The distinction between the mental operations of abstraction and exclusion plays an important part in Descartes’ philosophical methodology. He does not give an explicit account of this distinction in any of his published works, though he does explain it in a letter to Gibieuf of January 19, 1642 (AT III 474, CSMK 201), and he touches on it in a letter to Mesland of May 2, 1644 (AT IV 129, CSMK 236).

In the case of abstraction, we focus our attention on oneidea, while turning our attention away from the contents of a richer idea of which it is a part. For example, we focus our attention on the shape of some object, while turning our attention away from the extension of the object. We can tell that this operation is an abstraction from the fact that we can focus our attention on the shape without paying any attention to the extension, though we cannot without absurdity deny that the shape has that extension or that the extension has that shape. In the case of exclusion, by contrast, we focus our attention on two ideas, and deny the one of the other. We can focus our attention, for example, on the thought and extension of some human being, and deny that the thought is extended and that the extension is thought. We can tell that this operation is an act of exclusion by the fact that we can deny the one of the other without absurdity. Descartes sometimes calls exclusion “negation.”

For Descartes, the operation of exclusion is an indispensable instrument for determining the connections between ideas and the items they stand for. If we can mutually exclude the idea of an F and the idea of a G, then there is a real distinction between an F and a G in the sense that an F can exist independently of a G, and vice versa. If we cannot make this mutual exclusion, then there is only a modal distinction or a conceptual distinction between an F and a G, and the ideas of F and G can be distinguished only by an abstraction (see distinction [real, modal, rational]).