1.2.2. Truth conditions and propositions

When judging the validity of an argument, what we need to know about its premises and conclusion are the truth values of these sentences in various possible worlds. This information about a sentence is an aspect of its meaning that we will call its truth conditions. That is, when we are able to tell, no matter what possible world we might be given, whether or not a sentence is true, we know the conditions under which the sentence is true; and, when we know those conditions, we can tell whether or not it is true in a given possible world.

It will also be convenient to be able to speak of this kind of meaning or aspect of meaning as an entity in its own right. We will do this by speaking of the truth conditions of a sentence as encapsulated in the proposition expressed by the sentence. This proposition can be thought of as a way of dividing the full range of possible worlds into those in which the sentence is true and those in which it is false—i.e., into the possibilities it leaves open and the ones it rules out. And we can picture a proposition as a division of an area representing the full range of possibilities into two regions.

Fig. 1.2.2-1. A proposition dividing the full range of possible worlds into possibilities ruled out and possibilities left open.

Since knowing what possibilities are in one of these regions tells us that the rest are in the other region, we know what proposition is expressed by a sentence when we know what possibilities it rules out—or know what possibilities it leaves open. And focusing on one or the other of these sets of possibilities may be helpful in certain contexts.