Bivalence and States of Affairs
It is sometimes maintained that bivalence fails for certain kinds of sentences or propositions. What I will argue is that if bivalence holds for states of affairs it holds for sentences and propositions. Moreover, it is plausible that bivalence does hold for states of affairs, so we can conclude that it also holds for sentences and propositions.
By “state of affairs” I mean “possible condition of objects”, i.e. ways objects might be. States of affairs can be said to obtain or not to obtain: if they obtain they are called facts, while if they fail to obtain they are merely possible (sometimes impossible). For instance, there is the state of affairs of my cup having coffee in it, which happens to be actualized (a fact). Now I want to say that any such state of affairs either obtains or does not obtain—there is no other alternative. States of affairs are bivalent. There may be truth-value gaps for statements but there are no obtainment-value gaps for states of affairs. Either coffee is in the cup or it’s not in the cup. This says nothing about propositions or sentences; it is purely a point about how the world can be. Reality either is a certain way or it isn’t. There may be exceptions, such as vagueness and borderline cases, but generally speaking states of affairs either obtain or don’t. What I want to argue is that in cases in which states of affairs are bivalent propositions about them must be bivalent too. The only way for bivalence to fail for propositions is for it to fail for states of affairs.
The argument is simple: propositions are representations of states of affairs and their truth-value depends completely on whether the represented state of affairs obtains or not. If the state of affairs obtains the proposition is true, while if it does not obtain the proposition is false—and the state of affairs either obtains or it doesn’t (bivalence). This is intended to rule out a certain kind of interpretation of sentences about non-existent things, such as “The king of France is bald”: we cannot say that this sentence expresses a proposition that is neither true nor false. For every proposition represents a state of affairs that either obtains or does not—so the question must be whether the state of affairs represented by this sentence obtains or not. According to Russell’s theory, it does not obtain, so the proposition is false. According to Strawson’s theory, we cannot say whether the state of affairs obtains or not, because it lacks a constituent object to instantiate properties or fail to instantiate them. But we should not characterize this as a case of a proposition that is neither true nor false, since every proposition must represent a state of affairs subject to bivalence. And we need not speak that way: we can say instead that the sentence simply fails to express a proposition, since it depicts no determinate state of affairs. Then we can indeed conclude that the sentence suffers from truth-value gaps, since it expresses no proposition—and hence no proposition that is neither true nor false.  The same would be true of “Vulcan was hit by lightning”: since there is no such planet, there is no such possible state of affairs, and hence nothing to make true the proposition that Vulcan was struck by lightning. The right thing to say is that there is no state of affairs here and hence there is no proposition representing a state of affairs—on pain of allowing for propositions that represent no state of affairs. Propositions and states of affairs go hand in hand: there is no sense in the idea of a proposition that does not represent the world as being a certain way, i.e. certain objects having certain properties. So bivalence for states of affairs carries over to bivalence for propositions (but not sentences, i.e. meaningful strings of words).
Knowledge of states of affairs is another matter entirely: it is not true that every state of affairs is either known to obtain or known not to obtain, since we may be ignorant about reality. But propositions don’t represent (stand for) our knowledge of reality or its lack; they represent reality. Therefore propositions are bivalent, because reality is. If bivalence fails for a proposition, it must always be because it fails for reality; it cannot fail for a proposition yet hold for the state of affairs the proposition represents. Propositions stand for states of affairs, and they are true or false according to whether the state of affairs obtains or not. Given that states of affairs either obtain or don’t obtain, propositions must either be true or false—never neither.