An Argument For A Neutral Free Logic

I argue for a neutral free logic is a logic wherein sentences containing non-referring terms do not have truth value. The primary support for this conclusion comes by way of criticism of the alternatives. If every sentence of the form `a = a\u27 is a logical truth and is consequently knowable a priori then it will follow absurdly that `a exists\u27 is knowable a priori. There are several alternatives for avoiding this intolerable conclusion and I argue that, with the exception of neutral free logic which holds that `a = a\u27 can lack truth value, their successes are not sufficient to outweigh their shortcomings. One option is to reject the closure of a priori knowability. However, there are no plausible counterexamples to a carefully stated closure principle. Another option is to try to avoid the conclusion by rejecting the validity of `something is a, so a exists.\u27 However, this response, in its strongest form relies on an implausible ambiguity in the quantifiers `all\u27 and `some.\u27 One could avoid the intolerable conclusion if `a = a\u27 does not imply that `something is a.\u27 There are two main possibilities for this approach: positive free logic and supervaluational logic. The former absurdly abandons one of the most obviously valid argument forms in the history of the study of logic. The latter, despite its technical sophistication and apparent utility, mischaracterizes truth. Furthermore, I argue that the intuitions that recommend supervaluational semantics can be explained by appeal only to resources available to the neutral free logician. Also, the intolerable conclusion might be avoided by maintaining that `a = a\u27 is false rather than truth-valueless (or neutral). Such a logical system is a negative free logic. Its primary support comes from the principle of bivalence. I argue that bivalence and its syntactic relative, the law of excluded middle, are not well justified. The only remaining alternative for avoiding the intolerable conclusion is neutral free logic. There are several possible varieties of neutral free logic that, very roughly stated, vary with respect to how permissive they are of true statements containing non-referring names. I argue for the least possible permissivity, and offer criticism of the intuitions that suggest the more permissive stances