An axiom is a proposition asserted without proof within a formal system, serving as a starting point for deductive reasoning. Its parameters are: (1) it must be self-consistent within the system it grounds, (2) it must be non-derivable from other axioms in that system, and (3) its acceptance is conventional — chosen by the system's authors, not discovered as a natural fact. It persists through codification in formal languages, transmission across generations of practitioners, and the stability of the deductive frameworks it anchors. [formal: axioma | substrate: mind | horizon: a life | explicit: yes | epoch: 0.38]
Accepted ontology entry
axiom
An axiom is a proposition asserted without proof within a formal system, serving as a starting point for deductive reasoning. Its parameters are: (1) it must be self-consistent within the system it grounds, (2) it must be non-derivable fro…
Definition
Why it is in scope
A foundational proposition accepted as true within a formal system, serving as a starting point for reasoning and derivation. Human-made as a methodological choice — the selection of axioms is a deliberate act of convention that structures entire deductive frameworks and persists through teaching, formalization, and the systems they ground.
Names and aliases
- axiomen · CANONICAL
Relations from this entry
- cmrehumxg00i3g8vu5x5px5v2DEPENDS_ON →
axiom cannot function without logic — an axiom is a foundational proposition whose role is to serve as a starting point within a logical system. Remove logic and axioms lose their purpose and meaning. Constitutive necessity per Law 8.
- cmrwwgaob01kosoacf6wtlkdcINSTANCE_OF →
An axiom IS a specific kind of proposition — a proposition accepted as self-evidently true without proof, serving as a starting point for reasoning. A competent speaker would call an axiom 'a type of proposition.' Direction: specific→general per Law 9.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Jul 17, 2026, 9:37 AM UTC
- Content hash
- 424a76d09693800243a690ba081c57c826657bd4f10ff731ee0d9b7f56d3ad51