On super- and subvaluationism: a classicist's reply to Hyde
Ken Akiba · Mind · 1999
Dominic Hyde (1997) has presented a new logical system for vague words that employs paraconsistent logic. He called it subvaluationism, in analogy with supervaluationism Fine (1975) and others have made popular. Hyde maintained that subvaluationism is substantially different from supervaluationism, and is at least as good for a logic of vagueness. In this note, I shall argue for the following: First, we may reasonably take Hyde's so-called subtruth not as truth simpliciter, as Hyde does, but just as possible truth in a certain sense of possible. Second, we also may take supertruth in supervaluationism as the dual of subtruth, a kind of necessary truth; we do not have to take it as truth simpliciter, either. We can regard superand subvaluationism essentially as duals. Finally, if we interpret superand subtruth this way, we can make inference rules for vague words much simpler and in compliance with classical logic. The logic of superand subvaluationism can be regarded not as an alternative to classical logic but as an extension of it. We do not need non-classical logic to understand vagueness. Superand subvaluationism make use of the notion of (admissible) An of a vague predicate (or singular term) is an interpretation under which a particular precise extension (or denotation) is assigned to the word. Even a vague sentence is either true or false on an (In what follows I shall drop the adjective for the sake of simplicity and just say precisification when I mean admissible precisification. What is and what not has been a matter of controversy, but I set aside that problem.) According to supervaluationism, a sentence is supertrue if and only if it is true on all precisifications, superfalse if and only if it is false on all precisifications, and neither supertrue nor superfalse if and only if it is true on some precisifications and false on the others. According to subvaluationism, a sentence is subtrue if and only if it is true on some precisifications, and subfalse if and only if it is false on some precisifications. If a sentence is true on some precisifications and false on the others, it is considered both subtrue and subfalse. In both theories, all logical truths are superor subtrue because they are true on all (thus, some)