ΑΞΙΩΜΑ
Axioma — «worth, honor, rank» — from Homer to today has preserved its double meaning: social worth and scientific principle. Aristotle made it a cardinal term of logic: an axiom is a self-evident principle that needs no proof and serves as the foundation of every science. In its mathematical form — Euclid drew his inspiration from him — the axiom becomes the cornerstone of every axiomatic system. In modern logic, Hilbert and his successors developed the axiomatic program as a guide to mathematics.
REPORT ERRORDefinition
According to the Liddell-Scott-Jones Lexicon, τὸ ἀξίωμα means «that of which one is thought worthy, honor, glory, dignity, a request, a principle». It is formed from the verb ἀξιόω (to deem worthy, request), from ἄξιος (worthy). The first meaning is social: a person's worth, their position in the community, the honor due to them.
In philosophical and scientific usage, axioma becomes a technical term. Aristotle in the Posterior Analytics (A 2, 72a16-17) defines axioms as «common principles» — primary principles one must know before learning anything else. They are self-evident, not demonstrated, and are used as the basis of all proofs. Examples: «the same thing cannot simultaneously belong and not belong to the same thing» (principle of non-contradiction), «if equals be subtracted from equals, the remainders are equal» (mathematical common notion).
In the mathematical tradition, especially in Euclid, the axiom is the common notion valid in every science, in distinction from postulates (αἰτήματα) that hold only in a specific field. This distinction continued in scholastic philosophy and changed dramatically in the 19th-20th c., when Hilbert and the axiomatic method shaped modern mathematics.
Etymology
Cognates: ἄξιος, ἀξιῶ, ἀξία, ἀξίωσις, ἀξιόλογος, ἀξιοπρεπής. Latin parallels: dignus, dignitas, axioma (loanword). Related logical terms: ἀρχή, ὑπόθεσις, αἴτημα (postulate), ὁρισμός (definition), κοινὴ ἔννοια (common notion).
Main Meanings
- Social worth, honor — The oldest meaning — social standing, prestige, the honor accorded to someone.
- Request, demand — What someone requests or demands, especially in conversations or diplomatic exchanges.
- Maxim, apothegm — A short condensed statement expressing a truth, close to an aphorism.
- Aristotelian axiom — The primary, self-evident principle that needs no proof and is used as the foundation of every science.
- Euclidean common notion — In the mathematical tradition, the principle valid in all sciences, distinct from postulates (αἰτήματα) of a specific branch.
- Stoic axioma (proposition) — In Stoic logic, any assertoric proposition — a statement that is true or false. Different from the Aristotelian term.
- Modern axiom — In modern mathematical logic, the initial propositions of an axiomatic system, not necessarily self-evident but functionally fundamental.
- Political axiom — In political texts, the central position or principle that a political faction or theory considers non-negotiable.
Philosophical Journey
Axioma traverses the entire history of logic and mathematics, from social prestige to a technical foundation of science.
Lexarithmic Analysis
The lexarithmos of the word ΑΞΙΩΜΑ is 912, from the sum of its letter values:
912 decomposes into 900 (hundreds) + 10 (tens) + 2 (units).
The 18 Methods
Applying the 18 traditional lexarithmic methods to the word ΑΞΙΩΜΑ:
| Method | Result | Meaning |
|---|---|---|
| Isopsephy | 912 | Base lexarithmos |
| Decade Numerology | 3 | |
| Letter Count | 6 | |
| Cumulative | 2/10/900 | Units 2 · Tens 10 · Hundreds 900 |
| Odd/Even | Even | Feminine force |
| Left/Right Hand | Right | Divine (≥100) |
| Quotient | — | Comparative method |
| Palindromes | No | |
| Onomancy | — | Comparative |
| Sphere of Democritus | — | Divination with lunar day |
| Zodiacal Isopsephy | Venus ♀ / Aries ♈ | 912 mod 7 = 2 · 912 mod 12 = 0 |
Isopsephic Words (912)
The LSJ lexicon contains a total of 91 words with lexarithmos 912. For the full catalog and AI semantic filtering, see the interactive tool.
Sources & Bibliography
- Liddell, H. G., Scott, R., Jones, H. S. — A Greek-English Lexicon. Oxford: Clarendon Press, 1940, s.v. ἀξίωμα.
- Aristotle — Posterior Analytics A 2 (72a16-17), Metaphysics Γ 3 (1005b19). Loeb Classical Library.
- Euclid — Elements, Book I (common notions). Ed. J. L. Heiberg, Teubner.
- Mates, Benson — Stoic Logic. University of California Press, 1953.
- Hilbert, David — Grundlagen der Geometrie. Leipzig: Teubner, 1899.
- Spinoza, Benedict de — Ethica, ordine geometrico demonstrata. Amsterdam, 1677.
- Tarski, Alfred — Introduction to Logic and to the Methodology of Deductive Sciences. Oxford University Press, 1941.