Anna Mahtani

Dutch book and accuracy arguments are used to justify certain rationality constraints on credence functions. Underlying these dutch book and accuracy arguments are associated theorems, and I show that the interpretation of these theorems can vary along a range of dimensions. Given that the theorems can be interpreted in a variety of different ways, what is the status of the associated arguments? I consider three possibilities: we could aggregate the results of the differently interpreted theorems in some way and motivate rationality constraints based on this aggregation; we could be permissive and accept the conclusions of the dutch book and accuracy arguments under all interpretations of the associated theorems; or we could select one uniquely correct interpretation of the dutch book/accuracy theorem and use that to justify certain rationality constraints. I show that each possibility faces problems, and conclude that dutch book and accuracy theorems cannot be used to justify any principle of rationality.

The ex ante Pareto principle has an intuitive pull, and it has been a principle of central importance since Harsanyi’s defence of utilitarianism (to be found in e.g. (Harsanyi 1977)). The principle has been used to criticize and refine a range of positions in welfare economics, including egalitarianism and prioritarianism. But this principle faces a serious problem. I have argued elsewhere (XXX) that the concept of ex ante Pareto superiority is not well defined, because its application in a choice situation concerning a fixed population can depend on how the members of that population are designated. I show in this paper that in almost all cases of policy choice, there will be numerous sets of rival designators for the same fixed population.

I explore two ways that we might complete the definition of ex ante Pareto superiority. I call these the ‘supervaluationist’ reading and the ‘subvaluationist’ reading. I reject the subvaluationist reading as uncharitable, and argue that the supervaluationist reading is the most promising interpretation of the ex ante Pareto principle. I end by exploring some of the implications of this principle for prioritarianism and egalitarianism.

In this paper I offer an alternative—the ‘dispositional account’—to the standard account of imprecise probabilism. Whereas for the imprecise probabilist an agent’s credal state is modelled by a set of credence functions, on the dispositional account an agent’s credal state is modelled by a set of sets of credence functions. On the face of it, the dispositional account looks less elegant than the standard account—so why should we be interested? I argue that the dispositional account is actually simpler, because the dispositional choice behaviour that fixes an agent’s credal state is faithfully depicted in the model of that agent’s credal state. I explore some of the implications of the account, including a surprising implication for the debate over dilation.

In this paper I investigate an alternative to imprecise probabilism. Imprecise probabilism is a popular revision of orthodox Bayesianism: while the orthodox Bayesian claims that a rational agent’s belief-state can be represented by a single credence function, the imprecise probabilist claims instead that a rational agent’s belief-state can be represented by a set of such functions. The alternative that I put forward in this paper is to claim that the expression ‘credence’ is vague, and then apply the theory of supervaluationism to sentences containing this expression. This gives us a viable alternative to imprecise probabilism, and I end by comparing the two accounts. I show that supervaluationism has a simpler way of handling sentences relating the belief-states of two different people, or of the same person at two different times; that both accounts may have the resources to develop plausible decision theories; and finally that the supervaluationist can accommodate higher-order vagueness in a way that is not available to the imprecise probabilist.

Sometimes a proposition is 'opaque' to an agent: (s)he doesn't know it, but (s)he does know something about how coming to know it should affect his or her credence function. It is tempting to assume that a rational agent's credence function coheres in a certain way with his or her knowledge of these opaque propositions, and I call this the 'Opaque Proposition Principle'. The principle is compelling but demonstrably false. I explain this incongruity by showing that the principle is ambiguous: the term 'know' as it appears in the principle can be interpreted in two different ways, as either basic-know or super-know. I use this distinction to construct a plausible version of the principle, and then to similarly construct plausible versions of the Reflection Principle and the Sure-Thing Principle.

Many have argued that a rational agent's attitude towards a proposition may be better represented by a probability range than by a single number. I show that in such cases an agent will have unstable betting behaviour, and so will behave in an unpredictable way. I use this point to argue against a range of responses to the ‘two bets’ argument for sharp probabilities.

The concept of ‘pareto superiority’ plays a central role in ethics, economics, and law. Pareto superiority is sometimes taken as a relation between outcomes, and sometimes as a relation between actions—even where the outcomes of the actions are uncertain. Whether one action is classed as (ex ante) pareto superior to another depends on the prospects under the actions for each person concerned. I argue that a person’s prospects (in this context) can depend on how that person is designated. Without any constraints on acceptable designators, then, the concept of pareto superiority is ill defined and gives inconsistent results. I consider various ways of completing the definition and draw out some surprising implications.

This paper is about the standard Reflection Principle (van Fraassen in J Philos 81(5):235–256, 1984) and the Group Reflection Principle (Elga in Nous 41(3):478–502, 2007; Bovens and Rabinowicz in Episteme 8(3):281–300, 2011; Titelbaum in Quitting certainties: a Bayesian framework modeling degrees of belief, OUP, Oxford, 2012; Hedden in Mind 124(494):449–491, 2015). I argue that these principles are incomplete as they stand. The key point is that deference is an intensional relation, and so whether you are rationally required to defer to a person at a time can depend on how that person and that time are designated. In this paper I suggest a way of completing the Reflection Principle and Group Reflection Principle, and I argue that so completed these principles are plausible. In particular, they do not fall foul of the Sleeping Beauty case (Elga in Analysis 60(2):143–147, 2000), the Cable Guy Paradox (Hajek in Analysis 65(286):112–119, 2005), Arntzenius’ prisoner cases (Arntzenius in J Philos, 100(7):356–370, 2003), or the Puzzle of the Hats (Bovens and Rabinowicz in Episteme 8(3):281–300, 2011).

In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of whether we have a Dutch Book Argument for Conditionalization is left open.

We present a new argument for the claim that in the Sleeping Beauty problem, the probability that the coin comes up heads is 1/3. Our argument depends on a principle for the updating of probabilities that we call ‘generalized conditionalization’, and on a species of generalized conditionalization we call ‘synchronic conditionalization on old information’. We set forth a rationale for the legitimacy of generalized conditionalization, and we explain why our new argument for thirdism is immune to two attacks that Pust (Synthese 160:97–101, 2008) has leveled at other arguments for thirdism.

The Reflection Principle can be defended with a Diachronic Dutch Book Argument (DBA), but it is also defeated by numerous compelling counter-examples. It seems then that Diachronic DBAs can lead us astray. Should we reject them en masse — including Lewis’s Diachronic DBA for Conditionalization? Rachael Briggs’s “suppositional test” is supposed to differentiate between Diachronic DBAs that we can safely ignore (including the DBA for Reflection) and Diachronic DBAs that we should find compelling (including the DBA for Conditionalization). I argue that Brigg’s suppositional test is wrong: it sets the bar for coherence too high and places certain cases of self-doubt on the wrong side of the divide. Given that the suppositional test is unsatisfactory, we are left without any justification for discriminating between Diachronic DBAs and ought to reject them all — including the DBA for Conditionalization.

I examine a range of popular solutions to the puzzle of imaginative resistance. According to each solution in this range, imaginative resistance occurs only when we are asked to imagine something that conflicts with what we believe. I show that imaginative resistance can occur without this sort of conflict, and so that every solution in the range under consideration fails. I end by suggesting a new explanation for imaginative resistance — the Import Solution — which succeeds where the other solutions considered fail.

Could a sentence be, say, 3rd order vague, but 4th order precise? In Williamson 1999 we find an argument that seems to show that this is impossible: every sentence is either 1st order precise, 2nd order precise, or infinitely vague. The argument for this claim is unpersuasive, however, and this paper explains why.

Timothy Williamson claims that margin for error principles govern all cases of inexact knowledge. I show that this claim is unfounded: there are cases of inexact knowledge where Williamson’s argument for margin for error principles does not go through. The problematic cases are those where the value of the relevant parameter is fixed across close cases. I explore and reject two responses to my objection, before concluding that Williamson’s account of inexact knowledge is not compelling.

Timothy Williamson's response to the question why we cannot know where the sharp boundaries marked by vague terms lie involves the claim that vague terms are unstable. Several theorists would not accept this claim, and it is tempting to think that this gives them a good objection to Williamson. By clarifying the structure of Williamson's response to the title question, I show that this objection is wrong-headed, and reveal a new line of attack.