Title:
No Variables
Abstract:
This paper defends the thesis that the logical form of quantified statements doesn't contain variables. I'll argue that this view solves the problems associated with variables—importantly Fine's so-called "Antinomy of the Variable"—by providing a fully compositional and extensional semantics for first-order quantification. I achieve this using de Bruijn indices both in the object and the meta-language to express variable binding. This results in an interesting view of logical form, which has far-reaching consequences, for example for Quine's dogma "to be is to be the value of a variable".