 Intensional. The way in which I-languages are ‘intensional’ for Chomsky needs a little explication. The concept of intension is familiar in logic and semantics, where ‘intensional’ contrasts with ‘extensional’. The extension of a predicate like blue is simply the set of all blue objects; the intension is the function that picks out in a given world the blue objects contained therein. In a similar way, the extension of a set can be distinguished from an intensional description of the set in terms of a function: the set of integer squares is {1, 4, 9, 16, 25, 36, …}, and the intension could be given in terms of the one-place function f such that f(n) = n × n. One difference between the two accounts of squaring is that the intensional one could be applied to a different domain (any domain on which the ‘×’ operation is defined: on the rationals rather than the integers, for example, the extension of the identically defined function is a different and larger set containing infinitely many fractions).