Descartes sought to avoid these difficulties through the clarity and absolute certainty of geometrical-style demonstration. In geometry, theorems are deduced from a set of self-evident axioms and universally agreed upon definitions. Accordingly, direct apprehension of clear, simple and indubitable truths (or axioms) by intuition and deductions from those truths can lead to new and indubitable knowledge. Descartes found this promising for several reasons. First, the ideas of geometry are clear and distinct, and therefore they are easily understood unlike the confused and obscure ideas of sensation. Second, the propositions constituting geometrical demonstrations are not probabilistic conjectures but are absolutely certain so as to be immune from doubt. This has the additional advantage that any proposition derived from some one or combination of these absolutely certain truths will itself be absolutely certain. Hence, geometry’s rules of inference preserve absolutely certain truth from simple, indubitable and intuitively grasped axioms to their deductive consequences unlike the probable syllogisms of the Scholastics.

In the first case, it would not be correct to say that A's being a triangle * caused* it to have three sides, since the relationship between triangularity and three-sidedness is that of definition. The property of having three sides actually determines A's state as a triangle. Nonetheless, even when interpreted counterfactually, the first statement is true. An early version of Aristotle's "four cause" theory is described as recognizing "essential cause". In this version of the theory, that the closed polygon has three sides is said to be the "essential cause" of its being a triangle. [17] This use of the word 'cause' is of course now far obsolete. Nevertheless, it is within the scope of ordinary language to say that it is essential to a triangle that it has three sides.