Cian Dorr

In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, whether a certain outcome is associated with a non-measurable region or a measurable one.

This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for identity), and some which take the view in the direction of fineness of grain (whose endpoint is the maximally fine-grained theory containing all distinctness claims compatible with Classicism). The third part introduces some techniques for constructing models of Classicism, and uses them to prove the consistency of many of the extensions of Classicism introduced in the second part.

In general, a given object could have been different in certain respects. For example, the Great Pyramid could have been somewhat shorter or taller; the Mona Lisa could have had a somewhat different pattern of colours; an ordinary table could have been made of a somewhat different quantity of wood. But there seem to be limits. It would be odd to suppose that the Great Pyramid could have been thimble-sized; that the Mona Lisa could have had the pattern of colours that actually characterizes The Scream; or that the table could have been made of the very quantity of wood that in fact made some other table. However, there are puzzling arguments that purport to show that so long as an object is capable of being somewhat different in some respect, it is capable of being radically different in that respect. These arguments rely on two tempting thoughts: first, that an object’s capacity for moderate variation is a non-contingent matter, and second, that what is possibly possible is simply possible. This book systematically investigates competing strategies for resolving these puzzles, and defends one of them. Along the way it engages with foundational questions about the metaphysics of modality.

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed.

Presupposing that most predicates do not correspond directly to genuine relations, I argue that all genuine relations are symmetric. My main argument depends on the premise that there are no brute necessities, interpreted so as to require logical and metaphysical necessity to coincide for sentences composed entirely of logical vocabulary and primitive predicates. Given this premise, any set of purportedly primitive predicates by which one might hope to express the facts about non-symmetric relations order their relata will generate an objectionable multiplication of possibilities. In the final section I give a different argument, based on the weaker premise that brute necessities should not be multiplied without necessity.

We defend the thesis that every necessarily true proposition is always true. Since not every proposition that is always true is necessarily true, our thesis is at odds with theories of modality and time, such as those of Kit Fine and David Kaplan, which posit a fundamental symmetry between modal and tense operators. According to such theories, just as it is a contingent matter what is true at a given time, it is likewise a temporary matter what is true at a given possible world; so a proposition that is now true at all worlds, and thus necessarily true, may yet at some past or future time be false in the actual world, and thus not always true. We reconstruct and criticize several lines of argument in favor of this picture, and then argue against the picture on the grounds that it is inconsistent with certain sorts of contingency in the structure of time.

Part One of my dissertation is about composite objects: things with proper parts, like plates, planets, plants and people. I begin chapter 1 by pointing out that if one were to judge by the way we normally speak about composite objects, one would suppose that we were all completely certain of a theory I call folk mereology. For instance, we seem to be completely convinced that whenever some things are piled up, there is an object---a pile---which they compose. I point out that folk mereology is neither an analytic truth nor a theory for which we have conclusive empirical evidence. So what are we to make of the feeling that it makes no sense to deny folk mereology? What this shows, I claim, is that the standard which an assertion about composite objects has to meet in order to be correct is not strict and literal truth, but something less demanding. ;In the last part of chapter 1 and in chapter 2, I argue that we have no evidence for the existence of composite objects, and that without such evidence we ought to believe that there aren't any composite objects. Chapter 3 is devoted to working out some details of a broadly "fictionalist" explanation of the fact that claims about composite objects can be correct without being strictly and literally true. ;In Part Two I defend a parallel view about complex attributes---properties, relations and propositions. In our ordinary talk about attributes, we seem to presuppose a theory according to which there are very many of these entities; but, as I argue in chapter 4, we cannot justifiably be certain that this theory is true. I conclude that in this case too, correct assertion diverges from strict and literal truth. Chapter 5 is devoted to an argument that there are in fact no complex attributes. Finally, in chapter 6, I develop a fictionalist account of the conditions under which ordinary assertions about attributes are correct

Argument that Q∃ expresses more than one proposition: (1) Q∃ expresses the proposition that Q∃ expresses some proposition that isn’t true. ((E)) (2) If Q ∃ expresses only true propositions, then the proposition that Q ∃ expresses some proposition that isn’t true is true. ((1)) (3) If Q∃ expresses only true propositions, then some proposition expressed by Q∃ is not true. (2, T) (4) Some proposition expressed by Q ∃ is not true. ((3)) (5) The proposition that Q ∃ expresses some proposition that isn’t true is true. (4, T) (6) Q∃ expresses at least one true proposition. (1,5) (7) Q∃ expresses at least two propositions. (3, 6) (A parallel argument shows that Q∀ expresses both true and false propositions

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'.

Let me regale you with yet another variant of the story of Sleeping Beauty. In this one, the experiment takes place in a room with a skylight, so that Beauty can see what the weather is like outside as soon as she wakes up. The weather can be in any one of n different states on any given day. Beauty regards each of these states as equiprobable; moreover, she takes there to be no correlation between the weather on Monday and the weather on Tuesday, or between the weather on either day and the coin-toss. The rest of the story works as usual: Beauty will be awoken on Monday, after which a coin will be tossed; if it lands Tails, she will be woken again on Tuesday having had her memories of the Monday awakening erased; otherwise, she will stay asleep until Wednesday.1 The weather is the only source of variation in her wakings, so if it should happen that the weather is the same on Monday and Tuesday, her total evidence will be exactly the same on both wakings

I motivate and briefly sketch a linguistic theory of vagueness, on which the notion of indeterminacy is understood in terms of the conventions of language: a sentence is indeterminate iff the conventions of language either forbid asserting it and forbid asserting its negation, under the circumstances, or permit asserting either. I then consider an objection that purports to show that if this theory (or, as far as I can see, any other theory of vagueness that deserved the label "linguistic" were true, there would be no such thing as indeterminacy. I respond to this objection by arguing on independent grounds against its main premise, the widely-accepted claim that if it is indeterminate whether P, no human being knows whether P. I defend an alternative view according to which, when it is indeterminate whether P, it is often also indeterminate whether we know that P.

Suppose a sentence of the following form is true in a certain context: ‘Necessarily, whenever one believes that the F is uniquely F if anything is, and x is the F, one believes that x is uniquely F if anything is’. I argue that almost always, in such a case, the sentences that result when both occurrences of ‘believes’ are replaced with ‘has justification to believe’, ‘knows’, or ‘knows a priori’ will also be true in the same context. I also argue that many sentences of the relevant form are true in ordinary contexts, and conclude that a priori knowledge of contingent de re propositions is a common and unmysterious phenomenon. However, because of the pervasive context-sensitivity of propositional attitude ascriptions, the question what it is possible to know a priori concerning a given object will have very different answers in different contexts

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.

This paper considers how counterfactuals should be evaluated on the assumption that determinism is true. I argue against Lewis's influential view that the actual laws of nature would have been false if something had happened that never actually happened, and in favour of the competing view that history would have been different all the way back. I argue that we can do adequate justice to our ordinary practice of relying on a wide range of historical truths in evaluating counterfactuals by saying that, in typical cases, history would have been only *very slightly* different until shortly before the relevant time. The paper also draws some connections between the puzzle about counterfactuals under determinism and the debate about whether determinism entails that no-one can ever do otherwise than they in fact do.

In this paper I attempt two things. First, I argue that one can coherently imagine different communities using languages structurally similar to English, but in which the meanings of the quantifiers vary, so that the answers to ontological questions, such as ‘Under what circumstances do some things compose something?’, are different. Second, I argue that nevertheless, one can make sense of the idea that of the various possible assignments of meanings to the quantifiers, one is especially fundamental, so that there is still room for genuine debate as regards the answers to ontological questions construed in the fundamental way. My attempt to explain what is distinctive about the fundamental senses of the quantifiers involves a generalisation of the idea that claims of existence are never analytic.<br>.

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 sort

Seth Yalcin has pointed out some puzzling facts about the behaviour of epistemic modals in certain embedded contexts. For example, conditionals that begin ‘If it is raining and it might not be raining, … ’ sound unacceptable, unlike conditionals that begin ‘If it is raining and I don’t know it, … ’. These facts pose a prima facie problem for an orthodox treatment of epistemic modals as expressing propositions about the knowledge of some contextually specified individual or group. This paper develops an explanation of the puzzling facts about embedding within an orthodox framework