Word: axiom (noun)

Associations

An axiom is a statement or idea that is accepted as true without needing proof. It is often used in math, logic, or philosophy as a starting point for reasoning.

• In math: "The axiom that through any two points there is exactly one straight line." This is a basic truth used to build other ideas.
• In everyday speech: "Honesty is an axiom in good relationships." Meaning honesty is a basic, accepted truth.
• In logic: "The axiom 'if A equals B and B equals C, then A equals C' is fundamental." This is a rule accepted without proof to build arguments.

Synonym: principle.
Difference: A principle is a general truth or rule, often learned from experience, while an axiom is usually a self-evident truth accepted without proof, especially in formal systems.

Substitution

You can replace "axiom" with:

• principle (more general, sometimes less strict)
• postulate (used especially in math, similar meaning)
• rule (more informal, less formal than axiom) Example: "The principle of gravity" instead of "The axiom of gravity" (but gravity is a scientific law, not an axiom).

Deconstruction

The word "axiom" comes from the Greek word "axioma," meaning "that which is thought worthy or fit" or "a self-evident truth."
It has no prefix or suffix here, just the root "axiom," which relates to value or worth in Greek.

Inquiry

• Can you think of some axioms in everyday life or in your studies?
• How is an axiom different from a fact or an opinion?
• Why do you think axioms are important in math or science?
• Have you heard phrases like "It's an axiom that..."? What does that mean in conversation?