|March 31, 1596 (La Haye en Touraine (now Descartes), Indre-et-Loire, France)
|February 11, 1650 (Stockholm, Sweden)
|Cartesianism, Rationalism, Foundationalism
|Metaphysics, Epistemology, Science, Mathematics
|Cogito ergo sum, method of doubt, Mathesis Universalis, Cartesian coordinate system, Cartesian dualism, ontological argument for God's existence; regarded as a founder of Modern philosophy
|Plato, Aristotle, Anselm, Aquinas, Ockham, Suarez, Mersenne, Pyrrho
|Spinoza, Arnauld, Malebranche, Pascal, Locke, Leibniz, More, Kant, Husserl
René Descartes (March 31, 1596 – February 11, 1650), also known as Cartesius, was a noted French philosopher, mathematician, and scientist. Dubbed the "Founder of Modern Philosophy" and the "Father of Modern Mathematics," he ranks as one of the most important and influential thinkers of modern times. For good or bad, much of subsequent western philosophy is a reaction to his writings, which have been closely studied from his time down to the present day. Descartes was one of the key thinkers of the Scientific Revolution in the Western World. He is also honoured by having the Cartesian coordinate system used in plane geometry and algebra named after him.
Descartes frequently contrasted his views with those of his predecessors. In the opening section of the Passions of the Soul, he goes so far as to assert that he will write on his topic "as if no one had written on these matters before". Nevertheless many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his natural philosophy, he differs from the Schools on two major points: first, he rejects the analysis of corporeal substance into matter and form; second, he rejects any appeal to ends—divine or natural—in explaining natural phenomena. In his theology, he insists on the absolute freedom of God’s act of creation.
Descartes was a major figure in 17th century continental rationalism, later advocated by Baruch Spinoza and Gottfried Leibniz, and opposed by the empiricist school of thought, consisting of Hobbes, Locke, Berkeley, and Hume. Leibniz, Spinoza and Descartes were all versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well. As the inventor of the Cartesian coordinate system, Descartes founded analytic geometry, that bridge between algebra and geometry crucial to the invention of the calculus and analysis. Descartes' reflections on mind and mechanism began the strain of western thought that much later, impelled by the invention of the electronic computer and by the possibility of machine intelligence, blossomed into, e.g., the Turing test. His most famous statement is Cogito ergo sum (French: Je pense, donc je suis or in English: I think, therefore I am), found in §7 of Principles of Philosophy (Latin) and part IV of Discourse on Method (French).
On March 31, 1596, Descartes was born in La Haye en Touraine (now Descartes), Indre-et-Loire, France. When he was 1 year old, his mother died of tuberculosis. His father was a judge in the High Court of Justice. At the age of ten, he entered the Jesuit Collège Royal Henry-Le-Grand at La Flèche. After graduation, he studied at the University of Poitiers, earning a Baccalauréat and Licence in law in 1616, in accordance with his father's wishes that he become a lawyer.
Descartes never actually practiced law, however, and in 1618 he entered the service of Prince Maurice of Nassau, leader of the United Provinces of the Netherlands. His intention was to see the world and to discover the truth.
Here he met Isaac Beeckman, who sparked his interest in mathematics and the new physics, particularly the problem of fall of heavy bodies. On November 10, 1619, while traveling in Germany and thinking about using mathematics to solve problems in physics, Descartes had a vision in a dream through which he "discovered the foundations of a marvelous science" . This became a pivotal point in young Descartes' life and the foundation on which he develops analytical geometry. He dedicated the rest of his life to researching this connection between mathematics and nature.
In 1622 he returned to France, and during the next few years spent time in Paris and other parts of Europe. He arrived in La Haye in 1623, selling all of his property, investing this remuneration in bonds which provided Descartes with a comfortable income for the rest of his life. Descartes was present at the siege of La Rochelle by Cardinal Richelieu in 1627. He left for Holland in 1628, where he lived and changed his address frequently until 1649.
In 1633, Galileo was condemned by the Catholic Church, and Descartes abandoned plans to publish Treatise on the World, his work of the previous four years.
Although Descartes never married, he fathered a daughter, the issue of an affair with a woman named Helene; Francine, born in 1635 and baptized on August 7 of the same year. Much to Descartes' distress, she died in 1640 at the age of 5.
Descartes continued to
Descartes is often regarded as the first modern thinker to provide a philosophical framework for the natural sciences as these began to develop. In his Meditations on First Philosophy he attempts to arrive at a fundamental set of principles that one can know as true without any doubt. To achieve this, he employs a method called methodological skepticism: he doubts any idea that can be doubted.
He gives the example of dreaming: in a dream, one's senses perceive stimuli that seem real, but do not actually exist. Thus, one cannot rely on the data of the senses as necessarily true. Or, perhaps an "evil demon" exists: a supremely powerful and cunning being who sets out to try to deceive Descartes from knowing the true nature of reality. Given these possibilities, what can one know for certain?
Initially, Descartes arrives at only a single principle: thought exists. Thought cannot be separated from me, therefore, I exist (Meditations on First Philosophy). Most famously, this is known as cogito ergo sum, ("I think, therefore I am"). (These words do not appear in the Meditations, although he had written them in his earlier work Discourse on Method).
Note; Descartes was also sceptical of memory, as that has also been known to be manipulated, and can be doubted, so the 'cogito' argument can only apply to the present. The phrase is therefore more accurately (but less famously) translated as; "I am thinking, therefore I exist"
Therefore, Descartes concludes that he can be certain that he exists. But in what form? He perceives his body through the use of the senses; however, these have previously been proven unreliable. So Descartes concludes that the only undoubtable knowledge is that he is a thinking thing. Thinking is his essence as it is the only thing about him that cannot be doubted. Descartes defines "thought" (cogitatio) as "what happens in me such that I am immediately conscious of it, insofar as I am conscious of it". Thinking is thus every activity of a person of which he is immediately conscious.
To further demonstrate the limitations of the senses, Descartes proceeds with what is known as the Wax Argument. He considers a piece of wax: his senses inform him that it has certain characteristics, such as shape, texture, size, color, smell, and so forth. When he brings the wax towards a flame, these characteristics change completely. However, it seems that it is still the same thing: it is still a piece of wax, even though the data of the senses inform him that all of its characteristics are different. Therefore, in order to properly grasp the nature of the wax, he cannot use the senses: he must use his mind. Descartes concludes:
In this manner, Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and instead admitting only deduction as a method. Halfway through the Meditations, he offers an ontological proof of a benevolent God (through both the ontological argument and trademark argument). Because God is benevolent, he can have some faith in the account of reality his senses provide him, for God has provided him with a working mind and sensory system and does not desire to deceive him; however, this is a contentious argument, as his very notion of a benevolent God from which he developed this argument is easily subject to the same kind of doubt as his perceptions. From this supposition, however, he finally establishes the possibility of acquiring knowledge about the world based on deduction and perception. In terms of epistemology therefore, he can be said to have contributed such ideas as a rigorous conception of foundationalism and the possibility that reason is the only reliable method of attaining knowledge, as others said before him, though not as clearly as he did, and the rationalist answer to scepticism which other rationalists have elaborated on.
In Descartes' system, knowledge takes the form of ideas, and philosophical investigation is the contemplation of these ideas. This concept would influence subsequent internalist movements as Descartes' epistemology requires that a connection made by conscious awareness will distinguish knowledge from falsity. As a result of his Cartesian doubt, he sought for knowledge to be "incapable of being destroyed", in order to construct an unshakeable ground from which all other knowledge can be based on. The first item of unshakeable knowledge that Descartes argues for is the aforementioned cogito, or thinking thing.
Descartes also wrote a response to skepticism about the existence of the external world. He argues that sensory perceptions come to him involuntarily, and are not willed by him. They are external to his senses, and according to Descartes, this is evidence of the existence of something outside of his mind, and thus, an external world. Descartes goes on to show that the things in the external world are material by arguing that since God would not deceive him as to the ideas that are being transmitted, and that God has given him the "propensity" to believe that such ideas are caused by material things. Skeptics have responded to Descartes' proof for the external world by positing a brain in a vat thought experiment, in that Descartes' brain may be connected up to a machine which simulates all of these perceptions.
Descartes's theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent problem, thus permitting the evolution of that branch of modern mathematics . This appears even more astounding considering that the work was just intended as an example to his Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences (Discourse on the Method to Rightly Conduct the Reason and Search for the Truth in Sciences, known better under the shortened title Discours de la méthode).
Descartes' rule of signs is also a commonly used method in modern mathematics to determine possible quantities of positive and negative zeros of a function.
Descartes also made contributions in the field of optics; for instance, he showed by geometrical construction using the Law of Refraction that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°). 
Collected works in French:
Collected English translations: