coextensivity

Coextensivity is a concept in logic and philosophy, particularly in the philosophy of language, that describes a specific relationship between two concepts or predicates. Two concepts or predicates are said to be coextensive if they apply to exactly the same set of entities or individuals. In simpler terms, if every object that has property A also has property B, and every object that has property B also has property A, then A and B are coextensive.

For example, the concepts "creature with a heart" and "creature with kidneys" are often considered coextensive in biology, as all known creatures with hearts also have kidneys, and vice versa. If coextensivity holds, then the two predicates can be substituted for each other in many logical contexts without changing the truth value of a statement. However, coextensivity does not imply synonymy. Synonymy suggests that two words or phrases have the same meaning, which is a semantic relationship, whereas coextensivity is a referential relationship – it concerns what the concepts *pick out* in the world.

The concept of coextensivity is important for understanding how language refers to the world and how we can make logical inferences. It is also relevant in discussions about identity, definitions, and the nature of properties. While empirical coextensivity can be a contingent fact about the world, logical coextensivity would imply that the concepts are necessarily the same in their application.