When I was a child I viewed everything from a child's point of view. If I was afraid of the dark it was because I believed that monsters dwelled under my bed and in my closets. If I was afraid of loud noises it is because I believed with all my little heart that they led to danger. As I aged and learned more about the world that I live in I came to know that monsters do not exist and loud noises do not always spell danger, therefore as my knowledge and understanding of the world changed so did my beliefs and philosophies of the world.
             In the same way that my increasing maturity about the world change the way I think so has the field of philosophy in general. In ancient times Socrates was considered the world's greatest teacher of philosophy because of his wisdom and intellect. As the years moved forward after his death however, mankind matured and gained much more wisdom into the way the world actually operates and with that wisdom and knowledge came new styles and methods of philosophy as well. The words and beliefs of Socrates should be considered foundational stepping stones or blueprints for later philosophers such as Rene Descartes.
             For someone to be able to contrast and compare the methods of philosophy between Socrates and Descartes it is important to understand the life and workings of each man. Rene Descartes was perhaps the most celebrated philosopher of his time and was also a most well known mathematician(René Descartes: Discourse on Method (1637) http://www.wsu.edu:8080/~wldciv/world_civ_reader/world_civ_reader_2/descartes.html).
             Descartes method of philosophy includes many of the mathematic principles that he is so fond of. "Descartes proposes a method of thought incorporating the rigor of mathematics but based on intuitive truths about what is real, basic knowledge which could not be wrong (like the axioms of geometry). He calls into question everything that he thinks he has learned throu...