Cian Dorr

In "The Case for Comparability," we argue that every comparative expression "F" obeys Comparability: if two things are at least as F as themselves, then one of them must be at least as F as the other. One of our arguments appeals to the apparent validity of the Strong Monotonicity schema: x is F; y is not F; so, x is more F than y. Erik Carlson and Olle Risberg claim that this argument is not valid, that it begs the question, and that the appearances favoring Strong Monotonicity—at least, for the adjective "good"—can be explained away. This paper defends our argument against these objections.

This chapter argues that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on _ad infinitum_. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts of the nature of vagueness and definiteness.

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.

The conclusion of this chapter is that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on ad infinitum. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts of the nature of vagueness and definiteness.

Mark Johnston (2016, 2017) has argued on ethical grounds against a wide variety of "naturalistic" world views, which imply that 'in our close vicinity, there are many persisting things all ontologically on a par, very similar in their features and such that they come into being and cease to exist at various times'—'personites', for short. Johnston argues that if personites exist, their intrinsic properties are compatible with their being people and thus having moral status; but since moral status is an intrinsic matter, this implies that personites enjoy the same kind of moral status as people, a conclusion which leads to various bizarre ethical consequences. In response, we defend the view that although personites exist, they lack moral status, and have intrinsic properties (including modal properties) which no person could have. We also isolate a different argument for the moral status of certain personites, based on the claim that they instantiate properties which 'person' could very easily have expressed; we show how this argument can be resisted by adopting a pluralistic semantics, on which predicates like 'person' and 'being with moral status' express many properties even at the actual world.

In the course of proving a tenability result about the probabilities of conditionals, van Fraassen (1976) introduced a semantics for conditionals based on ω-sequences of worlds, which amounts to a particularly simple special case of ordering semantics for conditionals. On that semantics, ‘If p, then q’ is true at an ω-sequence just in case q is true at the first tail of the sequence where p is true (if such a tail exists). This approach has become increasingly popular in recent years. However, its logic has never been explored. We axiomatize the logic of ω-sequence semantics, showing that it is the result of adding two new axioms to Stalnaker’s logic C2: one, Flattening, which is prima facie attractive, and, and a second, Sequentiality, which is complex and difficult to assess, but, we argue, likely invalid. But we also show that when sequence semantics is generalized from ω-sequences to arbitrary (transfinite) ordinal sequences, the result is a more attractive logic that adds only Flattening to C2. We also explore the logics of a few other interesting restrictions of ordinal sequence semantics. Finally, we address the question of whether sequence semantics is motivated by probabilistic considerations, answering, pace van Fraassen, in the negative.

There is a common practice of providing natural-language ‘glosses’ on sentences in the language of higher order logic: for example, the higher-order sentence ∃X(X Socrates) might be glossed using the English sentence ‘Socrates has some property’. It is widely held that such glosses cannot be strictly correct, on the grounds that the word ‘property’ is a noun and thus, if meaningful at all, should be meaningful in the same way as any other noun. Against this view, this paper argues that natural languages feature pervasive type-ambiguity in such a way that the relevant English sentences are in fact semantically equivalent to the higher-order sentences of which they serve as ‘glosses’. It also responds to some objections that have often been taken to be fatal to such type-ambiguity, such as the challenge of accounting for the meaning of ‘mixed disjunctions’ like ‘Either Mars or the property of being red is interesting’.

I explicate and defend the claim that, fundamentally speaking, there are no numbers, sets, properties or relations. The clarification consists in some remarks on the relevant sense of ‘fundamentally speaking’ and the contrasting sense of ‘superficially speaking’. The defence consists in an attempt to rebut two arguments for the existence of such entities. The first is a version of the indispensability argument, which purports to show that certain mathematical entities are required for good scientific explanations. The second is a speculative reconstruction of Armstrong's version of the One Over Many argument, which purports to show that properties and relations are required for good philosophical explanations, e.g. of what it is for one thing to be a duplicate of another.

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.

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.

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.

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.