extension/intension

The extension of a predicate is the class of objects that it describes: the extension of ‘red’ is the class of red things. The intension is the principle under which it picks them out, or in other words the condition a thing must satisfy to be truly described by the predicate. Two predicates (‘…is a rational animal’, ‘…is a naturally featherless biped’) might pick out the same class but they do so by a different condition. If the notions are extended to other items, then the extension of a sentence is its truth-value, and its intension a thought or proposition; and the extension of a singular term is the object referred to by it, if it so refers, and its intension is the concept by means of which the object is picked out. A sentence puts a predicate or other term in an extensional context if any other predicate or term with the same extension can be substituted without it being possible that the truth-value changes: if John is a rational animal, and we substitute the co-extensive ‘is a naturally featherless biped’, then John is a naturally featherless biped. Other contexts, such as ‘Mary believes that John is a rational animal’, may not allow the substitution, and are called intensional contexts.