# An Argument For A Neutral Free Logic

## Access Type

Open Access Dissertation

January 2015

Dissertation

Ph.D.

Philosophy

Michael McKinsey

## Abstract

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' is a logical truth and is consequently knowable a priori then it will follow absurdly that `a exists' 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' 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.' However, this response, in its strongest form relies on an implausible ambiguity in the quantifiers `all' and `some.' One could avoid the intolerable conclusion if `a = a' does not imply that `something is a.' 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' 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.

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