a self-evident truth that requires no proof.
a universally accepted principle or rule.
Logic, Mathematics. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023
How to use axiom in a sentence
With an ATP, a programmer can code in all the rules, or axioms, and then ask if a particular conjecture follows those rules.How Close Are Computers to Automating Mathematical Reasoning? | Stephen Ornes | August 27, 2020 | Quanta Magazine
Gödel’s main maneuver was to map statements about a system of axioms onto statements within the system — that is, onto statements about numbers.
By the first theorem, this set of axioms would then necessarily be incomplete.
We’ve learned that if a set of axioms is consistent, then it is incomplete.
It would mean that there exists a sequence of formulas built from these axioms that proves the formula that means, metamathematically, “This set of axioms is consistent.”
Whether or not Hippocrates ever actually said “First, do no harm,” the axiom is central to medical ethics.
Jakes says he believes in the axiom that the act of forgiveness is not really a gift to others as much as it is a gift to oneself.Bishop T.D. Jakes on His New Book and Whitney Houston’s Death | Allison Samuels | March 10, 2012 | THE DAILY BEAST
It's Tip O'Neill's famous axiom in reverse: now all politics is national.
It is a generally accepted axiom that a public man cannot afford to be modest in these go-ahead days of "boom."The Doctor of Pimlico | William Le Queux
This truth is as old as Homer, and its proofs are as capable of demonstration as a mathematical axiom.The Book of Anecdotes and Budget of Fun; | Various
By this, OLeary understood that he was definitely adopted by virtue of the axiom of what was his was theirs.The Woman Gives | Owen Johnson
That was an axiom on which was founded a vigorous war against all capillary adornments.The British Expedition to the Crimea | William Howard Russell
He starts with the axiom that the whole amount of attention a reader can give at any moment is limited and fixed.English: Composition and Literature | W. F. (William Franklin) Webster
British Dictionary definitions for axiom
a generally accepted proposition or principle, sanctioned by experience; maxim
a universally established principle or law that is not a necessary truth: the axioms of politics
a self-evident statement
logic maths a statement or formula that is stipulated to be true for the purpose of a chain of reasoning: the foundation of a formal deductive system: Compare assumption (def. 4)
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Scientific definitions for axiom
A principle that is accepted as true without proof. The statement For every two points P and Q there is a unique line that contains both P and Q is an axiom because no other information is given about points or lines, and therefore it cannot be proven. Also called postulate
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Cultural definitions for axiom
In mathematics, a statement that is unproved but accepted as a basis for other statements, usually because it seems so obvious.
The New Dictionary of Cultural Literacy, Third Edition Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.