Aristotelian science is based on a method of demonstration and syllogism. It proceeds from first principles that are assumed to be certain, and from these first principles it logically deduces other results that are, in turn, treated as certain. The criteria for certainty are not very high, and the logical deductions are often quite faulty. Therefore, Aristotelian science embarrasses itself by making a number of grave errors. The new scientific method is based on a system of hypothesis and experiment. Theories are not taken as certain, just probable, and they are rendered increasingly probable the more experiential evidence there is to confirm them. Descartes is only part of the way into this new worldview. Most of his scientific inquiries follow this model, but he still feels it important to claim to have first principles that these scientific results follow from logically, and he feels it important to argue that these principles are absolutely certain.

Descartes had been brought up in an educational method that claimed it would teach him everything he needed to know in order to pursue knowledge and get by in the world. Having completed his Jesuit education, Descartes found that he knew everything his teachers wanted to teach him, but that he was far from satisfied with the knowledge it gave him. In particular, he felt he had no grounds for having any certainty with regard to what he had learnt. Descartes's philosophy is, to a large extent, motivated by a desire to find certainty. This leads him to reject all the precepts and principles of Aristotelian philosophy as not good enough, and to employ skeptical doubt in his search for a more solid foundation for knowledge.

The four principles are: (1) Not to accept anything as true unless it is evident, (2) to break problems down into parts and to work on the parts individually, (3) to start with the easiest knowledge and build toward more difficult matters, and (4) always to check over work and be wary of any errors. These principles are supportive of a foundationalist epistemology, which begins with certain simple, self-evident truths, and builds upon them. Descartes seems to assume that knowledge can be analyzed into parts and then built up from simple foundations. These assumptions lead him to believe that there must be certain self-evident first principles upon which all his philosophy can rest, and that all his subsequent conclusions can follow from these first principles.