How we know what we know and how we can trust that knowledge are important issues in philosophy. Plato and Descartes each have a fundamental mistrust of the material world, which is perceived through the senses. Knowledge acquired through the senses is not to be fully trusted, for it includes a subjective element that is placed between the real world and what we believe the real world to be. For Plato, what we perceive is only a shadow of reality, while for Descartes, reason is the only way of obtaining truth, especially the ordered reason of mathematics.
One of the most famous statements of a theory of knowledge comes in Plato's Republic in Book VI. He introduces the figure of the divided line, with one half representing the visible order and the other the intangible. Lavine describes the divided line as follows:
A vertical line is divided into four segments, each of which from the lowest to the highest represents a level of knowledge. Each level of knowledge--imagining or conjecture, belief, understanding, reason--has its own objects and its own method for knowing them. The basic division, however, is between knowledge, whose objects are in the intelligible world, and opinion, whose objects are in the visible world (Lavine 31).
This division is a ranking of knowledge according to the degree of reliability that can be placed in it, and it is clearly based on a belief that knowledge is possible.
Following Plato, Descartes sets forth a theory of rationalism in which reason is held up as the most important element in human nature and as the only means to certainty in knowledge. Descartes denies the power of the senses to perceive knowledge because of an awareness that the senses are flawed and that they are not to be trusted. He questions whether the senses provide any knowledge. For Descartes, reason is the only road to knowledge, and he uses mathematics as his model:
By using the method of mathematics, phil...