In the Fifth Meditation, triangles represent the way that people can achieve certain knowledge about the world through rationality. The Meditator uses triangles as an example to illustrate the difference between the clear and distinct truths of mathematics and the ordinary ideas about the world that people form in their everyday lives. He points out that it’s impossible to doubt the basic principles of a triangle’s geometry—like the fact that it has three sides, that its angles sum to 180 degrees, and that its largest angle is opposite its longest side. Such principles still hold true under the evil demon thought experiment, even if none of what the Meditator is perceiving turns out to be real at all. In fact, triangles’ basic properties would stay the same even if there were no real triangles anywhere in the world: they’re necessary truths of geometry, basic elements of the shape’s fundamental nature. For Descartes, true knowledge must be just as clear, distinct, and certain as these basic geometrical principles. This helps explain his lifelong dedication to studying geometry: for him, geometry is the model for how the sciences should operate. They should construct a systematic body of knowledge about the world by building out from basic, rational principles.
Triangles Symbol Timeline in Meditations on First Philosophy
