Title: Descartes
1Descartes
- The Man Who Would Be Aristotle
2René 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.
3Descartes 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.
4Descartes 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.
5A 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
6Descartes 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.
7Undertook 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.
8Descartes 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.
9The 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. - ...
10Cogito, 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.
11Dualism 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.
12The 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.
13Res 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.
14Res 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.
15Motion 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.
16Inertial 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.
17Projectile 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.
18Straight 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.
19Relentless 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.
20Vortex Theory
- Where (Aristotelian) Logic leads.
- If natural motion was in straight lines, why did
the planets circle the Sun?
21Vortex 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.
22Living 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.
23The Human Body as a Machine
- Living bodies were merely very complicated
systems of levers and pulleys with mechanisms
like gears and springs.
24Automata
- 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.
25The 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?
26The 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.
27The 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.
28God 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.
29The 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.
30Analytic 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.
31Cartesian 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.
32Analytic 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.
33Capturing Projectile Motion in an equation
34The 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.
35The 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.
36La 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.
37La 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.
38La 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.
39La 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.
40The 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.