Abstract According to Russellianism, the content of a Russellian thought, in which a person ascribes a monadic property to an object, can be represented as an ordered couple of the object and the property. A consequence of this is that it is not possible for a person to believe that a is F and not to believe b is F, when a=b. Many critics of Russellianism suppose that this is possible and thus that Russellianism is false. Several arguments for this (...) claim are criticized and it is argued that Russellians need not appeal to representational notions in order to defeat them. Contrary to popular opinion, the prospects for a pure Russellianism, a Russellianism without representations, are in fact very good. (shrink)

Among theories of personal identity over time the simple view has not been popular among philosophers, but it nevertheless remains the default view among non philosophers. It may be construed either as the view that nothing grounds a claim of personal identity over time, or that something quite simple (a soul perhaps) is the ground. If the former construal is accepted, a conspicuous difficulty is that the condition of causal dependence between person-stages is absent. But this leaves such a view (...) open to an objection from the failure to provide a condition of individuation. If, on the other hand something like a soul is said to ground personal identity over time, such an account turns out to be more suited to a kind of continuity view. (shrink)

Abstract Theories are metaphysically equivalent just if there is no fact of the matter that could render one theory true and the other false. In this paper I argue that if we are judiciously to resolve disputes about whether theories are equivalent or not, we need to develop testable criteria that will give us epistemic access to the obtaining of the relation of metaphysical equivalence holding between those theories. I develop such ?diagnostic? criteria. I argue that correctly inter-translatable theories are (...) metaphysically equivalent, and what we need are ways of determining whether a putative translation is correct or not. To that end I develop a number of tools we can employ to discern whether a translation is a correct one. (shrink)

In this chapter I outline some metaphysical views about time, and about persistence, and discuss how they can help us clarify our thinking about life and death.

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

Timothy Williamson has defended the claim that any philosophically satisfying conception of modality that encompasses possible worlds semantics (PWS) commits us to the Barcan Formula. His argument depends on the assumption that the domain of what there is (the domain of the actual world) has to be identified with the domain D(@), where @ is the index or possible world that in PWS represents , or stands for , the actual world. I work out an interpretation of the relation between (...) PWS and possible worlds terminology that makes it plausible to reject that assumption. (shrink)

Time passes; sometimes swiftly, sometimes interminably, but always it passes. We see the world change as events emerge from the shroud of the future, clandestinely slinking into the past almost immediately as though they are reluctant to meet our gaze: children are born, old friends and relatives die, governments once full of youthful enthusiasm wane. If the Earth were sentient, it might feel itself being torn apart as tectonic plates diverge, and chuckle as it outlived species upon species of transient (...) parasites. How could anyone possibly deny that time passes? (shrink)

There seems to be a distinction between primary and secondary properties; some philosophers defend the view that properties like colours and values are secondary, while others criticize it. The distinction is usually introduced in terms of essence; roughly, secondary properties essentially involve mental states, while primary properties do not. In part because this does not seem very illuminating, philosophers have produced different reductive analyses in modal terms, metaphysic or epistemic. Here I will argue, firstly, that some well-known examples fail, and (...) also that there are deep reasons why such approaches should do so. Secondly, I will argue that it is acceptable to remain satisfied with the non-reductive account in terms of essence. To that end, I will indicate how such an explication could be put to use to support the claim that properties like colours and values are secondary. In a series of recent writings, Kit Fine has argued that essence cannot be reductively analysed in modal terms. Fine offers some examples to motivate his claim. I suggest that the primary/secondary distinction constitutes a philosophically interesting illustration. (shrink)

Dispositional monists believe that all properties are essentially causal. Recently, an overdetermination argument has been proposed by Trenton Merricks to support nihilism about ordinary objects. I argue that this argument can be extended to target both nihilism about ordinary objects and nihilism about physical particles when dispositional monism is assumed. It implies that a philosopher who both endorses dispositional monism and takes seriously the overdetermination argument should not believe in the existence of physical particles. I end up by discussing possible (...) objections. I suggest, then, that if we live in a world that is inhabited by causal properties but not by chairs and tables, then we also live in a world without electrons and quarks, a world of dispositional properties, that is, a world of causal fields. (shrink)

Closest-possible-world analyses of counterfactuals suffer from what has been called the ‘problem of counterpossibles’: some counterfactuals with metaphysically impossible antecedents seem plainly false, but the proposed analyses imply that they are all (vacuously) true. One alleged solution to this problem is the addition of impossible worlds. In this paper, I argue that the closest possible or impossible world analyses that have recently been suggested suffer from the ‘new problem of counterpossibles’: the proposed analyses imply that some plainly true counterpossibles (viz., (...) ‘counterlogicals’) are false. After motivating and presenting the ‘new problem’, I give reasons to think that the most plausible objection to my argument is not compelling. (shrink)

Abstract Non-reductive physicalism is currently the most widely held metaphysic of mind. My aim in this essay is to show that supervenience physicalism?perhaps the most common form of non-reductive physicalism?is not a defensible position. I argue that, in order for any supervenience thesis to ground a legitimate form of physicalism, it must yield the right sort of determination relation between physical and non-physical properties. Then I argue that non-reductionism leaves one without any explanation for the laws that are implied by (...) supervenience theses that deliver this determination relation. (shrink)

Nelson Pike’s article, “Divine Omniscience and Voluntary Action,” is one of the most influential pieces in contemporary Philosophy of Religion. Published over forty years ago, it has elicited many different kinds of replies. We shall set forth some of the main lines of reply to Pike’s article, starting with some of the “early” replies. We then explore some issues that arise from relatively recent work in the philosophy of time; it is fascinating to note that views suggested by recent work (...) in this area and related areas of metaphysics have implications for Pike’s argument - implications perhaps not previously noticed. (shrink)

This dissertation is divided into two parts. In the first part I defend substantivalism. I do this by offering, in chapter 1, a counterpart-theoretic defense of substantivalism from Leibniz’ shift arguments. Then, in chapter 2, I defend substantivalism from the hole argument and argue, against the consensus, that the question of haecceitism is irrelevant to substantivalism in the context of general relativity. In the second part of the dissertation I defend supersubstantivalism. I do this by offering, in chapter 3, an (...) argument against dualistic substantivalism. The argument appeals to plausible principles of modal plenitude to show that the dualist is committed to a range of problematic possibilities. Then, in chapter 4, I consider a range of supersubstantivalist positions. I conclude by arguing for a version of supersubstantivalism I call compresence supersubstantivalism. (shrink)

All physical theories, from classical Newtonian mechanics to relativistic quantum field theory, entail propositions concerning the geometric structure of spacetime. To give an example, the general theory of relativity entails that spacetime is curved, smooth, and four-dimensional. In this dissertation, I take the structural commitments of our theories seriously and ask: how is such structure instantiated in the physical world? Mathematically, a property like 'being curved' is perfectly well-defined insofar as we know what it means for a mathematical space to (...) be curved. But what could it mean to say that the physical world is curved? Call this the problem of physical geometry. The problem of physical geometry is a plea for foundations--a request for fundamental truth conditions for physical-geometric propositions. My chief claim is that only a substantival theory of spacetime--a theory according to which spacetime is an entity in its own right, existing over and above the material content of the world--can supply the necessary truth conditions. (shrink)

Is the world internally connected by a web of necessary connections or is everything loose and independent? Followers of David Hume accept the latter by upholding Hume’s Dictum, according to which there are no necessary connections between distinct existences. Roughly put, anything can coexist with anything else, and anything can fail to coexist with anything else. Hume put it like this: “There is no object which implies the existence of any other if we consider these objects in themselves.” Since Hume’s (...) day, Hume’s Dictum has played a major role in philosophy, especially in contemporary metaphysics. In ruling out necessary connections, Hume’s Dictum implies that causal relations and the laws of nature are contingent. It makes other demands on our metaphysics of science as well; for example, it places restrictions on our metaphysics of counterfactuals, dispositions, and explanation. The principle has applications in other areas too. Hume’s Dictum places constraints on our theories of abstract objects and moral properties. For example, Hume’s Dictum rules out the view that moral properties are distinct from, but necessarily connected to, non-moral properties. While Hume’s Dictum is a prominent principle in metaphysics, few Humeans have defended the principle at length. It is assumed more often than it is argued for. As a result, Hume’s Dictum no longer enjoys the reputation it once did. It’s common to hear complaints about the lack of arguments in support of Hume’s Dictum. Moreover, philosophers are increasingly willing to defend views that are at odds with Hume’s Dictum. A striking example of this is the recent explosion of interest in views that take causal relations and the laws of nature to be necessary. Humeans can no longer afford to be complacent. An extended defense of Hume’s Dictum is called for, and that’s what this dissertation aims to offer. This dissertation has three parts. In the first part, I lay out some preliminaries and offer a precise formulation of Hume’s Dictum. In the second part, I develop three arguments in favor of Hume’s Dictum. In the final part, I defend Hume’s Dictum against objections. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

John MacFarlane explores how we might make sense of the idea that truth is relative. He provides new, satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis, including what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do.

This book is about the idea that some true statements would have been true no matter how the world had turned out, while others could have been false. It develops and defends a version of the idea that we tell the difference between these two types of truths in part by reflecting on the meanings of words. It has often been thought that modal issues—issues about possibility and necessity—are related to issues about meaning. In this book, the author defends the (...) view that the analysis of meaning is not just a preliminary to answering modal questions in philosophy; it is not merely that before we can find out whether something is possible, we need to get clear on what we are talking about. Rather, clarity about meaning often brings with it answers to modal questions. In service of this view, the author analyzes the notion of necessity and develops ideas about linguistic meaning, applying them to several puzzles and problems in philosophy of language. Meaning and Metaphysical Necessity will be of interest to scholars and advanced students working in metaphysics, philosophy of language, and philosophical logic. [See my homepage for a sample chapter.]. (shrink)

The philosophy of necessity and possibility has flourished in the last half-century, but much less attention has been paid to the question of how we know what can be the case and what must be the case. Many friends of modal metaphysics and many enemies of modal metaphysics have agreed that while empirical discoveries can tell us what is the case, they cannot shed much light on what must be the case or on what non-actual possibilities there are. In this (...) paper, in contrast, I discuss and defend naturalistic approaches to discovering the facts about necessity and possibility. After some remarks about what methodological naturalism in philosophy might amount to, I argue that naturalistic method in modal investigations may not need to be particularly revisionary of much of what is currently being done in modal investigation. I then discuss a number of respects in which a naturalistic orientation in modal investigation may improve on our current epistemic situation. (shrink)

Physicalism is the thesis that everything is physical, or as contemporary philosophers sometimes put it, that everything supervenes on, or is necessitated by, the physical. The thesis is usually intended as a metaphysical thesis, parallel to the thesis attributed to the ancient Greek philosopher Thales, that everything is water, or the idealism of the 18th Century philosopher Berkeley, that everything is mental. The general idea is that the nature of the actual world (i.e. the universe and everything in it) conforms (...) to a certain condition, the condition of being physical. Of course, physicalists don't deny that the world might contain many items that at first glance don't seem physical — items of a biological, or psychological, or moral, or social nature. But they insist nevertheless that at the end of the day such items are either physical or supervene on the physical. (shrink)

Much of the debate about identity in recent decades has been about personal identity, and specifically about personal identity over time, but identity generally, and the identity of things of other kinds, have also attracted attention. Various interrelated problems have been at the centre of discussion, but it is fair to say that recent work has focussed particularly on the following areas: the notion of a criterion of identity; the correct analysis of identity over time, and, in particular, the disagreement (...) between advocates of perdurance and advocates of endurance as analyses of identity over time; the notion of identity across possible worlds and the question of its relevance to the correct analysis of de re modal discourse; the notion of contingent identity; the question of whether the identity relation is, or is similar to, the composition relation; and the notion of vague identity. A radical position, advocated by Peter Geach, is that these debates, as usually conducted, are void for lack of a subject matter: the notion of absolute identity they presuppose has no application; there is only relative identity. Another increasingly popular view is the one advocated by Lewis: although the debates make sense they cannot genuinely be debates about identity, since there are no philosophical problems about identity. Identity is an utterly unproblematic notion. What there are, are genuine problems which can be stated using the language of identity. But since these can be restated without the language of identity they are not problems about identity. (For example, it is a puzzle, an aspect of the so-called “problem of personal identity”, whether the same person can have different bodies at different times. But this is just the puzzle whether a person can have different bodies at different times. So since it can be stated without the language of personal “identity”, it is not a problem about identity, but about personhood.) This article provides an overview of the topics indicated above, some assessment of the debates and suggestions for further reading. (shrink)

The goal of this essay is twofold. First, it provides a quick look at the foundations of modern relational mechanics by tracing its development from Julian Barbour and Bruno Bertotti's original ideas until present-day's pure shape dynamics. Secondly, it discusses the most appropriate metaphysics for pure shape dynamics, showing that relationalism is more of a nuanced thesis rather than an elusive one. The chapter ends with a brief assessment of the prospects of pure shape dynamics in light of quantum physics.

Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity, QG), but also to characterise this new theory and shape expectations of what it is to achieve. Here, we first evaluate how particular types of singularities may suggest an incompleteness of current theories. We then classify four different 'attitudes' towards singularities in the search for QG, and show, through examples in the physics literature, that these lead to (...) different scenarios for the new theory. Two of the attitudes prompt singularity resolution, but only one suggests the need for a theory of QG. Rather than evaluate the different attitudes, we close with some suggestions of factors that influence the choice between them. (shrink)

In On the Plurality of Worlds (Lewis 1986), David Lewis imposes a condition on realist theories of modality which he calls ‘plenitude’. Lewis apparently assigns this condition considerable importance, and uses it to motivate his Humean principle of recombination, but he never says exactly what plenitude amounts to. This chapter first sets aside some obvious ways of reconstructing the plenitude criterion which do not fit with the textual evidence. An objection to modal realism due to John Divers and Joseph Melia (...) (Divers and Melia 2002) is diagnosed as equivocating between an overly-demanding plenitude constraint and a weaker constraint which fails to establish their conclusion. An alternative deflationary interpretation of the plenitude condition has it following from an application of standard theoretical virtues to a modal realist’s total theory; Lewis’ correspondence provides new evidence in support of this interpretation. The deflationary plenitude criterion also has broader application, beyond Lewisian modal realism. (shrink)

Lynne Baker’s case for the incompatibility of naturalism with the first-person perspective raises a range of questions about the relationship between naturalism and the various properties involved in first-person perspectives. After arguing that non-qualitative properties—most notably, haecceities like being Lynne Baker—are ineliminably tied to first-person perspectives, this paper considers whether naturalism and non-qualitative properties are, in fact, compatible. In doing so, the discussion focus on Shamik Dasupgta’s argument against individuals and, in turn, non-qualitative properties. Several strategies for undermining Dasgupta's argument (...) are considered, drawing on de re laws and haecceitistic possibilities. Finally, an analogy is drawn between naturalism and platonism regarding mathematical entities and naturalism's parallel commitment to individuals. I conclude that naturalists are obliged to posit non-qualitative properties. (shrink)

We care not only about what experiences we have, but when we have them too. However, on the B-theory of time, something’s timing isn’t an intrinsic way for that thing to be or become. Given B-theory, should we be rationally indifferent about the timing per se of an experience? In this paper, I argue that B-theorists can justify time-biased preferences for pains to be past rather than present and for pleasures to be present rather than past. In support of this (...) argument, I appeal to the doctrine of temporal parts or “four-dimensionalism” for short. When held in conjunction with a certain evaluative principle about whose experiences matter, four-dimensionalism reconciles B-theory with some time-biased preferences. (shrink)

This chapter analyzes several key themes in Kant’s views about modality. We begin with the pre-critical Only Possible Argument in Support of a Demonstration of the Existence of God, in which Kant distinguishes between formal and material elements of possibility, claims that all possibility requires an actual ground, and argues for the existence of a single necessary being. We then briefly consider how Kant’s views change in his mature period, especially concerning the role of form and thought in defining modality. (...) Kant’s mature views, however, present two difficult interpretive puzzles. The first puzzle concerns whether Kant has a generally reductive view of modality. While Kant’s views on logical modality, the role of actuality in grounding possibility, and the relation of modality to cognition all suggest reduction, we argue that the categorial status of modal concepts and the difficulty in even identifying amodal grounds for modal facts all suggest a non-reductive view. The second puzzle concerns whether Kant accepts modal facts or properties at the noumenal level. While Kant’s appeal to noumenal necessary connections, the contingency of noumenal willing, and the idea of a necessary noumenal being suggest that he endorses noumenal modality, his claims that modal concepts express only relations to the faculty of cognition and his claim that modal concepts arise from our distinctive psychological structures, we argue, suggest that he rejects noumenal modality. We conclude by considering potential solutions to these puzzles. (shrink)

It seems natural to ask why the universe exists at all. Modern physics suggests that the universe can exist all by itself as a self-contained system, without anything external to create or sustain it. But there might not be an absolute answer to why it exists. I argue that any attempt to account for the existence of something rather than nothing must ultimately bottom out in a set of brute facts; the universe simply is, without ultimate cause or explanation.

Quantifier variance is a well-known view in contemporary metaontology, but it remains very widely misunderstood by critics. Here we briefly and clearly explain the metasemantics of quantifier variance and distinguish between modest and strong forms of variance (Section I), explain some key applications (Section II), clear up some misunderstandings and address objections (Section III), and point the way toward future directions of quantifier-variance-related research (Section IV).

In this paper I explore irrealist alternatives to orthodox realism about grounding, and claim that at least some of these alternatives represent fertile areas for future discussion.

Could I have been someone other than who I am? Philosophers from Williams to Nagel to Lewis have been tempted to answer 'yes', but how can we make sense of such a view? I argue that to say that it is contingent who I am is to say that it is contingent what perspective I have, in a distinctively metaphysical sense of perspective.

First-order normative theories concerning what’s right and wrong, good and bad, etc. and metanormative theories concerning the nature of first-order normative thought and talk are widely regarded as independent theoretical enterprises. This paper argues that several debates in metanormative theory involve views that have first-order normative implications, even as the implications in question may not be immediately recognizable as normative. I first make my claim more precise by outlining a general recipe for generating this result. I then apply this recipe (...) to three debates in metaethics: the modal status of basic normative principles, normative vagueness and indeterminacy, and the determination of reference for normative predicates. In each case I argue that certain views on each issue carry first-order normative commitments, in accordance with my recipe. (shrink)

In this paper, I present a categorial theory of meaning which asserts that the meaning of a sentence is the function from the actualization of some potentiality or the potentiality of some actuality to the truth of the sentence. I argue that it builds on the virtues of David Lewis’s Possible World Semantics but advances beyond problems that Lewis’s theory faces with its distinctly Aristotelian turn toward actuality and potentiality.

This is a slightly opinionated review of three main factions in metaontology: Quineans, Carnapians, and Meinongians. Emphasis is given to the last camp, as the metaontological aspect of Meinongianism has been underappreciated. The final section then offers some general remarks about the legitimacy of ontology, touching on ideas I have developed in other publications.

A primer on the philosophical issues relating to phenomenal consciousness, part of a collection of new papers by scientists and philosophers on the constitution of consciousness.

It’s a platitude that a picture is realistic to the degree to which it resembles what it represents (in relevant respects). But if properties are abundant and degrees of resemblance are proportions of properties in common, then the degree of resemblance between different particulars is constant (or undefined), which is inconsonant with the platitude. This paper argues this problem should be resolved by revising the analysis of degrees of resemblance in terms of proportion of properties in common, and not by (...) accepting a sparse theory of properties or by denying that degree of realism is degree of resemblance (in relevant respects). (shrink)

Existence as reflected in natural language is not a univocal notion, but divides into different modes of being, such as existence (as, roughly, endurance) and occurrence. One aim of the paper is to distinguish sharply between abstract artifacts and non-existent objects (e.g., plans vs. planned events that fail to occur); another is to argue for validity as a mode of being distinct from existence, as well as for corresponding distinctions among non-being.

I explore a challenge that idealisations pose to scientific realism and argue that the realist can best accommodate idealisations by capitalising on certain modal features of idealised models that are underwritten by laws of nature.

In the Phaedrus, Socreates sympathetically describes the ability “to cut up each kind according to its species along its natural joints, and to try not to splinter any part, as a bad butcher might do.” (265e) In contemporary philosophy, Ted Sider (2009, 2011) defends the same idea. As I shall put it, Plato and Sider’s idea is that limning structure is an epistemic goal. My aim in this paper is to articulate and defend this idea. First, I’ll articulate the notion (...) of a structural proposition (§1), and the notion of an epistemic goal (§2), where I’ll assume that epistemic goals are species of accuracy. Then (§3), I’ll argue against some proposals for understanding the idea that limning structure is an epistemic goal: limning structure is neither an aim of belief (§3.1), nor of inquiry (§3.2), nor of concept possession (§3.3). Importantly, non-structural belief is not thereby inaccurate; belief does not “aim” at being structural. Next (§4), I’ll propose a framework for understanding the idea that limning structure is an epistemic goal, and defend that idea. What is required, to defend the view that limning structure is an epistemic goal, is the notion of (what I call) theorizing – a propositional attitude that, unlike belief, does “aim” at being structural (§4.1). I’ll argue that structural truths constitute a species of “important” truths (§4.2), and that apt theorizing is a species of understanding (§4.3). Finally (§5), I’ll discuss the possibility that there is no structure. (shrink)

We aim to provide the ontological grounds for an adequate account of persistence. We defend a perspectivalist, or moderate pluralist, position, according to which some aspects of reality can be accounted for in ontological terms only via partial and mutually complementary ontologies, each one of which captures some relevant aspect of reality. Our thesis here is that this is precisely the sort of ontological account that is needed for the understanding of persistence, specifically an account involving two independent ontologies, one (...) for continuants, and one for occurrents. (shrink)

Many people think that truth somehow depends upon the way things are. Yet, it has proven difficult to precisely explain the nature of this dependence. The most common view is that truth depends upon the way things are by corresponding to things. But this account relocates the difficulty: one now wonders what correspondence is. It is worth emphasizing that the question of how truth relates to reality is not only a question for correspondence theorists; theorists of all stripes may wonder (...) how truth and reality connect. There are many reasons one might care to have an analysis of how truth relates to reality. Here are two. First, an analysis would help philosophers better understand how truth could depend upon the way things are. Why is it that when Joe shoves his cat off his pillow, the proposition that Joe's cat is on his pillow switches from true to false? It may seem puzzling that an abstract thing, such as a proposition, should be affected by physical changes to concrete particulars. How does that happen? The difficulty of seeing just how true propositions are able to systematically relate to reality will be called "the Problem of Matching." A thorough analysis of the relationship between truth and reality would effectively solve the Problem of Matching. (shrink)

I give two arguments for the claim that all events which occur at the actual world and are such that they could be caused, are also such that they must actually be caused. The first argument is an improvement of a similar argument advanced by Alexander Pruss, which I show to be invalid. It uses Pruss’s Brouwer Analog for counterfactual logic, and, as a consequence, implies inconsistency with Lewis’s semantics for counterfactuals. While (I suggest) this consequence may not be objectionable, (...) the argument founders on the fact that Pruss’s Brouwer Analog has a clear counterexample. I thus turn to a second, “Lewisian” argument, which requires only an affirmation of one element of Lewis’s analysis of causation and one other, fairly weak possibility claim about the nature of wholly contingent events. The final section of the paper explains how both arguments escape objections from supposed indeterminacy in quantum physics. (shrink)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove (...) the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (shrink)