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. (shrink)

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. (shrink)

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.

We tell a story where an agent who chooses in such a way as to make the greatest possible profit on each of an infinite series of transactions ends up worse off than an agent who chooses in such a way as to make the least possible profit on each transaction. That is, contrary to what one might suppose, it is not necessarily rational always to choose the option that yields the greatest possible profit on each transaction.

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.. (shrink)

A situated observer is an observer as modeled within the world characterized by one’s physical theory. A physical theory arguably only makes empirical predictions if it makes predictions for the records of a situated observer. In this spirit, one has a satisfactory solution to the measurement problem only if one has a formulation of quantum mechanics that makes the right empirical predictions for the records of a situated observer. Bohmian mechanics addresses the measurement problem by explaining what measurement records are, (...) how a situated observer might produce them, and why a situated observer should expect the standard quantum predictions. The notion of an effective wave function is crucial in understanding how the theory makes empirical predictions. (shrink)

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.

Empirical inquiry involves the coevolution of predictive theory and descriptive language. Here we consider how one might model this coevolution using the tools of evolutionary game theory. We will see how subsequently evolved languages might exhibit semantic drift, invention, and discard. These evolutionary models also illustrate how subsequently evolved languages might be incommensurable yet nevertheless provide faithful descriptions of nature. Finally, we will consider how a model for the coevolution of predictive theory and descriptive language accounts for endogenous epistemic norms.

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]. (shrink)

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.. (shrink)

Here we use generalized signaling games to model how one’s beliefs might coevolve with the language one uses to characterize those beliefs. We will start by considering how one might individuate pragmatic notions of truth and how such notions might coevolve with a descriptive language. We will then consider how agents might evolve a language that allows them to characterize their beliefs and degrees of belief. Finally, we will consider evolutionary conditions under which a principle of indifference that assigns equal (...) prior probability to each possibility that one can describe in one’s evolved language might in fact be successful. (shrink)