2008-08-13, Jonathan Schaffer, Truthmaker commitments, Indeed the whole point of Aristotle’s example of truth depending on being was that the truth of the proposition and the existence of the man are intensionally equivalent, yet there is an asymmetry of dependence. A term is treated either extensionally as a class of objects or intensionally as a set of properties. The ‘intent’ of the term ‘dog’ includes all the properties that are included in the intent of ‘mammal’. The intensional treatment of ‘dogs are mammals’ interprets this sentence as true because the semantic interpretation of the subject is a superset of the interpretation of the predicate. On the extensional treatment of the sentence, however, the sentence is true because the interpretation of the subject (the class of dogs) is a subset of the interpretation of the predicate (the set of mammals).
