Descartes

In the early 17th century a philosopher named Descartes, questioned his existence. His life was dedicated to the founding of a philosophical and mathematical system in which all sciences were logical.

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 that 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 exist. 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.

Descartes proves the existence of an all-powerful and perfect being. He reasoned that he is not perfect. 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 couldn't 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 Deity. 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. Descartes 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 its 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 came 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 monotonous. With the development of the exponent, larger numbers could be written with greater ease. This eventually led to the development of