indemonstrability

The indemonstrability of the axiom was accepted by the philosophers.

Definition

Noun (uncountable): The quality or state of being impossible to demonstrate or prove.

Usage Examples

• (The quality of being impossible to prove logically.)
• (The state of being beyond proof.)
• (The inability to demonstrate evidence for the statement.)

Advanced Usage

• "Indemonstrability of axioms": A concept in logic and mathematics referring to fundamental truths that cannot be proven because they serve as the foundation for all other proofs.

  • Euclid's geometry relies on the indemonstrability of its postulates. (The postulates are accepted without proof.)

• "Indemonstrability of moral values": In ethics, the idea that certain moral truths cannot be empirically demonstrated.

  • The indemonstrability of ethical principles often leads to debates about relativism. (The impossibility of proving moral claims.)

Variants and Related Words

• Indemonstrable (adjective): Not capable of being demonstrated or proved.

  • The theorem is indemonstrable within this system. (Cannot be proven.)

• Indemonstrably (adverb): In a manner that cannot be demonstrated.

  • The claim is indemonstrably false. (False in a way that cannot be shown.)

Synonyms

• Unprovability: the state of being impossible to prove.
• Undemonstrability: the quality of not being demonstrable.
• Ineffability: the quality of being beyond expression or proof (often used in mystical contexts).

Related Idioms

• Beyond proof: a phrase meaning something that cannot be demonstrated.

  • Some truths are beyond proof, like the existence of the self. (Indemonstrable.)

• Axiomatic: self-evident and thus requiring no proof, often implying indemonstrability.

  • The rule is considered axiomatic. (Accepted as indemonstrable.)