Hossein Jorjani
First publication: 2026 – 06 – 30
The history of the term axioma illustrates an important transformation in the foundations of knowledge, culminating in Francis Bacon’s redefinition of axioms as products of induction rather than self-evident truths.
The Greek term ἀξίωμα (axiōma) was employed by both Aristotle and Euclid, yet with markedly different intentions that illuminate a fundamental divergence between epistemology and formal logic.
For Aristotle, in the Posterior Analytics, axiōma designated a self-evident truth common to all the sciences, such as the Law of Non-Contradiction or the proposition that the whole is greater than the part. These axiōmata belonged to the broader class of archai—first principles (principia)—which also encompassed definitions and hypotheses. They were not derived from proof but grasped directly by nous, the intuitive intellect, and served as the epistemic foundations upon which demonstration was built. An Aristotelian axiom was therefore a universal and indemonstrable first truth, immediately known and applicable to all forms of knowledge.
Euclid, writing roughly half a century later, employed the same term in a more technical and mathematical sense. In the Elements, he distinguished between postulates (aitēmata), which are assumptions peculiar to geometry, and common notions (koinai ennoiai), which are general logical principles such as the equality of things equal to the same thing. An axiom was not justified by intuitive self-evidence but accepted without proof as a necessary starting point for demonstration. It could not itself be proved within the system, for it defined the boundaries of what could be proved.
The difference between the two usages lies chiefly in their function. Aristotle’s axioms were truths known immediately, the epistemological ground of all demonstration; Euclid’s were assumptions accepted immediately, the logical ground of mathematical demonstration. Later commentators often blurred this distinction, treating axioma and principium as interchangeable terms, a conflation that persisted through the Scholastic and early modern traditions.
Bacon’s axiomata represent a deliberate transformation of the concept. They are neither Aristotelian certainties apprehended by intellect nor Euclidean postulates posited for formal derivation. Rather, they are empirical generalizations established by legitimate induction, provisional yet progressively closer to the laws of nature.
Hossein Jorjani 