Jeffrey Barrett

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.

Lewis signaling games illustrate how language might evolve from random behavior. The probability of evolving an optimal signaling language is, in part, a function of what learning strategy the agents use. Here we investigate three learning strategies, each of which allows agents to forget old experience. In each case, we find that forgetting increases the probability of evolving an optimal language. It does this by making it less likely that past partial success will continue to reinforce suboptimal practice. The learning strategies considered here show how forgetting past experience can promote learning in the context of games with suboptimal equilibria.

This paper concerns how rule-following behavior might evolve in the context of a variety of Skyrms–Lewis signaling game, how such rules might subsequently evolve to be used in new contexts, and how such appropriation allows for the composition of evolved rules. We will also consider how the composition of simpler rules to form more complex rules may be significantly more efficient than evolving the complex rules directly. And we will review an example of rule following by pinyon and scrub jays as an illustration of the appropriation of a rule to a new context :142–150, 2013a; Barrett, Philos Sci, 2014). The proposal here is that the composition of rules might occur in a way that is precisely analogous to such simple appropriation. Finally, we will briefly consider how any finite truth-functional operation might evolve by the sequential appropriation of simpler rules.

Because of the conceptual difficulties it faces, quantum mechanics provides a salient example of how alternative metaphysical commitments may clarify our understanding of a physical theory and the explanations it provides. Here we will consider how postulating alternative quantum worlds in the context of Hugh Everett III’s pure wave mechanics may serve to explain determinate measurement records and the standard quantum statistics. We will focus on the properties of such worlds, then briefly consider other metaphysical options available for interpreting pure wave mechanics. These reflections will serve to illustrate both the nature and the limits of naturalized metaphysics.

A resolution of the quantum measurement problem would require one to explain how it is that we end up with determinate records at the end of our measurements. Metaphysical commitments typically do real work in such an explanation. Indeed, one should not be satisfied with one's metaphysical commitments unless one can provide some account of determinate measurement records. I will explain some of the problems in getting determinate records in relativistic quantum field theory and pay particular attention to the relationship between the measurement problem and a generalized version of Malament's theorem.

David Lewis (1969) introduced sender-receiver games as a way of investigating how meaningful language might evolve from initially random signals. In this report I investigate the conditions under which Lewis signaling games evolve to perfect signaling systems under various learning dynamics. While the 2-state/2- term Lewis signaling game with basic urn learning always approaches a signaling system, I will show that with more than two states suboptimal pooling equilibria can evolve. Inhomogeneous state distributions increase the likelihood of pooling equilibria, but learning strategies with negative reinforcement or certain sorts of mutation can decrease the likelihood of, and even eliminate, pooling equilibria. Both Moran and APR learning strategies (Bereby-Meyer and Erev 1998) are shown to promote successful convergence to signaling systems. A model is presented that illustrates how a language that codes state-act pairs in an order-based grammar might evolve in the context of a Lewis signaling game. The terms, grammar, and the corresponding partitions of the state space co-evolve to generate a language whose structure appears to reflect canonical natural kinds. The evolution of these apparent natural kinds, however, is entirely in service of the rewards that accompany successful distinctions between the sender and receiver. Any metaphysics grounded on the structure of a natural language that evolved in this way would track arbitrary, but pragmatically useful distinctions.

A field-theoretic version of Wigner’s friend (1961) illustrates how the quantum measurement problem arises for field theory. Similarly, considering spacelike separate measurements of entangled fields by observers akin to Wigner’s friend shows the sense in which relativistic constraints make the measurement problem particularly difficult to resolve in the context of a relativistic field theory. We will consider proposals by Wigner (1961), Bloch (1967), Helwig and Kraus (1970), and Bell (1984) for resolving the measurement problem for quantum field theory. We will conclude by considering the possibility of giving up rich dynamical explanation in the context of a many-maps formulation of relativistic quantum field theory.

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.

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 concerns two composite Lewis-Skyrms signaling games. Each consists in a base game that evolves a language descriptive of nature and a metagame that coevolves a language descriptive of the base game and its evolving language. The first composite game shows how a pragmatic notion of truth might coevolve with a simple descriptive language. The second shows how a pragmatic notion of probability might similarly coevolve. Each of these pragmatic notions is characterized by the particular game and role that it comes to play in the game.

Accuracy in the philosophical theory of rationality demands that we recognize particular beliefs as arising within the context of larger units, the cultural or conceptual schemes, patterns, or practices, involvement in which itself provides standards and grounds for their rational evaluation. At the same time, though, a satisfactory account of rationality cannot hold the standards, values, or commitments of one particular culture, practice, or conceptual scheme, even one’s own, immune from rational criticism. In order to accurately and responsibly picture the shape of our commitments and the dynamics of their revision over time, in other words, the theory of rationality must reconcile the immanence of reason to particular cultural and conceptual units with its transcendence of them. This raises a deep and far-ranging problem of perspective. In his perspicuous presentation of it, Hilary Putnam put the problem this way: There are two points that must be balanced, both points that have been made by philosophers of many different kinds: (1) talk of what is ‘right’ and ‘wrong’ in any area only makes sense against the background of an inherited tradition; but (2) traditions themselves can be criticized … On the one hand, there is no notion of reasonableness at all without cultures, practices, procedures; on the other hand, the cultures, practices, procedures we inherit are not an algorithm to be slavishly followed. As Mill said, commenting on his own inductive logic, there is no rule book which will not lead to terrible results ‘if supposed to be conjoined with universal idiocy.’ Reason is, in this sense, both immanent (not to be found outside of concrete language games and institutions) and transcendent (a regulative idea that we use to criticize the conduct of all activities and institutions). (p. 431). As Putnam argues, it is difficult to find a standpoint of theory from which the contrasting claims of immanence and transcendence can be reconciled..

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.

Skyrms-Lewis signaling games illustrate how meaningful language may evolve from initially meaningless random signals (Lewis, Convention 1969; Skyrms 2008). Here we will consider how incommensurable languages might evolve in the context of signaling games. We will also consider the types of incommensurability exhibited between evolved languages in such games. We will find that sequentially evolved languages may be strongly incommensurable while still allowing for increasingly faithful descriptions of the world.

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 are concerned here with explaining how successful rule-following behavior might evolve and how an old evolved rule might come to be successfully used in a new context. Such rule-following behavior is illustrated in the transitive judgments of pinyon and scrub-jays (Bond et al., Anim Behav 65:479–487, 2003). We begin by considering how successful transitive rule-following behavior might evolve in the context of Skyrms–Lewis sender–receiver games (Lewis, Convention. Harvard University Press, Cambridge, 1969; Skyrms, Philos Sci 75:489–500, 2006). We then consider two ways that an agent might come to use an old evolved rule in a new context. The first involves the agent evolving successful dispositions for one concrete type of experience, then associating a new type of experience with the old evolved dispositions. The second involves the agent evolving dispositions that represent a general inferential schema, then composing these dispositions with others in a way that allows the agent to make inferences concerning a new concrete type of experience.

We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves one no choice but to restrict the use of a certain class of implicational rules including modus ponens.

This article concerns how rule-following behavior might evolve, how an old evolved rule might come to be appropriated to a new context, and how simple concepts might coevolve with rule-following behavior. In particular, we consider how the transitive inferential rule-following behavior exhibited by pinyon and scrub jays might evolve in the context of a variety of the Skyrms-Lewis signaling game, then how such a rule might come to be appropriated to carry out inferences regarding stimuli different from those involved in the original evolution of the rule, and how this appropriation involves a step toward the evolution of basic ordinal concepts.

α-recursion lifts classical recursion theory from the first transfinite ordinal ω to an arbitrary admissible ordinal α [10]. Idealized computational models for α-recursion analogous to Turing machine models for classical recursion have been proposed and studied [4] and [5] and are applicable in computational approaches to the foundations of logic and mathematics [8]. They also provide a natural setting for modeling extensions of the algorithmic logic described in [1] and [2]. On such models, an α-Turing machine can complete a θ-step computation for any ordinal θ < α. Here we consider constraints on the physical realization of α-Turing machines that arise from the structure of physical spacetime. In particular, we show that an α-Turing machine is realizable in a spacetime constructed from R only if α is countable. While there are spacetimes where uncountable computations are possible and while they may even be empirically distinguishable from a standard spacetime, there is good reason to suppose that such nonstandard spacetimes are nonphysical. We conclude with a suggestion for a revision of Church’s thesis appropriate as an upper bound for physical computation.

There is good reason to suppose that our best physical theories are false: In addition to its own internal problems, the standard formulation of quantum mechanics is logically incompatible with special relativity. There is also good reason to suppose that we have no concrete idea concerning what it might mean to claim that these theories are approximately or vaguely true. I will argue that providing a concrete understanding the approximate or vague truth of our current physical theories is not a task for traditional epistemology; rather, this is only possible in the context of ongoing empirical inquiry. [Note #1].

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.

The bare theory is the standard von Neumann·Dirac formulation of quantum mechanics without the collapse postulate but with the eigenvalueeigenstate link. Albert (1992, 1i6-125) presented the bare theory as one way of understanding EverettRi7;s relative-state interpretation. At first glance, it looks as if the bare theory cannot possibly account for our experience. After all, at the end of a measurement an observer will typically be in a superposition of having recorded mutually incompatible results, which on the standard interpretation of states (the interpretation provided by the eigenvalue-eigenstate..

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.

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.

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.