Intension and Extension

Extensions

Here is a basic package of views about what extensions are. The extension of a predicate is the set of objects that it applies to. The extension of “is a rabbit” is the set of rabbits, for example, and the extension of “runs” is the set of running things. The extension of a name is the thing it is the name of. The extension of “George W. Bush” is a certain ex-president, for example. The extension of a sentence is a truth-value: normally there are thought to be two truth-values, True and False. Sometimes it is thought that an extension is the thing, or things, “out there” in the world that are picked out by pieces of language.

In the years since Gottlob Frege first presented this package of views about extensions, some theorists have offered slightly different accounts of the extensions of these expressions. Some people are suspicious of sets, or of giving sets a role in the meanings of ordinary pieces of language. They might interpret the extension of a predicate as the things, collectively, that the word applies to (the rabbits are the extension of “rabbit”). Other people think that the extension of a predicate is only the set of things that the predicate applies to in this possible world, and reserve the set of all actual and possible things the predicate applies to for the role of an intension. (See the suggestion by David Lewis in 1970 about extensions.)

As well as disputes about what sort of things should be considered to be the extensions of predicates, names, and sentences, there have also been theories that extend the notion of extension to other parts of language. Quantifier expressions (“all cats,” “most sailors,” etc.) are assigned extensions in some kinds of generalized quantifier theory. Descriptions (“the first King of England,” “a cat in my garden”) are sometimes assigned extensions, either by treating them as a kind of quantifier expression or by treating their extensions as the things they apply to. Extensions could be attributed to other pieces of language as well.

Intensions

Intensions, on the other hand, are often treated as features of meaning that determine the extensions of words. The intension of a predicate might be a concept or something that describes the things that fall under the predicate. Or it might be a property, such that things fall in the extension of the predicate if they possess that property. Or it might be a function from possible worlds to extensions—given the relevant possible world as an input, it delivers the extension of the expression as an output. On this conception of the intension of predicates, these intensions would in effect code information about which things would have which features, given different alternatives to this world.

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