Descartes

1. Descartes The Man Who Would Be Aristotle

2. René Descartes • 1596-1650 • Born in Touraine, France • Educated by Jesuits in traditional Aristotelian philosophy. • Took a law degree, but decided that real knowledge came from experience, so he became a soldier to be around “real” people. • Joined the Dutch army and then later moved to the Bavarian army. • Apparently was a well respected officer.

3. Descartes gives up on soldiers • After some years in the army, Descartes decided that “real” people didn’t know much either. • He retired from the army to devote himself to thinking about mathematics and mechanics, which he believed would lead to true knowledge.

4. Descartes a convert to Copernicus • Wrote a book about the Copernican system (The World) akin to Galileo's, but suppressed its publication when Galileo was condemned by the Inquisition. • It was not published until after his death.

5. A Dutch immigrant • Settled in Holland where he had more intellectual freedom than in France. • In 1649 moved to Stockholm to join the court of Queen Christina of Sweden, where, after a few months, he caught pneumonia and died. Descartes, at right, tutoring Queen Christina

6. Descartes’ Dream • Back when Descartes was being a soldier, he spent one winter night in quarters with the Bavarian army on the shore of the Danube, November 10, 1619. • The room was very hot. Descartes reported having three feverish dreams during the night. In these, he said later, he discovered the “foundations of a marvelous new science,” and realized that his future career lay in mathematics and philosophy. • He pondered this for nine more years before finally taking action, leaving the army and settling in Holland to think and write for the next 20 years.

7. Undertook to build a new systematic philosophy • In 1628 decided to create a new system of philosophy based on certainty (to replace Aristotle). • Certainty meant mathematics. • Descartes’ goal was to replace Aristotle’s common sense system with something organized like Euclid.

8. Descartes’ Principles of Philosophy • Published in 1644 • Organized like Euclid. • Sought to find a starting place, a certainty, which he would take as an axiom, and build up from that. • All his assertions are numbered and justified, just like Euclid’s propositions.

9. The Principles of Philosophy • Part 1: Of the Principles of Human Knowledge • 1. That whoever is searching after truth must, once in his life, doubt all things; insofar as this is possible. • 2. That doubtful things must further be held to be false. • ...

10. Cogito, ergo sum • Part 1: continued • 7. That it is not possible for us to doubt that, while we are doubting, we exist; and that this is the first thing which we know by philosophizing in the correct order. • Accordingly, this knowledge, I think, therefore I am [cogito, ergo sum] is the first and most certain to be acquired by and present itself to anyone who is philosophizing in correct order.

11. Dualism asserted • Part 1: continued • 8. That from this we understand the distinction between the soul and the body, or between a thinking thing and a corporeal one. • Note that this follows immediately after his “cogito, ergo sum” assertion.

12. The two worlds • Descartes assertion divides the world into two totally separate compartments: • Res cogitans – the world of the mind. • Res extensa – the world of things that take up space.

13. Res cogitans • The world of the mind. • Descartes wrote extensively about this, what is now considered his psychological and/or philosophical theory. • The main point for science is that it does not directly affect the physical world.

14. Res extensa • The world of extension, i.e., the physical world, was, for Descartes, totally mindless. • Therefore purpose had no place in it. • Res extensa obeyed strictly mechanical laws. • Compare Aristotle’s natural motion.

15. Motion in Res Extensa • Part II: Of the Principles of Material Objects • 36. That God is the primary cause of motion; and that He always maintains an equal quantity of it in the universe. • This is the principle ofconservation of motion – there is a fixed quantity of motion in the universe that is just transferred from one thing to another.

16. Inertial motion • Part II: continued • 37. The first law of nature: that each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move. • This is the principle of inertia, which, along with conservation of motion, asserts that motion is a natural thing requiring no further explanation. • Compare this to Aristotle, for whom all motion required an explanation.

17. Projectile motion • Part II: continued • 38. Why bodies which have been thrown continue to move after they leave the hand....having once begun to move, they continue to do so until they are slowed down by encounter with other bodies. • Descartes here disposes of Aristotle’s antiperistasis problem. A projectile keeps moving because it is natural that it do so.

18. Straight line motion • Part II: continued • 39. The second law of nature: that all movement is, of itself, along straight lines; and consequently, bodies which are moving in a circle always tend to move away from the centre of the circle which they are describing. • Anything actually moving in a circle is always tending to go off on a tangent. Therefore the circular motion requires a cause.

19. Relentless Mechanism • Inertial motion was natural. • Pushes and pulls transferred motion from one body to another. • Everything in Res extensa worked like a machine (e.g. windmill, waterwheel, clock). • Forces were occult – i.e. came from another world, therefore forbidden as an explanation.

20. Vortex Theory • Where (Aristotelian) Logic leads. • If natural motion was in straight lines, why did the planets circle the Sun?

21. Vortex Theory, 2 • Answer: They are pushed back toward the centre by all the invisible bits that fill the universe. • The universe is spherical and full. • Think of water in a bucket.

22. Living bodies are machines • The soul belongs to Res cogitans. • Anything in the physical world must be mechanical. • All living things are merely complex machines. • Animals were mere machines, no matter how much emotion they appeared to show.

23. The Human Body as a Machine • Living bodies were merely very complicated systems of levers and pulleys with mechanisms like gears and springs.

24. Automata • French clockmakers produced toy automata that made the mechanical body conceivable. • The monk kicks his feet, beats his chest with one hand, waves with the other, turns his head, rolls his eyes, opens and shuts his mouth.

25. The Human Condition • Since human being had souls and also had volition, there must be some communication for them between Res cogitans and Res extensa. • But how is this possible if the worlds are totally separate?

26. The Pineal Gland • In Descartes’ time, anatomists had discovered a tiny gland in the human brain for which they knew no purpose. • It was not known to exist in the brains of other animals. (It does.) • This was the Pineal Gland (it was shaped like a pine cone). • Aha!, thought Descartes. This is the seat of communication for the soul and the body.

27. The Pineal Gland in action • Descartes’ idea was that the pineal gland received neural transmissions from the body, communicated them to the soul, which sent back instructions to the body.

28. God the clockmaker • Descartes, the Jesuit-trained philosopher and lifelong Catholic, saw God’s role as being the creator of the universe and all its mechanisms. • God, the Engineer. • This became a popular theological position for scientists.

29. The Analysis of Res Extensa • Among Descartes’ most useful contributions to science were the tools he developed for studying the physical world. • Most important among these is the development of a new branch of mathematics: Analytic Geometry.

30. Analytic Geometry • A combination of geometry, taken from Euclid, and algebra, taken from Arab scholars, and traceable back to ancient Egypt. • Geometry was generally used to solve problems involving lines and shapes. • Algebra was most useful for finding numerical answers to particular problems. • Descartes found a useful way for them to work together.

31. Cartesian Coordinates • The extended world can be divided into indefinitely smaller pieces. • Any place in this world can be identified by measuring its distance from a fixed (arbitrary) beginning point (the origin) along three mutually perpendicular axes, x, y, and z.

32. Analytic Geometry • Geometric figures and paths of moving bodies can be described compactly with Cartesian coordinates. • A circle: x2 + y2 = 102 = 100 • This is a circle of radius = 10. • Every point on the circle is a distance of 10 from the centre. • By the Pythagorean theorem, every point (x, y) on the circle makes a right triangle with the x and y axes.

33. Capturing Projectile Motion in an equation

34. The Discourse on Method • Descartes’ revolutionary amalgamation of algebra and geometry was published as an appendix to his best known single work, the Discourse on Method of Rightly Conducting Reason in the Search for Truth in the Sciences, published in 1637. • Unlike the later Principles of Philosophy, which he wrote in Latin, the Discourse on Method was written in French and was intended for a general audience.

35. The Discourse on Method, 2 • The Discourse is itself not a formal philosophical treatise (though it is the work of Descartes that is most studied by philosophy students), but an autobiographical account of how Descartes arrived at his philosophical viewpoint, intended as a preface for the three works that followed. • It, like the Principles of Philosophy contains the argument from “I think, therefore I am.” • Now, the Discourse is studied extensively and the three appendices, which were intended to be the main subject matter, are ignored completely. • The three appendices are La Dioptrique (about light and optics), Les Météores(about the atmosphere—meteorology), and La Géométrie.

36. La Géométrie • In fact, the original La Géométrie was written in a confusing and disorganized way, with proofs only indicated, with the excuse that he left much out “in order to give others the pleasure of discovering for themselves.”

37. La Géométrie, 2 • This shortcoming was remedied by the Dutch mathematics professor, Frans van Schooten, who translated La Géométrie into Latin and added explanatory commentary that itself was more than twice the length of the original La Géométrie. • It was the Latin version that became the standard text that established analytic geometry in the universities of western Europe.

38. La Géométrie, 3 • Some of the innovations of La Géométrie: • It introduced the custom of using the letters at the end of the alphabet, x, y, z, for unknown quantities and those at the beginning, a, b, c, …, for constants. • Exponential notation: x2, y3, etc., was introduced. • Products of numbers, e.g. x2 or abc, were treated as just numbers, not necessarily areas or volumes, as was done in Greek geometry.

39. La Géométrie, 4 • We think of Cartesian coordinates as perpendicular axes, but in La Géométrie, they were merely two lines that met at an arbitrary angle, but then defined any point on the plane (or three lines, defining any point in space). • In the above diagram, the horizontal line from the vertex to the first diagonal line is arbitrarily given the value 1. The first diagonal has value a and the horizontal line from the vertex to the second diagonal has value b. Then, Descartes shows that the length of the second diagonal line is ab.

40. The Mechanical Philosophy • Though it is Newton’s systematic account of celestial mechanics that really established the mechanical viewpoint, Descartes’ works were the vanguard of the new mechanical philosophy whereby the educated public began to think of Nature as a large machine that ran on mechanical principles which could be expressed in mathematical laws. • Quoting Descartes: “the rules of mechanics…are the same as those of nature.