw that understanding the concept of a natural power requires a full-fledged theory of the nature of bodies and the laws governing their motion, and that getting this right should enable him to explain all kinds of phenomena, both in the heavens and on Earth.

The Galileo Affair and Its Aftermath (1633–1637)

Descartes never published The World, despite having worked hard on it for years and having achieved results he was very proud of. In 1616 the Church condemned as false and contrary to Scripture the Copernican doctrines that Earth moves and that the Sun is motionless. It prohibited a book by Paolo Foscarini that taught this doctrine, and suspended Nicolaus Copernicus's On the Revolutions of the Heavenly Spheres "until it should be corrected." Also, Cardinal Robert Bellarmine, in a private meeting with Galileo Galilei, ordered him to abandon the Copernican view. Descartes knew that the Copernican view had been censured. He probably did not know about Galileo's meeting with Bellarmine. He seems to have heard rumors that, in spite of the censure, some continued to teach the Copernican view "publicly, even in Rome."

In 1623 a Florentine cardinal friendly to Galileo became Pope Urban VIII. After discussions with the new pope, Galileo got permission to write a treatise on the Copernican system, provided he treat it as a mathematical hypothesis, no more than a convenient predictive device. Galileo apparently decided to test the limits of this permission. He wrote a dialogue in which one participant defended the Copernican theory, another defended the Ptolemaic theory, and a third played the role of uncommitted inquirer. His spokesman in the dialogue does not claim certainty for the Copernican theory. Moreover, he permitted his representative of orthodoxy to have the last word, proclaiming that, however plausible the pro-Copernican arguments might be, we can never know with certainty what the true explanation of the phenomena is. God, in his infinite power and wisdom, might have produced the phenomena in any number of ways. Finally, in the preface he claimed that his work treated the heliocentric theory as "a pure mathematical hypothesis," adopted for astronomical convenience, and that he was writing only to demonstrate that Italians were well aware of the scientific case for Copernicanism, and that the prohibition of 1616 had not been issued in ignorance. After long negotiations with the censors, he secured permission to publish his Dialogue Concerning the Two Chief World Systems in 1632.

But his precautions proved insufficient. It was evident to careful readers that he had crossed the line between hypothetical consideration and advocacy. In the spring of 1633 he was tried by the Inquisition on the charge of "vehement suspicion of heresy." What this language meant, in this case, was that he had presented views contrary to Scripture as if they were probable, but that there was some doubt as to whether he had the evil intention necessary for conviction of formal heresy. Found guilty in June, he was sentenced to house arrest for the rest of his life and required to abjure his errors.

In November 1633 Descartes wrote to Mersenne that he had tried to buy a copy of Galileo's Dialogue, which he heard had been published the year before. But when he looked for it, he learned that it had been confiscated and burned. He was so astonished, he said, "that I almost decided to burn all my papers, or at least, to let no one see them. For I could not imagine that he, who is an Italian, and even (as I hear) favored by the Pope … could have been made a criminal simply because he wanted (as doubtless he did) to establish the movement of the earth" (Adam and Tannery I, p. 270–271). The doctrine of the Earth's movement, Descartes writes, is so connected with the other parts of his own World that he could not detach it without making the remainder very unsatisfactory. If that doctrine is false, "all the foundations of my philosophy are, too, for they demonstrate it quite evidently." When he learned several months later that Galileo had been condemned "even though he pretended that he proposed [the Copernican system] only hypothetically" (Adam and Tannery I, p. 270–271) he was especially concerned, since he had adopted a similar device himself, representing himself as merely telling a story about how God could have created a world like ours, while conceding that Genesis tells us how he did create it.

It is not clear what stage The World was in at this time. Descartes said that he had been on the point of sending it to Mersenne as a New Year's present, if it could be copied in time. Perhaps it was nearer completion than the surviving parts would suggest. For a while Descartes held out hope that there may be a way to publish it. Perhaps this action of the Inquisition had not yet been ratified by the pope or by a Church council. If so, it may not have the full authority of the Church behind it. But eventually Descartes decided to abandon his treatise for the time being and adopt a different plan. He decided to publish a semiautobiographical treatise on method, to be supplemented by three short treatises demonstrating the power of his method: Optics, Meteorology, and Geometry.

The Discourse on Method and its Essays (1637)

At age forty-one, with only thirteen more years to live, Descartes published his first works. Thus began the public career that would earn him a reputation as the father of modern philosophy. As we have noted, Descartes's Discourse on the Method of Conducting One's Reason Well and Searching for Truth in the Sciences is partly autobiographical, but it is not very reliable in this regard, for it omits important events (such as his relation with Beeckman, his three dreams, and his encounter with Chandoux); it projects into the past ideas that Descartes probably had only at a later date (such as the idea of overturning all his past opinions to reconstruct his beliefs on firmer foundations); and it is silent on ideas that Descartes feared might cause his readers to raise objections he did not want to deal with (such as the creation of the eternal truths). Descartes himself warned us not to take his work too seriously as autobiography when he wrote that he was presenting it "only as a history, or, if you prefer, a fable." Descartes wanted us to read his work for its moral, for examples of conduct to imitate or avoid. But he also cautioned us that both fables and history have their dangers: Fables may make us think that something is possible when it is not, and even the most accurate histories, because of their selectivity, may make us conceive plans beyond our powers.

Examples of conduct to imitate would be examples of how to conduct our reason when we seek truth in the sciences. Descartes offered four rules that he said he found sufficient in this search:

1) never accept anything as true which he did not know evidently to be true, including nothing in his judgments except what has presented itself so clearly and distinctly to his mind that he had no reason to doubt it;

2) divide the difficulties he was examining into as many parts as possible;

3) conduct his thoughts in an orderly way, beginning with the simplest objects, and ascending gradually to the most complex; and

4) make enumerations so complete and reviews so comprehensive that he was sure he had not left anything out. (Adam and Tannery VI, p. 18–19)

Presented thus baldly, these rules probably do not give enough direction to be very useful. And in a letter to Mersenne in February 1637, Descartes disclaimed any intention to teach his method in the Discourse. His purpose there was only to talk about it, and his purpose in the scientific essays that accompanied the Discourse was to show what could be accomplished through its use. Even the essays do not, for the most part, purport to show the method at work. As Descartes explained in a letter to Antoine Vatier in February 1638, "I could not show the use of this method in [the three scientific treatises] because it prescribes an order for investigating things which is rather different from the one I thought I had to use to explain them" (Adam and Tannery I, p. 559). But Descartes made one exception to this generalization. He told Vatier he had given a sample of the method in his discussion of rainbows in the eighth chapter of Meteorology.

In that chapter Descartes began by noting that rainbows occur not only in the sky but also in the air near us, whenever there are many drops of water in the air illuminated by the Sun. We know this from our experience with fountains. He inferred from this that the rainbow arises only from the way light rays interact with drops of water, and from there move toward our eyes. Previously in the Meteorology he had shown that these drops are round; he also knew, presumably from experience, that the occurrence of a rainbow is independent of the size of the drops. These reflections suggested an experiment that enabled him to examine the phenomenon close up, in circumstances he could control.

He filled a large, round flask with water and positioned it so that the Sun was coming from behind him as he faced it. Then he situated himself in relation to the flask so that he observed a bright red spot at its bottom. He discovered that a line drawn from his eye to the bottom of the flask made about a 42-degree angle with a line drawn from the Sun to the flask's bottom. Furthermore, no matter how he moved—nearer to the flask or further away, to the right or to the left, even if he made the flask revolve around his head—he always saw a red spot at the bottom, so long as the angle between his line of vision and the line of the Sun's rays remained about 42 degrees. If he increased the angle, the red disappeared. If he decreased it slightly, the spot did not cease to be colored, but divided into two less brilliant parts of different colors (yellow, blue, etc.). From this he inferred that if all the air in that direction were filled with such round drops of water, a red spot would appear in each drop where the angle between the Sun's rays and the line of vision was about 42 degrees, producing a continuous circle of red spots. Similar circles of other colors would be generated in drops that were at slightly more acute angles.

Through further experiments with the flask, Descartes discovered that the red spot did not disappear when the light source was blocked, so long as light was permitted to enter at the top of the flask and leave at the bottom, and so long as certain paths within the flask were not blocked. He inferred that the appearance of red at the bottom was caused by refraction of the Sun's rays as they enter at the top of the flask, their reflection from a point at the back of the flask, and their refraction again at the bottom of the flask as they leave it to move toward the eye. He proposed a similar explanation for the production of the secondary bow, which appeared at an angle of about 52 degrees and had its colors arranged in reverse order. This, he inferred, arises from a combination of two refractions and two reflections.

So far the phenomena Descartes was trying to account for depended essentially on the refractive index of water in relation to air, a figure that he could calculate accurately. And so far his explanation of the phenomena was basically right. But he still had not explained what he called the principal difficulty: Why do only those rays refracted at a certain angle cause certain colors to appear? To resolve this difficulty, he undertook a series of experiments with a prism, a similar object also known to produce a spectrum of colors. The prism differed in various ways from his flask, and these differences enabled him to eliminate as irrelevant certain features of the flask. To produce a spectrum of colors, it is not necessary that the medium through which the light passes have a curved surface, or that the light strike that medium at a particular angle, or that it be reflected, or that it be refracted more than once. But it is necessary that the light be refracted at least once.

At this point Descartes invoked his theory of the nature of light, that it is the action or movement of particles of air (the element), which must be imagined as little balls. These balls have two motions, one in the direction of their propagation, the other rotational. Different degrees of rotational motion produce different color sensations when they strike the eye. The differences in the colors produced when light is refracted arise from the fact that the refractive process imparts different degrees of rotational motion to the light particles. (For further details, see Gaukroger 1995, chap. 6.)

This part of Descartes's explanation has not fared well. But the example remains interesting in a number of respects. First, it illustrates Descartes's second and third rules: dividing a complex problem into as many parts as possible till you reach something simple and easy to understand, and then retracing your steps back to the complex phenomenon you were originally interested in. The complex phenomenon is the rainbow. The simple object is the individual drop of water seen to have one of the colors of the rainbow. By using a model of the simple object, which we can observe close up and manipulate, we can determine the conditions for its being seen as having the color it has, and we can determine how changing those conditions might produce different colors (or no colors at all). We then reconstruct the complex phenomenon from the simple model by recognizing that if we observed a mass of such simple objects in the sky, the ones observed at the right angle for producing a particular color would form a continuous circle of that color, and that other concentric circles of different colors would also be produced at different angles.

But this example also warns us that if we use the concepts of intuition and deduction to analyze our solution of this problem, we need to understand those concepts very broadly. Our understanding of how the simple objects behave involves a priori elements, insofar as we make use of geometry to deal with certain aspects of the problem (such as the shape of the bow). But it also involves numerous appeals to experience. It is by careful experiment that we determine that the same color is produced so long as the same angle is preserved, or that a double refraction, combined with reflection, is involved in producing the primary bow, or that the refractive index of water in relation to air has the particular value it has. Our ordinary experience of fountains initially suggests a way of breaking the complex phenomenon down into simple elements. Experience is also involved, no doubt, in the theory of matter that Descartes's theory of light invokes. There is no a priori reason why there must be exactly three elements, having the properties that Descartes assumed they have. A priori considerations of simplicity and intelligibility speak for this theory when it is compared with the scholastic forms and qualities. But those considerations would not be sufficient to warrant acceptance of the theory if it were not capable of explaining a wide range of phenomena, as Descartes clearly thought it is.

The rules of the Discourse, then, are quite similar to the rules of the Regulae, provided that we interpret the concepts of the Regulae freely. But one notable feature of the Discourse is the absence of any explicit discussion of intuition and deduction. The ghosts of these concepts are present in the first rule, insofar as Descartes advises us to never accept as true anything we don't know to be evidently true, making no judgments except those that present themselves so clearly and distinctly to our minds that we have no reason to doubt them. This excludes reliance on merely probable assumptions. But it does not explicitly mention intuition or deduction. And it suggests a problem we have so far not considered, because so far it has not seemed to arise in the writings we have considered.

Throughout his work Descartes was clearly a foundationalist, at least in the minimal sense that he thought some of our beliefs are based on other beliefs we have, whereas some are not based on others. We can call the ones not based on others basic beliefs. Our basic beliefs provide the foundations for our system of beliefs; our derivative beliefs, the superstructure. This metaphor of our system of beliefs as like a building, which has foundations and a superstructure and might collapse if the foundations are not solid, is prominent in the Discourse and in the Meditations, but is only implicit in the Regulae, where Descartes presents arithmetic and geometry as the only genuine sciences yet discovered, superior to all other alleged sciences because of the certainty of their initial assumptions and the care with which mathematicians derive from those assumptions only conclusions clearly seen to follow from them.

But the Regulae does not have a criterion for distinguishing the absolutely certain from the merely probable. It assumes that mathematics is more certain than the other sciences because it is concerned with objects so pure and simple that it need make no assumptions that experience has rendered uncertain. At that point, that is all that Descartes thought it necessary to say to justify reliance on the assumptions of mathematics. But in the Discourse (and the Meditations ), he is concerned with a problem his earlier work had not considered. It is not the problem of the creation of the eternal truths, but a different skeptical problem.

We are not born with fully mature cognitive faculties. Rather our faculties develop gradually as we grow to adulthood. While they are developing, we accept, uncritically, many propositions from parents, teachers, and others whose authority we have come to respect. Then we learn, sadly, that these are not perfectly reliable sources. The propositions we accepted in this way can seem quite obvious. Nevertheless, they lack a firm foundation, and we can be mistaken about them, even when they seem most obvious. This reflection gives us a reason, not only for doubting the specific propositions we have accepted from others and everything based on them, but also for wondering whether our cognitive faculties, our basic capacities for distinguishing truth from falsity, are as reliable as we thought they were.

The Discourse not only identifies this problem; it offers a solution for it. Descartes was not content, in this work, simply to say that the basic beliefs we acquire through intuition are indubitable or evident. He wanted to show that we perceive some propositions so clearly and distinctly that there is no reason to doubt them, even on a generous conception of what might constitute a reason for doubt. So in Part IV of the Discourse he embarked on a project of rejecting as false anything in which he could "imagine the least doubt." This is what is called the method of doubt. He was very permissive in what he counted as a ground of doubt. He was prepared to allow that even "the most extravagant suppositions of the skeptics" provide some ground for doubt. If a belief can survive that permissive a test, we cannot reasonably demand anything more certain as a foundation for our beliefs. If we are to doubt, we must have some reason to doubt. But if we want what survives our attempt to doubt to be absolutely certain, we must be thorough about the attempt; we must allow even the most improbable possibilities to count as reasons for doubt.

This might seem to be a quixotic quest if Descartes had not apparently discovered something that resists his attempts to doubt it: that he, who is engaged in this methodical doubt, and thus is thinking, exists. So we encounter what is commonly referred to as "Descartes's cogito," a label deriving from the Latin version ("Cogito, ergo, sum ") of an inference that appears in the Discourse in French: "Je pense, donc, je suis " ("I think; therefore, I exist").

Though there is something very compelling about that inference, it is not clear exactly what Descartes was claiming as his initial certainty. In the Regulae he had cited both "I think" and "I exist" as truths known certainly by intuition; if that's their status, then either proposition might be a suitable foundation for demonstrations. In the Discourse he seems to be inferring his existence from his thought, as if he can be certain of his existence because he can be certain that he thinks—and, moreover, certain that to think, it is necessary to exist (Adam and Tannery VI, p. 32–33). This suggests that his affirmation of his existence is the conclusion of the following demonstration:

(1) To think, it is necessary to exist.

(2) I think.

(3) Therefore, I exist.

This way of thinking about the cogito naturally raises the question of how Descartes can be certain of the premises of this demonstration. The Discourse does not explicitly ask that question, but it does have what looks like an answer to it, as far as the first premise is concerned, where Descartes says that he sees very clearly that (1) is true. Though the Discourse has not offered any theory of intuition, this looks like an appeal to intuition, a faculty whose reliability we might have thought was put in doubt when Descartes questioned the certainty of simple mathematical truths.

The Discourse does not even seem to answer the question as it concerns the certainty of the second premise. But in a letter that Descartes wrote to Henri Reneri in 1638, the answer seems to be that when we are thinking, we cannot doubt that we are thinking (Adam and Tannery II, p. 38). This may suggest the following argument for the certainty of (2):

(4) When we think, we cannot doubt that we think.

(5) I am thinking.

(6) Therefore, I cannot doubt that I am thinking.

But though Descartes often seems to accept (4), or propositions equivalent to it, there are times when he seems to reject such claims. Earlier in the Discourse he had written that "many people don't themselves know what they believe; for the act of thought by which one believes a thing being different from the act by which one knows that one believes it, the one often occurs without the other" (Adam and Tannery VI, p. 23). Moreover, the argument consisting of propositions (4) to (6), if offered as a demonstration of the certainty of (2), looks hopelessly question-begging: it assumes the truth (and certainty) of the proposition whose certainty it claims to prove. So the cogito argument of the Discourse, in spite of its fame and wide appeal, is problematic. Fortunately, the argument takes a different, and more attractive, form in the Meditations, as we shall see below.

The remainder of part IV gives a quick sketch of the argument Descartes would develop more fully and accurately in the Meditations. Having found one proposition that he knew to be true and certain, he provisionally formed a general rule: Whatever we conceive very clearly and very distinctly is true. Reflecting on his nature as a doubter, and hence as imperfect, he asked how he could have acquired his ideas of things other than himself. Most of them, he thought, he could have generated himself. But the idea of God is an exception. An imperfect being cannot cause itself to have the idea of a perfect being. So God must be the cause of his idea of God. God, therefore, must exist. To this causal argument he added a version of the ontological argument: If God is a perfect being, as we conceive him to be, then he cannot lack the perfection of existence. Having established the existence of God, he proceeded to argue that because everything real and true in us comes from a perfect being, the general rule he had provisionally adopted is correct: All our clear and distinct ideas must be true. And even those ideas that are not clear and distinct must have some foundation in truth. This account of Descartes's metaphysics raises issues that are best pursued in the discussion below of the Meditations.

Parts V and VI of the Discourse are primarily concerned with Descartes's World, which, he wrote, "certain considerations" prevent him from publishing. He tantalizes us with a summary of its contents, omitting any explicit mention of its Copernicanism, but strongly hinting that the Church's condemnation of Galileo is the reason that he could not publish at that time. He did not mention either the Church or Galileo by name, but what he did say must have left little doubt in the minds of informed readers: "People to whom I defer and who have no less authority over my actions than my reason has over my thoughts have disapproved an opinion in physics, published not long ago by someone else" (Adam and Tannery VI, p. 60). Descartes did not say whether he accepted this opinion, but he did say that before the authorities' censure he had not noticed anything in the work "prejudicial either to religion or to the state," so nothing would have prevented him from publishing this opinion himself if his reason had convinced him it was true. This censure, he said, made him fear that he might have made some mistake in his own theories. And that, combined with a fear of getting involved in time wasting controversies, made him decide not to publish, at least at that time.

Descartes had clearly not given up all hope of publishing The World during his lifetime. He even suggested that he had a duty to publish it: If, as he thought, he was on the path to developing a correct and comprehensive physics, giving an account not only of the heavens, but of all the principal kinds of bodies here on Earth, the potential benefits would be enormous. Such a science would enable us to become "the masters and possessors of nature." It would offer the hope of discovering new ways to maintain our health and prolong our lives. He saw only two obstacles to his achieving this goal: the brevity of life and the lack of observations. Though he presented the foundations of his physics as a priori ("To discover in general the principles or first causes of everything that exists or can exist in the world …, I considered nothing but God alone, who created the world"), he reported that as he proceeded from the first causes, through the first and most ordinary effects deducible from them, to more particular things, he found that the only way he could discover the causes of the particular effects was to construct what Bacon called crucial experiments.

Descartes's principles were so general that there were many ways he could deduce the effects from them. To determine which, among many possible ways to produce the effects, was the one God had chosen, he needed to set up situations where the alternative theories would have different observable consequences. To do that he would need money for research. Part 6 of the Discourse was, among other things, an appeal for money from public-spirited citizens who saw the value of his work and wished to aid him. But the whole project of the Discourse and its essays was also intended to generate such interest in his project that the Church would feel obliged to permit him to publish his World during his lifetime. Failing that, he would publish posthumously.

Other matters in Parts V and VI of the Discourse merit more discussion than they can receive here: Descartes's discoveries regarding the circulation of the blood, which he made independently of William Harvey, and his affirmation that the fundamental laws of nature are necessary truths that must be observed in any world that God might have created. Here we must limit ourselves to noting his provocative doctrine that animals are nothing but machines. In the portions of The World dealing with humankind, Descartes had tried to show that God could have produced machines that would have looked and behaved just as the human body does, using only matter of the kind Cartesian physics allows and the laws that follow from God's nature. Descartes aimed to give a mechanistic explanation of many different animal functions, all the functions, in fact, that humans share with the lower animals. He did not think mechanism could explain all human activities. Some, notably the intelligent use of language, could be explained only by the presence of a rational soul embedded in the machine. We can be certain from their language use, Descartes thought, that the human-looking bodies around us are inhabited by rational souls. (He was not troubled by the problem of other minds.) But nonhuman animals, which do not display intelligent language use, lack a rational soul; they are nothing but complex machines, lacking even sensations of the kind we have.

This doctrine had a strong impact, most of it in ways that Descartes would not have welcomed. Some thought it absurd to draw such a sharp distinction between humans and the rest of the animal kingdom. Some accused the Cartesians of being cruel to animals, or at least of having no good reason not to be. And some argued that Descartes was right about lower animals, but wrong to think that humans are fundamentally different. They too are nothing but very complex machines.

The Start of Controversy (1637–1641)

After publishing the Discourse and its essays in June 1637, Descartes spent the next few years responding to criticisms of his work and, toward the end of the period, preparing to publish his Meditations. The criticism of the 1637 publications tended to focus, not on metaphysics or epistemology, but on his commitment to mechanistic explanations in science: of light, of the circulation of the blood, of animal behavior. In the early part of this period he tried to reassure friends in the Jesuit order that his work does not contain dangerous innovations. He boasted to Vatier (Adam and Tannery I, p. 564) that the faith had never been so strongly supported by human reasons as it was by his, and that transubstantiation, "which the Calvinists criticize as impossible to explain by the ordinary philosophy, is very easily explained by mine." But by 1640, the Jesuit priest Pierre Bourdin's criticism of his Optics had persuaded Descartes that he had to 'go to war with the Jesuits (Adam and Tannery III, p. 752).

By that point Descartes had already begun revising his "little treatise" on metaphysics (the future Meditations on First Philosophy ) and planned to circulate it privately among twenty or thirty theologians before making it public so that he could learn from their criticisms what needed to be corrected or added before publication (Adam and Tannery II, p. 622). Descartes told Mersenne that his book on metaphysics was to contain "all the foundations of my physics," but cautioned him not to tell people that, "for those who favor Aristotle might make more difficulty about approving them. I hope that readers will gradually get used to my principles, and recognize their truth, before they notice that they destroy Aristotle's principles" (January 28, 1641; Adam and Tannery III, p. 298).

Descartes was particularly keen to have the Sorbonne's approval of his work. This may seem out of character, for in the Discourse he said that since God has given each of us some capacity for distinguishing truth from falsity, he felt obliged not to be content with accepting the opinions of others (Adam and Tannery VI, p. 27). Presumably this is an obligation we all have. But experience had persuaded him that he needed the support of the authorities to get people to read his work carefully and to free himself from having to reply to quibbling, malicious critics (Adam and Tannery III, p. 184, 237–238).

When the Meditations first appeared in August 1641, the original plan had changed. Instead of circulating his work first among twenty or thirty theologians to get objections that might lead to changes, Descartes delegated most of the preliminary circulation of the work to Mersenne, who selected a smaller number of critics, not all theologians. Instead of modifying the text in the light of this criticism, Descartes left the text largely untouched, publishing the objections he received and his replies after the main text. Each critic could see the preceding objections and replies in composing his own.

The author of the first set of objections was a Dutch Catholic theologian named Johan van Kater (Johannes Caterus). Mersenne himself is generally credited with having written some or all of the anonymous second and sixth sets of objections. The third, fourth, and fifth sets of objections were written by Thomas Hobbes, Antoine Arnauld, and Pierre Gassendi, respectively. Those were the only objections included in the first edition. When the second edition appeared in 1642, there was an additional set of objections, by Father Bourdin, accompanied by Descartes's irate replies. Descartes was not a man to suffer fools gladly, and he found it easy to believe that his critics were fools. Sometimes he was right.

Meditations on First Philosophy (1641)

The title page of the first edition claims that Descartes was publishing it "with the approval of the learned" and that in his work he would demonstrate both the existence of God and the immortality of the soul. Neither of these claims was true. Though he and Mersenne tried, they were not able to get the approval of the Theology Faculty at the Sorbonne. While Descartes did offer several arguments for the existence of God, he did not even attempt to prove the immortality of the soul. Both these mistakes were corrected on the title page of the second edition, which appeared in the following year. But it is puzzling that they were made in the first place. Some have blamed them on Mersenne, who saw the work through the press. He is supposed to have hastily inferred from the Dedicatory Letter to the Theology Faculty that Descartes intended to prove the immortality of the soul. But in December 1640 Descartes warned Mersenne not to expect a proof of immortality in the Meditations. Descartes thought the most he could prove was that the mind is distinct from the body, not subject to die when the body does. Since God is omnipotent, he can always annihilate the mind (Adam and Tannery III, p. 265–266). The title page of the second edition claimed only a proof that mind and body are really distinct, and it dropped any claim to be approved by the learned.

The Meditations is a work with multiple agendas. No reasonable interpreter doubts that Descartes wanted to establish the religious conclusions announced on the title page of the second edition. But the First Meditation emphasizes a different aim: establishing something firm and lasting in the sciences. It is that project that has preoccupied most English-language students of Descartes and made the Meditations one of the most commonly used texts in modern universities. The project involves more than just validating our reliance on clear and distinct ideas. As Descartes said in a letter to Mersenne (January 28, 1641), he also wanted to accustom people to the foundations of his physics and destroy Aristotelian natural philosophy.

The First Meditation begins by recalling the project of the Discourse : ridding ourselves of all past beliefs. Descartes assumed that if a belief survives a thorough attempt to doubt it, and is permissive in what it counts as a valid ground of doubt, it will qualify as indubitable and provide a proper foundation for reconstructing our system of beliefs. If the fact that a belief is indubitable is to make it a proper foundation for a new system of beliefs, that indubitability cannot be a merely psychological matter. But facts about what we can and cannot believe are relevant to determining what is indubitable. We cannot doubt a belief at will. We must have some reason for doubt. That reason need not be probable enough to make the belief improbable. But if, after a thorough search for some reason, we cannot find even a slight reason for doubt, our inability to doubt the proposition is more than just a psychological fact about us.

How are we to proceed? If we had to question each of our beliefs individually, it would be an endless task to doubt them all. Fortunately, many of our beliefs are based on other beliefs. If we shake the foundation, we shake everything that rests on it. Most, if not all, of our beliefs are based on trust in the senses. Descartes actually said, early in the First Meditation, that all his past beliefs were. But when Frans Burman questioned him about this, he explained that the "I" who speaks to us in the Meditations is a man who is first beginning to philosophize, someone who holds the opinions anyone might hold, if he has not reflected critically on his beliefs. Call this fictional person "the meditator." Descartes does not endorse all the opinions the meditator expresses, any more than the author of a dialogue endorses all the opinions his characters express. Before the First Meditation is over, reflection will lead the meditator to drop this empiricist assumption. but in the beginning, empiricism rules.

The meditator briefly considers common cases of sense deception as a ground of doubt, but dismisses them because they support doubts only about small or distant objects, not a more general doubt about all material objects. More serious, he thinks, are the skeptical implications of dreaming. Each night, when he falls asleep, he dreams. In those dreams he has experiences just as vivid as his most vivid waking experiences. Or at least if there is a difference between his dreams and his most vivid waking experiences, it is not discernible during the dream. Only afterward, when he wakes up, does he realize that he was dreaming. So it is possible, for all he knows, that he is dreaming now, no matter how convincing his present experience seems to be. If this doubt can be raised about any sense experience, no matter how vivid, then no belief based on sense experience can be certain. And if all justified beliefs are based on sense experience, then no belief is certain.

That seems to be the conclusion the meditator reaches during the first stage of his reflections. But the Meditations are a dialogue within the meditator's mind, a dialogue between his skeptical side and his dogmatic side. After reflection it occurs to the meditator that perhaps arithmetic and geometry, those sciences that deal with the simplest and most general objects and care little whether their objects exist in nature, might not be affected by the dream argument. Sense experience is our primary means of knowing what is in nature. But if the mathematical sciences do not require objects actually existing in nature, they may not depend on sense experience. If they do not, they will not be impugned by an argument that shows sense experience to be unreliable. Moreover, it seems impossible that truths so clear should be suspected of falsity.

The meditator then reflects on the implications of a belief he has long held: that there is a God, who can do all things, and who has made him what he is. If there is such a being, it seems he might have created him (the meditator), not only with deceptive perceptions of everything around him (so that he seems to see Earth, a sky, and other extended objects even though there are no such things), but also with mistaken beliefs about even the simplest truths of mathematics—so that it seems evident that two added to three makes five, though this proposition is false. Of course, the meditator also believes that God is supremely good, and that such a being would not want him to be deceived. But the meditator does, after all, make mistakes. Evidently, if the meditator was created by a good God, it is consistent with God's goodness to permit him sometimes to be deceived. Couldn't it be consistent with God's goodness to make him always be deceived? Moreover, dropping the assumption that God created the meditator does not help. The less perfect his cause, the less reason he has to think that his cognitive faculties are not flawed.

The meditator has no answer to these arguments. He concludes that a legitimate doubt can be raised about all his former beliefs and that he has powerful (validas ) and carefully considered (meditatas ) reasons for these doubts. The reasons are powerful not because of their probability, but because of their scope, because they cast doubt on all kinds of beliefs, sense-based or not. The meditator insists that his former beliefs remain highly probable, more reasonable to believe than to deny. Later he will characterize the doubt based on the possibility of a deceiving God as "slight (tenuis ) and … metaphysical." Many critics have asked how Descartes knows that the premises of his skeptical arguments are true. The answer is that he does not, and need not, claim to know that. Since the meditator is seeking absolute certainty, the only epistemic requirement for a legitimate ground of doubt is that the doubt not be one that he has compelling reasons to reject.

In the Second Meditation, having resolved to set aside as false anything that admits even the slightest doubt, Descartes claims to finds his Archimedean point, a proposition that resists all attempts to doubt it, on which he can build his revised system of beliefs. His initial certainty is the existence of the self. But the argument for the certainty of his existence takes a different form than it had in the Discourse. The famous inference—"I think; therefore, I exist"—does not appear. Instead, the cogito paragraph concludes with the words "This proposition, I am, I exist, is necessarily true as often as I utter it or conceive it in my mind" (Adam and Tannery VII, p. 25).

This formulation, combined with the absence of any explicit inference and some obscure remarks Descartes makes in the second set of replies, has led some readers to think Descartes is claiming intuitive certainty for the proposition "I exist." But we must remember that in the Discourse and the Meditations Descartes was writing for readers who had not read the Regulae. In neither the Discourse nor the Meditations does he introduce intuition as a central concept in his epistemology. Moreover, like the Discourse, but unlike the Regulae, the Meditations has raised as yet unresolved doubts about those paradigms of intuitive knowledge, the simplest truths of mathematics.

There is an alternative to seeing the existence of the self as something which, if known at all, must be known either by intuition or by inference from intuitions. As the cogito paragraph opens, the meditator is reviewing his situation. He has rejected the existence of all bodies, but perhaps there is something incorporeal whose existence he cannot doubt. God, perhaps? But God does not yet qualify as an indubitable being; at this stage the meditator thinks he himself might be the cause of his thoughts about God. What about himself? Is his existence so bound up with the existence of his body that he cannot exist without it? No. If he has convinced himself of something (say that there are no bodies), then he must exist, whether bodies exist or not. Perhaps a supremely powerful deceiver is deceiving him about everything (including his own existence). But if the deceiver is deceiving him, then he exists.

The italics here emphasize two cogito -like conditionals that each have an antecedent hypothesizing some thought process that the meditator may be involved in (convincing himself, being deceived by the deceiver) and a consequent affirming his existence. The meditator does not commit to either of the antecedents. The point is that whatever skeptical hypothesis he entertains, and whether he is responsible for his beliefs or the deceiver is, it follows from that hypothesis that he exists. Descartes hit on a way to justify accepting something as a first principle without incurring reasonable accusations of dogmatism: if the truth of a proposition follows from any skeptical hypothesis that could validly be invoked to cast doubt on it, then it's permissible to accept that proposition as certain without other argument, specifically, without having to deduce it from some prior certainty and without having to appeal to an infallible faculty of intuition.

Any valid ground of doubt must entail the existence of the doubter. Although valid doubts need to satisfy only a weak epistemic requirement (that we not have compelling reasons to reject them), there is another condition they must also satisfy: They must explain, conjecturally at least, how the person engaged in the search for truth could be mistaken. But if they do that, they must say something of the form "Perhaps, but you could be mistaken because God is deceiving you, or you are dreaming, or you are yourself the source of this thought, etc." The skeptic, if he is rationally, and not dogmatically, skeptical in his attempt to cast doubt on our beliefs, must argue that there is some reason why things seem to us as they do, even though things are not as they seem. As soon as he does that, he concedes that we are thinking, and hence that we exist.

Descartes used the same procedure when he took up the next problem in the Second Meditation: What is this self whose existence the meditator is now certain of? The meditator starts from the beliefs that he assumes a beginner in philosophy would have and asks which of them, if any, can survive radical doubt. The meditator thinks that he is something that has both a body (something with shape and location, occupying space so as to exclude other bodies, perceptible to the senses, and movable by other bodies that come in contact with it) and a soul (a fine substance, like air or fire, infused throughout the body and responsible for nutrition, motion, sensation, and thinking).

Not many of these prereflective beliefs can survive the hypothesis that some supremely powerful malicious being is deceiving him. The meditator has already rejected, until it can be reestablished on firmer ground, the belief that there are bodies. So the self whose existence he is certain of is apparently not something corporeal, nor can it engage in functions requiring the existence of a body. Nutrition and movement must go. At first it seems that sensation too must go, since sensation apparently presupposes the existence of sense organs. Only thought remains. Just as the existence of the self follows from any hypothesis entertained to cast doubt on it, so (trivially) does its thinking. If Descartes's procedure for identifying indubitable first principles is sound, he could have taken "I think" as a first principle and demonstrated "I exist" from that principle. Perhaps that is why he sometimes gives the appearance of doing that.

To say that the meditator is a thinking being is to attribute a number of different activities to him: that he understands many propositions, affirms some, denies others, and suspends judgment about still others. All this is implicit in the dialogue between his skeptical side and his dogmatic side. And on reflection, even sensation is something whose occurrence he cannot deny. Not having a body, he may not have sense organs, but he cannot deny that it sometimes seems to him as if he were perceiving something through some organ of the body he thought he had. And such seeming is a purely mental occurrence, immune to skeptical doubt. The skeptic assumes it in his attempt to explain why we had the ill-founded beliefs we had about bodies.

Toward the end of the Second Meditation, Descartes indulges in what looks like a digression. Though the meditator has not yet resolved his doubts about the existence of bodies, he says that he will give in to his natural inclination to believe that he knows bodies (which he can imagine and sense) more distinctly than he knows this mysterious self (which he can neither imagine nor sense). So he decides to examine one particular body, a piece of wax, to see what he knows distinctly in that object. He describes its properties: size, shape, color, hardness, temperature, taste, fragrance, etc. Then he takes the wax near a fire and notes the changes it undergoes in these changed circumstances. All its sensible properties change. What was cold becomes warm; what was hard becomes soft; and so on. But the wax, he says, remains (numerically) the same, in spite of its qualitative changes. No one doubts this. He concludes that the wax is not to be identified with any of its changing sensible properties. What he imagines distinctly in the wax is nothing but an extended something, capable of changing its shape, and capable of change in general.

Descartes draws a number of conclusions from this experiment. First, the wax, and bodies in general, are known, not by the senses or the imagination, but by the mind alone. The wax is capable of changing in many more ways than either the meditator's senses or imagination can encompass. Only the mind can grasp the wax. Second, the mind is better known than the body. Whenever the meditator judges, on the basis of sense evidence, that the wax exists, those sensations do not establish the existence of the wax. But they do establish the existence of the thinking being that judges that the wax exists.

What appears here to be a digression, not necessary to establish the main announced conclusions of the Meditations, does serve Descartes's unannounced purpose of insinuating the foundations of his physics. Just as the middle section of the Second Meditation clarified our prereflective concept of the soul, or mind, paring away the inessential to lay bare the essential property of thought, so the concluding section clarifies our prereflective concept of body. After the wax passage we know not to think of the sensible properties of bodies as essential to them. The only first-order property essential to any body is that it is extended. We also know not to think of bodies as inherently perceptible by the senses.

The wax passage serves another nonobvious purpose. It is characteristic of Descartes's method in the Meditations that he does not formally define his central concepts, but lets them emerge in informal ways. One of Descartes's central concepts is that of a clear and distinct idea, which he first mentioned prominently at the beginning of the Third Meditation, where he proposed his criterion of truth: Whatever he perceives clearly and distinctly is true. He did not define "clarity" and "distinctness" until he wrote his Principles of Philosophy (and even then the definitions are not very helpful). But the wax passage gives us a paradigm of what it is to acquire a clear and distinct idea. When the meditator begins to reflect on the wax, his idea of it is imperfect and confused. After he considers more attentively what the wax consists in and eliminates the inessential, his idea is clear and distinct.

The Third Meditation illustrates another way in which the process of acquiring clear and distinct ideas can work. When the meditator introduced the idea of God in the First Meditation, he explained the content of that idea by enumerating several attributes that he took God to have, among them that he created the meditator, that he can do all things, that he is supremely good, and that he is a source of truth. The problem the meditator faced was that he was not sure that all these attributes are united in one being. Perhaps he was created by an omnipotent being who is not supremely good and, far from being a source of truth, is a deceiver.

The idea of God is central to both arguments for the existence of God in the Third Meditation. At the heart of those arguments is the contention that the only possible explanation for the meditator's possessing an idea of God is that God does exist and has implanted an idea of himself in the meditator, much as a craftsman might stamp his mark on his work. But what exactly is the content of that idea? Descartes offers three answers to that question in the Third Meditation. The first two involve lists of divine attributes: God is supreme, eternal, infinite, omniscient, omnipotent, and the creator of all things apart from himself (Adam and Tannery VII, p. 40); God is an infinite substance, independent, supremely intelligent, supremely powerful, and has created the meditator and everything else that exists, if there is anything else (Adam and Tannery VII, p. 45). The French translation of the Meditations, which appeared in 1647, adds immutability to both lists.

These varying lists have several notable features: All three include the idea that God is the creator and that he is omnipotent. The two lists in the Third Meditation both omit the attributes that gave trouble in the First Meditation, that God is supremely good and the source of truth. And the Third Meditation lists both include infinity, an attribute that will play an important part in the arguments for God's existence. But no two lists are identical. This highlights a problem to which the Third Meditation will suggest a solution. We cannot adequately explain the content of the idea of God by listing his attributes. We may know where to begin: with his being the creator and being omnipotent. But we do not know where to stop. If God is absolutely infinite, not only are his individual attributes infinite in themselves, he must have infinitely many of them. No finite mind will be able to list them all. And as we learned in the First Meditation, there may be disagreement about some candidates. If God created the meditator and is omnipotent but the meditator makes mistakes and is imperfect in other ways, is God supremely good and a source of truth?

The solution that the Third Meditation proposes is that God is best understood as a supremely perfect and infinite being (Adam and Tannery VI, p. 46), where this implies that he must have all perfections and only perfections. This formula is a generalization from the various lists of attributes, each of which is a perfection. It is a useful way of summing up those lists, since it covers attributes that may have been omitted, either inadvertently or because of the limitations of the mind compiling the list. But most important, it provides a criterion for deciding what should be on the list and what should not. If an attribute is a perfection, it should be; if it is not, it shouldn't be.

Is there such a perfect being? Descartes first addressed this question in the Third Meditation, mounting two arguments, each starting from the assumption that we have an idea of God of the kind described. In the third set of objections Thomas Hobbes challenged the claim that we have an idea of God. But Descartes replied that Hobbes's challenge depends on confusing ideas with images. Since God is an infinite being, we can, of course, have no image of God. But that does not mean that we cannot have an idea of him. "Whenever I express something in words and understand what I am saying, it is certain, from this very fact, that there is in me an idea of the thing the words signify" (Adam and Tannery VII, p. 160). If a theist affirms, and an atheist denies, the existence of God, and if they both understand what they are saying, they both have an idea of God.

But how can the mere fact that we have an idea of God lead to a proof of his existence? In the Third Meditation the arguments are causal. They depend first on the general causal maxim that there must be at least as much reality in the total efficient cause as there is in the effect (Adam and Tannery VII, p. 40). It was an axiom of ancient philosophy, which Descartes endorsed, that something cannot come from nothing. A stone that previously did not exist cannot now begin to exist unless it is produced by something in which there exists, "either formally or eminently," whatever is in the stone. Descartes never really explained what the quoted qualification means. It's clear that he did not think that the cause needs to have the same properties as the effect. If it did, then God, who is incorporeal, would not be able to create extended objects. It is also clear that if the cause does not have the same properties, it must have properties "of at least equally great perfection." There cannot be heat in an object not previously hot except from something that is "of an order at least as perfect as is the heat" (Adam and Tannery VII, p. 40). That language clearly does not mean that the cause needs to have heat in it. But it is unclear what restriction the language does place on possible causes.

From this general causal maxim the meditator infers a causal principle applying specifically to ideas: The cause of an idea must contain at least as much formal reality as the idea contains objective reality. If we understood what formal reality is, we would understand what objective reality is, since objective reality can be defined in terms of formal reality. Objective reality is a property of ideas as representative entities that is correlated with the formal reality of their objects. An idea that represents its object as possessing a very high degree of formal reality will have more objective reality than one that represents its object as possessing a lower degree of formal reality. To say that an idea has objective reality is not to say that its object exists. All ideas have some degree of objective reality, even though some ideas have non-existent objects. Similarly, all objects have some degree of formal reality, even though some objects do not exist.

Descartes's point is that all ideas have some content, and their content requires causal explanation. In the first set of replies, he illustrates this with the example of someone who has the idea of a machine with a highly intricate design. The person might have acquired the idea of that machine by observing a real machine with that design. But perhaps there is no such machine. If not, we must seek some other cause for his conception of that object, perhaps in his extensive knowledge of mechanics. If he derived his idea of the machine neither from having observed such a machine nor from his knowledge of mechanics, he may have derived it from someone who had seen such a machine or had the requisite knowledge of mechanics. But whatever the cause, there must be a cause sufficient to produce that effect. The idea of God, as the idea of an infinite being possessing all the perfections that God is supposed to possess, has more objective reality than the idea of a finite substance does. Indeed, it has as much objective reality as it is possible for an idea to have, since its object has as much perfection as it is possible for an object to have.

Stripped to its essentials, the argument is as follows: 1) Each idea must have a cause possessing at least as much formal reality as the idea represents its object as having. 2) The idea of God represents its object as having the maximum possible formal reality. 3) Therefore, the only possible cause of our idea of God is a being that has the maximum possible formal reality (that is, equals all possible perfections). 4) Therefore, the idea of God must have God as its cause. 5) Therefore, God exists. This argument has generally not been well received by Descartes's readers, partly because of the obscurity of the causal principles involved, and partly because Descartes seems to have precluded himself from ever using such an argument.

The argument appeals to causal principles that Descartes said are known by natural light, a cognitive faculty whose deliverances cannot be doubted in any way. (Adam and Tannery VII, p. 38). As an example of one of the things so known, he gave the proposition: "From the fact that I doubt, it follows that I am." But just before he entered on this argument, he said that until he knew whether God exists and can be a deceiver, he could not be certain of anything (Adam and Tannery VII, p. 36). And he seemed there to regard the possibility of God's deception as a reason for doubting, not only simple truths of mathematics, but also the proposition "If I think that I am something, I am something"—a proposition that would presumably be known by that natural light whose deliverances are beyond doubt. It looks as though, to prove the reliability of the natural light, Descartes needs to construct a proof of the existence of a nondeceiving God. And to construct that proof, he needs to deploy premises known by the natural light, which he cannot be sure of until he is sure of his conclusion. The reasoning looks circular. The difficulty is known, therefore, as the Cartesian circle.

We will not have the materials to respond to this objection until we have considered the Fourth Meditation. But first we must note briefly that Descartes offers a second causal argument in the Third Meditation, beginning at the top of Adam and Tannery VII, p. 48. The focus of this argument is not on explaining the existence of the meditator's idea of God, but rather the meditator's own existence as a being possessing this idea. This argument has not persuaded many readers either, partly because it involves some of the same conceptual difficulties as the first argument. But it does introduce another restriction on causality, which had interesting consequences.

At one point in the argument the meditator considers the possibility that his existence as a being possessing the idea of God that he has, might be explained by saying that he has always existed, as he does now. This might not seem a plausible hypothesis, since few people are likely to think they have always existed. But Descartes's reason for rejecting it is curious. He replied that each person's life can be divided into countless parts, each completely independent of the others. From the fact that the meditator exists at one moment, it does not follow that he will exist at the next moment. Apparently he will not exist then, unless some cause creates him again at that time. The meditator thus requires a cause to sustain him in existence from one moment to the next, much as he requires a cause to bring him into existence, if he has not always existed. And that cause, of course, must be God.

What is interesting about this position is the assumption that for a cause to explain an effect, the existence of the effect must follow logically from the existence of the cause. The will of an omnipotent being can satisfy this requirement on causality. It is part of the notion of omnipotence that if an omnipotent being wills something, what it wills must occur. But no finite being appears able to satisfy the condition. For any supposed finite cause, it will always be possible for that being to exist without having the effect we suppose it to have. This restriction on causality looks like it will lead quickly to the occasionalist doctrine that no finite being is ever truly a cause, that God is the only real cause of anything that happens, apparent finite causes being merely occasions for his willing things to happen as they do. It is unclear whether Descartes saw that his argument might have these consequences.

At the end of the Third Meditation, having devoted most of his longest meditation to elaborating two complex arguments for the existence of God, Descartes makes a quick argument that God cannot be a deceiver. The God whose existence he has proven is a supremely perfect being, possessing all perfections and no defects. It is manifest by the natural light that all deception involves some defect. So God cannot be a deceiver. Of course, there is the awkward fact, noted in the First Meditation, that God's creatures do sometimes make mistakes. Not until the next meditation will Descartes attempt to reconcile his awareness of that with his conviction that a supremely perfect being created him.

The main line of response to this difficulty in the Fourth Meditation is a variation of a standard approach to the problem of evil: Though God created the meditator as he is, God is not responsible for the meditator's errors, because they arise from the meditator's misusing the free will God has given him. Free will is a good great enough to compensate for whatever evil is involved in the meditator's mistakes. If the meditator exercised his free will properly, he would not make mistakes.

In the Third Meditation, Descartes classified his thoughts into three kinds: ideas, which, though not images, are like images insofar as they represent their objects as possessing certain properties; volitions or emotions, which involve having an idea of an object and also having some affective attitude toward it (wanting it, disliking it, fearing it, etc.); and judgments, which involve having an idea of an object and affirming or denying something about that object. Only judgments can be true or false. The most common mistake the meditator makes is to judge that things outside him are as his ideas represent them. When they are not, as is often the case, he errs. But error, like any judgment, always involves an act of the will, either affirming something or denying it. The meditator makes judgments he does freely. If he makes a mistake, it is his fault, not God's.

The notion of freedom used here requires some examination. Within one sentence, Descartes suggests two very different conceptions of freedom. The sentence reads as follows:

The will, or freedom of choice …, consists only in this, that we can do something or not do it (that is, affirm or deny, pursue or flee, the same thing), or rather, only in this, that when the intellect proposes something to us for affirmation or denial, pursuit or avoidance, we are so inclined that we do not feel we are determined to it by any external force. (Adam and Tannery VII, p. 57; emphasis added)

This puzzling sentence presents difficulties both of translation and of interpretation. But what Descartes seems to mean by it is that the first clause (before "or rather") describes one (indeterminist) way we can be free, and the second clause (after "or rather") describes another way we can be free (without assuming indeterminism).

Descartes's view seems to be this: Much of the time, when we affirm something, we could have denied it, and when we deny it, we could have affirmed it (or neither affirmed it nor denied it). This will be true under a variety of circumstances: We might have no evidence one way or the other; we might have evidence each way, but the evidence might not favor one way over the other; or the evidence for the proposition might outweigh the evidence against it, perhaps quite strongly, without being conclusive. In all these cases we will have the power to decide either way, and will be free under the first clause of Descartes's definition. This is often called a liberty of indifference, though that term has misleading connotations. It may suggest either that we have no evidence one way or the other, or that our evidence one way is no stronger than our evidence the other way. As Descartes conceived this liberty, that will not always be true. In cases where our evidence for a proposition is strong but inconclusive, as is our sense evidence for the existence of material objects, denial or suspension of judgment will be difficult, but not impossible.

But sometimes, Descartes thought, we find that we cannot help judging as we do. In the Second Meditation, when the meditator was examining whether there was anything in the world and noticed that it followed from the fact that he was examining this that he existed, he could not but judge that what he understood so clearly was true. He was not aware of any external force compelling him to judge thus. Rather, a great inclination of his will followed from a great light in his intellect. He seemed to be all the more free the less indifferent he was. This is what is sometimes called a liberty of spontaneity,a notion that suggests that the absence of external constraint is sufficient for freedom. It is not necessary for our freedom that we have the power to act differently than we do.

Descartes wanted to allow both a liberty of indifference and a liberty of spontaneity. When we do not have clear and distinct ideas, we possess a liberty of indifference. We can judge either way. When we do have clear and distinct ideas, we cannot judge otherwise, but we are still judging spontaneously, and not under any kind of coercion. The absence of external coercion does not imply that there is no external causation of our judgments. Descartes explicitly allowed that God might be disposing the meditator's innermost thoughts to judge the way he did. That will not diminish his liberty of spontaneity, though it will mean that he no longer has a liberty of indifference.

Some critics have found Descartes's theory of judgment highly implausible. Benedict de Spinoza argued that Descartes was confusing judgments with utterances when he supposed that we might have a liberty of indifference in some of the cases where he claimed it. It is one thing to say that one's experiences of the external world might have no more basis than a dream, and quite another to actually believe it. The first is easy; the second may well be impossible. Again, is the liberty of indifference that Descartes requires to relieve God of responsibility for our errors compatible with his doctrine that God is continuously creating us at each moment of time? The doctrine of continuous creation seems to make us completely dependent on God; a liberty of indifference seems to make us at least partially independent of God.

For all the time that Descartes spent arguing that we have a liberty of indifference with respect to some ideas, in the final analysis he seems not to have relied on that liberty to reconcile God's goodness with the occurrence of error. At the end of the Fourth Meditation he conceded that God could easily have brought it about that the meditator would never make a mistake without losing his freedom. All God would have to do is to give the meditator clear and distinct ideas about everything he would ever have to make judgments about, or to implant in him a firm resolution to make judgments only about things he perceived clearly and distinctly. In the closing paragraphs of the Fourth Meditation it looks like Descartes's solution to the problem of error does not depend on free will at all, but on the thought that, although the meditator might be better if he never made mistakes, it is possible that the world as a whole is better for having in it beings who make mistakes. Variety is the spice of the universe.

Nevertheless, the doctrine of judgment in the Fourth Meditation has considerable systematic importance. The method of doubt requires that we suspend judgment about everything we have the slightest reason to doubt, that we withhold our assent from things we do not perceive clearly and distinctly. Moreover, it is arguable that Descartes's vindication of reason depends on our in ability to refrain from assenting to things we do perceive clearly and distinctly. As noted above, when Descartes was arguing in the Third Meditation that God exists and is not a deceiver, he frequently justified the assumptions of those arguments as things "manifest by the natural light." And it's not clear how, given the arguments of the First Meditation, he can repose confidence in that, or any other, cognitive faculty until he has first determined whether God exists and is a deceiver.

Since the mid-twentieth century, at least, commentators have been reluctant to accuse Descartes of blatant circularity. But there is no consensus about how he escapes the accusation. Here is one try. It is not controversial that Descartes thought that our clear and distinct ideas compel assent when we are attending to them. We may be able to doubt simple propositions of mathematics when we consider them under some general rubric, like "the things which seem most evident to me." But when we are actually focusing on a particular simple proposition of mathematics, we cannot in fact doubt it. It compels our assent. The same is true, Descartes thought, of some metaphysical propositions, such as "So long as I think I am something, I am something," and "If I exist now, then it will not be true at some later time that I never existed."

The arguments for God's existence and nondeception in the Third Meditation are constructed from two kinds of propositions. One kind reports the contents of the meditator's consciousness, specifically, the fact that he has an idea of God. This is a presupposition of the dialogue with the skeptic and amenable to the defense offered above for the propositions "I exist" and "I think." The other kind are general propositions, such as "A cause must have at least as much reality or perfection as its effect," and "Deception is a defect." If we perceive these things clearly and distinctly, we will not be able to doubt them when we attend to them. Descartes may not have thought that they are self-evident, in the sense that they command assent as soon as we understand the terms. But if they do not command assent, then we have not yet perceived them clearly and distinctly. We are confused in some way, perhaps by badly understood experiences that seem to refute the principles.

Suppose that we are able to construct an argument that God exists and is not a deceiver, relying entirely on propositions about contents of our consciousness that we cannot doubt and on general propositions that we perceive clearly and distinctly, which we also cannot doubt when we attend to them. If we perceive all these premises clearly and distinctly, and see equally clearly their connection with the conclusion, we cannot doubt the conclusion.

A skeptic might now say, "I understand that you cannot doubt that God exists and is not a deceiver. But that's just a fact about you. It doesn't mean the proposition is not worthy of doubt. Perhaps your creator is an omnipotent demon and this conviction of yours is just another of his tricks." On the interpretation offered here, Descartes would say that once he has a compelling argument to the conclusion that he has been created by a God who is not a deceiver, it is no longer enough to offer the mere supposition that a demon might be deceiving us when we assent to ideas that we cannot in fact doubt. In the First Meditation the hypothesis that an omnipotent creator might deceive us, even about matters most evident to us, constituted a valid ground of doubt, because we had no compelling argument against it. By the end of the Fourth Meditation we do have a compelling argument against it. So it no longer constitutes a valid ground of doubt. The validity of a ground of doubt is situational. What constitutes a valid ground of doubt at one stage of the argument, when we have no compelling argument against it, will no longer be valid when we do have such an argument. Descartes makes this clear in his reply to the seventh set of objections (Adam and Tannery VII, p. 473–474).

It may help to consider the Pyrrhonian skepticism that we find in Montaigne's Apology for Raymond Sebond. The Pyrrhonist advocates what Montaigne calls the principle of equipollence: For every argument in favor of a proposition, there is an equally strong argument against it. Montaigne's criterion for the strength of an argument is psychological persuasiveness. When someone who holds the principle of equipollence is confronted with a compelling argument that we have been created by a nondeceiving god, he can no longer cast doubt on that conclusion simply by hypothesizing the possibility of deception by an omnipotent being. He must produce an equally strong and compelling argument for the opposite conclusion. Absent such an argument, Descartes is entitled to his conclusion.

There is one other respect in which the situation at the end of the Fourth Meditation is different from the situation at the beginning of the Third Meditation. Now we have a clear and distinct idea of God. At the beginning of the Third Meditation we conceived of God simply as an omnipotent creator who was supposed to be supremely good and is the source of all truth. But we didn't see any necessary connection between these attributes, and we worried that we might have been created by a being who possessed some of these attributes, but not all of them. By the end of the Fourth Meditation we understand that what God is, essentially, is a supremely perfect being, who has all the perfections and no defects. Once we have seen this, we see that the hypothesis of an omnipotent deceiver is incoherent. It is not even a hypothesis that we can consider as a possibility.

In the Fifth Meditation, Descartes had two items on his agenda: considering the nature of material things and arguing once more for the existence of God. His most urgent task if he is to recover from his doubts, he said, is to determine whether he can have any certainty about material things. Before he could decide whether such things really exist, he needed to consider what distinct ideas he had of them. He prepared the ground for this consideration in the Second Meditation, where he identified extension as the one first-order property that remains constant in the wax as it changes. There his focus was on a particular body. Here it is on what he calls "continuous quantity … or the extension of this quantity—or rather, of the thing quantified—in length, breadth and depth." (Adam and Tannery VII, p. 63). So we are to think of geometrical space (continuous quantity) as a material substance extended in three dimensions, of which particular bodies are parts, each possessing its own size, shape, and position, and distinguished from the other parts by their varying motions. (Here again, Descartes is insinuating fundamental propositions of his physics.)

When Descartes reflected on his ideas of extended objects, he realized that he had countless ideas of geometrical objects, objects that may not exist anywhere outside his mind but that nevertheless have a definite nature, "a true and immutable nature," independent of his mind. He could demonstrate properties of these shapes, even though he might never have observed any shapes of the kind whose properties he was demonstrating. He may have observed triangles; it's unlikely that he ever observed a chiliagon (a thousand-sided polygon). But he could determine what its properties are, even if there are no chiliagons to observe. Whenever he saw clearly and distinctly that some property belongs to the true and immutable nature of some thing, that property really does belong to that thing. He had a clear and distinct idea of God as a supremely perfect being. He understood that to be supremely perfect, a being must possess all perfections, and that existence is a perfection. He inferred, then, that God must possess the perfection of existence.

This version of the ontological argument depends on a Platonic philosophy of mathematics, which Pierre Gassendi criticized in the fifth set of objections. Gassendi complained first that it seemed to him that it is hard to maintain that there are true and immutable natures apart from God. He imagined Descartes replying that he was only saying what they say in the schools, that the essences of things are eternal, and that there can be true propositions about them. But Gassendi did not understand how there can be an essence of something—his example is man—if there are no things of that kind. At one point he seemed willing to concede that there is a sense in which "Man is an animal" can be true even if no men exist. But he said that the statement is true only if it is understood conditionally: "If something is a man, it is an animal." And he gave an analysis of that conditional that makes its truth apparently require the existence of some men:

When man is said to be of such a nature that he cannot exist without being an animal, it is not on that account to be imagined that such a nature is something or is somewhere outside the intellect. The meaning is only that for something to be a man, he must be like the rest of those things to which we give the same name, man, on account of their mutual similarity. (Adam and Tannery VII, p. 320)

Gassendi also questioned whether existence is a perfection: "Existence is not a perfection either in God or in anything else; it is that without which no perfections can be present. … What does not exist has no perfections or imperfections. … If a thing lacks existence, we do not say it is imperfect … but say instead that it is nothing at all" (Adam and Tannery VII, p. 323). Though Gassendi focused on the idea that existence might be a perfection, his reasoning would seem to exclude its being a property of any kind. He treated existence not as something which is predicated of a thing, but as a precondition of any predication.

When Descartes replied, he was puzzled about what category Gassendi wanted to put existence in. Existence seemed to him analogous to omnipotence, something that can be predicated of a thing, and that therefore is a property. But then he rejected Gassendi's conditional analysis of essential predications. Gassendi's example, man, was one of the "universals of the dialecticians," that is, the Scholastic philosophers. Descartes preferred to focus on essences that we understand clearly and distinctly, like those of geometric figures. We cannot understand the latter essences the way the Scholastics and Gassendi did, as based on concepts abstracted from experience of instances of the concept, because there are no instances for us to experience. This is true not only for such unfamiliar figures as chiliagons, but also for such apparently common figures as triangles. The problem is that nothing in our experience strictly satisfies the definition of a triangle, which requires, among other things, that it be composed of straight lines. The lines we experience turn out, when examined closely, not to be perfectly straight. But we can recognize the figures we experience as approximations of the ideal geometric figures because we have ideas of the ideal figures from another source.

Descartes's objections to Gassendi's analysis of essential predication probably go deeper than his opposition to the scholastic theory that our concepts are formed by abstraction from experience. It seems likely that he would reject any conditional analysis of essential predications, even if it was not spelled out in abstractionist terms. Gassendi had complained that the essences Descartes was talking about could not have an immutable and eternal nature apart from God. Descartes replied that he did not claim that the essences of things exist independently of God. He conceived of them rather as depending on the will of God, and as being immutable only because God's will is immutable. Although Descartes did not explicitly invoke his doctrine of the creation of the eternal truths in the body of the Meditations itself –(he may have presupposed it in the Third Meditation), he did make it explicit in his replies to objections. (It comes up again in the sixth set of replies.) Reflection on the reasons that may have led Descartes to his doctrine of the creation of the eternal truths may also suggest a reason why he would reject Gassendi's conditional analysis of essential predications.

One problem that scholastic philosophers faced when they thought about essential predications was that, according to the orthodox theory of universal propositions, they have existential import. "All men are animals" entails that there are men. But if "All men are animals" is a necessary truth, so are its entailments. However, "There are men" is supposed to be a contingent truth, made true at the creation by God's will. Descartes may have been moved to compare the eternal truths with the laws that a king establishes in his kingdom because a king's laws depend for their validity not on the existence of violators of those laws, but only on the authority of their source. The king's prohibition on dueling does not depend on there being any duelists. Descartes may have felt that a conditional analysis of essential predications avoided one problem only to raise another equally difficult problem. On the hypothesis that there are no men, "If anything is a man, it is an animal" is a conditional whose antecedent is false. If this is a material conditional, it is true in such circumstances, as is the conditional "If anything is a man, it is a plant." If it is a modal conditional, it is unclear what the truth conditions for such conditionals are (if they have any).

Gottfried Wilhelm Leibniz raised an equally serious problem when he argued that Descartes needed to supplement his ontological argument with a proof that the concept of God is consistent. Arguably, that is what Descartes was trying to do, in a limited way, in the Fourth Meditation. That meditation tried to resolve an inconsistency that had threatened his concept of God since the First Meditation: that God was a perfect being who was nonetheless supposed to have created a very imperfect being. But emphasizing human freedom as a solution to that problem, even if it is not Descartes's final solution, only raised the question of whether human freedom is compatible with God's omnipotence, a problem Descartes would address in his Principles of Philosophy.

In the Sixth Meditation there are two announced items on the agenda: establishing the existence of bodies and proving that mind and body are distinct. The first step in approaching the latter problem is to recognize (1):

(1) Whatever I clearly and distinctly understand can be made by God as I understand it.

The thought here seems to be that if I understand something clearly and distinctly, it must be free of contradiction, and that God, being omnipotent, can create anything that does not involve a contradiction. From (1) it follows that (2):

(2) If I clearly and distinctly conceive myself as a thinking, non-extended thing, then God can create me as a thinking, nonextended thing.

Similarly, (3) also follows from (1):

(3) If I clearly and distinctly conceive of body as an extended, non-thinking thing, God can create it as an extended, nonthinking thing.

In the Second Meditation Descartes' meditator, in his reasoning, achieved a state in which he satisfied the antecedents of (2) and (3). He had a clear and distinct idea of the wax as an extended thing, to which he did not ascribe any thought, and a clear and distinct idea of himself as a thinking thing, to which he did not ascribe anything corporeal. So he infers (4) and (5):

(4) God can create me as a thinking thing, apart from my or any other body.

(5) God can create my or any other body as an extended thing, apart from me or any other thinking thing.

To show that two things are really distinct, it does not matter what power is required to create them as separate substances. According to the definition of a real distinction, two things are really distinct if they are substances and it's possible for each to exist without the other. So this is sufficient to prove that:

(6) I and my body are really distinct substances.

It is not obvious what is wrong with this argument, though it certainly has not lacked critics.

In the fourth set of objections Antoine Arnauld proposed the following counterexample. An individual might clearly and distinctly perceive that a triangle inscribed in a semicircle is right-angled, but not be aware of the Pythagorean theorem, according to which the square on the hypotenuse of a right-angled triangle must equal the sum of the squares on the other two sides. So he might doubt or deny that a particular triangle inscribed in a semicircle has the Pythagorean property. From Descartes's first assumption (1), he might infer (2′):

(2′) If I clearly and distinctly conceive the triangle inscribed in a semicircle as right-angled, but doubt or deny that this triangle has the Pythagorean property, then God can create a triangle inscribed in a semicircle that does not have that property.

The antecedent of this conditional might well be true, it seems, but the consequent attributes to God a power he cannot have, even if we accept Descartes's doctrine of the creation of the eternal truths. Even if God could have created a different nature for triangles, the immutability of his will entails that he cannot now create a triangle with a different nature (Adam and Tannery V, p. 160). Descartes replied at length to Arnauld's objection without ever seeming to meet the point. It is not obvious what he should have said to defend himself.

Though Descartes regarded mind and body as substances capable of existing apart from one another, he was also anxious to insist that he is very closely united to his body, "as it were, intermingled with it," (Adam and Tannery VII, p. 81), so that he composes one thing with it. His bodily sensations taught him this: He feels pain when this body is damaged, hunger when it needs food, thirst when it needs drink. He does not feel these sensations when similar things happen to other bodies. So, he said, nature taught him that he is not merely present to his body as a sailor is present to his ship. He thereby rejected what the medievals regarded as the excessive dualism of Plato. Bodily sensations are nothing but confused modes of thinking arising from the union of mind and body. It is not clear that this doctrine of mind-body union is compatible with the doctrine that mind and body are distinct. This was to become a major topic of debate after the publication of the Meditations, as we shall see.

Descartes's attempt to prove the existence of bodies has generated not so much debate as dismissal. God, he said, had given him a great propensity to believe that his sensations are caused by material things and no faculty for recognizing any alternative source for them. So Descartes did not see how God could be cleared of the charge of being a deceiver if his sensations were caused by something incorporeal. There must be corporeal things. They may not have all the properties he grasped by sensation, since there is much in those properties that is obscure and confused. But they must have all the properties he understands clearly and distinctly, that is, all the properties that are the subject of pure mathematics.

It is indeed hard to see how a perfectly good God could permit such a massive delusion. But Descartes here has weakened the conditions under which God can be judged to be a deceiver. In the Fourth Meditation, God would have been a deceiver if we had false beliefs that we could not help having. Now God is a deceiver even if we have false beliefs that we can help having, provided we are strongly inclined to believe them and have no way of telling that they are false. Perhaps the proper conclusion from this argument is that it is improbable that our belief in material objects is false. When we are dealing with beliefs that we could help having, we probably need to know something about God's purposes before we can decide whether or not he would be a deceiver if we held false beliefs under those circumstances. Descartes did not think that we can know what God's ends are. But probably the main reason the argument has not found much favor is that it does not seem that we should have to accept this complex theistic argument to see the existence of bodies as certain.

We should note an important negative conclusion that Descartes reaches in the Sixth Meditation: Even if we have been created by a nondeceiving God, we have no justification for believing that the things we perceive by the senses have all the properties we are inclined to ascribe to them. The properties of which we have confused and obscure ideas—the heat we attribute to hot bodies, the color we attribute to green bodies, and in general what later philosophers were to call "the secondary qualities of things"—these properties, insofar as we think of them as properties of external objects, need not resemble in any way the ideas we have of them. There must be some differences in the things themselves, between a hot object and a cold one, or between a red object and a green one. But so long as there is a systematic correlation between the differences in external objects and the differences in our sensations, we needn't suppose that there is anything in the objects themselves resembling color or heat. This was one of the fundamental principles of Descartes's physics that he slipped into the Meditations.

Continued Controversy (1641–1644)

Even before the publication of the Meditations in August 1641, Descartes had begun work on his next major publication, his Principles of Philosophy (1644), which he sometimes referred to in the correspondence as his "summa of philosophy" or as his "philosophy" or as his "physics." His aim was to produce "a complete textbook" of his philosophy, combining metaphysics, physics, and biology, in the form of theses, "where, without any excess words, I will just present all my conclusions, with the true premises from which I derive them" (Adam and Tannery III, p. 233). There would be none of the false starts that gave the Meditations their dialectical character. When he first began planning this work, he thought of publishing it with a standard textbook of scholastic philosophy on which he would comment. He had selected Eustachius of St. Paul's Summa philosophiae for this purpose, but gave up that aspect of the project after Eustachius's death in December 1640. Clearly, he had decided that he could be more open about his anti-Aristotelianism, and could present his cosmology in a way that would escape condemnation.

When the second edition of the Meditations appeared in May 1642, it added not only Father Bourdin's objections and Descartes's replies, but also a letter from Descartes to Father Jacques Dinet, a former teacher at La Flèche and now the head of the Jesuit order in France, complaining about his treatment by Bourdin. Descartes had reason to be upset by Bourdin: He was long-winded, sarcastic, and unsympathetic in his interpretation of Descartes's views. Descartes said he showed the acumen of a bricklayer, not a Jesuit priest. And he wrote bad Latin. Though Descartes seems to have had a genuine affection for some members of the Jesuit order and respect for the quality of education the society provided in its schools, he was prone to see conspiracy in its members' actions. He worried that Bourdin's critique was not the opinion of one Jesuit priest, but represented a consensus among the Jesuits. He urged Dinet to read the Meditations himself—or if he did not have the time for that, to assign the task to members of the society more competent than Bourdin—and to let him know if they saw problems in his project. Dinet delegated the task to Father Etienne Charlet, formerly the rector at La Flèche and later Dinet's successor as head of the Jesuits in France, who was to write to Descartes about his works. It appears that Charlet eventually demonstrated his personal good will toward Descartes and his work, but left him uncertain about the attitude of the society as a whole.

Descartes also included in his letter to Dinet an account of a controversy he was embroiled in at the University of Utrecht. In 1641 a follower of his, Henricus Regius, professor of medicine at the University, had engaged in a disputation there in which he presented his version of Cartesian natural philosophy, going further than Descartes judged it wise to go. Regius said that the union of mind and body was an accidental one, rather than substantial, and also denied the existence of substantial forms, those formal aspects of things that in scholastic natural philosophy were supposed to make them the kinds of things they are and explain their characteristic behavior. For these positions Regius came under attack from the rector of the university, Gisbert Voetius, who took the opportunity to hurl a few barbs in Descartes's direction as well.

Regius felt he needed to reply publicly, and Descartes advised him on what to say. Though Descartes thought Regius meant something acceptable when he declared that the union of soul and body was accidental—namely that mind and body are really distinct from one another, each capable of existing without the other—he warned Regius that the Scholastics would interpret this language differently, and that the best thing would be to claim ignorance of scholastic terminology and to say that the disagreement between them was only verbal. Regarding substantial forms, Descartes thought Regius should say that he did not wish to reject them absolutely, and that he meant merely that he had no need to invoke them in his scientific explanations. Saying that fire possesses the form of fire does not help us in any way to understand its ability to burn wood. This was the stance Descartes had taken, leaving it to his readers to draw the conclusion that if substantial forms were explanatorily useless, there was no reason to postulate them.

When Regius published his reply, he only made matters worse. The university condemned the new philosophy and forbade Regius to teach his course on physical problems. "Utrecht University, the first in the world to allow one of its professors to teach Cartesianism, was also the first that forbade its teaching" (Verbeek 1992, p. 19). When Descartes criticized Voetius in his letter to Father Dinet, Voetius responded by arranging for Martin Schoock, a professor at Groningen and a disciple of his, to write a book that accused Descartes, among other things, of atheism and of fathering numerous illegitimate children. (Descartes did, in fact, have one illegitimate child, a daughter whom he was quite fond of but who died in 1640, at the age of five.) The full story of the Utrecht affair—which ultimately involved lawsuits for libel, charges of perjury, and a prohibition on any discussion of Descartes, pro or con—is too complex to tell here (for further details, see Verbeek 1992).

Principles of Philosophy (1644)

The Principles was Descartes's most systematic work and the one his contemporaries went to for a definitive statement of his philosophy. It consists of four parts, the first dealing with metaphysics and epistemology, the second with general principles of physics, the third with celestial phenomena, and the fourth with terrestrial phenomena. Since Descartes himself preferred the exposition of his metaphysics and epistemology in the Meditations to the one he gave in Part I of the Principles, and since the science that dominates the remainder of the work is primitive by modern standards, most recent students of Descartes have neglected the Principles. Here we must limit ourselves to noting only a few of the many things it adds to what we know from our survey of Descartes's other works.

Among the additions is a metaphor that Descartes used in the Preface to the French translation of 1647: "The whole of philosophy is like a tree, whose roots are metaphysics, whose trunk is physics, and whose branches are all the other sciences, which reduce to three principal sciences, medicine, mechanics and morals" (Adam and Tannery IX-B, p. 14). This passage illustrates Descartes's conception of the close connection among disciplines that we now regard as quite separate, his ambition to found the sciences in metaphysics, and his hope that his foundational work would have practical consequences. Particularly intriguing is his ambition to derive a moral philosophy from his metaphysics and physics. We will see what that led to when we come to his last major work, The Passions of the Soul.

One delicate issue the Principles raises is the question of the extent of the universe. Copernicus had not claimed that the world was infinite, but later Copernicans, such as Giordano Bruno, did. Though we do not know the specific grounds for the Church's execution of Bruno in 1600, it seems likely that this was one of them. Since Descartes identified matter with (Euclidean) space, it might seem that he too would be committed to the infinity of the physical universe. But in the Principles (pt. I, secs. 26–27), he said that he was not. He reserved the term "infinite" for God alone and designated things in which he could discover no limits—such as the extension of the world and the divisibility of matter—indefinite. Nevertheless, later in the Principles (pt. II, sec. 21), he passed from denying knowledge that there are any limits to the extent of the world to affirming knowledge that there are no limits to its extent. When he later began to develop his moral philosophy, he listed, as one of the truths most useful to us, the proposition that we must beware of supposing that there are limits to the extent of the world God created (Principles, pt. III, sec. 1). Descartes supposed that an appreciation of the vastness of God's creation would aid us in detaching ourselves from the things of this world (Adam and Tannery IV, p. 292).

Another theologically sensitive issue that Descartes dealt with in Part 1 is the problem of reconciling human freedom with God's omnipotence (secs. 37–41). Descartes's conception of freedom here seems to be more single-mindedly indeterminist than it was in the Meditations. If we are to deserve praise for our actions, we must be in some special way the author of those actions, and not have been determined to so act by our maker. We must have been able to do otherwise. That we have the power to assent or not to assent in many cases is as evident as any first principle, though this is not innate knowledge, but something we learn from what we experience within ourselves. On the other hand, now that we know God, we see that his power is so immense that it would be impious to think we could ever do something he had not foreordained.

Recent discussion of the problem of reconciling human freedom with God's attributes has tended to focus on showing that human freedom is consistent with divine foreknowledge. Descartes was more worried about showing it to be consistent with God's omnipotence. Perhaps Descartes thought that his identification of God's will with his intellect ruled out the possibility that he might foreknow without foreordaining. In any case, the solution that Descartes proposed is that we should maintain both our freedom and God's foreordination, even though we do not see how they could be compatible. God's power is infinite; our intellects are finite. So we should not expect to understand how they can be compatible, and we cannot give up two such certain truths merely because of a defect in our understanding. Had Descartes continued to allow the liberty of spontaneity that he recognized in the Fourth Meditation, it seems that he would not have needed to take this position.

In part II of the Principles, Descartes laid the groundwork for a version of Copernicanism that was supposed to avoid the censured claim that Earth moves. In sections 13 and 24 he gave a relativistic account of what we ordinarily mean when we say that a body moves: It changes its place, which is defined as its position relative to other bodies taken to be at rest. We will get different answers to the question of whether something is moving, depending on which other bodies we take as our frame of reference. Suppose that a man is sitting on the stern of a ship headed down river to the sea. We say that he is at rest if we consider his constant relation to the part of the ship where he is sitting. We say that he is moving if we consider his relation to the shore, since he is continually moving away from some parts and toward others. If we think that Earth is rotating on its axis and moving just as much from west to east as the ship is moving from east to west, we say that he is not moving—our frame of reference now being certain bodies in the heavens that we suppose to be motionless. But if we think that there are no such motionless points anywhere in the universe, we will conclude that nothing has a permanent place, except insofar as it is determined by our thought. In part II, section 13, Descartes foreshadowed an argument that, he said, makes it probable that there are no genuinely fixed points in the universe. We get that argument in part III, section 29, where he contended that if we follow ordinary usage, there is no reason to say it is the stars that are at rest rather than Earth.

Descartes seems to reject ordinary usage. In part 2, section 25, he said that if we want to understand motion "according to the truth of the matter," we ought to define it as "a transfer of one part of matter, or of one body, from the neighborhood of those bodies immediately touching it, considered as resting, to the neighborhood of other bodies " (emphasis added). So he treats the immediately surrounding bodies as a privileged reference frame. On this definition, Earth, strictly speaking, is at rest, even though there is admittedly a sense in which it is moving round the Sun. In Descartes's cosmology, it is at rest in relation to the fluid matter immediately surrounding it, which carries it round the Sun, just as a ship, neither driven by the wind nor hindered by an anchor, might be at rest in relation to the water around it, though it is imperceptibly carried out to sea by the tide (pt. III, sec. 26–28). Of course, as Descartes noted, the same thing can be said of all the other planets.

Cartesian scholars have often suspected Descartes of adopting this strict definition of motion simply because he could then claim that in his cosmology the Earth did not move, permitting him to adopt a basically Copernican astronomy without suffering the fate of Galileo. Descartes anticipated that his denial that the Earth moves might be judged to be "merely verbal," intended to avoid censure. But he said that a careful reading of his work should remove that suspicion (Adam and Tannery V, p. 550). In any event, it is arguable that he had serious reasons, internal to his philosophy, for wanting to define motion in a way that would escape the relativism he saw in the common conception of motion. Motion is supposed to do a great deal of work in his mechanistic physics. As he said in the Principles, "All the variety in matter, all the diversity of its forms, depends on motion" (pt. II, sec. 23). To make that kind of explanatory use of motion, he needed it to be something that really exists in bodies, not something that is in them or not, depending on how you look at them. But his solution to the problem is highly problematic, and not only because it did not in the end protect him from condemnation by the Church. (For more on this complex issue, see Garber 1992, chap. 6.)

We cannot leave this all-too-brief discussion of the Principles without noting that at the end Descartes commented on the epistemological status he took his scientific theories to have. He claimed that they are at least morally certain, that is, certain enough that it would be reasonable to act on them (or perhaps unreasonable not to act on them), even if they are not absolutely or metaphysically certain (pt. IV, sec. 205). His principles explain so many phenomena that it hardly seems possible that they could be false. And some of his principles, he thought, are absolutely certain, because they are grounded in his certainty that God is supremely good and is not a deceiver (pt. IV, sec. 206). He mentioned mathematical demonstrations, the existence of material things, and "all evident reasonings about material things." He clearly hoped that his readers would find even more of his conclusions metaphysically certain.

Royal Admirers, Continuing Conflicts (1644–1648)

Descartes dedicated his Principles of Philosophy to Princess Elisabeth, the daughter of Frederick V (formerly the Elector Palatine and briefly King of Bohemia) and Elisabeth Stuart (sister of Charles I of England). They had begun to correspond in 1643, after Descartes learned that the princess, who was living in exile in the Hague, had read his Meditations with approval. She pressed him with acute questions about the relation between mind and body, eliciting some surprising answers. Later their correspondence turned to questions of ethics and psychology, which prompted Descartes to write his last major work, The Passions of the Soul (1649), also dedicated to her. Though the extravagant mutual flattery that pervades their correspondence may be mere courtly etiquette, readers have sometimes wondered if Descartes did not harbor an affection for this sad, lovely, intelligent young woman that might have led to a romance, had not the difference in their ages, social station, and religion made that impossible. In any event, she proved to be a stimulating student.

Elisabeth began their correspondence by raising an issue that was to become central in the subsequent development of Cartesianism: How, in voluntary motion, can the mind, as a nonextended thing, cause its body, an extended thing, to move (Adam and Tannery III, p. 661)? Her paradigm for an intelligible causation of motion—and Descartes's paradigm too, we might have thought—involves the impact of one body on another, with the cause transmitting some of its motion to the body that begins to move. Impact requires contact, which requires extension in both cause and effect. A nonextended thing cannot have an impact on an extended one.

Descartes replied by saying that what explains the mind's power to move the body is its union with the body (Adam and Tannery III, p. 664). The notion of the union of mind and body is a primitive one, like extension and thought, which cannot be explained in terms of anything more fundamental. But Descartes thought that we demonstrate our possession of this notion when we attribute to so-called "real qualities," like weight, a force that moves bodies toward the center of Earth. Although we have no knowledge of weight, except as a force of a sort that has this effect, we find no difficulty in thinking of it as moving a body, even though we do not think that it does so by actually touching one surface against another. We find this easy to conceive because we experience in ourselves a power to move the body, and we infer that bodies possess qualities that have analogous powers. We call these qualities "real," meaning thereby that we conceive of them as being really distinct from the body that has them, and hence as a kind of substance. (In fact, as Descartes explained elsewhere, we think of them as a kind of spiritual substance, since we attribute goal-oriented behavior to them.)

Unsatisfied with this explanation, Elisabeth pointed out that real qualities are a disreputable part of scholastic natural philosophy that Cartesian physics aims to replace (Adam and Tannery III, p. 684). Descartes promised to give a proper mechanical explanation of such phenomena as the fall of heavy bodies to Earth, so that it will not be necessary to explain the mind's power to move the body in terms of occult qualities, powers known only by their effects. Since Elisabeth did not really understand weight, she could not use its supposed causal powers to help her understand how the soul might act on the body. It would be easier for her, she confessed, to grant extension to the soul than to suppose that an immaterial being has the ability to move and be moved by a material one. In his reply (Adam and Tannery III, p. 694), Descartes gave her permission to do just that: to think of the soul as an extended being! Thinking of the soul as extended is just thinking of it as united to the body. Elisabeth was not satisfied with this reply either, which hardly seems consistent with saying that we have a clear and distinct idea of the mind as a thinking, nonextended substance. But she got no more from Descartes on this subject.

Later their correspondence turned to ethical questions, and Descartes recommended that they discuss Seneca's "De Vita Beata" (On the happy life). Elisabeth's life as a princess in exile was not a happy one. Descartes hoped that reading Seneca would help her overcome her depression. Evidently, he had not read Seneca, or had not read him recently, when he made that suggestion. When he did, he did not find much useful there. But when he made his own recommendations for achieving happiness, they had a distinctly Stoic flavor: We should use our reason to consider without passion the value of all the perfections, both of body and of soul, so that we can always choose the better. We should cultivate a firm and constant resolution to carry out what reason recommends as best without being diverted by our passions. Virtue consists in sticking to this resolution, and virtue, Descartes thought, is the path to contentment. But before long he decided that he needed to examine the passions in more detail, so that he could define them. This led to the first draft of his Passions of the Soul, written in the winter of 1645–1646.

While these positive developments were occurring, the controversy with Voetius continued and spread to the University of Leiden, where Jacob Revius, the dean of the Staten college at the University, attacked Descartes, and Adriaan Heereboord, Revius's subdean in the college, defended him. This time the principal issues were not so much Descartes's rejection of key ideas in scholastic philosophy as the positive doctrines of his own philosophy:

• Whether the method of doubt leads to skepticism—a reasonable concern, considering the problems Descartes faced in getting beyond the cogito
• Whether Descartes was guilty of blasphemy even to suggest the possibility that God might be a deceiver—not so reasonable, it seems, since Descartes had shown sensitivity to the issue by substituting the demon for God at the end of the First Meditation and had gone on to argue that the hypothesis of a deceiving God involves a contradiction
• Whether Descartes was guilty of atheism in rejecting the Thomistic versions of the cosmological argument for God's existence and replacing them with less satisfactory arguments of his own—a possibly reasonable concern, though the details of the critic's arguments show a poor understanding of Descartes's conception of an idea of God
• Whether Descartes was guilty of Pelagianism for excessively exalting free will

The principal basis for this last accusation was Descartes's claim, in the Fourth Meditation, that he experienced within himself a freedom of choice so great that he could not conceive of the idea of a greater freedom (Adam and Tannery VII, p. 57). It is above all in virtue of his freedom that he understood how he might have been made in the image of God.

The accusation of Pelagianism had come up in the correspondence with Mersenne as early as 1637 (Adam and Tannery I, p. 366). Descartes was always puzzled by it, since he understood the Pelagian heresy to involve the claim that an individual, using only his own natural powers, without a special act of divine grace, can achieve salvation. He knew that he had never made this claim, and he was happy to reject it when the situation required (Adam and Tannery III, p. 544). Nevertheless, when the curators at the University of Leiden forbade any discussion of Descartes's views, pro or con, and Descartes appealed to them, complaining that he must be permitted to defend himself against misrepresentation, the rector of the University, who was well disposed to Descartes, advised him to drop the appeal. The matter might be brought before an ecclesiastical council, where his opponents would surely win, not because of what he had said about freedom of the will, but "because they believe he is a Jesuit in disguise" (Verbeek 1992, p. 47). This was ironic, in view of the trouble Descartes was having with the Jesuits in France, but it was not the last of the ironies arising from Descartes's ambiguous position on free will, as we shall see later.

These were busy years for Descartes. One matter that occupied him was seeing that his principal Latin works were translated into French, so that they could be read by a broader audience. Various friends did the translations: Louis Charles d'Albert, Duke of Luynes, did the Meditations ; Claude Clerselier, Objections and Replies ; and the abbot Claude Picot, the Principles. The translations were published in 1647. In each case Descartes is supposed to have reviewed them, presumably correcting anything he found faulty and occasionally adding text to explain his views more clearly. In principle, this means we might prefer the French translations of his works to the Latin originals. But it is not clear how much weight we can put on the French variations. We cannot know how carefully he reviewed the translations. Substantial variations almost certainly come from his hand. Smaller ones are doubtful. Older translations of Descartes into English blended the Latin and French texts. The now standard translation listed in the bibliography (Cottingham, Stoothoff, Murdoch, and Kenny) properly takes the Latin as the primary text, noting variations in the French.

In 1647 or 1648 Descartes initiated a quarrel with his former follower, Henricus Regius, who had developed positions at odds with Cartesian philosophy. Descartes first criticized Regius in the preface he wrote for the French translation of the Principles and later in the short work Notae in programma quoddam (Notes on a Program; also known as Comments on a Certain Broadsheet), published in 1648 and notable for its clarification of Descartes's views on innate ideas. Also in 1648, Descartes sat down for a long interview with a young Dutch theology student named Frans Burman. Burman prepared well for the interview, carefully reading Descartes's published works and asking probing questions about them. His record of Descartes's answers is a valuable source of information about Descartes's views, though sometimes it is not clear that Burman accurately transcribed what Descartes said.

Toward the end of this period, Descartes entered into a correspondence with Queen Christina of Sweden, who was making her court in Stockholm a center for learning. Most of their correspondence was conducted through Pierre-Hector Chanut, the French ambassador, and there is none of the give and take that makes his correspondence with Elisabeth so interesting. But Descartes's relationship with Christina was momentous in other ways, as we shall see.

The Passions of the Soul (1649)

The Passions of the Soul is Descartes's most serious attempt to provide the moral philosophy promised in the preface to the French edition of the Principles. In a prefatory letter, Descartes said that he will treat the passions "only as a natural philosopher," not "as a rhetorician, or even as a moral philosopher." But this is somewhat misleading. Although the work begins with a quick course in Cartesian physiology (secs. 1–16), and broader and narrower definitions of the passions that emphasize their close connection with the body (secs. 17, 25, 27–29), it ends by making a moral evaluation of the passions that smacks more of Aristotelian moderation than Stoic rigor: The passions are all good in their nature; all we need do is to avoid their excess and misuse (sec. 211). Indeed, all the good and evil of this life depend only on the passions (sec. 212).

In the broad sense, the passions of the soul are perceptions the soul receives from the things they represent (sec. 17). Sometimes the things these perceptions represent are in the soul itself, as when we perceive our volitions, imaginations, etc. (sec. 19). Sometimes the things they represent are either in our body or in some external object that acts on our body. This category includes bodily sensations, sensations of external objects, and passions in the narrow sense. These last are defined as excitations of the soul that, though in fact proximately caused by some movement of the animal spirits, are not perceived as having that proximate cause, but are referred to the soul itself (sec. 27).

Descartes maintained that there are six "simple and primitive" passions: wonder, love, hatred, desire, joy, and sadness (sec. 69). All other passions are either combinations of the primitive passions or particular species of them. Like sensations, the passions help to preserve the mind-body union: Their use "consists in this alone, they dispose the soul to will the things nature tells us are useful and to persist in this volition" (sec. 52). They are nature's way of telling us what is useful to us and what is harmful, motivating us to pursue what is useful and avoid what is harmful. The sensation of fear incites the will to flight; the sensation of boldness incites the will to fight.

The connection between the movements of the animal spirits and the excitations of the soul they cause and sustain is no more perspicuous here than it was in the correspondence with Elisabeth. Descartes identified the locus of interaction as the pineal gland, selected for this role, it seems, because it is the only part of the brain that is not double, and because a slight movement of this gland can greatly alter the movements of the animal spirits and, conversely, a slight movement of the animal spirits can greatly alter the movement of this gland (secs. 31–32). But how a particular movement of the pineal gland can affect the soul and how an action of the soul can move the pineal gland are mysteries shrouded in silence. The connections, apparently, are established "by nature" (secs. 44, 50), that is, we assume, the will of God.

Descartes, it seems, thought that for the most part the regularities God has put in place work well for us. But just as in the Sixth Meditations, our bodily sensations can sometimes lead us astray, causing us to want drink, say, when drink would be harmful to us, so can our passions sometimes lead us astray. "When we feel the blood stirred up, we should be warned and remember that everything which presents itself to the imagination tends to deceive the soul, and to make the reasons favoring the object of its passion appear much stronger than they are, and the opposing reasons much weaker" (sec. 211). If the passion favors some object that does not require immediate action, we should refrain from making any immediate judgment and distract ourselves with other thoughts, until our blood has cooled. If it incites us to an action requiring immediate action, we should reflect on the reasons that oppose that action, and follow them even if they seem weaker. This, Descartes said, is "the general remedy for all the excesses of the passions, and the easiest to put into practice" (sec. 211). Descartes is not at his best when he is doing moral philosophy.

Death and Condemnation (1649–1663)

In July 1649, in response to an invitation from Queen Christina, Descartes embarked for Stockholm, where he was to enhance the reputation of her court as an intellectual center and provide the queen with lessons in philosophy. This Swedish adventure did not end happily. When Descartes first arrived in October, his duties were minimal. But by mid-January he was required to give Christina five-hour lessons in philosophy, three mornings a week, beginning at five in the morning. Within two weeks he came down with pneumonia. By February 11, 1650, he had died.

Thirteen years later Descartes's works were placed on the Catholic Church's Index of Prohibited Books. For a long time it was unclear what the grounds for this condemnation were, but recently the Archives of the Congregation for the Doctrine of the Faith have been opened, permitting a clearer view of the Church's reasons and procedures. The Holy Office assigned two outside consultants to read Descartes's works and report on them: Joannes Tartaglia, to read the Discourse on Method (and its essays) and the Meditations (with the Objections and Replies ); and Stephanus Spinula, to read The Principles of Philosophy and The Passions of the Soul. On the whole, the censors (especially Tartaglia) seem to have done their work carefully, attributing to Descartes only doctrines he actually held, or at least doctrines that might reasonably be inferred from what he wrote.

The censors found much to object to. Some were propositions in Cartesian physics where Descartes knew he was pushing the bounds of orthodoxy: the denial of substantial forms and real qualities; the doctrine that Earth moves, while the Sun is immobile; the doctrine that the physical universe has no limits. Others were fundamental doctrines of Cartesian epistemology: that the existence of the self as a thinking thing is the first evident truth, from which all other evident truths derive; that we cannot clearly understand what is true unless we know clearly that God exists and cannot deceive us; and that the standard Thomistic versions of the cosmological argument are unsatisfactory ways of proving God's existence.

Particularly interesting are the objections to two doctrines relating to human freedom: that the soul can easily acquire an absolute power over all its passions; and that freedom of the will does not require freedom from necessity, but only freedom from constraint. The first of these was a proposition that Spinoza also sharply criticized, in the Preface to part V of his Ethics. The second was one of five Jansenist propositions that the Church had censured in 1653. So while the Dutch Protestants accused Descartes of Pelagianism (the doctrine that the will is not bound to sin but is capable of choosing good or evil), the Catholic Church condemned him for Jansenism, that is, for siding with those within the Church who thought that in their reaction against Lutheran/Calvinist denial of free will the Jesuit theologians had succumbed to Pelagianism. The gate to doctrinal orthodoxy is narrow indeed.

See also Anselm, St.; Aristotelianism; Aristotle; Arnauld, Antoine; Augustine, St.; Berkeley, George; Cartesianism; Cosmological Argument for the Existence of God; Degrees of Perfection, Argument for the Existence of God; Galileo Galilei; Gassendi, Pierre; Hintikka, Jaakko; Hobbes, Thomas; Husserl, Edmund; Kant, Immanuel; Leibniz, Gottfried Wilhelm; Locke, John; Malebranche, Nicolas; Matter; Mind-Body Problem; More, Henry; Newton, Isaac; Nicholas of Cusa; Ontological Argument for the Existence of God; Pascal, Blaise; Plato; Reid, Thomas; Ryle, Gilbert; Skepticism; Spinoza, Benedict (Baruch) de; Wittgenstein, Ludwig Josef Johann.

Bibliography

works by descartes

Discourse on Method, Optics, Geometry, and Meteorology. Translated by Paul Olscamp. Indianapolis, IN: Library of Liberal Arts, 1965. The only complete English translation of the scientific essays published with the Discourse.

Oeuvres. 11 vols., edited by Charles Adam and Paul Tannery. Paris: J. Vrin, 1974–1986. This is the standard edition of the texts in their original languages. All references to Descartes's works in this entry are to volume and page of this edition, cited as "Adam and Tannery."

Treatise of Man. Cambridge, MA: Harvard University Press, 1972. The French text with translation and commentary by Thomas Steele Hall.

Descartes' Conversation with Burman. Translated by John Cottingham. Oxford, U.K.: Clarendon Press, 1976.

Descartes: His Moral Philosophy and Psychology. Translated by John Blom. New York: New York University Press, 1978. The only English language edition of Descartes's correspondence with Elisabeth that gives her letters to Descartes as well as his replies to her.

Le monde, ou Traité de la lumière (The World ). French text with English translation by Michael Mahoney. New York: Abaris, 1979.

Principles of Philosophy. Translated by Valentine Rodger Miller and Reese P. Miller. Dordrecht, Netherlands: D. Reidel, 1983. The only complete English translation of this work.

Philosophical Writings. 3 vols. Translated by John Cottingham, Robert Stoothoff, Dugald Murdoch, and (in vol. 3), Anthony Kenny. Cambridge, U.K.: Cambridge University Press, 1985–1991. The best comprehensive English language edition. It gives the volume and page numbers of the Adam and Tannery edition in the margins.

The Passions of the Soul. Translated by Stephen Voss. Indianapolis, IN: Hackett, 1989.

biography

Baillet, Adrien. The Life of Monsieur Descartes. Translated by S. R. London: 1653. Available through Early English Books Online (http://eebo.chadwyck.com/home).

Gaukroger, Stephen. Descartes: An Intellectual Biography, Oxford, U.K.: Clarendon Press, 1995.

works on descartes

Alanen, Lilli. Descartes' Concept of Mind. Cambridge, U.K.: Harvard University Press, 2003.

Ariew, Roger. Descartes and the Last Scholastics. Ithaca, NY: Cornell University Press, 1999.

Ariew, Roger, John Cottingham, and Tom Sorell. Descartes' "Meditations": Background Source Materials. Cambridge, U.K.: Cambridge University Press, 1998.

Ariew, Roger, Dennis Des Chene, Douglas Jesseph, Tad Schmaltz, and Theo Verbeek. Historical Dictionary of Descartes and Cartesian Philosophy. Lanham, MD: Scarecrow Press, 2003.

Ariew, Roger, and Marjorie Grene. Descartes and His Contemporaries, "Meditations," Objections and Replies. Chicago: University of Chicago Press, 1995.

Armogathe, Jean-Robert, and Vincent Carraud. "The First Condemnation of Descartes' Oeuvres : Some Unpublished Documents from the Vatican Archives." Oxford Studies in Early Modern Philosophy 1 (2003): 67–109.

Baker, Gordon, and Katharine Morris. Descartes' Dualism. London: Routledge, 1996.

Broughton, Janet. Descartes' Method of Doubt. Princeton, NJ: Princeton University Press, 2002.

Clarke, Desmond. Descartes' Philosophy of Science. Manchester, U.K.: Manchester University Press, 1982.

Cottingham, John, ed. The Cambridge Companion to Descartes. Cambridge, U.K.: Cambridge University Press, 1992.

Cottingham, John, ed. Reason, Will, and Sensation. Oxford, U.K.: Clarendon Press, 1994.

Curley, Edwin. Descartes against the Skeptics. Cambridge, MA: Harvard University Press, 1978.

Frankfurt, Harry. Demons, Dreamers, and Madmen. Indianapolis, IN: Bobbs-Merrill, 1970.

Garber, Daniel. Descartes' Metaphysical Physics. Chicago: University of Chicago Press, 1992.

Garber, Daniel. Descartes Embodied: Reading Cartesian Philosophy through Cartesian Science. Cambridge, U.K.: Cambridge University Press, 2001.

Gaukroger, Stephen, ed. Descartes: Philosophy, Mathematics, and Physics. Sussex, U.K.: Harvester Press, 1980.

Hatfield, Gary. Routledge Philosophy Guidebook to Descartes and the "Meditations." London: Routledge, 2003.

Kenny, Anthony. The Anatomy of the Soul: Historical Essays in the Philosophy of Mind. Oxford, U.K.: Basil Blackwell, 1973.

Kenny, Anthony. Descartes: A Study of His Philosophy. New York: Random House, 1968.

Koyré, Alexandre. From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins University Press, 1957.

Matthews, Gareth. Thought's Ego in Augustine and Descartes. Ithaca, NY: Cornell University Press, 1992.

Menn, Stephen. Descartes and Augustine. Cambridge, U.K.: Cambridge University Press, 1998.

Rorty, Amélie Oksenberg, ed. Essays on Descartes' "Meditations." Berkeley: University of California Press, 1986.

Schuster, John. "Descartes' mathesis universalis, 1619–1628." In Descartes: Philosophy, Mathematics, and Physics, edited by Stephen Gaukroger. Sussex, U.K.: Harvester Press, 1980.

Verbeek, Theo. Descartes and the Dutch: Early Reactions to Cartesian Philosophy, 1637–1650. Carbondale: Southern Illinois University Press, 1992.

Voss, Stephen, ed. Essays on the Philosophy and Science of Descartes. Oxford, U.K.: Oxford University Press, 1993.

Weber, Jean-Paul. La constitution du texte des "Regulae." Paris: Société d'édition d'enseignement supérieur, 1964.

Williams, Bernard. Descartes: The Project of Pure Enquiry. Harmondsworth, U.K.: Penguin, 1978.

Williston, Byron, and André Gombay, eds. Passion and Virtue in Descartes. Amherst, NY: Humanity Books, 2003.

Wilson, Margaret Dauler. Descartes. London: Routledge and Kegan Paul, 1978.

Edwin Curley (2005)