Suppose that only propositions can be true or false. In a much earlier post I expressed a suspicion of conjunctive definitions. But if bivalence is right, then the following definition of falsity seems very plausible:
- x is false iff x is a proposition and x is not true.
I could say that the suspicious conjunctiveness shows that in fact this isn't the right definition of falsity. Instead, I should have a definition friendlier to non-bivalent views, such as that x is false if and only if not-x is true. I am not sure I want to do that, though.
Another move would be to dig in my heels and say that there are two properties. There is falsity and falsity*. x is false* iff x is not true. x is false iff x is a proposition and x is false*. Chairs are false*, but only a proposition can be false. The more basic and natural property is falsity*. But English, for whatever pragmatic reason, has a single word for "false" and lacks a single word for "false*". Thus the English "false" denotes a less basic property, but this has some pragmatic explanation. However, in philosophizing, we should work as much as possible with the more basic concept, that of falsity*. Extending truth to sentences and beliefs, we then get to say that "All mimsy were the borogoves" is false*, just as my computer and "The sky is now pink" are false*.