Worlds and Intensions

A pervasive feature of natural languages is that sentences depend for their truth value on the context or situation in which they are evaluated. For example, sentences like ‘It is raining’ and ‘I am glad’ cannot be assigned truth values unless the time, place of utterance, and the identity of the speaker is known. The same sentence may be true in one situation and false in another. In modal language, where we consider how things might have been, sentences may be evaluated in different possible worlds.

In the standard extensional semantics, truth values are assigned directly to sentences, as if the context had no role to play in their determination. This conflicts with what we know about ordinary language. There are two ways to solve the problem. The first is to translate the content of a sentence uttered in a given context into a corresponding sentence whose truth value does not depend on the context. For example, ‘It is raining’ might be converted into, for example, ‘It is raining in Houston at 12:00 EST on Dec. 9, 1997 ‥’. The dots here indicate that the attempt to eliminate all context sensitivity may be a never-ending story. For instance, we forgot to say that we are using the Gregorian Calendar, or that the sentence is to be evaluated in the real world.