Enumeration

Summary

The concept of enumeration is introduced by Descartes within the context of his discussions on method, playing central roles in both the analysis and synthesis of ideas. The earliest and clearest discussion of the concept is found in the unpublished Rules for the Direction of the Mind (1628). The concept is also mentioned in his first published work, Discourse on Method (1637). A close examination of the concept of enumeration shows that it also plays an important role in his accounts of clarity and distinctness, which are important concepts in Cartesian epistemology.

Commentators have traditionally understood enumeration in its standard sense, namely, as the numbering or listing of items (Curley 1986). This may explain why the significance of the concept in Cartesian philosophy has been overlooked. When seen in connection with Descartes’ employment of common natures, the enumeration appears to be akin to a logical partition (Smith 2001, 2010). The elements of ideas are what Descartes calls in the Rules the “simple natures” (Marion 1999). So, an enumeration of ideas might be best understood as a partition of the simple natures.

We produce an enumeration of objects whenever we place each object of inquiry into exactly one class, where the union of the classes produced is the original set of objects with which we began. For example, suppose that we wish to produce an enumeration of a bunch of marbles on a table. We will produce an enumeration of the marbles if, and only if, we place each marble in exactly one jar (a jar in this case will be analogue to a class), where the union of (the contents of) the jars will be the original bunch of marbles on the table.

The sorting is accomplished by applying a specific kind of relation: an equivalence relation. Such relations are reflexive, symmetric, and transitive. For example, x is the same color as y is an equivalence relation. If those marbles on the table are monochromatic, applying this equivalence relation to the marbles will sort them – marbles of the same color will be placed in the same jar. So, if “A is the same color as B” is true, then marbles A and B are placed in the same jar.