How to use axiom in a sentence

39 example sentences · noun

Axiom means a seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved. Example: “The axioms of political economy cannot be considered absolute truths.”

Examples of axiom by meaning

nounA seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot...

Any publicity, runs the axiom, is good publicity.1963 February, “Nobody runs this railway, mate”, in Modern Railways, page 73
"As above, so below" is an axiom from Hermetic mysticism, and in this Hermetic vision of physiology the tongue is connected through the spinal column to the penis.1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London...
Can we then find axioms as self-evident as those of Arithmetic, on which we can build as on a sure foundation, which could be shaken only by a scepticism which should attack the whole fabric of our knowledge?1999, Bertrand Russell, edited by Charles R. Pigden, Russell on Ethics: Selections from the Writings of Bertrand Russell, London; New York...

nounA fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from...

The axioms read as follows.1992, Colin McLarty, “Rudimentary Structures in a Category”, in Elementary Categories, Elementary Toposes (Oxford Logic Guides; 21)...
The axioms of arithmetic imply that when you expand (a + b)², for example, you get a² + 2ab + b² in the following way: (a + b)² is equal to (a + b)(a + b).2022 August 7, Alec Wilkinson, “Could learning algebra in my 60s make me smarter?”, in The Guardian, archived from the original on 22 Mar...

nounAn established principle in some artistic practice or science that is universally received.

The axioms of political economy cannot be considered absolute truths.

More sentences with axiom

The axiom of choice is equivalent to the proposition that every infinite cardinal is an aleph.From the entry aleph
Only formal proofs, which derive theorems logically from their given axioms, are considered satisfactory in modern mathematics.From the entry formal
S has no axiom of extensionality and identity is absent from the other S axioms.From the entry s
The axiom of choice is logically equivalent to the assertion that every vector space has a basis.From the entry axiom of choice
But the ZF axioms of which the hierarchy is an intuitive model involve impredicative quantifications.2011, Adam Rieger, “9: Paradox, ZF, and the Axiom of Foundation”, in David DeVidi, Michael Hallett, Peter Clark, editors, Logic…. From the entry axiom of power set
Most striking is the axiom of power set in tandem with the axiom of separation.2011, Adam Rieger, “9: Paradox, ZF, and the Axiom of Foundation”, in David DeVidi, Michael Hallett, Peter Clark, editors, Logic…. From the entry axiom of power set
That's not to say that developers who use the class won't still misgeneralize the getting-vs-storing axiom.2005, Damian Conway, Perl Best Practices. From the entry misgeneralize
In contrast, there are weak forms of the axiom of choice that are not provable.2000, Bruno Poizat, translated by Moses Klein, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, page 169. From the entry axiom of choice
Doesn't anyone remember the axiom that what wins on Sunday sells on Monday?1991 July 3, Al Pearce, “General Motors likely to reduce NASCAR funds”, in Daily Press, Virginia, US, retrieved 15 Oct 2018. From the entry what wins on Sunday sells on Monday
The truth of other axiomata would have to be defined in terms of the truth of these.1985, William Kneale, Martha Kneale, The Development of Logic, page 53. From the entry axiomata
It is an axiom of agricolation that the soil must be made suitable for the crop.1912, Central Conference of American Rabbis, Centennial Convention. From the entry agricolation
Take, for example, the axiom "Never give declarer a ruff-and-sluff."2008, Phillip Alder, “The Just-So Story of a Justified Ruff-and-Sluff”, in The New York Times. From the entry ruff
These axiomata themselves are self-evident to us; we do not feel that they need proving and recognize them intuitively.2003, J. J. Van Der Leeuw, Conquest of Illusion, page 52. From the entry axiomata
The finite axiom of choice is not an axiom, but rather a theorem that can be proved from the other axioms.2000, Bruno Poizat, translated by Moses Klein, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Springer…. From the entry axiom of countable choice
Suppose we have any axiom of the form: (2) For every Tweedledee there is a Tweedledum R-related to it.1989, Jon Barwise, The Situation in Logic, page 189. From the entry Tweedle-dum
Axioms of the form (2) cut two ways.1989, Jon Barwise, The Situation in Logic, page 189. From the entry Tweedle-dum
If you practice in an exclusive area and have chairfuls of well-healed clients, this axiom probably does not apply.1981, Aldon J. Hilton, Winning the dental insurance game: operations manual, page 110. From the entry chairful
It should almost be a lighting axiom therefore, that brilliant underhead light sources are taboo for esthetic purposes.1931, Lighting - Volumes 20-21, page 14. From the entry underhead
Opposed to codes that qualify, and overcodes that bring codes into a single resonance, axioms function by directly conjugating unqualified and decoded flows themselves.2012, Thomas Nail, Returning to Revolution: Deleuze, Guattari and Zapatismo, →ISBN, page 94. From the entry overcode
Part of establishing a foundation for geometry was demonstrating that the axioms were consistent – that they could never lead to contradictions.2008, Charles Petzold, “Centuries of Progress”, in The Annotated Turing: A Guided Tour through Alan Turing’s Historic Paper on…. From the entry consistent
As we have mentioned before, the structure of Euclidean geometry, as formalized through the axioms of Hilbert, produces an archimedean ordered field.2008 November, Ambar N. Sengupta, “Notes in Introductory Real Analysis”, in www.math.lsu.edu, retrieved 13 Jul 2012. From the entry real number system
In the domain of valuations which are supervaluations with respect to a certain partial valuation the axioms of classical logic remain valid.2008 October 8, Holger Andreas, “Another Solution to the Problem of Theoretical Terms”, in Erkenntnis, volume 69, number 3, →DOI. From the entry supervaluation
The existence of the empty set is entailed, in the presence of the axiom scheme of separation, by the existence of any set whatever.2004, Michael Potter, Set Theory and its Philosophy, Oxford University Press, page 58. From the entry empty set
In the first years of independence this nationalist ideology was sometimes applied in a dogmatic manner similar to that of the former axioms.2003, Andreas Kappeler, “The Russian Empire and Its Nationalities in Post-Soviet Historiographies”, in Hayashi Tadayuki, editor, The…. From the entry Armenophobic
In fact, there can be no proof of the parallel postulate that relies only on the other axioms and postulates of Euclid.1998, David A. Singer, Geometry: Plane and Fancy, Springer, page 16. From the entry parallel postulate
Here, then, is an example of an arithmetical statement that may be true, but may be non-derivable from the axioms of arithmetic.1989, Ernest Nagel, James R. Newman, Godel's Proof. From the entry non-derivable
A hemispheric axiom has it that when a dictator falls afoul of Washington, his opponents are emboldened to try to topple him.1957 December 15, “Still in Business”, in Time. From the entry afoul
How intensely postulatory these axioms are, is best seen when we consider what is too often neglected, viz. the limits of their use.1902, Henry Cecil Sturt, Personal Idealism, Axioms as Postulates. From the entry postulatory
Second, it suggests an axiom so puritan that I hesitate to express it: On Twitter, ideas are so commodified that to say something is simultaneously to amplify it.2020 January 17, Robinson Meyer, “Why Twitter May Be Ruinous for the Left”, in The Atlantic. From the entry commodified
Whereas, on the “multiverse” interpretation, Modal Realism acknowledges physical possibilities only--and worse, (assuming either axiom S5 or axiom B) each possibilium ends up as a necessary physical existent.2011, T Parent, Modal Realism and the Meaning of 'Exist'. From the entry possibilium
Knopfmacher gives an interesting exposition of abstract analytic number theory wherein many of the results of classical number theory are generalized in a suitable context of semigroups satisfying certain axioms.2006, R. Sivaramakrishnan, Certain Number-Theoretic Episodes In Algebra, Taylor & Francis (Chapman & Hall/CRC), page 339. From the entry abstract analytic number theory
Thus at last mathematics is shown to be a completely contradictionless and scientifically unassailable system, and the final reduction of every mathematical proposition to the axioms of logic is completed.2004, Rudolf Metz, A Hundred Years of British Philosophy, Volume 14. From the entry contradictionless
And they seem to work, in the sense that in a sufficiently strong set theory it can be shown that Peano's axioms have (up to isomorphism) a unique model (cf.1996, Moshe Machover, Set Theory, Logic and Their Limitations, Cambridge University Press, →ISBN, page 282. From the entry ambient

Meaning of axiom

noun A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
noun A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).
noun An established principle in some artistic practice or science that is universally received.

Full definition of axiom

Questions about axiom in a sentence

How do you use axiom in a sentence?: Axiom is used as a noun. For example: “The axioms of political economy cannot be considered absolute truths.”
What is a short sentence with axiom?: “The axioms read as follows.”
What does axiom mean?: Axiom means a seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.

Adapted from Wiktionary: axiom (page history and authors) and the entries each sentence comes from. Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws chose the sentences, left out offensive ones and quotations older than 1900, and marked the word in each. Wiktionary data of 2026-09-02.

Last updated: 2026-09-02

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