Reasons, Coherence, and Group Rationality

Philosophy and Phenomenological Research, EarlyView

Degree supervaluational logic

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There???s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy. It applies the methodology above to focus on degree logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allow degrees of consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical???all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail

Betting on Quantum Objects

Dutch book arguments have been applied to beliefs about the outcomes of measurements of quantum systems, but not to beliefs about quantum objects prior to measurement. In this paper, we prove a quantum version of the probabilists' Dutch book theorem that applies to both sorts of beliefs: roughly, if ideal beliefs are given by vector states, all and only Born-rule probabilities avoid Dutch books. This theorem and associated results have implications for operational and realist interpretations of the logic of a Hilbert lattice. In the latter case, we show that the defenders of the eigenstate-value orthodoxy face a trilemma. Those who favor vague properties avoid the trilemma, admitting all and only those beliefs about quantum objects that avoid Dutch books.Comment: 26 pages, 3 figures, 1 table; improved operational semantics, results unchange

Dilating and contracting arbitrarily

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a precise state arbitrarily

Measuring the Consequences of Rules: A Reply to Smith

In ‘Measuring the Consequences of Rules’, Holly Smith presents two problems involving the indeterminacy of compliance, which she takes to be fatal for all forms of rule-utilitarianism. In this reply, I attempt to dispel both problems

A subjectivist’s guide to deterministic chance

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies

Cluelessness

Decisions, whether moral or prudential, should be guided at least in part by considerations of the consequences that would result from the various available actions. For any given action, however, the majority of its consequences are unpredictable at the time of decision. Many have worried that this leaves us, in some important sense, clueless. In this paper, I distinguish between ‘simple’ and ‘complex’ possible sources of cluelessness. In terms of this taxonomy, the majority of the existing literature on cluelessness focusses on the simple sources. I argue, contra James Lenman in particular, that these would-be sources of cluelessness are unproblematic, on the grounds that indifference-based reasoning is far less problematic than Lenman (along with many others) supposes. However, there does seem to be a genuine phenomenon of cluelessness associated with the ‘complex’ sources; here, indifference-based reasoning is inapplicable by anyone’s lights. This ‘complex problem of cluelessness’ is vivid and pressing, in particular, in the context of Effective Altruism. This motivates a more thorough examination of the precise nature of cluelessness, and the precise source of the associated phenomenology of discomfort in forced-choice situations. The latter parts of the paper make some initial explorations in those directions

Epistemic irrelevance in credal nets: the case of imprecise Markov trees

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.Comment: 29 pages, 5 figures, 1 tabl