Language and Intension

The complement, in many Philosophies of Language, of Extension is Intension. While the Extension of a word is given as the set of all objects to which the term applies, its Intension is the set of properties shared by every object to which it applies. Hence, standard dictionary definitions are Intensional, and examples such as 'unicorn', which has an Intension, but no Extension, support theories which assert the primacy of Intensionality in Language. Cassirer's contrast of grasping to pointing suggests the relation between Intension and Extension, respectively, with possession as its basis, i. e. to know the dictionary definition of a word is to possess its meaning, and, thereby, is to possess information about any object to which the word applies. Now, just as, in Formaterialism, linguistic Extension is a mode of the Material Principle of an Individual, Exposition, linguistic Intension is a mode of the Formal Principle, Propriation, i. e. 'becoming-one's-own'. Hence, that an Individual is constituted by both Principles, in combination, suggests that Language is both Intensional and Extensional.