axiomatism.com

Glossary

axiom-related terms are organized by etymology, Derivation, Compound, and future derivation possibilities.Based on the international standards in the Guideline (ISO 1087, ISO 704, ISO 24613, etc.).

1. Etymology

OED: axiom, n. (OED).

axiom

Pronunciation (OED)
British /ˈaksiəm/(AK-see-uhm)|U.S. /ˈæksiəm/(AK-see-uhm)
Etymology
A borrowing from French. Etymons: French axiome. Further from Latin axiōma, Ancient Greek ἀξίωμα (axiōma).
Prefix Axi-
Axi-: From Greek ἄξιος (axios). Meaning "worthy, fitting, of equal weight."
Suffix -om
-om: Greek -μα (-ma). Suffix forming abstract nouns. Denotes result or object. Noun as the result of ἀξιόω (axióō, to deem worthy).
Origin
Ancient Greek ἀξίωμα (axiōma)
Meaning
From ἀξιόω (axióō) "to deem worthy." Meaning "self-evident truth," "proposition worthy of assertion."
Earliest use
First attested 1578 in John Lyly (OED).
Definition
A proposition accepted as true without proof. A foundational claim from which an axiomatic system proceeds.

Reference Dictionaries

Dictionaries used to verify that terms in Derivation and Compound are established.

2a. Derivation

Established terms formed with affixes (-ic, -ization, -ity, etc.). Verified primarily against OED.

  • axiomata

    -ata (pl.)OEDWiktionary, OED (axiomata media), Oxford Reference

    Plural of axiom (Greek/Latin form). Like lemma → lemmata. Used in philosophy and classical contexts. Rarer than axioms.

  • axiomatic

    -icOEDOED, Merriam-Webster, OALD

    Based on axioms; axiomatic. Adjective. From Greek axiomatikos, 1797.

  • axiomatically

    -allyOEDOED, OALD

    In an axiomatic manner; as a self-evident truth. Adverb.

  • axiomatize

    -izeOEDOED

    To axiomatize. Verb. Base for axiomatization.

  • axiomatization

    -izationOEDOED, Merriam-Webster

    The reconstruction of a theory as a set of axioms. Axiomatization clarifies the structure of a theory. First attested c. 1931.

  • axiomatizing

    -ingOEDOED

    The act or process of axiomatizing. Present participle/gerund of axiomatize. Refers to the work of reconstructing a theory as a set of axioms.

  • axiomatics

    -icsMerriam-Webster

    (1) A set of axioms; an axiomatized system. (2) The study or theory of axioms and axiomatic systems.

  • axiomaticity

    -ityMerriam-Webster

    The degree to which a domain is formalized by axioms.

  • axiomatism

    -ismWiktionary, Merriam-Webster

    The doctrine or practice of basing systems on axioms. The axiomatic approach or method.

2b. Compound

Compound terms combining two or more words. Verified primarily against OED axiom/axiomatic compounds.

  • axiomatic system

    OED (axiomatic)OED, Oxford Reference, Merriam-Webster

    A formal system consisting of axioms and inference rules. Examples: Euclidean geometry, Peano arithmetic, ZFC set theory.

  • axiomatic method

    OED (axiomatic)OED, Oxford Reference, Britannica

    The procedure of deriving an entire system logically from axioms. Originates in Aristotelian syllogism and Euclidean geometry.

  • axiom of choice

    OED (axiomatic)Merriam-Webster, Wikipedia, Stanford Encyclopedia

    A fundamental axiom of set theory. Asserts the existence of a choice function that selects one element from each set in a family of non-empty sets. Zermelo 1904.

  • axiom schema

    OED (axiomatic)Oxford Reference, Wikipedia

    A formal pattern representing infinitely many axioms. Used in first-order predicate logic.

3. Future Derivation Possibilities

Candidates for future adoption and definition, based on ISO 704 neologism principles.

  • axiom-ness

    axiom + -ness

    axiom-ness; axiomatic quality. Nominalization (-ness) expressing intuitive property. Example: [Category: Noun, Aspect: Intuitive]

  • axiom-omorphism

    axiom + -omorphism

    Correspondence of axiomatic structures across logical systems. Example: a mapping that connects the logic of number theory and geometry. Close to the formal implementation of Common Logic (ISO/IEC 24707).

  • axiom-odynamics

    axiom + -odynamics

    Axiom dynamics. Description of the energy or flow derived from axioms to theorems.

  • iso-axiomatic

    iso- + axiomatic

    Having the same axiomatic structure. From Greek ἴσος (isos) "equal, same" + axiomatic. Enables instant identification of phenomena (management, quantum mechanics, social structure) that share the same axiomatic form.