Jeffrey Barrett

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.

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

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

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

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

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

Skyrms-Lewis sender-receiver games with invention allow one to model how a simple mathematical language might be invented and become meaningful as its use coevolves with the basic arithmetic competence of primitive mathematical inquirers. Such models provide sufficient conditions for the invention and evolution of a very basic sort of arithmetic language and practice, and, in doing so, provide insight into the nature of a correspondingly basic sort of mathematical knowledge in an evolutionary context. Given traditional philosophical reflections concerning the nature and preconditions of mathematical knowledge, these conditions are strikingly modest

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.

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..

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.

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.

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.

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

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.