Quantificational Logic and Empty NamesSkip other details (including permanent urls, DOI, citation information)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. Please contact firstname.lastname@example.org to use this work in a way not covered by the license. :
For more information, read Michigan Publishing's access and usage policy.
The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as $\exists xt = x$; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia.