# axiom

## Definitions

• WordNet 3.6
• n axiom (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
• n axiom a saying that is widely accepted on its own merits
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Webster's Revised Unabridged Dictionary
• Axiom (Logic & Math) A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, “The whole is greater than a part;” “A thing can not, at the same time, be and not be.”
• Axiom An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.
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Century Dictionary and Cyclopedia
• n axiom A self-evident, undemonstrable, theoretical, and general proposition to which every one who apprehends its meaning must assent. The Greek word was probably applied by Plato (though it does not occur in his dialogues in this sense) to certain first premises of mathematics; and this continues to be the ordinary use of the term. It was extended by Aristotle to similar principles supposed to underlie other branches of knowledge. The axioms or “common notions” of Euclid, as given in English translations, are twelve in number, viz.:
• n axiom Any higher proposition, obtained by generalization and induction from the observation of individual instances; the enunciation of a general fact; an empirical law. This use originated with Bacon, influenced probably by the employment of axiom by the Stoics to mean any proposition.
• n axiom In logic, a proposition, whether true or false: a use of the term which originated with Zeno the Stoic. Synonyms Maxim, Truism, etc. See aphorism.
• n axiom one of those generalizations of ordinary experience which nobody doubts, and which are soon replaced by scientific formulations, which latter are also, but less properly, termed middle axioms.
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Chambers's Twentieth Century Dictionary
• n Axiom aks′yum a self-evident truth: a universally received principle in an art or science
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## Quotations

• Maxwell Maltz
“It is an old psychological axiom that constant exposure to the object of fear immunizes against the fear.”
• Aneurin Bevan
“It is an axiom, enforced by all the experience of the ages, that they who rule industrially will rule politically.”
• Albert Einstein
“The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.”
• Sir Arthur Conan Doyle
“It has long been an axiom of mine that the little things are infinitely the most important.”
• Abraham Lincoln
“The principles of Jefferson are the definitions and axioms of free society.”

## Etymology

Webster's Revised Unabridged Dictionary
L. axioma, Gr. , that which is thought worthy, that which is assumed, a basis of demonstration, a principle, fr. , to think worthy, fr. , worthy, weighing as much as; cf. , to lead, drive, also to weigh so much: cf F. axiome,. See Agent (a.)
Chambers's Twentieth Century Dictionary
Gr. axiōmaaxio-ein, to think worth, to take for granted—axios, worth.

## Usage

### In literature:

What are your Axioms, and Categories, and Systems, and Aphorisms?
"Sartor Resartus, and On Heroes, Hero-Worship, and the Heroic in History" by Thomas Carlyle
On the other hand, it is a political axiom that the first duty of any statesman is to his own people.
"Mr. Grex of Monte Carlo" by E. Phillips Oppenheim
The system is evolved in a series of theorems in severely demonstrative order out of the definitions and axioms which we have translated.
"Short Studies on Great Subjects" by James Anthony Froude
The true principle may be stated in the form of an axiom.
"Albert Gallatin" by John Austin Stevens
Agnes herself was trying to prove that axiom; but Trix had never tried to restrain herself.
"The Corner House Girls at School" by Grace Brooks Hill
The English school of philosophy have already attacked this problem in connection with the origin of axioms.
"The Mind and the Brain" by Alfred Binet
The axiom of Christian faith is that whatever we do not obtain we do not require.
"Expositions of Holy Scripture" by Alexander Maclaren
This has become well nigh the axiom for Norwegian politics.
"The Swedish-Norwegian Union Crisis" by Karl Nordlund
You have to begin with one hedgehog, that's an axiom.
"Burr Junior" by G. Manville Fenn
Why then, when it comes to this particular axiom of irrational common-sense, does he balk and sheer off?
"The Complex Vision" by John Cowper Powys
This you may take as an axiom.
"Woman" by William J. Robinson
Heavens, with what pained looks, with what platitudes and proverbs, with what reproofs and axioms and sentiments!
"The Daughters of Danaus" by Mona Caird
Theological dicta were, to the thinkers of those days, that which the axioms and definitions of Euclid are to the geometers of these.
"Harvard Classics Volume 28" by Various
In chemistry, also, the axiom fails.
"The Short-story" by William Patterson Atkinson
Then he said no more, scorning to demonstrate an axiom.
"St. Cuthbert's" by Robert E. Knowles
So here is a theory which South African practice proved to be more often wrong than right being treated as an axiom at Gallipoli!
"Gallipoli Diary, Volume 2" by Ian Hamilton
Where we have no legal principles or courts to decide, we must fall back on legal axioms.
"Memoirs" by Charles Godfrey Leland
That is an axiom I have frequently heard fall from the lips of my dear mistress.
"Aunt Rachel" by David Christie Murray
That saying has been proven again and again till it has become an undisputed axiom.
"Policing the Plains" by R.G. MacBeth
All Euclid is in the definitions and axioms and postulates at the beginning.
"Expositions of Holy Scripture" by Alexander Maclaren
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### In poetry:

But, keeping still the end in view
To which I hoped to come,
I strove to prove the matter true
By putting everything I knew
Into an axiom:
"Phantasmagoria Canto VI ( Dyscomfyture )" by Lewis Carroll

### In news:

Newt quotes a political axiom about the last week of an election from Democratic operative James Carville to make his point.
Months later, after just three full-team minicamp practices, the axiom about perception versus reality seems to apply perfectly here.
The Axiom Epic 80/500 home theater speaker system, shown here finished in Mansfield Beech.
It is an axiom of conventional wisdom about the Middle East that the government of Israel is a hard-line opponent of peace that must be pressured and cajoled to deal with the Palestinians for the sake of the survival of its people.
There is a well known axiom that states that the eyes are the window to the soul.
Here are some easy adjustments, provided by Axiom Audio, that you can make over the weekend to boost your system's performance.
If that old axiom is indeed true, then the trophy case at Canfield High School may need to clear some space.
We try out that axiom at shop in Orange.
It's an age-old axiom for truck drivers: if you see signs of trouble ahead, start slowing down, because time and space is what you need to safely maneuver your big rig out of danger.
There's an old axiom in music that says you have your whole life to make your first record and under a year to make your second.
An axiom in advertising is that sex sells.
Axiom Audio Epic Midi 400 Speakers.
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Badawi destroy all prophets the axiom ep.
Axiom Audio's custom-matched outdoor speakers can help solve your dilemma of electronics clashing with aesthetics.
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### In science:

I if it satisﬁes the axioms that will be listed below. (It is important that the functions fp,q be deﬁned on the whole circle S 1 since axiom (A7) below might otherwise be violated in the applications.) Notice that fp,q is deﬁned for p 6= q if and only if p, q ∈ ¯I and fp,p is deﬁned if and only if p ∈ I .
Sextactic points on a simple closed curve
Then the triple (R, ∂, Y + (·, z)) forms a conformal algebras if and only if Axiom (2.5), and Axiom (2.6) acting on V hold for u, v ∈ V .
Simple Conformal Algebras Generated by Jordan Algebras
Then this Γ satisﬁes the above four axioms: It is easy to see that our Γ saitsﬁes Axioms 1, 3 and 4.
Definability of initial segments
Note ﬁrst, that no ways are known now for direct generalizations of Wightman axioms or, in euclidean approach, Osterwalder-Schrader axioms (although, axioms of S -matrix type can be generalized in different directions - topological ﬁeld theory, diagrams of string theory).
Gibbs and Quantum Discrete Spaces
Topological quantum ﬁeld theory Axioms of topological quantum ﬁeld theory as introduced in resemble more axioms of S -matrix theory, than give models of the space-time structure.
Gibbs and Quantum Discrete Spaces
Informally, the set of axioms and deduction rules generates all ‘theorems’; for example, we cannot take as axioms all true statements about natural numbers as this set is not computably enumerable.
Incompleteness, Complexity, Randomness and Beyond
The ﬁrst, respectively the second, axiom of a pre-dialgebra of type I is equivalent to the ﬁrst, respectively the second, axiom of a dendriform algebra with ≺ associative.
Coassociativity breaking and oriented graphs
Proof: a ≺ (b ≻ c) = 0 ⇔ a ⊣ (b ⊢ c − b ⊣ c) = 0, which proves that the ﬁrst axiom of a pre-dialgebra of type I is equivalent to the ﬁrst axiom of a dendriform algebra.
Coassociativity breaking and oriented graphs
The third, respectively the second, axiom of a pre-dialgebra of type III is equivalent to the third, respectively the second, axiom of a dendriform algebra with ≻ associative.
Coassociativity breaking and oriented graphs
Proof: (of the theorem 5.32) In the case of a pre-dialgebra of type I, the proof is completed by noticing that the third axiom of a dendriform algebra with ≺ associative is not enough to prove the third axiom of a dialgebra.
Coassociativity breaking and oriented graphs
Indeed, stability and composition axioms for a pre-topology are statisﬁed, but the base change axiom is not.
From HAG to DAG: derived moduli spaces
Note that in the limit ψ → ±π the braided Hopf algebra axioms reduce to the ordinary/super Hopf algebra axioms.
Generalized exclusion and Hopf algebras
Note that these axioms bear remarkable similarity to the axioms of R´enyi’s entropy.
Information theory and generalized statistics
Obviously, in the q → 1 limit the Jackson sum reduces to ordinary S (A ∩B ) = S (A)+ S (B |A) and above axioms boil down to Shannon– Khinchin axioms of classical information theory .
Information theory and generalized statistics
In the axiomatization proposed in (Levesque et al. 1998), axioms are divided into domain axioms and domain independent foundational axioms for situations.
Logic-Based Specification Languages for Intelligent Software Agents
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