Jeffrey Barrett

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.

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.

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.

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.

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.

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.

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.

We consider how cue-reading, sensory-manipulation, and signaling games may initially evolve from ritualized decisions and how more complex games may evolve from simpler games by polymerization, template transfer, and modular composition. Modular composition is a process that combines simpler games into more complex games. Template transfer, a process by which a game is appropriated to a context other than the one in which it initially evolved, is one mechanism for modular composition. And polymerization is a particularly salient example of modular composition where simpler games evolve to form more complex chains. We also consider how the evolution of new capacities by modular composition may be more efficient than evolving those capacities from basic decisions.

Insofar as empirical inquiry involves the coevolution of descriptive language and theoretical commitments, a satisfactory model of empirical knowledge should describe the coordinated evolution of both language and theory. But since we do not know what conceptual resources we might need to express our future theories or to provide our best future faithful descriptions of the world, we do not now know even what the space of future descriptive options might be. One strategy for addressing this shifting-resource problem is to track the predictive and linguistic dispositions of inquirers rather than to track their theories and conceptual resources directly. Sender-predictor games, a variant of Skyrms–Lewis sender-receiver games, provide very simple models for the coordinated coevolution of predictive and linguistic dispositions. Such models explain how it is possible for (1) predictive and descriptive dispositions of inquirers to coevolve, (2) term-wise incommensurable, but nevertheless descriptively faithful languages, to sequentially evolve, and (3) a sort of underdetermination to occur where inquirers might satisfy their descriptive and predictive aims by revising their linguistic dispositions, their theoretical dispositions, or both. Such models also provide an elementary characterization of what it might mean for descriptions of the world to be faithful and hence for empirical inquiry to be successful. In doing so they provide a relatively weak, but perfectly clear, endogenous account of epistemic norms.

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.