This is the rule of clarity and distinctness. Before accepting any proposition, Descartes demands that it be seen with a kind of intellectual vision so clear that no doubt can attach to it. The enemies of this clarity are precipitancy — jumping to conclusions before they are fully examined — and prejudice — accepting conclusions because they come from authorities or long tradition rather than from the evidence itself. The first rule is a demand for intellectual honesty and patience.
The second rule is analytical: divide every problem into as many parts as necessary for its adequate solution. Complex questions are almost never resolvable in one step; they must be broken down until each element is small enough to be seen clearly. The third rule is synthetical: begin with the simplest and most easily knowable things, then ascend step by step to the more complex.
Descartes took these two rules from mathematics — from the method of geometric analysis and algebraic reasoning that he had found uniquely reliable. His ambition was to extend this same rigour to all fields of inquiry: to philosophy, physics, medicine, and moral life. The method is not specifically mathematical, but it shares with mathematics the demand that each step follow necessarily from what preceded it.
The fourth rule is review: make enumerations so complete and surveys so general that nothing is left out. This is the quality-control step — the check that the analysis has been thorough and the synthesis complete. Taken together, the four rules constitute a method for approaching any question with the kind of systematic rigour that Descartes admired in mathematics. Their influence on the development of the natural sciences, on Enlightenment epistemology, and on the rational ideal of systematic inquiry can hardly be overstated.
The four rules of method are set out in Part II of the Discourse on the Method, in the context of a discussion of Descartes' intellectual biography. The same method underlies the Meditations and the scientific works, including the Geometry and the Dioptrics appended to the Discourse.
