Temporally Continuous Probability Kinematics
Creators: name: Blackwell, Kevin
Publisher: name: My University
Year: 2020
Subjects: subject: formal epistemology
subject: updating rules
subject: diachronic and synchronic norms of rationality
subject: temporally continuous updating
subject: Jeffrey's Probability Kinematics
subject: rationality and personhood
subject: Philosophy
subject: FOS: Philosophy, ethics and religion
subject: Humanities
subject: FOS: Humanities

description: The heart of my dissertation project is the proposal of a new updating rule for responding to learning experiences consisting of continuous streams of evidence. I suggest characterizing this kind of learning experience as a continuous stream of stipulated credal derivatives, and show that Continuous Probability Kinematics is the uniquely coherent response to such a stream which satisfies a continuous analogue of Rigidity – the core property of both Bayesian and Jeffrey conditionalization. In the first chapter, I define neighborhood norms of rationality with reference to Kenny Easwaran’s definition of neighborhood properties. I summarize and comment on some of the key arguments in the dispute between time-slice epistemologists, who argue that there are no fundamentally diachronic norms of rationality, and the proponents of diachronic norms. I am sympathetic to two of the key motivations often given in support of the synchronist position: mentalist internalism and the idea that metaphysical disputes about the identity of persons in bizarre puzzle cases should not play a central role in epistemologists’ assessments of the rationality of agents. However, I argue that time-slice epistemology cannot adequately address the rationality of temporally-extended processes like reasoning and learning. Neighborhood norms present a viable third way between these two positions, capturing much of the spirit of the previously-discussed synchronist motivations while still providing just enough temporal structure to meaningfully guide and evaluate temporally-extended rational processes. Continuous Probability Kinematics is an example of one such neighborhood norm. In the second chapter, I develop my updating rule CPK and establish many of its core properties. Of special note here are the deep connections to Jeffrey’s Probability Kinematics, as well as some key differences. The net result of any CPK updating process will always be representable as a Jeffrey shift on the refined partition generated by the propositions that the agent is receiving direct evidence concerning. However, one crucial difference is that CPK provides an intuitive account of how to combine the effects of learning experiences that are each about fundamentally different underlying partitions. In CPK’s formalism, an agent can receive simultaneous evidence streams about an arbitrary (finite) number of propositions, which can themselves be evidentially related in any way. At any given instant, the result of the combination is a simple sum of the effects that learning about the individual propositions would have separately. CPK is concerned with a novel kind of learning experience and involves a novel characterization of evidence. The third and final chapter of this dissertation is concerned with explaining what this characterization of evidence means and with arguing that it can be the basis for genuine learning. I begin by characterizing learning experiences in terms of the Value of Information, and prove a Value of Information theorem for CPK learning experiences under the assumption of a Martingale constraint on the agent’s prior distribution over the signals that they might receive. I examine Timothy Williamson’s arguments that evidence must be propositional and express my skepticism. I then explore two different routes to model agents who update by CPK as if they are learning some propositional content and updating the rest of their credences by Bayesian conditionalization on this content. The second of these two routes provides a very interesting lens to reexamine the evidential commitments that underwrite updating by CPK, which I analyze.