41 pages • 1 hour read
René DescartesDiscourse on Method and Meditations on First Philosophy
Nonfiction | Book | Adult | Published in 1637A modern alternative to SparkNotes and CliffsNotes, SuperSummary offers high-quality Study Guides with detailed chapter summaries and analysis of major themes, characters, and more.
Symbols & Motifs
Mathematical Objects
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.
Material Objects
Unlike mathematical objects, material or corporeal objects present a different problem within Descartes’s overall philosophy. They present the problem of an experience the nature of which we cannot be certain because material objects are subject to perpetual modification. Perhaps the most used example is a ball of wax, which is featured in both the First and Second Meditations.
Moreover, unlike the certainty by which we grasp the nature of the triangle, material objects are of an opposite nature and present the human mind with no guarantee as to the correct judgments we may make of them. Hence, Descartes’s long passages that describe the ball of wax as sometimes hot and sometimes cold, sometimes hard and sometimes soft, and so forth. Or, as Descartes himself writes:
Let us consider it attentively, and setting aside everything that does not belong to the wax, let us see what remains. Indeed nothing remains, except something extended, flexible and malleable. Now, what does that mean: flexible and malleable? Is it not that I imagine that this wax, being round, is capable of becoming square, and of passing from a square to a triangular figure? No indeed, it is not that, for I conceive of it as capable of undergoing an infinity of similar changes, and as I could not embrace this infinity by my imagination, consequently this conception I have of the wax is not the product of the faculty of imagination (108-09).
This reference to the material object of wax serves as a contrast between what can be expected, in terms of knowledge, between material and mathematical objects.
