How vagueness could cut out at any order

Timothy Williamson has shown that the B axiom for 'definitely' (α → Δ¬Δ¬α) guarantees that if a sentence is second-order vague in a Kripke model, it is nth order vague for every n. More recently, Anna Mahtani has argued that Williamson's epistemicist theory of vagueness does not support the B axiom, and conjectured that if we consider models in which the “radius of accessibility” varies between different points, we will be able to find sentences that are nth-order vague but (n+1)th-order precise, for any n. This paper bolsters Mahtani's argument, shows her conjecture to be true, and shows that imposing certain further natural constraints on "variable radius" models does not change the situation

Physical Geometry and Fundamental Metaphysics

I explore some ways in which one might base an account of the fundamental metaphysics of geometry on the mathematical theory of Linear Structures recently developed by Tim Maudlin (2010). Having considered some of the challenges facing this approach, Idevelop an alternative approach, according to which the fundamental ontology includes concrete entities structurally isomorphic to functions from space-time points to real number

Of Numbers and Electrons

According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world is just as it in fact is, then T’ bear on this claim. It concludes that, while analogies with theories that attempt to eliminate unobservable concrete entities provide good reason to regard theories of the former sort as explanatorily bad, this reason does not apply to theories of the latter sor

Solving a Paradox of Evidential Equivalence

David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads. We argue that if you should have any conditional credence at all, it should be 1/2

How to Be a Modal Realist

This paper investigates the form a modal realist analysis of possibility and necessity should take. It concludes that according to the best version of modal realism, the notion of a world plays no role in the analysis of modal claims. All contingent claims contain some de re element; the effect of modal operators on these elements is described by a counterpart theory which takes the same form whether the de re reference is to a world or to something else. This fully general counterpart theory can validate orthodox modal logic, including the logic of 'actually'

Contingent Existence and Iterated Modality

A discussion of a view, defended by Robert Adams and Boris Kment, according to which contingent existence requires rejecting many standard principles of propositional modal logic involving iterated modal operators

Self-locating Priors and Cosmological Measures

We develop a Bayesian framework for thinking about the way evidence about the here and now can bear on hypotheses about the qualitative character of the world as a whole, including hypotheses according to which the total population of the world is infinite. We show how this framework makes sense of the practice cosmologists have recently adopted in their reasoning about such hypotheses

Illusions of gunk

The possibility of gunk has been used to argue against mereological nihilism. This paper explores two responses on the part of the microphysical mereological nihilist: (1) the contingency defence, which maintains that nihilism is true of the actual world; but that at other worlds, composition occurs; (2) the impossibility defence, which maintains that nihilism is necessary true, and so gunk worlds are impossible. The former is argued to be ultimately unstable; the latter faces the explanatorily burden of explaining the illusion that gunk is possible. It is argued that we can discharge this burden by focussing on the contingency of the microphysicalist aspect of microphysical mereological nihilism. The upshot is that gunk-based arguments against microphysical mereological nihilism can be resisted

Philosophical Perspectives, 17, Language and Philosophical Linguistics

Is a glass that is two-thirds full pretty full? We don't want to say 'Yes'; we don't want to say 'No'. This reluctance on our part seems very different in character and origin from our reluctance to answer 'Yes' or 'No' to questions like 'Is there intelligent life on other planets in our galaxy?'. A natural thing to say is that while in the latter case our reluctance is due to ignorance, in the former case it has nothing to do with ignorance: even someone who knew all the relevant facts wouldn't want to say 'Yes' or 'No' to the question 'Is a glass that is twothirds full pretty full?' Characteristically, when a is a borderline case of the predicate 'F', we are motivated to avoid either asserting or denying the sentence 'a is F' by considerations that have nothing to do with ignorance. In the first two sections of this paper, I will try to show how this ''no-ignorance theory'' can be developed into an illuminating account of the nature of vagueness and semantic indeterminacy. The remainder of the paper will be spent addressing what I take to be the most important objection to the no-ignorance theory. Why don't we say 'Yes' or 'No' to borderline questions? A and B have instituted a simple signalling system. A explores the jungle, looking for fruit-bearing trees. When she finds such a tree, she makes a noise: either a hoot or a yelp. (A and B's vocal apparatus doesn't allow them to make any other sounds.) When B hears a hoot or a yelp, he comes to believe that A has found a fruit-bearing tree. Moreover, he takes the noise he hears as evidence relevant to the question how much fruit is on the tree in question: if the noise was a hoot, he favours hypotheses according to which the tree has more fruit; if it was a yelp, he favours hypotheses according to which the tree has less fruit. But even when this evidence is taken into account, his credences remain smoothly distributed: the hypothesis that the tree has n fruit never receives much more or less credence than the hypothesis that the tree has n + 1 fruit. This situation is depicted i