Definite enough

Reference occurs when someone refers another person to something—or to some things (the first thing that Russell looked at, after thinking about Cantor’s paradox, was reference). Reference is fundamental to language (and mathematics). And even before creatures had language, there was being seen to be looking at something. There was pointing and then naming and thinking. But for Russell, names were definite descriptions, and vagueness was a logical problem. I think that vagueness is not so much a problem in logic, as the possibility of a logical solution to most if not all of the philosophical problems in logic. Consider, for example, the Lottery paradox:

If I believe, of each ticket, that it won’t win, then I believe that none of the tickets will win. Whereas, I know that one of them will win.

But I actually believe, of each ticket, that it very probably won’t win, and when I describe those beliefs with that amount of precision, there is no paradox. What about the Preface paradox; or more simply, the likelihood of some of my beliefs being wrong? I certainly believe all of my beliefs, so my belief that some of them are likely to be wrong might appear paradoxical. However, as soon as I come to the realisation that some of my beliefs are likely to be wrong, I find that I am holding those beliefs less strongly. For a more epistemological problem:

I can see very clearly that there is a horse trotting past a tree, outside my window (I live in a village in Bedfordshire), so I know that there is a horse there. I could conceivably be looking at a painted zebra that is about to be eaten by an alien stick-insectoid, though: that is a logical possibility. And if I don’t know how rare such creatures are, how can I know how unlikely this possibility is?

Well, I can simply assume that it is unlikely, until I get evidence to the contrary. We naturally assume that things remain more or less the same, in the absence of evidence to the contrary, when we name things. And we only have to be definite enough for the purposes of communication. We do not need a precise definition of “horse” in order to know that something is a horse, so why would we need to rule out all conceivable stick-insectoids?
......Quite generally, the power of natural language lies in its flexibility, which derives from the inherent vagueness of its terms: our words arrive sufficiently well defined for their usual uses, but they can always be defined with more precision if that becomes necessary. The ubiquity of vagueness in natural language is not a logical problem (as Russell believed), it is the possibility of a logical solution to most if not all of our philosophical problems.
......Philosophers have a strong bias towards bivalence because as we philosophize we clarify, aiming to maintain an adequate bivalence. But intuitions that logic ought to be bivalent are therefore quite compatible with logic not being perfectly bivalent. After all, questions of truth are essentially questions of how well our words describe the world; so, the logical primitive is not True (or T, in some mathematical model of logical reasoning) but True Enough. When we say “that’s true” we usually mean that it’s true enough. And it is implausible that statements are bound to be either true enough or else sufficiently false.