Discourse on Method and Meditations on First Philosophy

Perhaps one of the most used examples by Descartes throughout both his Discourse on Method and Meditations on First Philosophy are mathematical objects, and especially that of the triangle. The reason for Descartes’s continued reference back to the triangle has to do with how he understands the nature of truth. According to Descartes, triangles are a good image of the criteria for truth because even if we never encounter a triangle in nature or the material world, it does nothing to detract from the fact that a triangle is a shape with three sides, two of which are equal to two right angles. In other words, the criteria for truth is the logical consistency of an idea independent of any possible object that may correspond with its definition. Additionally, this criteria of logical consistency establishes a firm basis for human rational inquiry, insofar as what it refers to is not something in the world but rather the basis upon which we make legitimate use of our ability to reason and make judgments about ourselves and the world. It is for this reason that Descartes, who was a mathematician himself, continuously comes back to the image of triangles and mathematical objects to illustrate his arguments.