Imprecise Quantification

Following David Lewis (1986), Ted Sider (2001) has famously argued that unrestricted first-order quantification cannot be vague. His argument was intended as a type of reductio: its strategy was to show that the mere hypothesis of unrestricted quantifier vagueness collapses into the claim that unrestricted quantification is precise. However, this short article considers two natural reconstructions of the argument, and shows that each can be resisted. The theme will be that each reconstruction of the argument involves assumptions which advocates of vague quantification have independent reason to reject.

Unrestricted Quantification and Natural Theology: Is "the World" on the Index?

The first section of this paper introduces talk about absolutely everything – the world as a totality – as an integral element in the project of natural theology, as it has been presented by Fergus Kerr and Denys Turner respectively. The following section presents talk about the world as a totality of facts as a theme in philosophical logic and outlines a problem it has given rise to there. After confronting the solution originally suggested by Bertrand Russell and defended by David Armstrong, the paper points to key elements of the solution presented by Wittgenstein in Tractatus Logico-Philosophicus. I show how Wittgenstein’s answer to the question of unrestricted quantification draws on his notion of showing and the inexpressible. Against this background, the concluding section draws attention to an important difference in ambition between Kerr’s and Turner’s description of the prospects for natural theology.