Abstract. 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 (1969)] [Skyrms (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 priors may simply fail to apply to one's model of evolving inquiry.
Description, Prediction, and ExpectationBelief-revision models of knowledge describe how to update one's degrees of belief as one considers new evidence. On a Bayesian model, for example, one fixes a descriptive language, sets coherent prior probabilities over a set of hypotheses expressed in the language, then updates one's degrees of belief as one conditions on new evidence. While such an account of reflective inquiry has many virtues, it has nothing to say concerning how to assign prior probabilities to meaningful hypotheses. This is the problem of priors.On reflection, one might, however, find the problem of priors itself puzzling.While it is indeed unclear what procedure one should adopt in assigning prior expectations to hypotheses expressed in a fixed descriptive language, it is similarly unclear how one might ever come to use such a language without already having a rich set of expectations. The symmetry of these reflections suggests a strategy.We will consider how it might be possible for basic expectations to coevolve with a simple descriptive language. More specifically, we will consider how simple for coordinated prediction might also also provide a core set of well-tuned posterior expectations that might then be available to constrain subjective degrees of belief should the agent turn to reflective inquiry.We will consider the story in three parts.
Part I: The Coevolution of Description and PredictionA sender-predictor game is a variety of Skyrms-Lewis signaling game.2 In a sender-predictor game, however, the agents coevolve both descriptive and predictive dispositions. We will refer to these are the agents' first-order dispositions. Their second-order dispositions determine how they update their first-order dispositions as they learn from experience.