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steven feldman

on 22 February 2013

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Transcript of Descartes

Another way Descartes described geometry algebraically.
Describing points by their relationship to axis.
Equations describe all points on a curve.
Algebraic vs Transcendental curves Accept nothing as true unless it is evident
Divide any given problem into the greatest possible number of parts
Start with simple objects and then move towards increasingly complex objects of study
Constantly review any progress that has been made to insure that no mistakes were made photo credit Nasa / Goddard Space Flight Center / Reto Stöckli 1596-1650 René Descartes Born: March 31, 1596
La Haye, France
1 of 5 children
Parents: Jaochim Descartes and Jeanne Brochard
Father: lawyer and magistrate
Mother: Passed away while Descartes was a baby
Descartes and siblings move in with Grandmother The Final Years Philosophy Mathematics The Creator of Analytic Geometry: Geometry in the coordinate plane.
Combined Algebra and Geometry Early years Education Jaochim cared to provide children with proper education
Sent to Jesuit college at age 8
Fragile health allowed for him to attend class late every morning
A habit he kept for the rest of his life
Subjects studied prepared him well to become a philosoper
University of Poiters - 1615
Spent 4 years earning Baccalaureate in law
Influential teacher at University: mathematics and logic to understand world Military Major Works 1618: Enlisted in Dutch Army
Army of Prince Maurice of Nassau
Corps of Engineers Four Laws Discourse on Method of Rightly Conducting the Reason and Seeking truth in the Sciences Meditations on First Philosophy While stationed in Breda, introduced to Dutch mathematician and scientist, Issac Breeckman
Student/teacher relationshp
Rekindle interest in math and science
Teaches Lipsius' theories
3 dreams - a landmark moment in his life
Leaves army in 1619 Contains six meditations
Written as though he was meditating for six days
The meditations are revolved around Descartes's metaphysical system Life After War Fascinated with Lipsius' ideals
switches focus: law to natural philosophy
1628: begins work on Regulae ad Directionem Ingenii
Published in 1637 - 1st establishing his philosophies Recognition November, 1628:
Debate with Chandoux
Chandoux: science based on probability
Descartes: certainty provides scientific knowledge
Later that year he moves to Holland Le Monde (The World) Abandons Regulae ad Directionem Ingenii
In Holland, begins work on Le Monde
"Dioptrique" and "Meteors" - later become part of "Le Monde"
1633: "Le Monde" is ready for publication
Backed out - feared treatment that Galileo received from Catholic authorities Meditation 1: Concerning Those Things That Can Be Called into Doubt Developed method as a reaction to his education in Aristotelian philosophy
Absence of knowledge and certainty
November 10, 1619
Questioned all previous beliefs and thoughts
Discards everything except for the fact that he exists
Arguments to show God exist Discourse The Existence of God -Deception Some of "Le Monde" was added to "Discourse"
Published 1937
Builds following of students interested in Cartesian Science
Then puts a hold on work to take care of family
Domestic servant: Helene
Daughter: Francine - He had been mislead in his past and he believed it was prudent that we never completely trust those who have deceived us before Meditations Before Descartes -Descartes was very concerned with metaphysics ,which is the study of being (root) Must exist because we can conceive a God
Impossible for imperfect being to conceive of a perfect being by himself
All perfect in the world must come from God Epistemology of Descartes 1639: Descartes begins work on Meditiations
Includes all of the foundations of his physics
1640: Goes to Leiden for publication
Interrupted by unexpected death of daughter (father and sister die later same year as well).
1641: official publication
Hopes of becoming a textbook (for teachers)
1642: publication of 2nd edition and "Objections and Replies" Notation was different.
Geometry was most important. -We should doubt all that can be doubted, to find only that which is certain (build with firm foundation) -Senses can deceive us, so how can we believe anything we see, hear, feel, taste, or touch. This leaves us with doubt The Determinate Problem - In dreams there are clearly no senses that are certain; all is possible in a dream-- except math Finite number of solutions.
Line Segment. Indeterminate Problem Locus Problems (the Pappus Problem)
A locus is a set of points that satisfies a certain condition. There can be an infinite amount of solutions - If I am being deceived while I dreaming, then my beliefs are unreliable SO............ Cartesian Doubt Problem from Ancient Greece
This is a simplified problem, Descartes actually solved a Pappus Line Problem with "n" lines.
In other words, he used Algebra to find universal solution to this geometric problem.
This is important because Descartes described geometry algebraically.
Descartes used Algebra to solve numerous Geometric problems (many of which involved conics) Cartesian Geometry Accept nothing as true unless it is evident
Divide any given problem into the greatest number of parts to make for a simpler analysis
Start with the simplest of objects, and slowly progress towards more complex objects of study
Constantly review any progress made to ensure that nothing is left out -Cartesian doubt is a systematic process of being skeptical about (or doubting) the truth of one's beliefs Principia Philosophiae (Principles of Philosophy) - Descartes ultimately erased all of his beliefs that he was not certain of, so he could determine for himself what was true - He even thought that a god like demon might be feeding his brain with these false beliefs. 1643: Moves to North Holland
Completes new textbook
Began in 1640, published in 1644
Makes arguments by means of metaphysics -He believes that if we can answer the simple questions first, then we will be able to build up and get the right answers 1649: Offered and accepts a position in Queen Christina's court
1650: Provides philosophical teachings to Queen
5 hours a day, 3 days a week at 5 AM In Conclusion Passions -Descartes thought that everything you experience in your everyday life could, in fact, be an illusion
-Your senses can be deceived, and therefore you cannot prove that your senses are lying to you and you can't prove they are not.
-But If you can think, it proves you exist since something that does not exist cannot doubt its own existence. Therefore, you exist
-This is the basis of his adapted famous quote, "Cogito, ergo, sum" or, "I think, therefore, I am" Correspondence with Princess Elizabeth
1650: Publishes "Passions"
Main argument: "Passion of the soul" is a direct result of brain activity
Passions lead to actions
Controlling the passions is a necessity
February, 1650: Falls ill
February 11th, 1650: respiratory infection causes death Thoughts on Death Allowed to arrive late to school as a child because of sickness
5 AM classes with Queen
Possible death correlation Overview Published in 1644 in Latin
Synthesis on Discourse on method and Meditations on First Philosophy
Dedicated to Elisabeth of Bohemia Four Parts I. Account of Epistemology and Metaphysics
II. Principles of physics
III. Develop theory of structure of the universe and solar system.
IV. Investigates the origins of the earth as well as other earthly phenomena Meditation 2 Argument that our mind is more certainly known than the body - It is possible that all external objects could be false, including my body, as a result of an evil demon -However, I can not be deceived about my nature as a thinking thing -Even corporeal objects, such as the body, are known much more distinctly through the mind -The wax argument -Therefore, our mind is much more clearly known to us than our body -Descartes used what is today known as Cartesian Doubt Meditation 3 -Descartes proposes that there are three types of ideas Innate Fictitious Adventitious -God = Innate Principles of Nature Replace Aristotelian curriculum in French and English Universities
In the absence of external forces, an objects movement will be uniform and in a strait line.
Degrees of knowledge
Clear and evident ideas
Use of senses
What we learn when talking with other men
Writings from men capable of giving good instruction
Search for the first causes* Laws of Physics -Argues that he had a clear and distinct idea of God and that his perfect idea of a perfect being could not be caused by anything less than the existence of a perfect being Meditation 4 -Explains the possibility of error -God is not a deceiver and he created me, but I am often in error. -How is it possible that I can make errors even though I am a product of the perfect God? -Intellect vs. Will - Can't blame God for free will which it is possible for us to abuse and enables us to fall into error -Avoid error Meditation 5 Key Concepts We can trust our clear and distinct perceptions to tell us the truth about the world.
God is responsible for the workings of our perceptions and he would not purposefully lead man astray
God created human beings' mind and body separately
Matter is infinitely divisible
Space and body are the same thing Rule of Signs A technique for determining the number of positive and negative real roots of a polynomial.
The number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by a multiple of 2.
The number of negative roots is the number of sign changes after multiplying the coefficients of odd-power terms by −1, or fewer than it by a multiple of 2. Descartes argues the existence of God once again Corporeal objects are properties concerned with extension, duration and movement (external objects) Ideas of god are the only ideas that imply God's existence (just like math) -Perfection includes existence -So God exists -Ontological Argument Meditation 6 -The existence of material things and the real distinction between mind and body Sources http://www.math4all.nl/MathAdore/Images/Descartes.jpg
http://prezi.com/at7eljbdaxfl/rene-descartes/ -Do material things exist? -Imagination vs. intellect -Imagination is not necessary, you would still be the same Intellect-mind turns towards self imagination-mind turns towards body -These object must come from external reality or from God himself -And if these things didn’t exist then God would be deceiving us This leads to..... Therefore Descartes starts his work with only what he know to be true - Dualism -Descartes proves God's existence and that he is not a deceiver
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