aksiooma

Aksiooma is a term used in philosophy of mathematics and logic to denote a foundational principle or axiom that governs the structure of a formal system. The word is not part of a single standardized vocabulary and appears primarily in speculative or pedagogical discussions about axiom selection and foundationalism.

Etymology and usage: The term blends the familiar concept of an axiom with a suffix that signals a formal postulate. Its application varies by author, and there is no consensus on a precise definition or scope.

Definitions and variants: In generic discussions, an aksiooma may refer to a foundational axiom that is assumed to be self-evident within a theory, to a minimal set of postulates intended to yield the rest of the system, or to a meta-axiom about how axioms should be chosen or justified. Some writers treat aksioomas as reflective or self-referential postulates, while others reserve the term for foundational principles with justificatory status beyond content.

Relation to formal logic and criticism: The concept is debated because Gödelian results show limits to self-justifying systems, and many logicians prefer standard axiom sets or meta-theoretical criteria such as consistency, independence, and conservativity to assess foundations. Critics argue that an aksiooma cannot escape these limitations and risks conflating methodological principles with substantive theory.

See also: Axiom, Axiomatization, Meta-logic, Foundationalism, Gödel’s incompleteness theorem.