Rene Descartes
Philosopher and Mathematician
French
1596-1650
Descartes was a "jack of all trades", making major contributions to the areas of anatomy, cognitive science, optics, mathematics and philosophy. Underlying his methodology is the belief that all science is based on mathematics. This is manifested in his unification of ancient geometry and his new algebra based on the Cartesian coodinate system.
For Descartes, certainty in philosophy and in mathematics is gained through understanding. We may know that two apples and two apples make four apples, but Descartes believed that mathematics transcends the senses. There is an overall mathematical order in the universe that is independent of the senses.
Senses were at the center of his Meditations on First Philosophy, a work in which Descartes explores the concepts of self, God and mind. He begins by shaking our belief in what our senses tell us about the external world; if our perceptual beliefs are all part of an illusion created by a malicious deceiver, what can we trust? His answer is that we can doubt, and that the deceiver cannot cause us to doubt our own existence. Hence his famous dictum "cogito ergo sum" (I think therefore I am). However, the I is not a physical thing; it is an immaterial mind.
Thus begins Cartesian Dualism, the theory that there are two fundamental types of entities : mind and matter. Physical bodies exist extended in space. However, minds are entirely immaterial and nonspatial; such an entity is the referent of "I" whenever that pronoun is used. We cannot be deceived as to our own existence as minds, whatever the ministrations of the evil demon. For, even when I am in a state of hallucination supposedly induced by the demon, I am still thinking (even if only by entertaining false beliefs, or wondering whether I can trust my senses).