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 didnt 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 Aristotles 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 Euclids 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 Aristotles 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 of conservation 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 Aristotles
  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 Gods 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
  atmospheremeteorology), 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 Newtons 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 mechanicsare
  the same as those of nature.