axiomatically

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axiomatically

This principle is axiomatically true in the field of logic.

Definition

Adverb: 1. In a way that is based on or derived from an axiom; in a self-evident or unquestionable manner. It describes something that is accepted as true without needing proof because it is a fundamental principle. 2. As an obvious or necessary consequence; as a matter of logical certainty. It indicates that a statement follows directly and undeniably from established principles.

Usage

The adverb "axiomatically" is used to modify a verb, an adjective, or a whole clause to state that something is true based on a fundamental, self-evident truth. It is formal and often used in academic, philosophical, mathematical, or logical contexts. * It is placed before the adjective or past participle it modifies. * It can be used at the beginning of a sentence to modify the entire statement that follows.

Examples
  • Modifying a verb/statement:
  • Modifying an adjective:
  • Sentence-initial use: Axiomatically, a democratic government derives its power from the consent of the governed.
Advanced Usage
  • In logic and mathematics: Used to describe a proposition that is taken as a starting point for reasoning, from which other statements are logically derived.
    • In Euclidean geometry, it is axiomatically accepted that parallel lines never meet.
  • In philosophical argument: Used to assert a foundational premise that is not argued within the current context but is treated as given.
    • The author begins from the axiomatically held belief in the inherent dignity of every person.
Variants and Related Words
  • Axiom (n): A statement or proposition that is regarded as being established, accepted, or self-evidently true.
  • Axiomatic (adj): 1. Self-evident or unquestionable. 2. Relating to or containing axioms.
    • It is axiomatic that energy cannot be created or destroyed.
Synonyms
  • Self-evidently
  • Necessarily
  • Obviously (in a logical sense)
  • Fundamentally
  • By definition
Antonyms
  • Debatably
  • Questionably
  • Contingently
  • Empirically (derived from observation/experiment rather than pure logic)
axiomatically

This principle is axiomatically true in the field of logic.

Adverb
  1. on the basis of axioms
    • this is axiomatically given

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