axiom
AK-see-um
/ˈæk.si.əm/
A statement or proposition accepted as self-evidently true without proof, serving as a foundation for further reasoning.
An axiom cannot be proven from within its own system because it is the foundational starting rule upon which all other proofs depend.
The story behind the word. From Greek 'axioma', meaning 'that which is thought worthy', derived from 'axios' (worthy). An axiom is a truth so fitting and worthy that it commands acceptance without needing a formal demonstration.
Word relationships
- postulate: A postulate is an assumed rule specific to a certain discipline, while an axiom is often considered universally self-evident.
- truism: A truism is an obvious or cliché statement, whereas an axiom serves as a formal structural foundation for proof.
- theorem: A theorem is a proposition that must be proven using axioms and logical rules.
Commonly confused with
- maxim: A maxim is a short rule of personal conduct or moral wisdom, while an axiom is a foundational truth in logic or math.
Word family
- axiomatic (adjective): Self-evident or unquestionable.
- axiomatically (adverb): In an axiomatic manner.
Collocations
- fundamental axiom
- accepted axiom
- build on an axiom
- self-evident axiom
Idioms & expressions
- take as an axiom
Example sentences
- "Euclidean geometry begins with a set of basic axioms, such as the statement that a straight line segment can be drawn between any two points." Mathematics
- "We hold these truths to be self-evident, that all men are created equal, is treated as an axiom of modern democratic theory." Political Philosophy
Memory hook
AXIOM = ACTS as the home foundation for logic. A foundation truth that needs no proof.
When not to use
Avoid calling a temporary assumption or controversial opinion an axiom; an axiom must be accepted as fundamentally self-evident within its framework.
Fun facts
- In 1931, Kurt Gödel shocked mathematicians by proving that no system of axioms can ever be completely self-contained and comprehensive (Gödel's Incompleteness Theorems).
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