René Descartes

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René Descartes
It is not enough to have a good mind. The main thing is to use it well.

René Descartes (March 31, 1596February 11, 1650) was a highly influential French philosopher, mathematician, physicist and writer. He is known for his influential arguments for substance dualism, where mind and body are considered to have distinct essences, one being characterized by thought, the other by spatial extension. He has been dubbed the "Father of Modern Philosophy" and the "Father of Modern Mathematics." He is also known as Cartesius.

See also
Discourse on the Method (1637)
Meditations on First Philosophy (1641)
Principles of Philosophy (1644)


  • M. Desargues puts me under obligations on account of the pains that it has pleased him to have in me, in that he shows that he is sorry that I do not wish to study more in geometry, but I have resolved to quit only abstract geometry, that is to say, the consideration of questions which serve only to exercise the mind, and this, in order to study another kind of geometry, which has for its object the explanation of the phenomena of nature... You know that all my physics is nothing else than geometry.
  • Me tenant comme je suis, un pied dans un pays et l’autre en un autre, je trouve ma condition très heureuse, en ce qu’elle est libre.
  • So blind is the curiosity by which mortals are possessed, that they often conduct their minds along unexplored routes, having no reason to hope for success, but merely being willing to risk the experiment of finding whether the truth they seek lies there.
    • Rules for the Direction of the Mind: IV
  • The entire method consists in the order and arrangement of the things to which the mind’s eye must turn so that we can discover some truth.
    • Rules for the Direction of the Mind: X.379
    • As quoted in Clarke, Desmond M. (2006). Descartes : a Biography. Cambridge Press. p. 67. ISBN 978-0-521-82301-2. 
  • No more useful inquiry can be proposed than that which seeks to determine the nature and the scope of human knowledge. ... This investigation should be undertaken once at least in his life by anyone who has the slightest regard for truth, since in pursuing it the true instruments of knowledge and the whole method of inquiry come to light. But nothing seems to me more futile than the conduct of those who boldly dispute about the secrets of nature ... without yet having ever asked even whether human reason is adequate to the solution of these problems.
  • Mais apud me omnia fiunt Mathematicè in Natura
    • Loosely translated: With me, everything turns into mathematics.
    • More closely translated as: but in my opinion, all things in nature occur mathematically.
      • Note: "Mais" is French for "but" and the "but in my opinion" comes from the context of the original conversation. apud me omnia fiunt Mathematicè in Natura is in latin.
    • Sometimes the Latin version is incorrectly quoted as Omnia apud me mathematica fiunt.
    • Sources: Correspondence with Mersenne note for line 7 (1640), page 36, Die Wiener Zeit page 532 (2008); StackExchange Math Q/A Where did Descartes write...

Le Discours de la Méthode (1637)[edit]

Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences
  • Je pense, donc je suis.
    • I think, therefore I am.

Quotes about Descartes[edit]

  • Descartes maintained his confidence in the instantaneity of light. ...Yet in his derivation of the law of refraction, Descartes reasoned that light travelled faster in a dense medium than in one less dense. He seems to have had no qualms about comparing infinite magnitudes!
  • Among the earliest thinkers of the seventeenth and eighteenth centuries, who employed their mental powers toward the destruction of old ideas and the up-building of new ones, ranks Rene Descartes. Though he professed orthodoxy in faith all his life, yet in science he was a profound sceptic. He found that the world's brightest thinkers had been long exercised in metaphysics, yet they had discovered nothing certain; nay, they had even flatly contradicted each other. ...The certainty of the conclusions in geometry and arithmetic brought out in his mind the contrast between the true and false ways of seeking the truth. He thereupon attempted to apply mathematical reasoning to all sciences.
  • His philosophy has long since been superseded by other systems, but the analytical geometry of Descartes will remain a valuable possession forever.
    • Florian Cajori, A History of Mathematics (1893)
  • His Geometry is not easy reading. An edition appeared subsequently with notes by his friend De Beaune, which were intended to remove the difficulties.
    • Florian Cajori, A History of Mathematics (1893)
  • It is frequently stated that Descartes was the first to apply algebra to geometry. This statement is inaccurate, for Vieta and others had done this before him. Even the Arabs sometimes used algebra in connection with geometry.
    • Florian Cajori, A History of Mathematics (1893)
  • In the Greek geometry the idea of motion was wanting but with Descartes it became a very fruitful conception. ...This geometric idea of co-ordinate representation, together with the algebraic idea of two variables in one equation having an indefinite number of simultaneous values, furnished a method for the study of loci, which is admirable for the generality of its solutions. Thus the entire conic sections of Apollonius is wrapped up and contained in a single equation of the second degree.
    • Florian Cajori, A History of Mathematics (1893)
  • Descartes' geometry was called "analytical geometry," partly because unlike the synthetic geometry of the ancients it is actually analytical in the sense that the word is used in logic; and partly because the practice had then already arisen, of designating by the term analysis the calculus [i.e., symbolic calculation or computation] with general quantities.
    • Florian Cajori, A History of Mathematics (1893)
  • The first important example solved by Descartes in his geometry is the "problem of Pappus"... Of this celebrated problem the Greeks solved only the special case... By Descartes it was solved completely, and it afforded an excellent example of the use which can be made of his analytical method in the study of loci. Another solution was given later by Newton in the Principia.
    • Florian Cajori, A History of Mathematics (1893)
  • Methods of drawing tangents were invented by Roberval and Fermat... Descartes gave a third method. Of all the problems which he solved by his geometry, none gave him as great pleasure as his mode of constructing tangents. It is profound but operose, and, on that account, inferior to Fermat's. His solution rests on the method of Indeterminate Coefficients, of which he bears the honour of invention. Indeterminate coefficients were employed by him also in solving bi-quadratic equations.
    • Florian Cajori, A History of Mathematics (1893)
  • In mechanics Descartes can hardly be said to have advanced beyond Galileo. ...His statement of the first and second laws of motion was an improvement in form, but his third law is false in substance. The motions of bodies in their direct impact was imperfectly understood by Galileo, erroneously given by Descartes, and first correctly stated by Wren, Wallis, and Huygens.
  • Descartes implicitly assumed a complete correspondence existed between the real numbers and the points of a fixed axis. ...tacitly, because it seemed so natural as to go without saying, he accepted it as axiomatic that between the points of a plane and the aggregate of all pairs of real numbers there can be established a perfect correspondence. Thus the Dedekind-Cantor axiom, extended to two dimensions, was tacitly incorporated in a discipline which was created two hundred years before Dedekind and Cantor saw the day. This discipline became the [tool and] proving-grounds for all achievements of the following two centuries: the calculus, the theory of functions, mechanics, and physics. Nowhere did this discipline, analytic geometry, strike any contradictions; and such was its power to suggest new problems and forecast the results that wherever applied it would soon become the indispensable tool of investigation.
  • The famous problems of antiquity [doubling the cube, angle trisection, and squaring the circle]... were now disposed of by Descartes in a matter-of-fact statement that any problem which leads to an equation of the first degree is capable of a geometric solution by straight-edge only; that a straight-edge [and] compass construction is equivalent to the solution of a quadratic equation; but that if a problem leads to an irreducible equation of degree higher than the second, its geometrical solution is not possible by means of a ruler and compass only.
  • This momentous finding of nonlocality has, in common with that of Einstein concerning time, the additional feature that it disproves the validity, not of a "view of the World", but of a deeply ingrained concept. And this brings me to the second reason. It is that this disproof of a deeply ingrained concept pointed in fact in a direction quite consonant with my own line of thought. In a way, it brings us back to Descartes, for, as we all know, Descartes was the first scientist who dared to question our common views, including even all the notions that had always seemed so primitive and obvious that thinkers, scientists and so on never hesitated in making use of them. He found out that, at the start, he could doubt of everything but his own thinking, and in this, according to Hegel, he was a hero. Unfortunately he then constructed a grand metaphysical argument that led him to the view that, after all, since God is not a liar, the "obvious" realistic concepts must apply. He thereby founded mechanicism, which is the theory that, apart from thought, everything has to be described by the exclusive means of familiar concepts. We know, of course, how deficient such a view is. But I think Descartes' really significant contribution on these matters is not mechanicism. It is what I just said. In other words, it is the realization that a sharp distinction has to be made between rationality on the one hand and the use of seemingly obvious concepts on the other hand. And that therefore, if you are a rational person you cannot demand that science should be based exclusively on seemingly obvious concepts without first logically justifying this demand. This Descartes tried to do but, since his argument based on God not being a liar is now considered as not convincing enough, we are not bound to his conclusion. Indeed, I consider that we are not even bound to the idea that physics should be expressed in an ontological language, which was more or less Einstein's view. The older Einstein seems to have considered that Reality, and even physical objects in the plural, can be described as they really are, if not by familiar concepts, at least by unfamiliar ones, such as those borrowed from mathematics. I do not think this is necessarily true. I consider that mere predictive rules, such as the Born rule in quantum mechanics, count as fully fledged explanations, or, more precisely, as constituting, when all taken together, a first step in an explanation, the second step being the philosophical idea that these predictive rules dimly reflect some existing, largely hidden structures of Mind-Independent Reality. Of course, these speculations of mine go much further than nonlocality. But you understand that they receive some support from it.
    • Bernard d'Espagnat, "My Interaction with John Bell", in Quantum [Un]speakables (2002) edited by R.A. Bertimann, A. Zeilinger
  • Newton's proof of the law of refraction is based on an erroneous notion that light travels faster in glass than in air, the same error that Descartes had made. This error stems from the fact that both of them thought that light was corpuscular in nature.
    • John Freely, Before Galileo, The Birth of Modern Science in Medieval Europe (2012)
  • The Geometry is divided into three books. In the first book Descartes briefly explains his method. He says that every geometric problem may be reduced to a problem of straight lines; and he points out that, in order to find these lines, nothing more advanced is required than the five fundamental operations of Arithmetic, viz.: Addition, Subtraction, Multiplication, Division, and Root Extraction. He advises:—
    (1) That the problem should be imagined as done.
    (2) That then lines, whether known or unknown, which appear necessary in its solution, should be named.
    (3) And finally, that their relation to each other should be sought, and expressed by means of an equation or equations. Descartes strongly advocates this analytic treatment of Geometry as giving greater clearness and more continuity of argument, qualities lacking in the work of the Ancients, who probably did not understand where such reasoning would carry them, and whose isolated proofs were necessarily wanting in connection and generality.
  • It should be remembered that it was Descartes who systematised our Mathematical notation. He used the letters at the end of the alphabet as variables, and those at the beginning as constants, and he brought into general use our present system of indices. He also introduced the method of indeterminate co-efficients for the solution of equations.
  • There seems to me to exist a sort of rationalism which, by not recognizing these limits of the powers of individual reason, in fact tends to make human reason a less effective instrument than it could be. … This sort of rationalism is a comparatively new phenomenon, though its roots go back to ancient Greek philosophy. Its modern influence, however, begins only in the sixteenth and seventeenth century and particularly with the formulation of its main tenets by the French philosopher, René Descartes.
    • Friedrich Hayek, "Kinds of Rationalism", The Economic Studies Quarterly (1965)
  • Aristotle remarks in his Poetics that poetry is superior to history, because history presents only what has occurred, poetry what could and ought to have occurred, poetry has possibility at its disposal. Possibility, poetic and intellectual, is superior to actuality; the esthetic and the intellectual are disinterested. But there is only one interest, the interest in existing; disinterestedness is the expression for indifference to actuality. The indifference is forgotten in the Cartesian Cogito-ergo sum, which disturbs the disinterestedness of the intellectual and offends speculative thought, as if something else should follow from it. I think, ergo I think; whether I am or it is (in the sense of actuality, where I means a single existing human being and it means a single definite something) is infinitely unimportant. That what I am thinking is in the sense of thinking does not, of course, need any demonstration, nor does it need to be demonstrated by any conclusion, since it is indeed demonstrated. But as soon as I begin to want to make my thinking teleological in relation to something else, interest enters the game. As soon as it is there, the ethical is present and exempts me from further trouble with demonstrating my existence, and since it obliges me to exist, it prevents me from making an ethically deceptive and metaphysically unclear flourish of a conclusion.
  • Thus was the Nixon Administration first exposed to the maddening diplomatic style of the North Vietnamese. It would have been impossible to find two societies less intended by fate to understand each other than the Vietnamese and the American. On the one side, Vietnamese history and Communist ideology combined to produce almost morbid suspicion and ferocious self-righteousness. This was compounded by a legacy of Cartesian logic from French colonialism that produced an infuriatingly doctrinaire technique of advocacy.
    • Henry A. Kissinger, The White House Years
  • As a symbol of the power of absolutism, Versailles has no equal. It also expresses, in the most monumental terms of its age, the rationalistic creed—based on scientific advances, such as the physics of Sir Isaac Newton (1642–1727) and the mathematical philosophy of René Descartes (1596–1650)—that all knowledge must be systematic and all science must be the consequence of the intellect imposed on matter. The whole spectacular design of Versailles proudly proclaims the mastery of human intelligence (and the mastery of Louis XIV) over the disorderliness of nature.
    • Fred S. Kleiner, Gardner’s Art through the Ages: A Global History (2009)
  • "There is one basis of science," says Descartes, "one test and rule of truth, namely, that whatever is clearly and distinctly conceived is true." A profound psychological mistake. It is true only of formal logic, wherein the mind never quits the sphere of its first assumptions to pass out into the sphere of real existences; no sooner does the mind pass from the internal order to the external order, than the necessity of verifying the strict correspondence between the two becomes absolute. The Ideal Test must be supplemented by the Real Test, to suit the new conditions of the problem.
  • The one book that turned out to be perhaps the most influential in guiding Newton's mathematical and scientific thought was none other than Descartes' La Géométrie. Newton read it in 1664 and re-read it several times until "by degrees he made himself master of the whole." ...Not only did analytic geometry pave the way for Newton's founding of calculus... but Newton's inner scientific spirit was truly set ablaze.
  • By... confounding the properties of matter with those of space he arrives at the logical conclusion, that if the matter within a vessel could be entirely removed the space within the vessel would no longer exist. In fact he assumes that all space must be always full of matter.
  • The primary property of matter was indeed distinctly announced by Descartes in what he calls the "First Law of Nature": "That every individual thing, so far as in it lies, perseveres in the same state, whether of motion or of rest."
    • James Clerk Maxwell, Matter and Motion (1876)
  • Descartes... fell back on his original confusion of matter with space—space being, according to him, the only form of substance, and all existing things but affections of space. This error... forms one of the ultimate foundations of the system of Spinoza.
  • As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition.
  • “Do you know who first explained the true origin of the rainbow?” I asked.
    “It was Descartes,” he said. After a moment he looked me in the eye.
    “And what do you think was the salient feature of the rainbow that inspired Descartes’ mathematical analysis?” he asked.
    “Well, the rainbow is actually a section of a cone that appears as an arc of the colors of the spectrum when drops of water are illuminated by sunlight behind the observer.”
    “I suppose his inspiration was the realization that the problem could be analyzed by considering a single drop, and the geometry of the situation.”
    “You’re overlooking a key feature of the phenomenon,” he said.
    “Okay, I give up. What would you say inspired his theory?”
    “I would say his inspiration was that he thought rainbows were beautiful.”
    I looked at him sheepishly. He looked at me.
    “How’s your work coming?” he asked.
    I shrugged. “It’s not really coming.” I wished I was like Constantine. It all came so easily to him.
    “Let me ask you something. Think back to when you were a kid. For you, that isn’t going too far back. When you were a kid, did you love science? Was it your passion?”
    I nodded. “As long as I can remember.”
    “Me, too,” he said. “Remember, it’s supposed to be fun.” And he walked on.
    • Leonard Mlodinow, Feynman’s Rainbow: A Search for Beauty in Physics and in Life (2003)
  • Descartes … is distinguished from Bacon in respect of the thoroughness of his education in the Scholastic philosophy and in the profound impression that geometrical demonstration had upon his mind, and the effect of these differences in education and inspiration is to make his formulation of the technique of inquiry more precise and in consequence more critical. His mind is oriented towards the project of an infallible and universal method or research, but since the method he propounds is modelled on that of geometry, its limitation when applied, not to possibilities but to things, is easily apparent. Descartes is more thorough than Bacon in doing his scepticism for himself and, in the end, he recognizes it to be an error to suppose that the method can ever be the sole means of inquiry. The sovereignty of technique turns out to be a dream and not a reality. Nevertheless, the lesson his successors believed themselves to have learned from Descartes was the sovereignty of technique and not his doubtfulness about the possibility of an infallible method.
    • Michael Oakeshott, "Rationalism in Politics" (1947), published in Rationalism in Politics and other essays (1962)
  • I would inquire of reasonable persons whether this principle: Matter is naturally wholly incapable of thought, and this other: I think, therefore I am, are in fact the same in the mind of Descartes, and in that of St. Augustine, who said the same thing twelve hundred years before. ...I am far from affirming that Descartes is not the real author of it, even if he may have learned it only in reading this distinguished saint; for I know how much difference there is between writing a word by chance without making a longer and more extended reflection on it, and perceiving in this word an admirable series of conclusions, which prove the distinction between material and spiritual natures, and making of it a firm and sustained principle of a complete metaphysical system, as Descartes has pretended to do. is on this supposition that I say that this expression is as different in his writings from the saying in others who have said it by chance, as in a man full of life and strength, from a corpse.
  • Descartes subscribed to the doctrine of instantaneous propagation, but with him something new emerged: for his was the first uncompromisingly mechanical theory that asserted the instantaneous propagation of light in a material medium... Indeed, mechanical analogies had been used to explain optical phenomena long before Descartes, but the Cartesian theory was the first clearly to assert that light itself was nothing but a mechanical property of the luminous object and of the transmitting medium. It is for this reason that we may regard Descartes' theory of light as legitimate starting point of modern physical optics.
    • A. I. Sabra, Theories of Light, from Descartes to Newton (1981)
  • In the theory of the state of the seventeenth century, the monarch is identified with God and has in the state a position exactly analogous to that attributed to God in the Cartesian system of the world.
  • Descartes may have made a lot of mistakes, but he was right about this: you cannot doubt the existence of your own consciousness. That's the first feature of consciousness, it's real and irreducible. You cannot get rid of it by showing that it's an illusion in a way that you can with other standard illusions.
  • Despite Newton's belated appreciation of Euclid's geometry, he set it aside as an undergraduate and immediately turned to Descartes' Geometrie, a much more difficult text. Newton read a few pages... and immediately got stuck. ...The second time through, he progressed a page or two further before running into more difficulties. Again, he read it from the beginning, this time getting further still. He continued this process until he mastered Descartes' text. Had Newton mastered Euclid first, Descartes' analytic geometry would have been much easier to understand. Newton later advised others not to make the same mistake.
    But Descartes had ignited Newton's interest in mathematics, an interest that bordered on obsession.
    • Mitch Stokes, Isaac Newton (2010)
  • Man occupies a special place in the Cartesian scheme. He alone is endowed with mind. Descartes believed that animals did not possess one, that they were simply extremely complicated automatons. Other thinkers have rejected this point of view and proposed to endow all matter in the universe—living or inanimate—with consciousness. This "panpsychism" has been promoted by, among others, Teilhard de Chardin and, more recently by the British-American physicist Freeman Dyson, who holds that mind is present in every particle of matter.
  • The truth is sum, ergo cogito — I am, therefore I think, although not everything that is thinks. Is not consciousness of thinking above all consciousness of being? Is pure thought possible, without consciousness of self, without personality? Can there exist pure knowledge without feeling, without that species of materiality which feelings lends to it? Do we not perhaps feel thought, and do we not feel ourselves in the act of knowing and willing? Could not the man in the stove [Descartes] have said: "I feel, therefore I am"? or "I will, therefore I am"? And to feel oneself, is it not perhaps to feel oneself imperishable?
  • After Bruno's death, during the first half of the seventeenth century, Descartes seemed about to take the leadership of human thought... in promoting an evolution doctrine as regards the mechanical formation of the solar system... but his constant dread of persecution, both from Catholics and Protestants, led him steadily to veil his thoughts and even to suppress them. The execution of Bruno had occurred in his childhood, and in the midst of his career he had watched the Galileo struggle in all its stages. He had seen his own works condemned by university after university under the direction of theologians and placed upon the Roman Index. ...Since Roger Bacon, perhaps, no great thinker had been so completely abased and thwarted by theological oppression.


  • An optimist may see a light where there is none, but why must the pessimist always run to blow it out?
    • Michel de Saint-Pierre, as quoted in Cryptograms and Spygrams (1981) by Norma Gleason, p. 106; attributed to Descartes in The Athlete's Way : Training Your Mind and Body to Experience the Joy of Exercise (2008) by Christopher Bergland, p. 271.
  • Doubt is the origin of wisdom and Latin: Dubium sapientiae initium. This has been attributed to Descartes, including here previously, but no original attribution has been found. Descartes Meditationes de prima philosophia has been cited as the source of Dubium sapientiae initium, but this quote is not found in this work.

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