Descartes’ “common notions or axioms” – the terms are interchangeable in the Principles (cf. AT IXB 24, CSM I 209) – derive their name from the koinai ennoiai, later called axiomata, which follow the definitions and postulates of Euclid's Elements. Their conception is classical yet innovative. The idea that some strictly universal and necessary truths are both (a) self-evident or immediately clear and distinct for anyone “not blinded by preconceived opinions” (ibid.) and (b) primary in the sense of providing starting points for the deduction of other truths is largely traditional; original, on the other hand, is Descartes’ bold extension of their use from mathematics, logic, and natural science – to which the axiomatic method had been applied since antiquity (cf. Blanché 1973) – to metaphysics or first philosophy. But if Descartes routinely employed metaphysical axioms in his demonstrations, he was nonetheless reluctant to follow the axiomatic procedure of drawing logical consequences from a set of intuitively evident general definitions, axioms, and postulates, professing a preference for the analytic method of the Meditations over the synthetic method of the geometer (cf. AT VII 155–59, CSM 110–13) (see analysis versus synthesis). Still, the more geometrico “arguments” he reluctantly agreed to provide as an addendum to the Second Replies are the main source of the common notions listed here (AT VII 160–70, CSM 113–20)(see Geometrical Exposition).

Since (a) and (b) characterize Cartesian definitions as well, how do axioms and definitions differ? For one thing, definitions (see those of “mind,” “body,” and “God” in the Geometrical Exposition) articulate the content of innate ideas or basic concepts that are not simple and indefinable, like “thought,” and “existence,” both of which are best understood simply by experiencing inwardly that one thinks and exists (AT X 524, CSM II 418; cf. AT IXB 8, CSM I 195–96); axioms or common notions, by contrast, are primary propositions or innate truths. But since a Cartesian definition is a proposition or eternal truth about the essence of the thing defined, this cannot be the whole story. In the Principles I.48, Descartes distinguishes “things” (res) and their “affections,” both of which may exist outside the mind, from vertitates aeternae, which cannot.