Robin Yamaguchi Math 13 March 21, 1999 Rene Descartes In the recent hit movie The Net, the character played by Sandra Bullock has her identity erased.
Everyone doubted her existence. This was not, however, the first time someone’s existence was questioned. In the early 17th century a philosopher, who is named Descartes, questioned his own existence.
His life was dedicated to the founding of a philosophical and mathematical system in which all sciences were coherent. Descartes was born in 1596 in Touraine, France.His education consisted of attendance to a Jesuit school of La Fleche. He studied a liberal arts program which emphasized philosophy, the humanities, science, and math.
He then went on to the University of Poitiers where he graduated in 1616 with a law degree. Descartes also served as a volunteer in several different armies to broaden his horizons. After all of Descartes’ study and contemplation of math and science, he decided to find a single principle without doubt on which to build knowledge.His purpose in life became the development of a metaphysical theory that would prove the mathematical truth he had found. His analytical system of doubt led him to doubt everything in the world. He finally reached the conclusion that everything can be doubted except for one thing, his own existence. Even this was called into doubt and found true. Descartes rationalized that by doubting his own existence, he was thinking.
If he was thinking, then he must be existing. Then he contemplated whether he was awake or asleep. If he was asleep, then he was dreaming that he was thinking and therefore not existing. He decided that one could use sense perception to realize if one was awake of asleep.
Finally he concluded, “I think, therefore I am.” This became the basis for his entire system of beliefs. Descartes’ argument for existence was called “cogito ergo sum.” All of Descartes philosophical arguments were made by analytical means.He deduced the conclusion. According to Descartes, one’s existence must be because they cannot not exist.
By saying that one does not exist, that person is thinking and thus externalizing their thoughts through speech and must exist. Thereby, he proved by the converse statement of nonexistence that he does exist. Descartes did differentiate between existing and being, however, this will not be addressed accept to be mentioned. Next, Descartes must prove the existence of an omnipotent and perfect being.He reasoned that he is not perfect. Then the fact that a perfect thing exists. If he exists and is not perfect then that which is perfect also exists.
He says that this thing which is perfect is God. He says God exists because of his thoughts of God as an extension of God’s existence.After further philosophical reasoning he proved the existence of God. His proof of God has become the classic ontological proof used ever since. Descartes further proved that God cannot deceive anyone concerning anything. This proof was necessary in order to proceed on to other topics such as the world and it’s origins and laws. His God must also be omnipotent to do the things he wished to describe later, so he proved God to be omnipotent. The main literary work in which he published these proofs was his Meditations.
The other major philosophical work, which was publisher later, was his Discourse on Method. These two main works have paved the path for modern philosophy throughout the world. Although Descartes proved the existence of God, he did not believe him to be imminent, but rather, transcendent.
He was by definition a Deist. He believed that God created the world and the laws by which it works. Then, set the cosmos in motion by these natural laws and simply watches it operate.Once Descartes proved his own existence and that of God’s, he proceeded on to the sciences.
He showed that mathematics was the truest of all sciences. Descartes studied math intensely at the Jesuit school. His zeal for the subject continued into his later life.
Gradually, he became more and more disgusted with the current system of math.He sought to revise it and ended up revolutionizing it. Math today is based upon the Cartesian system. He is called the “Father of Modern Mathematics” for several reasons.
His major contribution is the application of algebra to geometry. In his treatise, Geometry, Descartes reveals his analytic geometry.Analytic geometry allows any curve to be addressed from an algebraic view by means of a coordinate system. This is taught to all beginning math students as the x,y plane. Any point, a Euclidean geometry undefined term, can be written by it’s x position and it’s y position. These positions are measured relative to the x-axis and the y-axis respectively. This is known as the Cartesian Coordinate System.From this simple beginning comes more complex ideas.
The equation of a line can now be know with only two points, a point and the slope of the line, or by the slope and the point at which the line crosses the y-axis, know as the y intercept. This in turn leads to quadratics and trigonometrics and so forth. All this allows curves to be studied in terms of their algebraic properties. Descartes’ other major mathematical contribution was the development of a shorthand notation for involution. Involution is the repeated multiplication of a given number, thus the notation was the exponent.Previously, involution was tedious. With the development of the exponent, larger numbers could be written with greater ease. This eventually led to the development of scientific notation which is a number multiplied by a power of ten.
Descartes ushered in the modern age of mathematics. Rene Descartes also contributed to other sciences. He studied the circulation of the blood at the same time as Harvey.
He performed many dissections of animals. It is rumored that someone asked to see his library and he pointed to a half dissected calf. The conclusions he reached were very similar to Harvey’s. Descartes discussed matter and regarded it as an extension of the mind. Similar to this is his view on heat, color, odor, and other sense perceptions. He said that they are only existent in one’s mind.
Two people do not see the same color, feel the same heat, smell the same odor, or anything else exactly the same.Therefore, these perceptions only have matter and exist in one’s mind. The personal life of Rene Descartes was a secluded one. He lived in the country and he kept his place of residence a secret. Only his closest friends knew his whereabouts. He corresponded with his friends regularly.One day a week was set apart as correspondence day.
Much of his time was spent contemplating the cosmos. The title of his first published work was very fittingly called Meditations. His publications were handled by a friend in the city. Descartes published several works anonymously.About this same time Galileo was found to be a heretic and Descartes would probably have been too had he not been so sly. He cleverly proposed a heliocentric theory as well as an evolutionary theory without being caught. A correspondent of Descartes’ was related to the queen of Sweden. This friend relayed the knowledge to the queen who was intrigued.
She sent a warship and an invitation to Descartes to visit her in Sweden.After much debate, Descartes agreed. He was required to rise early in the morning and teach the queen philosophy. He was not happy with his life there and longed for his home. In February of 1650, while nursing an ill friend, Rene Descartes caught pneumonia and died. Much of his work was later published by his other correspondents.Behind was left a legacy of philosophical thought that continues today.
The modern rationalistic movement was founded by Descartes. It is devoted to the reconciliation between the mechanical world and the spiritual God. Other members of this group include Spinoza and Leibniz. Descartes also inspired the Philosophes.These are French philosophers dedicated to the supremacy of human reason, popularization of science, and political and economic reform.
Other members of this movement were Voltaire and Montesquieu. From Descartes’ early scholastic achievements he was destined for greatness. He is known as the “Father of Modern Mathematics” and the “Father of Modern Rationalism.” His system of deductive reasoning has been adapted to almost every field of study. His major contributions to the field of math were the Cartesian coordinate system , the exponent, and the development of analytical geometry. His major contributions to the field of philosophy were the “cogito,” the system of doubt, and the classical ontological proof of God.Descartes has influenced thought throughout the ages. His works, especially Meditations, Geometry, and his Discourse on Method have become classics.
Rene Descartes, although he died at the premature age of 54, was a great mathematician and philosopher well disciplined in all genres. He will always be best remembered for proving his own existence by the statement, “I think, therefore I am.” Works Consulted Cantor, Norman F. and Peter L.Klein, eds. Seventeenth-Century Rationalism: Bacon And Descartes. London: Blaisdell, 1969. Kenny, Anthony.
Descartes: A study of his Philosophy.New York: Random House, 1968. “Analytic Geometry and Trigonometry.” Compton’s Living Encyclopedia. Compton’s Learning Company, 1996. On-line. America On-line.
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