Cian Dorr

Region R Question: How many objects — entities, things — are contained in R? Ignore the empty space. Our question might better be put, 'How many material objects does R contain?' Let's stipulate that A, B and C are metaphysical atoms: absolutely simple entities with no parts whatsoever besides themselves. So you don't have to worry about counting a particle's top half and bottom half as different objects. Perhaps they are 'point-particles', with no length, width or breadth. Perhaps they are extended in space without possessing spatial parts (if that is possible). Never mind. We stipulate that A, B and C are perfectly simple. We also stipulate that they are connected as follows. A and B are stuck together in such a way that when a force is applied to one of them, they move together 'as a unit'. Moreover, the two of them together exhibit behavior that neither would exhibit on its own — Perhaps they emit a certain sound, or glow in the dark — whereas C is..

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 lays out a novel proposal about the metaphysical foundations of (non-relativistic) quantum mechanics, which has some elements in common with Everett's “Many Worlds” interpretation and some elements in common with Bohm's ”Pilot Wave” interpretation. The view agrees with the Everettians that the quantum wavefunction can be interpreted be interpreted as a complete description of the world in fundamental terms. But it holds that this truth of this description suffices for the existence of an uncountable plurality of “worlds” of ordinary, non-fundamental objects, where each such “world” corresponds to a mapping of points of time to points of configuration space that obeys that Bohmian “Guidance Equation”.

In 1950, Quine inaugurated a strange new way of talking about philosophy. The hallmark of this approach is a propensity to take ordinary colloquial sentences that all of us utter routinely when we are not thinking about philosophy, or (more often) other sentences that very directly and obviously logically entail such sentences, and treat those sentences (i) as having a clear content, calling for little or no elucidation, and (ii) as proper objects of philosophical controversy. Questions like ‘are there numbers?’ and ‘are there tables?’ were now placed on a par with questions like ‘are there immaterial souls?’ and ‘are there sense-data?’. Of course philosophers have always had a propensity to say things that sound odd to vulgar ears. What was new with Quine was a systematic policty of privileging these kinds of formulations over more distinctively philosophical idioms. Jargon which had been central to the practice of metaphysics—’logical construction’, ’nothing over and above’, ‘reduce’, ‘ground’, ‘in virtue of’, ‘fundamental’, ‘consist in’...—were shifted to a much more peripheral role. The tradition inaugurated by Quine raises some hard interpretative questions for anyone who, like me and Dave, thinks that there is a range of different propositions that people brought up as English-speakers might be tempted to try to get across by uttering one of these sentences. On the one hand, Dave and I agree that the propositions that any ordinary, unphilosophical use of a sentence like ‘there are some free tables at the back of the café’ would be intended to get across are (in many cases) extremely obvious. The idea that when ontologists assert ‘there are no tables’, or treat this claim as calling for serious debate, they are intending to call into question propositions as obvious as that seems implausibly uncharitable. On the other hand, it is also a hallmark of the Quinean tradition that it claims to be using words in their ordinary sense, at least to the extent that (unlike its founder) it is willing to traffic in talk of meanings at all..

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.

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.

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.