axiom

/'æksiəm/

Thân thiện

An axiom is a fundamental principle in mathematics.

Definition

1. Noun:
   • A self-evident or universally accepted truth: An axiom is a statement or principle that is regarded as being established, accepted, or self-evidently true, often serving as a starting point for further reasoning or argument.
   • A fundamental proposition in logic or mathematics: In formal systems, an axiom is a basic assumption or postulate that is accepted without proof, forming the basis for deducing other truths (theorems).

Usage Examples

• General Truth:
  • It is an axiom in politics that all power corrupts.
  • "Honesty is the best policy" is treated as an axiom by many people.
• Logic/Mathematics:
  • Euclid's axioms form the foundation of classical geometry.
  • In that logical system, the axiom of choice is a controversial but fundamental postulate.

Advanced Usage

• "To take something as an axiom": To accept a statement as a fundamental, unquestionable truth.
  • In his philosophy, he takes human dignity as an axiom.
• "Axiomatic truth": A truth that is so evident it is considered an axiom.
  • The axiomatic truth of his argument made further debate pointless.

Variants and Related Words

• Axiomatic (adj): Self-evident or unquestionable.
  • It is axiomatic that a whole is greater than any of its parts.
• Axiomatically (adv): In a way that is self-evident or derived from axioms.
  • The conclusion follows axiomatically from the premises.

Synonyms

• Maxim: A short, pithy statement expressing a general truth or rule of conduct.
• Truism: A statement that is obviously true and says nothing new or interesting.
• Postulate: A thing suggested or assumed as true as the basis for reasoning, especially in logic or mathematics.
• Principle: A fundamental truth or proposition that serves as the foundation for a system of belief or behavior.

Related Phrases

• "As an axiom": Used to introduce a statement considered a fundamental truth.
  • We must start, as an axiom, from the belief in human rationality.

Học thuật

Noun

1. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
2. a saying that is widely accepted on its own merits

Từ đồng nghĩa

• maxim