Rule 12 holds that we must use our intellect, imagination, sense perception, and memory to their fullest extent. Using these tools well will help us to combine the matters we’re investigating with knowledge we already have. Rule 12 contains a lengthy, inaccurate description of how the brain works and how memories are made, the point being that the brain learns to intuit simple things from experience. Descartes concludes Rule 12 (and the first set of rules) by saying that a problem can only be classed as perfectly understood if three things happen: we know what kind of problem it is when we come across it, we know what we need to deduce the answer, and we can see that the kind of problem it is and the means to deduce the answer depend on one another. The method for solving these simple problems was to be outlined in the second set of rules, which was never completed.
The first three rules express the importance of certainty in Descartes’ thinking. Descartes stresses the value of “true and sound judgments” and “certain and evident cognition” and goes so far as to argue that studying something that only serves to raise more questions is more harmful than not studying at all. If the information in your mind is jumbled, it is impossible to create any cohesive system of thought, and, as a result, everything you think you know is open to doubt. Rule 4 lays the groundwork for the intellectual rebirth that Descartes discusses in Discourse on the Method. Descartes’ education was excellent, but it left him open to much doubt. He has read all the experts, and enjoyed learning from them, but he finds that all too often the experts disagree. If two learned people hold opposing views on the same topic, how can it be determined who is right? According to Descartes, at least one party is wrong in such situations, and more often that not, both are wrong. For if one were right, he should be able to prove his point to the other through irrefutable logic.
In Rules 5 and 6, Descartes lays out several theories that foreshadow other, grander thoughts he goes on to explain in Discourse on the Method and Meditations on First Philosophy. He asserts that every problem can be broken down into simple parts and that there exist parts so simple that they can’t be broken down into simpler parts. These “absolute” ideas can be accurately perceived just by looking at them. These absolutes prefigure Descartes’ later ideas of clear and direct perception. He ultimately concludes that whatever can be clearly and directly perceived is true. After breaking everything down into perfectly understandable parts, the next step is to figure out how the simple parts relate to one another. After that relation has been determined, the task is to understand out how the complicated parts relate to the simple parts. In these rules, Descartes insists that repeated review of the chain of relationships between all the parts of a problem makes it easy to see at a glance how any single part relates to all the others.
Descartes’ assurance, in Rule 8, that anyone can attain real knowledge by employing his method indicates that he was promoting the democratization of knowledge. Unlike most scholars of his time, Descartes occasionally switched from the scholarly language of Latin to publish in French, the language of his people. This, he always argued, was because a person who approached his writings with a mind unburdened by the prejudices that come with scholarship was the only person who would really be able to understand his points. Descartes held a firm belief in the native capacity for reason in every man. For Descartes, reason is what makes a man. So every man, from the lowliest plowherd to the most learned scholar, is endowed with the natural gift of reason. In fact, at this point in his career, Descartes felt that a plowherd, free of the burden of received ideas, might have an easier time using reason than a scholar.
Descartes often employs terms like “intuited,” “natural light,” and “clear and distinct perception” that don’t seem to fit in with his skeptical, rational view of the world. But these terms are used to describe a process that Descartes cannot fully explain. We intuit and have clear and distinct perceptions as a result of our reasoning. It happens when we have broken everything down so thoroughly that there appears in our mind something that we recognize to be true because it cannot be false. Reason, not divine inspiration, allows us to make these recognitions. Something intuited is grasped in the same way one would grasp a simple math equation. Descartes’ extensive work in geometry and algebra spurred his insistence that problems in the real world could be expressed in mathematical formulas, a radical view at the time that would revolutionize the way we study physics.