Axiom: meaning, definitions and examples

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axiom

[ˈæks.i.əm ]

Definitions

^{Context #1 | Noun}

mathematics

A statement or proposition that is regarded as being established, accepted, or self-evidently true.

Synonyms

postulate, principle, truth.

Which Synonym Should You Choose?

Word	Description / Examples
axiom	Suitable for use in mathematics, logic, or formal systems. An axiom is a statement accepted as true without proof. In geometry, one basic axiom is that through any two points, there is exactly one line
postulate	Often used in science and mathematics, a postulate is a statement assumed true without proof for the sake of building a theory. Einstein's theory of relativity is built on the postulate that the speed of light is constant in a vacuum
principle	Applicable in general discussions, philosophy, or everyday life. A principle is a fundamental truth or proposition that serves as the foundation for a system of belief or behavior. Honesty is a key principle that most people value in personal relationships
truth	Used in a broad range of contexts, from daily conversation to philosophical discourse. Truth is a statement or fact accepted as true. It is a universal truth that gravity causes objects to fall towards the earth

Examples of usage

The axiom of choice is a fundamental principle in set theory.
One of the axioms of Euclidean geometry states that parallel lines never meet.

^{Context #2 | Noun}

philosophy

A statement or proposition on which an abstractly defined structure is based, used to generate further statements and theorems.

Synonyms

fundamental, premise.

Which Synonym Should You Choose?

Word	Description / Examples
axiom	An axiom is a statement that is accepted as true without proof, often used in mathematics and philosophy. It is considered a self-evident or universally recognized truth. In geometry, the parallel postulate is an axiom that cannot be derived from other assumptions The principle of equality is often treated as an axiom in discussions of human rights
premise	A premise is a statement or idea that forms the basis for an argument or story. It is often used in logical reasoning, debates, and narrative structures. The premise of the argument was flawed from the start The movie's premise was intriguing, featuring a time-traveling detective
fundamental	Fundamental refers to something that is a basic and essential part of a larger system or concept. It is used in various fields such as science, education, and philosophy to indicate core principles or elements. Understanding the fundamental laws of physics is crucial for any scientist Reading and writing are fundamental skills in education

Word

Description / Examples

axiom

An axiom is a statement that is accepted as true without proof, often used in mathematics and philosophy. It is considered a self-evident or universally recognized truth.

In geometry, the parallel postulate is an axiom that cannot be derived from other assumptions
The principle of equality is often treated as an axiom in discussions of human rights

premise

A premise is a statement or idea that forms the basis for an argument or story. It is often used in logical reasoning, debates, and narrative structures.

The premise of the argument was flawed from the start
The movie's premise was intriguing, featuring a time-traveling detective

fundamental

Fundamental refers to something that is a basic and essential part of a larger system or concept. It is used in various fields such as science, education, and philosophy to indicate core principles or elements.

Understanding the fundamental laws of physics is crucial for any scientist
Reading and writing are fundamental skills in education

Examples of usage

In metaphysics, the principle of causality is considered an axiom for many philosophical arguments.

^{Context #3 | Noun}

general

An established rule or principle or a self-evident truth.

Synonyms

maxim, motto.

Which Synonym Should You Choose?

Word	Description / Examples
axiom	An axiom is a statement or proposition that is regarded as being established, accepted, or self-evidently true. It is often used in mathematics and philosophy. In Euclidean geometry, one common axiom is that through any two points, there is exactly one straight line. The axioms of logic are fundamental to mathematical proofs.
motto	A motto is a short sentence or phrase chosen as encapsulating the beliefs or ideals guiding an individual, family, or institution. It's often used in a symbolic or inspirational context. The school’s motto is 'Knowledge is Power.' The company’s motto, 'Customer First,' reflects its commitment to service.
maxim	A maxim is a short, pithy statement expressing a general truth or rule of conduct. It is often used in a moral or philosophical context. One common maxim is 'actions speak louder than words.' The maxim 'honesty is the best policy' is often quoted in ethical discussions.

Word

Description / Examples

axiom

An axiom is a statement or proposition that is regarded as being established, accepted, or self-evidently true. It is often used in mathematics and philosophy.

In Euclidean geometry, one common axiom is that through any two points, there is exactly one straight line.
The axioms of logic are fundamental to mathematical proofs.

motto

A motto is a short sentence or phrase chosen as encapsulating the beliefs or ideals guiding an individual, family, or institution. It's often used in a symbolic or inspirational context.

The school’s motto is 'Knowledge is Power.'
The company’s motto, 'Customer First,' reflects its commitment to service.

maxim

A maxim is a short, pithy statement expressing a general truth or rule of conduct. It is often used in a moral or philosophical context.

One common maxim is 'actions speak louder than words.'
The maxim 'honesty is the best policy' is often quoted in ethical discussions.

Examples of usage

The axiom 'treat others as you would like to be treated' is a common ethical guideline.

Interesting Facts

Etymology

The word comes from the Greek 'axioma', meaning 'that which is thought worthy or fit.'
It has been used in philosophical texts since the times of ancient Greece, framing foundational principles.
In mathematics, axioms form the starting point of logical reasoning, often paired with theorems and proofs.

Philosophy

Philosophers like Aristotle argued that certain axioms are self-evident, meaning they are obvious and don’t require proof.
In ethics, some foundational beliefs are considered axioms that guide moral reasoning and judgments.
Axioms help simplify complex systems by providing a basic set of accepted truths.

Mathematics

In mathematics, axioms are foundational statements accepted as true without proof, like 'through any two points, there is exactly one straight line.'
Euclidean geometry is built on five key axioms established by the Greek mathematician Euclid.
Different mathematical systems can have different axioms leading to unique geometric interpretations, such as non-Euclidean geometry.

Cultural References

In popular culture, axioms are often referenced in self-help books, indicating commonly accepted wisdom.
Quotations like 'The only thing we have to fear is fear itself' reflect axiomatic beliefs influencing society.
Axioms appear in various forms in literature, often as maxims or aphorisms that encapsulate important lessons.

Science

In scientific discourse, axioms can serve as assumptions for building theories; for example, the conservation of energy.
Einstein’s theories reshaped earlier axiomatic views of physics, introducing new foundational principles.
Scientific methods often accept certain axiomatic truths about the natural world to build upon in research.

Translations

Translations of the word "axiom" in other languages:

🇵🇹 axioma

🇮🇳 स्वयंसिद्ध सत्य

🇩🇪 Axiom

🇮🇩 aksioma

🇺🇦 аксіома

🇵🇱 aksjomat

🇯🇵 公理 (こうり)

🇫🇷 axiome

🇪🇸 axioma

🇹🇷 aksiyom

🇰🇷 공리 (공리)

🇸🇦 بديهية

🇨🇿 axiom

🇸🇰 axioma

🇨🇳 公理 (gōnglǐ)

🇸🇮 aksiom

🇮🇸 sjálfgefið

🇰🇿 аксиома

🇬🇪 აქსიომა

🇦🇿 aksiom

🇲🇽 axioma

Word Frequency Rank

At position #14,144, this word is part of sophisticated English vocabulary. It's useful for academic or professional contexts where precise language is needed.

...
14141 gotta
14142 overthrown
14143 fallow
14144 axiom
14145 turret
14146 motel
14147 boulder
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