Peter J. Lewis

The answer to the Monty Hall Problem that many people—including some well-trained mathematicians—initially give is incorrect. Nonetheless, there is little controversy among mathematicians and philosophers about what the correct answer is. However, many different arguments have been given for this answer. Although Bayes’s Theorem is the gold standard for carrying out probabilistic inferences, many mathematicians and philosophers try to give shorter and more intuitive arguments for the correct answer to the Monty Hall Problem. Unfortunately, as we argue in this paper, an unconscionably large number of these shortcut arguments involve bad reasoning. Thus, many people end up believing “the right answer for a wrong reason.” Moreover, since these arguments only yield the correct answer in a very restricted range of cases, people learn techniques that lead to false conclusions when they are applied to many other probabilistic inference problems. In this paper, we identify three distinct bad arguments for switching in the Monty Hall Problem that are commonly given by quite reputable sources. We show that these arguments yield incorrect answers when applied to slight variations of the Monty Hall Problem. And we identify exactly where each argument goes wrong. We argue that it would be much better to simply teach people to ask how likely the evidence is given each of the hypotheses.

Relational quantum mechanics (RQM) is an interesting alternative to the standard responses to the measurement problem in quantum mechanics. But it suffers from a distinctive kind of epistemic solipsism: an observer can’t in principle know anything beyond their immediate present experience. This makes RQM self-undermining: it takes away the evidence we have for believing in quantum mechanics in the first place. Recently, Adlam and Rovelli have proposed a solution to this problem in the form of a new postulate they call cross-perspective links. Here I argue that this postulate does indeed solve the skeptical problem, but it also removes those aspects of RQM that make it distinctively relational. Nevertheless, the result of equipping RQM with cross-perspective links is an interesting interpretation in its own right.

It has been suggested by some proponents of Bohm’s theory that it requires a special account of mental awareness--that the Bohmian solution to the measurement problem rests on direct awareness of the particle configuration in one's own brain. This suggestion leads to two criticisms of Bohm’s theory: first, that direct awareness of particle configuration is a highly implausible account of the mental; and second, that such direct awareness leads to violations of the quantum no-signalling theorem. I argue that Bohm’s theory requires no special account of mental awareness, and hence that neither of these problems arises.

Spontaneous collapse theories provide a promising solution to the measurement problem. But they also introduce a number of problems of their own concerning dimensionality, vagueness, and locality. In response to these problems, advocates of collapse theories have proposed various accounts of the primitive ontology of collapse theories—postulated underlying entities governed by the collapse theory and underwriting our observations. The most prominent of these are a mass density distribution over three-dimensional space, and a set of discrete “flash” events at space-time points. My argument here is that these primitive ontologies are redundant, in the sense that the structures exhibited by the primitive ontologies that allow them to solve the problems facing spontaneous collapse theories are also present in the wave function. But redundancy is not nonexistence; indeed, the fact that the relevant structures are already there in the wave function shows that the mass density ontology and the flash ontology exist whether they are explicitly postulated or not. By the same token, there is no need to decide between a wave function ontology, a mass density ontology and a flash ontology.

In a recent book, Anjan Chakravartty builds a case for a particular conception of the relationship of science to metaphysics. The main novel feature in his account of scientific ontology is his construction of a metaphysical distance measure. Some ontological claims are close to the science that informs those claims, and some are further away. The distance is a measure of the epistemic risk one takes in asserting the claim: the further from the empirical base, the greater the risk. But conversely, claims far from the empirical base can serve explanatory and unificatory purposes regarding claims closer in. Since different philosophers have different attitudes towards epistemic risk, Chakravartty endorses a pluralism about scientific ontology. Chakravartty illustrates his arguments concerning scientific ontology by considering what we can infer from the Standard Model of particle physics concerning the ontological status of the structures and entities it describes. I argue that, while this case study initially appears to support Chakravartty’s arguments, on closer inspection it suggests a more deflationary approach to scientific ontology.

Quantum mechanics arguably provides the best evidence we have for strong emergence. Entangled pairs of particles apparently have properties that fail to supervene on the properties of the particles taken individually. But at the same time, quantum mechanics is a terrible place to look for evidence of strong emergence: the interpretation of the theory is so contested that drawing any metaphysical conclusions from it is risky at best. I run through the standard argument for strong emergence based on entanglement, and show how it rests on shaky assumptions concerning the ontology of the quantum world. In particular, I consider two objections: that the argument involves Bell's theorem, whose premises are often rejected, and that the argument rests on a contested account of parts and wholes. I respond to both objections, showing that, with some important caveats, the argument for emergence based on quantum mechanics remains intact.

Just as Bell proposed that we excise the word “measurement” from physics, so I propose that we should excise the word “experience”: “experience” and its cognates should not appear in the formulation of any physical theory, including quantum mechanics and its various interpretations. The reasons are more or less the same as Bell gives for “measurement”: “experience” is a vague term, and experiencing systems are made out of atoms obeying quantum mechanics. Bell’s exhortation concerning “measurement” has largely been taken on board in the foundations of quantum mechanics. But appeals to “experience” remain—in part, I will argue, because of a bad argument that can be traced back to von Neumann, and in part because of mistaken impressions about the fundamentality of experience.

The Sleeping Beauty paradox in epistemology and the many-worlds interpretation of quantum mechanics both raise problems concerning subjective probability assignments. Furthermore, there are striking parallels between the two cases; in both cases personal experience has a branching structure, and in both cases the agent loses herself among the branches. However, the treatment of probability is very different in the two cases, for no good reason that I can see. Suppose, then, that we adopt the same treatment of probability in each case. Then the dominant ‘thirder’ solution to the Sleeping Beauty paradox becomes incompatible with the tenability of the many-worlds interpretation.

Pragmatism about quantum mechanics provides an attractive approach to the question of what quantum mechanics says. However, the conclusions reached by pragmatists concerning the content of quantum mechanics cannot be squared with the way that physicists use quantum mechanics to describe physical systems. In particular, attention to actual use results in ascribing content to claims about physical systems over a much wider range of contexts than countenanced by recent pragmatists. The resulting account of the content of quantum mechanics is much closer to quantum logic, and threatens the pragmatist conclusion that quantum mechanics requires no supplementation.

This dissertation is an investigation into the adequacy of the GRW theory of quantum mechanics as a solution to the measurement problem, and a comparison between the GRW theory and the other potential solutions. A new problem, the vagueness problem, is found to afflict a broad class of quantum mechanical theories, including the GRW theory. ;The standard theory of quantum mechanics and the measurement problem from which it suffers are sketched. The GRW theory of quantum mechanics is explained, along with how it is intended to solve the measurement problem. The major obstacle to the adequacy of the GRW theory in this regard, known as the tails problem, is presented. Two potential lines of response to the tails problem are outlined, namely modifying the GRW dynamics and modifying the interpretation rule connecting the language of the theory to everyday language. The first of these is quickly shown to be unworkable. The second is investigated in some detail. A defense of this line of response in terms of the inherent vagueness of the translation between the language of physical theory and everyday language is presented. However, it is argued that any modified interpretation rule which can adequately respond to the tails problem will violate intuitions concerning counting and the logic of parts and wholes. This is termed the vagueness problem. ;The extent of the vagueness problem among the other promising solutions to the measurement problem is investigated. It is demonstrated that the modal theories suffer from this problem, but Bohm-type hidden variable theories do not. It is argued that this gives us reason to prefer the hidden variable theories over their competitors. The empirical adequacy of the GRW theory is investigated. It is found that empirical considerations cannot at present decide between the GRW theory and its alternatives, although they may be able to do so eventually. ;The conclusion drawn is that because of the vagueness problem, the GRW theory and the modal theories cannot be regarded as fully satisfactory quantum mechanical theories, and that the Bohm-type hidden variable theories are to be preferred

A non-solipsist form of presentness is usually thought to require the non-relative co-presentness of space-like separated events, where this requirement further implies the non-relative simultaneity of these events. Since special relativity is thought to rule out any global, non-relative simultaneity, typical non-solipsist forms of presentness are taken to be inconsistent with special relativity. To address this problem, we re-explain the relationship between the non-solipsism of presentness and co-presentness by appealing to metaphysical indeterminacy. We propose presentness indeterminacy, the thesis that where an event, p, is determinately present, any event in space-like relation to p lacks a determinate tense. We argue that for many theories of time, indeterminate co-presentness is all that the non-solipsism of presentness requires. Since there is no determinate co-presentness, the inconsistency between presentness and special relativity in these theories disappears.

The accuracy-first program attempts to ground epistemology in the norm that one’s beliefs should be as accurate as possible, where accuracy is measured using a scoring rule. We argue that considerations of scientific progress suggest that such a monism about epistemic value is untenable. In particular, we argue that counterexamples to the standard scoring rules are ubiquitous in the history of science, and hence that these scoring rules cannot be regarded as a precisification of our intuitive concept of epistemic value.

It is possible that you are living in a simulation—that your world is computer-generated rather than physical. But how likely is this scenario? Bostrom and Chalmers each argue that it is moderately likely—neither very likely nor very unlikely. However, they adopt an unorthodox form of reasoning about self-location uncertainty. Our main contention here is that Bostrom’s and Chalmers’ premises, when combined with orthodoxy about self-location, yields instead the conclusion that you are almost certainly living in a simulation. We consider how this (surprising) conclusion might be resisted, and show that the analogy between Sleeping Beauty cases and simulation cases provides a new way of evaluating approaches to self-location uncertainty. In particular, we argue that some conditionalization-based approaches to self-location are problematically limited in their applicability.

In recent years there has been a robust but inconclusive debate over the existence and nature of indeterminacy in the world as described by quantum mechanics. I suggest that the inconclusive nature of the debate stems from starting from a metaphysical theory of indeterminacy. I propose instead framing the issue as a Carnapian explication project: start with the informal notion of indeterminacy used by physicists, and consider how best to make that concept precise. I defend a precisification based on von Neumann’s interpretation of quantum states, and consider the nature of the indeterminacy that results.

Accuracy-based arguments for conditionalization and probabilism appear to have a significant advantage over their Dutch Book rivals. They rely only on the plausible epistemic norm that one should try to decrease the inaccuracy of one’s beliefs. Furthermore, conditionalization and probabilism apparently follow from a wide range of measures of inaccuracy. However, we argue that there is an under-appreciated diachronic constraint on measures of inaccuracy which limits the measures from which one can prove conditionalization, and none of the remaining measures allow one to prove probabilism. That is, among the measures in the literature, there are some from which one can prove conditionalization, others from which one can prove probabilism, but none from which one can prove both. Hence at present, the accuracy-based approach cannot underwrite both conditionalization and probabilism.

In cases of animal mimicry, the receiver of the signal learns the truth that he is either dealing with the real thing or with a mimic. Thus, despite being a prototypical example of animal deception, mimicry does not seem to qualify as deception on the traditional definition, since the receiver is not actually misled. We offer a new account of propositional content in sender-receiver games that explains how the receiver is misled by mimicry. We show that previous accounts of deception, and of propositional content, give incorrect results about whether certain signals are deceptive.

Measures of epistemic utility are used by formal epistemologists to make determinations of epistemic betterness among cognitive states. The Brier rule is the most popular choice among formal epistemologists for such a measure. In this paper, however, we show that the Brier rule is sometimes seriously wrong about whether one cognitive state is epistemically better than another. In particular, there are cases where an agent gets evidence that definitively eliminates a false hypothesis, but where the Brier rule says that things have become epistemically worse. Along the way to this ‘elimination experiment’ counter-example to the Brier rule as a measure of epistemic utility, we identify several useful monotonicity principles for epistemic betterness. We also reply to several potential objections to this counter-example.

Deception has long been an important topic in philosophy. However, the traditional analysis of the concept, which requires that a deceiver intentionally cause her victim to have a false belief, rules out the possibility of much deception in the animal kingdom. Cognitively unsophisticated species, such as fireflies and butterflies, have simply evolved to mislead potential predators and/or prey. To capture such cases of “functional deception,” several researchers Machiavellian intelligence II, Cambridge University Press, Cambridge, pp 112–143, 1997; Searcy and Nowicki, The evolution of animal communication, Princeton University Press, Princeton, 2005; Skyrms, Signals, Oxford University Press, Oxford 2010) have endorsed the broader view that deception only requires that a deceiver benefit from sending a misleading signal. Moreover, in order to facilitate game-theoretic study of deception in the context of Lewisian sender-receiver games, Brian Skyrms has proposed an influential formal analysis of this view. Such formal analyses have the potential to enhance our philosophical understanding of deception in humans as well as animals. However, as we argue in this paper, Skyrms’s analysis, as well as two recently proposed alternative analyses, are seriously flawed and can lead us to draw unwarranted conclusions about deception.

Accuracy-based arguments for conditionalization and probabilism appear to have a significant advantage over their Dutch Book rivals. They rely only on the plausible epistemic norm that one should try to decrease the inaccuracy of one's beliefs. Furthermore, it seems that conditionalization and probabilism follow from a wide range of measures of inaccuracy. However, we argue that among the measures in the literature, there are some from which one can prove conditionalization, others from which one can prove probabilism, and none from which one can prove both. Hence at present, the accuracy-based approach cannot underwrite both conditionalization and probabilism.

Recently, Richard Healey and Simon Friederich have each advocated a pragmatist interpretation of quantum mechanics as a way to dissolve its foundational problems. The idea is that if we concentrate on the way quantum claims are used, the foundational problems of quantum mechanics cannot be formulated, and so do not require solution. Their central contention is that the content of quantum claims differs from the content of non-quantum claims, in that the former is prescriptive whereas the latter is descriptive. Healey also argues that claims about non-decoherent systems are largely devoid of content. I consider various objections to these claims, noting in particular the ways in which the application of pragmatism to quantum mechanics differs from previous examples of pragmatist therapy. I conclude that a pragmatist dissolution of the foundational difficulties of quantum mechanics is promising, but requires fairly radical changes to our understanding of the content of propositions and the extent of physical explanation.

The Doomsday Argument and the Simulation Argument share certain structural features, and hence are often discussed together. Both are cases where reflecting on one’s location among a set of possibilities yields a counter-intuitive conclusion—in the first case that the end of humankind is closer than you initially thought, and in the second case that it is more likely than you initially thought that you are living in a computer simulation. Indeed, the two arguments do have some structural similarities. But there are also significant disanalogies between the two arguments, and I argue that these disanalogies mean that the Simulation Argument succeeds and the Doomsday Argument fails.

Everettian accounts of quantum mechanics entail that people branch; every possible result of a measurement actually occurs, and I have one successor for each result. Is there room for probability in such an account? The prima facie answer is no; there are no ontic chances here, and no ignorance about what will happen. But since any adequate quantum mechanical theory must make probabilistic predictions, much recent philosophical labor has gone into trying to construct an account of probability for branching selves. One popular strategy involves arguing that branching selves introduce a new kind of subjective uncertainty. I argue here that the variants of this strategy in the literature all fail, either because the uncertainty is spurious, or because it is in the wrong place to yield probabilistic predictions. I conclude that uncertainty cannot be the ground for probability in Everettian quantum mechanics.

Putnam and Laudan separately argue that the falsity of past scientific theories gives us reason to doubt the truth of current theories. Their arguments have been highly influential, and have generated a significant literature over the past couple of decades. Most of this literature attempts to defend scientific realism by attacking the historical evidence on which the premises of the relevant argument are based. However, I argue that both Putnam's and Laudan's arguments are fallacious, and hence attacking their premises is unnecessary. The paper concludes with a discussion of the further historical evidence that would be required if the pessimistic induction is to present a serious threat to scientific realism.

It is widely acknowledged that the link between quantum language and ordinary language must be "fuzzier" than the traditional eigenstate-eigenvalue link. In the context of spontaneous-collapse theories, Albert and Loewer argue that the form of this fuzzy link is a matter of convention, and can be freely chosen to minimize anomalies for those theories. I defend the position that the form of the link is empirical, and could be such as to render collapse theories idle. This means that defenders of spontaneous-collapse theories must gamble that the actual form of the link renders such theories tenable

In quantum mechanics it is usually assumed that mutually exclusives states of affairs must be represented by orthogonal vectors. Recent attempts to solve the measurement problem, most notably the GRW theory, require the relaxation of this assumption. It is shown that a consequence of relaxing this assumption is that arithmatic does not apply to ordinary macroscopic objects. It is argued that such a radical move is unwarranted given the current state of understanding of the foundations of quantum mechanics.