Axiom Meaning: Definition, Examples, and Translations
๐ง
axiom
[หรฆks.i.ษm ]
Definitions
mathematics
A statement or proposition that is regarded as being established, accepted, or self-evidently true.
Synonyms
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.
|
| postulate |
Often used in science and mathematics, a postulate is a statement assumed true without proof for the sake of building a theory.
|
| 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.
|
| truth |
Used in a broad range of contexts, from daily conversation to philosophical discourse. Truth is a statement or fact accepted as true.
|
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.
philosophy
A statement or proposition on which an abstractly defined structure is based, used to generate further statements and theorems.
Synonyms
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.
|
| 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.
|
| 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.
|
Examples of usage
- In metaphysics, the principle of causality is considered an axiom for many philosophical arguments.
general
An established rule or principle or a self-evident truth.
Synonyms
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.
|
| 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.
|
| 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.
|
Examples of usage
- The axiom 'treat others as you would like to be treated' is a common ethical guideline.
Translations
To see the translation, please select a language from the options available.
Interesting Facts
Philosophy
- Philosophers like Aristotle argued that certain axioms are self-evident, meaning they are obvious and donโt 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.
- Einsteinโs 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.
Origin of 'axiom'
Main points about word origin
- 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.
The word 'axiom' originated from the Greek word 'axรญลma', meaning 'that which is thought worthy or fit'. It first appeared in English in the late 15th century. In mathematics and philosophy, axioms play a crucial role in establishing the foundation of theories and systems of thought.