Jeffrey Barrett

There is a long tradition of trying to find a satisfactory interpretation of Everett's relative-state formulation of quantum mechanics. Albert and Loewer recently described two new ways of reading Everett: one we will call the single-mind theory and the other the many-minds theory. I will briefly describe these theories and present some of their merits and problems. Since both are no-collapse theories, a significant merit is that they can take advantage of certain properties of the linear dynamics, which Everett apparently considered to be important, to constrain their statistical laws

We consider how an epistemic network might self-assemble from the ritualization of the individual decisions of simple heterogeneous agents. In such evolved social networks, inquirers may be significantly more successful than they could be investigating nature on their own. The evolved network may also dramatically lower the epistemic risk faced by even the most talented inquirers. We consider networks that self-assemble in the context of both perfect and imperfect communication and compare the behaviour of inquirers in each. This provides a step in bringing together two new and developing research programs, the theory of self-assembling games and the theory of network epistemology.

We consider two ways one might use algorithmic randomness to characterize a probabilistic law. The first is a generative chance* law. Such laws involve a nonstandard notion of chance. The second is a probabilistic* constraining law. Such laws impose relative frequency and randomness constraints that every physically possible world must satisfy. While each notion has virtues, we argue that the latter has advantages over the former. It supports a unified governing account of non-Humean laws and provides independently motivated solutions to issues in the Humean best-system account. On both notions, we have a much tighter connection between probabilistic laws and their corresponding sets of possible worlds. Certain histories permitted by traditional probabilistic laws are ruled out as physically impossible. As a result, such laws avoid one variety of empirical underdetermination, but the approach reveals other varieties of underdetermination that are typically overlooked.

I argue that a strong mind–body dualism is required of any formulation of quantum mechanics that satisfies a relatively weak set of explanatory constraints. Dropping one or more of these constraints may allow one to avoid the commitment to a mind–body dualism but may also require a commitment to a physical–physical dualism that is at least as objectionable. Ultimately, it is the preferred basis problem that pushes both collapse and no-collapse theories in the direction of a strong dualism in resolving the quantum measurement problem. Addressing this problem illustrates how the construction and evaluation of explanatorily rich physical theories are inextricably tied to the evaluation of traditional philosophical issues.

A many-worlds interpretation is of quantum mechanics tells us that the linear equations of motion are the true and complete laws for the time-evolution of every physical system and that the usual quantum-mechanical states provide complete descriptions of all possible physical situations. Such an interpretation, however, denies the standard way of understanding quantum-mechanical states. When the pointer on a measuring device is in a superposition of pointing many different directions, for example, we are to understand this as many pointers, each in a differentworld, each pointing in a different determinate direction. We ask here whether such talk makes any genuinely intelligible sense of the term world. We conclude that it does not.

This paper is concerned with the possibility and nature of relativistic hidden-variable formulations of quantum mechanics. Both ad hoc teleological constructions of spacetime maps and frame-dependent constructions of spacetime maps are considered. While frame-dependent constructions are clearly preferable, they provide neither mechanical nor causal explanations for local quantum events. Rather, the hiddenvariable dynamics used in such constructions is just a rule that helps to characterize the set of all possible spacetime maps. But while having neither mechanical nor causal explanations of the values of quantummechanical measurement records is a significant cost, it may simply prove too much to ask for such explanations in relativistic quantum mechanics.

argued that there are two options for what he called a realistic solution to the quantum measurement problem: (1) select a preferred set of observables for which definite values are assumed to exist, or (2) attempt to assign definite values to all observables simultaneously (1810–1). While conventional wisdom has it that the second option is ruled out by the Kochen-Specker theorem, Vink nevertheless advocated it. Making every physical quantity determinate in quantum mechanics carries with it significant conceptual costs, but it also provides a way of addressing the preferred basis problem that arises if one chooses to pursue the first option. The potential costs and benefits of a formulation of quantum mechanics where every physical quantity is determinate are herein examined. The preferred-basis problem How to solve the preferred-basis problem Relativistic constraints Conclusion.

Given Hugh Everett III's understanding of the proper cognitive status of physical theories, his relative-state formulation of pure wave mechanics arguably qualifies as an empirically acceptable physical theory. The argument turns on the precise nature of the relationship that Everett requires between the empirical substructure of an empirically faithful physical theory and experience. On this view, Everett provides a weak resolution to both the determinate record and the probability problems encountered by pure wave mechanics, and does so in a way that avoids unnecessary metaphysical complications. Taking Everett's goal to be showing the empirical faithfulness of the relative-state formulation agrees well with his characterization of his project as one of seeking a model for observation in the correlation structure described by pure wave mechanics and seeking a measure of typicality over this empirical substructure that covaries with our empirically warranted expectations. 1 Pure Wave Mechanics and Relative States2 Everett and Frank3 Everett on the Nature of Physical Theories4 Conditions for Empirical Faithfulness5 The Empirical Faithfulness of Pure Wave Mechanics6 Conclusion

Everett (1957a, b, 1973) relative-state formulation of quantum mechanics has often been taken to involve a metaphysical commitment to the existence of many splitting worlds each containing physical copies of observers and the objects they observe. While there was earlier talk of splitting worlds in connection with Everett, this is largely due to DeWitt’s (Phys Today 23:30–35, 1970) popular presentation of the theory. While the thought of splitting worlds or parallel universes has captured the popular imagination, Everett himself favored the language of elements, branches, or relative states in describing his theory. The result is that there is no mention of splitting worlds or parallel universes in any of Everett’s published work. Everett, however, did write of splitting observers and was willing to adopt the language of many worlds in conversation with people who were themselves using such language. While there is evidence that Everett was not entirely comfortable with talk of many worlds, it does not seem to have mattered much to him what language one used to describe pure wave mechanics. This was in part a result of Everett’s empirical understanding of the cognitive status of his theory

Everett's relative-state formulation of quantum mechanics is an attempt to solve the measurement problem by dropping the collapse dynamics from the standard von Neumann-Dirac theory of quantum mechanics. The main problem with Everett's theory is that it is not at all clear how it is supposed to work. In particular, while it is clear that he wanted to explain why we get determinate measurement results in the context of his theory, it is unclear how he intended to do this. There have been many attempts to reconstruct Everett's no-collapse theory in order to account for the apparent determinateness of measurement outcomes. These attempts have led to such formulations of quantum mechanics as the many-worlds, many-minds, many-histories, and relative-fact theories. Each of these captures part of what Everett claimed for his theory, but each also encounters problems.

Signaling games with reinforcement learning have been used to model the evolution of term languages (Lewis 1969, Convention. Cambridge, MA: Harvard University Press; Skyrms 2006, “Signals” Presidential Address. Philosophy of Science Association for PSA). In this article, syntactic games, extensions of David Lewis’s original sender–receiver game, are used to illustrate how a language that exploits available syntactic structure might evolve to code for states of the world. The evolution of a language occurs in the context of available vocabulary and syntax—the role played by each component is compared in the context of simple reinforcement learning

Belief-revision models of knowledge describe how to update one’s degrees of belief associated with hypotheses as one considers new evidence, but they typically do not say how probabilities become associated with meaningful hypotheses in the first place. Here we consider a variety of Skyrms–Lewis signaling game (Lewis in Convention. Harvard University Press, Cambridge, 1969; Skyrms in Signals evolution, learning, & information. Oxford University Press, New York, 2010) where simple descriptive language and predictive practice and associated basic expectations coevolve. Rather than assigning prior probabilities to hypotheses in a fixed language then conditioning on new evidence, the agents begin with no meaningful language or expectations then evolve to have expectations conditional on their descriptions as they evolve to have meaningful descriptions for the purpose of successful prediction. The model, then, provides a simple but concrete example of how the process of evolving a descriptive language suitable for inquiry might also provide agents with conditional expectations that reflect the type and degree of predictive success in fact afforded by their evolved predictive practice. This illustrates one way in which the traditional problem of priors may simply fail to apply to one’s model of evolving inquiry

In order to judge whether a theory is empirically adequate one must have epistemic access to reliable records of past measurement results that can be compared against the predictions of the theory. Some formulations of quantum mechanics fail to satisfy this condition. The standard theory without the collapse postulate is an example. Bell's reading of Everett's relative-state formulation is another. Furthermore, there are formulations of quantum mechanics that only satisfy this condition for a special class of observers, formulations whose empirical adequacy could only be judged by an observer who records her measurement results in a special way. Bohm's theory is an example. It is possible to formulate hidden-variable theories that do not suffer from such a restriction, but these encounter other problems

Lewis sender‐receiver games illustrate how a meaningful term language might evolve from initially meaningless random signals (Lewis 1969; Skyrms 2006). Here we consider how a meaningful language with a primitive grammar might evolve in a somewhat more subtle sort of game. The evolution of such a language involves the co‐evolution of partitions of the physical world into what may seem, at least from the perspective of someone using the language, to correspond to canonical natural kinds. While the evolved language may allow for the sort of precise representation that is required for successful coordinated action and prediction, the apparent natural kinds reflected in its structure may be purely conventional. This has both positive and negative implications for the limits of naturalized metaphysics

On Bohm''s formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm''s theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm''s theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm''s theory without the distribution postulate.

This paper is concerned with how a simple metalanguage might coevolve with a simple descriptive base language in the context of interacting Skyrms–Lewis signaling games Lewis. We will first consider a metagame that evolves to track the successful and unsuccessful use of a coevolving base language, then we will consider a metagame that evolves a truth predicate for expressions in a coevolving base language. We will see how a metagame that tracks truth provides an endogenous way to break the symmetry between indicative and imperative interpretations of the base language. Finally, we will consider how composite signaling games provide a way to characterize alternative pragmatic notions of truth.

Everett proposed resolving the quantum measurement problem by dropping the nonlinear collapse dynamics from quantum mechanics and taking what is left as a complete physical theory. If one takes such a proposal seriously, then the question becomes how much of the predictive and explanatory power of the standard theory can one recover without the collapse postulate and without adding anything else. Quantum mechanics without the collapse postulate has several suggestive properties, which we will consider in some detail. While these properties are not enough to make it acceptable given the usual standards for a satisfactory physical theory, one might want to exploit these properties to cook up a satisfactory no-collapse formulation of quantum mechanics. In considering how this might work, we will see why any no-collapse theory must generally fail to satisfy at least one of two plausible-sounding conditions.

There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules of inference between such statements. As shown in [1], the threat of paradoxes, such as the Curry paradox, requires care in implementing rules of inference in this context. As in any type-free logic, some traditional rules will fail. The first part of the paper develops a rich collection of inference rules that do not lead to paradox. The second part identifies traditional rules of logic that are paradoxical in algorithmic logic, and so should be viewed with suspicion in type-free logic generally.

There is good reason to suppose that our best physical theories, quantum mechanics and special relativity, are false if taken together and literally. If they are in fact false, then how should they count as providing knowledge of the physical world? One might imagine that, while strictly false, our best physical theories are nevertheless in some sense probably approximately true. This paper presents a notion of local probable approximate truth in terms of descriptive nesting relations between current and subsequent theories. This notion helps explain how false physical theories might nevertheless provide physical knowledge of a variety that is particularly salient to diachronic empirical inquiry

Everett wanted a formulation of quantum mechanics that (i) took the linear dynamics to be a complete and accurate description of the time-evolution of all physical systems and (ii) logically entailed the same subjective appearances predicted by the standard formulation of quantum mechanics. While most everyone would agree with this description of Everett’s project, there is little agreement on exactly how his relative-state formulation was supposed to work. In this paper, I consider two very different readings of Everett: the bare reading and the splitting-worlds reading. What distinguishes these is their interpretation of the wave function and how one accounts for the experiences of observers. The difficulty in interpreting Everett, however, is illustrated by the fact that neither reading is entirely compatible with his own description of his project.

In this paper I describe the history of the surreal trajectories problem and argue that in fact it is not a problem for Bohm's theory. More specifically, I argue that one can take the particle trajectories predicted by Bohm's theory to be the actual trajectories that particles follow and that there is no reason to suppose that good particle detectors are somehow fooled in the context of the surreal trajectories experiments. Rather than showing that Bohm's theory predicts the wrong particle trajectories or that it somehow prevents one from making reliable measurements, such experiments ultimately reveal the special role played by position and the fundamental incompatibility between Bohm's theory and relativity. They also provide a striking example of the theory-ladenness of observation

Hugh Everett III proposed his relative-state formulation of pure wave mechanics as a solution to the quantum measurement problem. He sought to address the theory’s determinate record and probability problems by showing that, while counterintuitive, pure wave mechanics was nevertheless empirically faithful and hence empirical acceptable. We will consider what Everett meant by empirical faithfulness. The suggestion will be that empirical faithfulness is well understood as a weak variety of empirical adequacy. The thought is that the very idea of empirical adequacy might be renegotiated in the context of a new physical theory given the theory’s other virtues. Everett’s argument for pure wave mechanics provides a concrete example of such a renegotiation

Quantum mechanics without the collapse postulate, the bare theory, was proposed by Albert (1992) as a way of understanding Everett's relative-state formulation of quantum mechanics. The basic idea is to try to account for an observer's beliefs by appealing to a type of illusion predicted by the bare theory. This paper responds to some recent objections to the bare theory by providing a more detailed description of the sense in which it can and the sense in which it cannot account for our experience.