Definition

1. Adjective:
   • Not having a common factor; lacking a common measure: In mathematics, two quantities are incommensurable if their ratio is an irrational number, meaning they cannot be expressed as a ratio of integers.
   • Impossible to measure or compare in value, size, or excellence: Used to describe things so fundamentally different in nature, quality, or kind that they cannot be meaningfully measured against each other using a common standard.

Usage Examples

• Adjective:
  • The value of a human life and the cost of a material good are incommensurable.
  • In geometry, the side of a square and its diagonal are incommensurable lengths.
  • The artist felt that commercial success and artistic integrity were incommensurable concepts.

Advanced Usage

• "incommensurable with": Used to state that one thing cannot be compared to another.
  • The suffering of war is incommensurable with any statistic.
  • His personal ethics were incommensurable with the company's profit-driven policies.

Variants and Related Words

• Incommensurability (noun): The quality or state of being incommensurable.
  • The debate highlighted the incommensurability of the two philosophical frameworks.
• Incommensurate (adjective): Often used similarly to mean out of proportion or inadequate. While closely related, "incommensurable" more strongly implies impossibility of comparison, whereas "incommensurate" often implies a lack of due proportion.
  • The punishment was incommensurate with the minor offense.

Synonyms

• Incomparable: So good or great that nothing can be compared to it (often positive, whereas incommensurable is neutral).
• Disparate: Essentially different in kind; not allowing comparison.
• Incompatible: (Of two things) so different in nature as to be incapable of coexisting or being compared.

Antonyms

• Commensurable: Measurable by the same standard; having a common factor.
• Comparable: Able to be likened to another; similar.

Related Concepts

• Incommensurable values: A philosophical concept where two or more values (like freedom and security) cannot be reduced to a single measure of value for rational comparison.
• Incommensurability (philosophy of science): The idea that competing scientific paradigms may be so different that they lack a common basis for comparison.

Adjective

1. not having a common factor
2. impossible to measure or compare in value or size or excellence