Descartes describes a growing trend in the youth of his generation, something that Thomas Kuhn calls a "paradigm shift." There was a growing dissatisfaction with, and skepticism toward, the scholastic philosophy that had been inherited from Aristotle. This is not so much to say that people stopped being interested in the things that previous generations had been interested in. Rather, people grew dissatisfied with a paradigm of knowledge, of an understanding of what knowledge was, of how it could be learned, and of what value it could have.
Aristotelian logic, and hence Aristotelian science, works according to a method of syllogism and demonstration. One starts with a premise that one knows with certainty by means of intuition, and then one deduces consequences from it by means of a syllogism. A syllogism is a kind of logical argument with three steps and three terms. For example, "All y's are z; x is a y; therefore, x is a z." If we are certain about the first two statements, then we can deduce the third statement with equal certainty.
According to Aristotle, and to the two thousand-year old tradition that used his ideas, scientific knowledge is certain knowledge deduced from certain premises. This is the kind of knowledge that Descartes was promised as a part of his education and that he came to find unsatisfying. We might be inclined to sympathize with Descartes on this one. Among the irrefutable demonstrations of Aristotelian philosophy are the assertions that the earth is the center of the universe, that women are naturally inferior to men, and that the world is made up of the four elements of earth, air, fire, and water.
Aristotelian scholasticism was not overthrown by a set of scientific discoveries. Rather, these discoveries were a result of a revolution in the way we think about science. Galileo and Descartes were two of the early exponents of a new scientific method that relies on hypothesis and experiment rather than on demonstration and syllogism. This method does not pretend to provide certainty, but only proposes theories and models that fit the facts and provide plausible explanations of natural phenomena. It took a long while before people came to accept that a sound theory, and not certainty, was the highest possible aspiration of science. For instance, one of the main arguments the Inquisition made against Galileo was that his claim that the earth went around the sun was not demonstrated knowledge. They were perfectly happy to accept that it was a plausible theoretical model, but they were trapped in an ancient worldview according to which theoretical models and demonstrations of certainty were two very different things. Galileo was accused of claiming that his model was a demonstration of certainty rather than a theoretical model.
The Discourse on the Method is thus a rather tricky book, because it is part of a revolution in its early stages. Descartes not only must pay lip service to Aristotelian philosophy, but he also has not entirely freed himself from that mindset. For instance, we find him arguing early on that we are all equally rational because reason is a form, and not an accident, of human nature. The distinction between form and accident is quintessentially Aristotelian. The idea is that we have essential properties—like reason—without which we would not be what we are. A human being without reason is not a human being. We also have accidental properties—like legs—without which we could still be human beings. As humans we can only differ with respect to our accidental properties, but not with respect to our form (our essential properties). Thus, we must all have reason, and have it to an equal extent.
This assertion also identifies Descartes as a rationalist philosopher. The early modern period in philosophy, of which Descartes is the founding father, was split roughly into two camps: the British empiricists and the Continental rationalists. Empiricists, such as John Locke, asserted that the mind is a blank slate at birth, and all knowledge comes from experience. Descartes, on the other hand, maintains that there is a certain something—our native intellect or reason—that we are born with and all share.