axiom
AK-see-um
/ˈæk.si.əm/
A statement or principle that is accepted as self-evidently true without requiring proof, serving as a foundation for further reasoning.
In mathematics and logic, axioms are starting rules that cannot be proven within the system itself (e.g., 'a straight line can be drawn between any two points').
The story behind the word. From Greek 'axios' (worthy or having weight). An axiom was a principle deemed so intrinsically worthy of belief that it required no lower demonstration to justify it.
Word relationships
- postulate: A postulate is an assumed starting truth for a specific argument; an axiom is held to be universally self-evident.
- theorem: A theorem is a proposition that MUST be mathematically proven using axioms.
Commonly confused with
- premise: Premises are arguments' specific starting inputs; axioms are basic self-evident truths accepted across an entire discipline.
Word family
- axiomatic (adjective): Self-evident or unquestionable.
- axiomatically (adverb): In a self-evident manner.
Collocations
- fundamental axiom
- basic axiom
- accepted axiom
- build on an axiom
Idioms & expressions
- self-evident axiom
Example sentences
- "Euclidean geometry is built upon five fundamental axioms from which all subsequent theorems are deduced." Mathematics
- "The declaration rests on the axiom that all human beings are born with inherent rights to freedom and dignity." Ethics
Memory hook
AXIOM is an ACT OF FAITH in logic: a truth so solid it acts as your starting ground. Self-evident starting point of truth.
When not to use
Do not use to describe a debated theory or an empirical claim that requires observational evidence.
Fun facts
- Albert Einstein revolutionized physics by challenging Isaac Newton's basic axiom that time passes at the same rate everywhere in the universe!
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