Note 13 — Chapter VII · ANALYTICA POSTERIORA I.

Aristot. Analyt. Post. I. ii. p. 72, a. 1-24; Themistius, Paraphr. I. ii. p. 10, ed. Spengel; Schol. p. 199, b. 44. Themistius quotes the definition of an Axiom as given by Theophrastus: Ἀξίωμά ἐστι δόξα τις, &c. This shows the difficulty of adhering precisely to a scientific terminology. Theophrastus explains an axiom to be a sort of δόξα, thus lapsing into the common loose use of the word. Yet still both he and Aristotle declare δόξα to be of inferior intellectual worth as compared with ἐπιστήμη (Anal. Post. I. xxiii.), while at the same time they declare the Axiom to be the very maximum of scientific truth. Theophrastus gave, as examples of Axioms, the maxim of Contradiction, universally applicable, and, “If equals be taken from equals the remainders will be equal,” applicable to homogeneous quantities. Even Aristotle himself sometimes falls into the same vague employment of δόξα, as including the Axioms. See Metaphys. B. ii. p. 996, b. 28; Γ. iii. p. 1005, b. 33.