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Axiomatic Meaning: Definition, Examples, and Translations

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axiomatic

[ˌaksēəˈmadik ]

Definition

Context #1 | Adjective

philosophy, mathematics

Axiomatic refers to something that is self-evident or universally accepted as true without requiring proof. In mathematics and logic, axiomatic systems are based on a set of axioms or statements assumed to be true. These axioms serve as the foundation for deriving further truths and theorems. The term is often used in discussions that emphasize the foundational principles of a particular theory or system.

Synonyms

fundamental, implicit, self-evident.

Examples of usage

  • In axiomatic geometry, the postulates are taken as given.
  • The principle is considered axiomatic in that field.
  • Many scientists rely on axiomatic truths in their research.

Translations

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Interesting Facts

Philosophy

  • In philosophical terms, an axiomatic system is a set of principles or statements from which other truths can be derived.
  • Famous philosophers like Euclid used axiomatic reasoning in geometry, establishing foundational truths that others would build upon.
  • Axioms are crucial in mathematics; they form the basis for proofs and logical arguments.

Mathematics

  • In mathematics, axioms are usually straightforward propositions assumed to be true, like 'through any two points, there is exactly one straight line.'
  • Different mathematical systems may have different sets of axioms, leading to various branches like Euclidean or non-Euclidean geometry.
  • The concept of an axiomatic framework allows for the exploration of complex ideas built on simple truths.

Psychology

  • Axiomatic beliefs can shape our worldview, as people often accept certain ideas without questioning them.
  • Cognitive biases may lead us to treat some axioms as more self-evident than they actually are, affecting decision-making.
  • In psychology, recognizing these axiomatic beliefs is vital for understanding how perspectives can differ between individuals.

Cultural References

  • In various cultures, sayings and proverbs often reflect axiomatic truths that guide social norms and behaviors.
  • Popular phrases like 'the sun rises in the east' are considered axiomatic truths universally accepted.
  • In literature, characters might rely on axiomatic truths that reflect societal values, adding depth to themes.

Origin of 'axiomatic'

Main points about word origin

  • The word comes from the Greek 'axioma', meaning 'that which is worthy' or 'self-evident'.
  • The suffix '-matic' comes from the Greek 'matikos', meaning 'of or related to', showing its relation to principles or norms.
  • It has been used in philosophical contexts since the 16th century.

The term 'axiomatic' comes from the Greek word 'axioma,' which means 'that which is thought worthy or fit.' The root 'axios' means 'worthy,' indicating that axioms are fundamental truths deemed to be universally accepted without proof. This concept was integrated into Western thought through the works of ancient philosophers like Euclid, who structured geometric principles based on axioms. Over time, the term evolved to encompass broader philosophical, logical, and mathematical discussions, emphasizing the idea that some truths are accepted as starting points for further reasoning. The use of 'axiomatic' has grown in contemporary discourse, often reflecting discussions around foundational principles in various fields, including ethics, finance, and science.

Word Frequency Rank

With rank #19,297, this word belongs to specialized vocabulary. While not common in everyday speech, it enriches your ability to express complex ideas.