Ted Sider has famously argued that existence, in the unrestricted sense of ontology, cannot be vague, as long as vagueness is modeled by means of precisifications. The first section of Chapter 9 exposes some controversial assumptions underlying Sider’s alleged reductio of vague existence. The upshot of the discussion is that, although existence cannot be vague, it can be super-vague, i.e. higher-order vague, for all orders. The second section develops and defends a novel framework, dubbed negative supervaluationary semantics, which makes room (...) for the possibility of super-vague existence. (shrink)

Precis of my book by this title, for a symposium.

In my book Four-dimensionalism (chapter 4, section 9), I argued that fourdimensionalism – the doctrine of temporal parts – follows from several other premises, chief among which is the premise that existence is never vague. Kathrin Koslicki (preceding article) claims that the argument fails since its crucial premise is unsupported, and is dialectically inappropriate to assume in the context of arguing for four-dimensionalism. Since the relationship between four-dimensionalism and the non-vagueness of existence is not perfectly transparent, I think the argument (...) would retain some interest even if the premise were wholly unsupported; it would show that anyone who accepts that premise (which seems reasonable enough to me though perhaps not to others) must accept four-dimensionalism. Still, Koslicki is right that my defense of the premise was thin. So I will now try to do better. The new defense will have further premises, which could ultimately be rejected by opponents of four-dimensionalism, and so the argument retains the form: anyone who thinks certain things (which seem reasonable enough to me though perhaps not to others) must believe four-dimensionalism. But that’s metaphysics for you. I should also say that, in addition to the material on vague existence, there is more in Koslicki’s excellent paper which I cannot discuss here. I agree with much of it;1 and where we disagree there are formidable challenges, some of which I hope to address in the future. (shrink)

There is little doubt that a second-order axiomatization of Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) is desirable. One advantage of such an axiomatization is that it permits us to express the principles underlying the first-order schemata of separation and replacement. Another is its almost-categoricity: M is a model of second-order ZFC if and only if it is isomorphic to a model of the form Vκ, ∈ ∩ (Vκ × Vκ) , for κ a strongly inaccessible ordinal.

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.