Near enough is good enough in the real world; and in particular, it is good enough for reference, a concept that lies at the heart of philosophical logic. Reference occurs when someone refers someone else to something. Even prior to language, there is a primitive kind of reference that involves being seen to be looking at something, of some commonsensical kind. Now, analytical philosophers usually move quickly from reference to definite descriptions, before getting bogged down in the problem of vagueness. But I would like to suggest that vagueness is not so much a problem at the cutting edge of mathematical logic, as the best way to resolve most problems in philosophical logic. For a very simple example, consider the Lottery paradox: I believe, of each ticket, that it won’t win, so logically I ought to believe the conjunction, that none of the tickets will win, whereas I know that one will win.
......The paradox is resolved if I describe my belief that it very probably won’t win at least that precisely. And similarly, consider the Preface paradox: Each statement in this post is here because I believe it, but I also believe that I have probably made at least one mistake. Also similar is the fact that I believe that what I am now looking at, out my window, is a horse trotting past a tree, even though it might, just possibly, be a painted zebra about to be eaten by an alien stick insect. And what is common to all such paradoxes is that they are most satisfyingly resolved by our clarifying our terms. And quite generally, the power of natural language lies in its flexibility, which derives, I think, from the inherent vagueness of its terms. There are endless examples, so I challenge the reader to come up with a term that could not be replaced by more precise terms if necessary.
......Such subtle vagueness is ubiquitous precisely because our terms are almost always definite enough, so long as we speak carefully enough. And since logic is essentially the study of correct reasoning, it should not ignore the natural-linguistic clarification procedures—such as philosophical analysis itself—that aim at no more than an adequate bivalence. We 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, and so the logical primitive is not T (true), 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.
Pruss and Rasmussen's Necessary Existence: Conclusion and Table of Posts - Pruss and Rasmussen conclude with an appendix providing "a slew of arguments" for the claim that there is a necessary being. These arguments are, for the m...
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