The problem of knowledge is a key one in philosophy, asking as it does whether there is anything we can really know and whether what we know can be said to be objectively true. Theories of knowledge come under the heading of epistemology. We perceive the world through our sense, but our senses can be deceived. The degree of deception involved also varies according to different views of the world. Some see this deception as absolute and deny that there can be any knowledge at all through the senses. Others admit knowledge acquired through the senses while recognizing that there are limitations. René Descartes was a rationalist, and his thinking was governed by his knowledge of and dedication to mathematics, which he believed could clear up the confusions and uncertainties of philosophy. In this regard, Descartes wished to attain certainty with reference to the external, physical objects in the world around us. Mathematics, he believed, could help philosophy achieve absolute certainty so that philosophy could then reach final and certain truth. He began with the now well-known proposition, "I think, therefore I am," and from this he built a philosophical structure striving for the aforementioned mathematical certainty. However, by the end of the Sixth Medication, Descartes concludes that our knowledge of external objects will always remain imperfect. This does not mean that the Meditations have failed, only that the conclusions to which they have come show the limitations of mathematics in making philosophical judgments and that the Meditations reaffirm the limitations of sensory perception.
There are only two mental operations by which true knowledge can be attained, says Descartes, and these are the methods of mathematics. Intuition is the understanding of self-evident principles. These are statements that are self-evident in that they prove themselves to reason, for to understand them is to know that they are absolute...