Associations to the word «Axiom»
AXIOM, noun. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
AXIOM, noun. (mathematics) (logic) (proof theory) A fundamental assumption that serves as a basis for deduction of theorems. Examples: "Through a pair of distinct points there passes exactly one straight line", "All right angles are congruent".
AXIOM, noun. An established principle in some artistic practice or science that is universally received.
AXIOM OF CHOICE, noun. (set theory) One of the axioms in axiomatic set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty.
AXIOM OF EXTENSIONALITY, noun. (set theory) One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements.
AXIOM SCHEMA, noun. (logic) A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
AXIOM SCHEMATA, noun. Plural of axiom schema
AXIOM SCHEME, noun. (logic) A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
AXIOM SCHEMES, noun. Plural of axiom scheme
AXIOM SYSTEM, noun. A set of axioms or axiom schemata from which theorems can be derived.
AXIOM, noun. A saying that is widely accepted on its own merits.
AXIOM, noun. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident.
To use the same words is not a sufficient guarantee of understanding; one must use the same words for the same genus of inward experience; ultimately one must have one's experiences in common.