Definition

1. Adjective:
   • Relating to or derived from axioms: Pertaining to a statement or principle that is accepted as true without proof, serving as a starting point for further reasoning.
   • Self-evident or unquestionably true: Describing something that is so clearly true that it needs no proof or justification.

Usage Examples

• Adjective:
  • The mathematician presented an axiomatical foundation for the theory. (The mathematician presented a foundation for the theory based on axioms.)
  • It is axiomatical that all points on a circle are equidistant from the center. (It is a self-evident truth that all points on a circle are equidistant from the center.)

Advanced Usage

• "axiomatical system": A logical system built upon a set of initial axioms.
  • Euclidean geometry is a classic example of an axiomatical system.
• "axiomatical approach": A method of reasoning or constructing a theory that begins with axioms.
  • The philosopher favored an axiomatical approach to ethics.

Variants and Related Words

• Axiomatic (adj): The more common form, with identical meaning.
  • It is an axiomatic truth.
• Axiom (n): A statement or proposition that is accepted as true.
  • One axiom of economics is that resources are scarce.
• Axiomatically (adv): In a way that is based on or relates to axioms.
  • The conclusion follows axiomatically from the premises.

Synonyms

• Self-evident: Clear without needing proof.
• Postulational: Based on postulates or assumed truths.
• Fundamental: Serving as a basic foundation.

Related Phrases

• Taken as axiomatic: Accepted as a basic, unquestionable truth.
  • In this field, it is taken as axiomatic that behavior is learned.

Adjective

1. of or relating to or derived from axioms
   • axiomatic physics
   • the postulational method was applied to geometry- S.S.Stevens