Published & Forthcoming Papers
Impossible Worlds and Partial Belief | Forthcoming in Synthese
The open-access published version is also available here
Abstract: One response to the problems of logical omniscience is to extend the space of possible worlds to include impossible worlds. It is natural to think that essentially the same strategy can be applied to standard probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. With only very weak assumptions about the space of worlds, most of the propositions which can be constructed from possible and impossible worlds are in an important sense inexpressible; whereas the probabilistic model seems committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic.
Ramsey Without Ethical Neutrality | 2017, Mind 126 (501): 1-51
The published version is available here
Abstract: Frank Ramsey’s ‘Truth and Probability’ sketches a proposal for the empirical measurement of credences, along with a corresponding set of axioms for a (somewhat incomplete) representation theorem intended to characterize the preference conditions under which this measurement process is applicable. There are several features of Ramsey’s formal system which make it attractive and worth developing. However, in specifying his measurement process and his axioms, Ramsey introduces the notion of an ethically neutral proposition, the assumed existence of which plays a key role throughout Ramsey’s system. A number of later representation theorems have also appealed to ethically neutral propositions. The notion of ethical neutrality has often been called into question—in fact, there seem to be good reasons to suppose that no ethically neutral propositions exist. In this paper, I present several new, Ramsey-inspired representation theorems that avoid any appeal to ethical neutrality. These theorems preserve the benefits of Ramsey’s system, without paying the cost of ethical neutrality.
A Representation Theorem for Frequently Irrational Agents | 2017, Journal of Philosophical Logic 46 (5): 467-506
The published version is available here
Abstract: The standard representation theorem for expected utility theory tells us that if a subject's preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities--and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility (given her preferences). However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being (amongst other things) always probabilistically coherent with infinitely precise degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board--that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles.
Probabilism, Representation Theorems, and Whether Deliberation Crowds out Prediction | 2017, Erkenntnis 82 (2): 379-399
The published version is available here
Abstract: Decision-theoretic representation theorems have been developed and appealed to in the service of two important philosophical projects: (i) in attempts to characterise credences in terms of preferences, and (ii) in arguments for probabilism. Theorems developed within the formal framework that Savage developed have played an especially prominent role here. I argue that the use of these 'Savagean' theorems create significant difficulties for both projects, but particularly the latter. The origin of the problem directly relates to the question of whether we can have credences regarding acts currently under consideration and the consequences which depend on those acts; I argue that such credences are possible. Furthermore, I argue that attempts to use Jeffrey's non-Savagean theorem (and similar theorems) in the service of these two projects may not fare much better.
Epistemic Two-Dimensionalism and Arguments from Epistemic Misclassification | 2013, Australasian Journal of Philosophy 91 (2): 375-389 (With Kelvin McQueen and Clas Weber).
The published version is available here
Abstract: Epistemic Two-Dimensional Semantics (E2D) claims that expressions have a counterfactual intension and an epistemic intension. Epistemic intensions reflect cognitive significance such that sentences with necessary epistemic intensions are a priori. We defend E2D against an influential line of criticism: arguments from epistemic misclassification. We focus in particular on the arguments of Speaks [2010] and Schroeter [2005]. Such arguments conclude that E2D is mistaken from (i) the claim that E2D is committed to classifying certain sentences as a priori and (ii) the claim that such sentences are a posteriori. We aim to show that these arguments are unsuccessful as (i) and (ii) undercut each other. One must distinguish the general framework of E2D from a specific implementation of it. The framework is flexible enough to avoid commitment to the apriority of any particular sentence; only specific implementations are so committed. Arguments from epistemic misclassification are therefore better understood as arguments for favouring one implementation of E2D over another, rather than as refutations of E2D.
Recent Work on Decision Theory | Invited for Analysis Reviews
Abstract: A review of some major topics of debate in normative decision theory from circa 2007 to 2019. Topics discussed include the ongoing debate between causal and evidential decision theory, decision instability, risk-weighted expected utility theory, decision-making with incomplete preferences, and decision-making with imprecise credences. (This is the slightly longer 'original draft'.)
The open-access published version is also available here
Abstract: One response to the problems of logical omniscience is to extend the space of possible worlds to include impossible worlds. It is natural to think that essentially the same strategy can be applied to standard probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. With only very weak assumptions about the space of worlds, most of the propositions which can be constructed from possible and impossible worlds are in an important sense inexpressible; whereas the probabilistic model seems committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic.
Ramsey Without Ethical Neutrality | 2017, Mind 126 (501): 1-51
The published version is available here
Abstract: Frank Ramsey’s ‘Truth and Probability’ sketches a proposal for the empirical measurement of credences, along with a corresponding set of axioms for a (somewhat incomplete) representation theorem intended to characterize the preference conditions under which this measurement process is applicable. There are several features of Ramsey’s formal system which make it attractive and worth developing. However, in specifying his measurement process and his axioms, Ramsey introduces the notion of an ethically neutral proposition, the assumed existence of which plays a key role throughout Ramsey’s system. A number of later representation theorems have also appealed to ethically neutral propositions. The notion of ethical neutrality has often been called into question—in fact, there seem to be good reasons to suppose that no ethically neutral propositions exist. In this paper, I present several new, Ramsey-inspired representation theorems that avoid any appeal to ethical neutrality. These theorems preserve the benefits of Ramsey’s system, without paying the cost of ethical neutrality.
A Representation Theorem for Frequently Irrational Agents | 2017, Journal of Philosophical Logic 46 (5): 467-506
The published version is available here
Abstract: The standard representation theorem for expected utility theory tells us that if a subject's preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities--and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility (given her preferences). However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being (amongst other things) always probabilistically coherent with infinitely precise degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board--that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles.
Probabilism, Representation Theorems, and Whether Deliberation Crowds out Prediction | 2017, Erkenntnis 82 (2): 379-399
The published version is available here
Abstract: Decision-theoretic representation theorems have been developed and appealed to in the service of two important philosophical projects: (i) in attempts to characterise credences in terms of preferences, and (ii) in arguments for probabilism. Theorems developed within the formal framework that Savage developed have played an especially prominent role here. I argue that the use of these 'Savagean' theorems create significant difficulties for both projects, but particularly the latter. The origin of the problem directly relates to the question of whether we can have credences regarding acts currently under consideration and the consequences which depend on those acts; I argue that such credences are possible. Furthermore, I argue that attempts to use Jeffrey's non-Savagean theorem (and similar theorems) in the service of these two projects may not fare much better.
Epistemic Two-Dimensionalism and Arguments from Epistemic Misclassification | 2013, Australasian Journal of Philosophy 91 (2): 375-389 (With Kelvin McQueen and Clas Weber).
The published version is available here
Abstract: Epistemic Two-Dimensional Semantics (E2D) claims that expressions have a counterfactual intension and an epistemic intension. Epistemic intensions reflect cognitive significance such that sentences with necessary epistemic intensions are a priori. We defend E2D against an influential line of criticism: arguments from epistemic misclassification. We focus in particular on the arguments of Speaks [2010] and Schroeter [2005]. Such arguments conclude that E2D is mistaken from (i) the claim that E2D is committed to classifying certain sentences as a priori and (ii) the claim that such sentences are a posteriori. We aim to show that these arguments are unsuccessful as (i) and (ii) undercut each other. One must distinguish the general framework of E2D from a specific implementation of it. The framework is flexible enough to avoid commitment to the apriority of any particular sentence; only specific implementations are so committed. Arguments from epistemic misclassification are therefore better understood as arguments for favouring one implementation of E2D over another, rather than as refutations of E2D.
Recent Work on Decision Theory | Invited for Analysis Reviews
Abstract: A review of some major topics of debate in normative decision theory from circa 2007 to 2019. Topics discussed include the ongoing debate between causal and evidential decision theory, decision instability, risk-weighted expected utility theory, decision-making with incomplete preferences, and decision-making with imprecise credences. (This is the slightly longer 'original draft'.)
Works in Progress
Unawareness and Implicit Belief: Possible Worlds Models of Informational Content | Conditionally accepted
Abstract: Possible worlds models of belief have difficulties accounting for unawareness, the inability an agent may have to entertain (and hence believe) certain propositions. Accommodating the possibility of unawareness is important for adequately modelling epistemic states, and representing the informational content to which agents have access given their explicit beliefs. In this paper, I use neighbourhood structures to develop an original multi-agent model of explicit belief, awareness, and informational content, along with an associated sound and complete axiom system. I also defend the model against the seminal impossibility result of Dekel et al. (1998), according to which three intuitive conditions preclude non-trivial unawareness on any `standard' model of knowledge or belief.
'Ramseyfying' Probabilistic Comparativism | Under revise & resubmit
Abstract: Comparativism is the view that the fundamental doxastic state consists in comparative probability judgments (e.g., judging p to be more likely than q), with numerical degrees of belief (e.g., believing p to some numerical degree x) seen as theoretical tools used to represent and reason about systems of comparative judgements that satisfy a minimum standard of rationality. In this paper, I develop a version of comparativism inspired by a suggestion made by Frank Ramsey in his `Probability and Partial Belief' (1929). I show how this `Ramseyan comparativism' can be used to weaken the (unrealistically strong) conditions of probabilistic coherence that comparativism traditionally relies on.
Betting Against the Zen Monk: On Preferences and Belief | Under review
Abstract: 'The degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it' (Ramsey 1931). that is, I think that the connection between partial beliefs and preferences is key to understanding what partial beliefs are, and how they're measured. But this view is not as popular as it once was: nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, or unpalatably anti-realist. Furthermore, cases like Eriksson & Hajek's (2007) preferenceless Zen monk have suggested to many philosophers that any account of partial belief that ties them too closely to preferences is hopelessly flawed. Using the Zen monk as a stalking horse, in this paper I provide a defence of preference-centric accounts of partial belief.
Comparativism and the Measurement of Partial Belief | Under review
Abstract: According to comparativism, an agent's beliefs consist fundamentally in a system of purely ordinal judgements of relative probability. (For example, the judgement that p is more probable than q, or that p and q are as probable as one another.) In this paper, I put forward three general challenges for comparativism, relating to its capacity to draw enough distinctions between doxastic states, its capacity to handle common instances of irrationality, and its capacity to handle interpersonal comparisons.
Don't Stop Believing: On the Rationality of Inquiry into the Moral Error Theory (with Jessica Isserow) | Under review; email me for a draft
Abstract: It's natural to think that there's value to improving the accuracy of one's beliefs. If beliefs are a map by which we steer our efforts to bring the world in line with our preferences, then, all else being equal, we should want a more accurate map. However, the world could be structured so as to punish learning with respect to certain topics; i.e., by coming to learn certain things, your situation as a whole may end up worse than it would have been otherwise. In this paper, we investigate whether the world is structured so as to punish learning specifically with respect to the moral error theory. We ask: If an ordinary human agent, with ordinary human preferences, had the option to learn whether the error theory is true, should she take it? We will argue that she should not.
Credal Sets and Strength of Belief | It'll be done when it's done
Abstract: I distinguish between several common ways to interpreting credal sets (i.e., sets of probability functions), which are often conflated--the supervaluational, interval, and intersectional interpretations. I discuss each in relation to the idea that the strength of a belief is a psychological quantity. I show that on the intersectional interpretation, but not on the supervaluational or interval interpretations, a number of very intuitive claims about strengths of belief become difficult to maintain, and the intersectional interpretation requires a more radical picture of the mind than is often realised by its proponents. Finally, I suggest the need for generalising the credal sets model, along with a mixed interval-supervaluational interpretation of the resulting model.
Abstract: Possible worlds models of belief have difficulties accounting for unawareness, the inability an agent may have to entertain (and hence believe) certain propositions. Accommodating the possibility of unawareness is important for adequately modelling epistemic states, and representing the informational content to which agents have access given their explicit beliefs. In this paper, I use neighbourhood structures to develop an original multi-agent model of explicit belief, awareness, and informational content, along with an associated sound and complete axiom system. I also defend the model against the seminal impossibility result of Dekel et al. (1998), according to which three intuitive conditions preclude non-trivial unawareness on any `standard' model of knowledge or belief.
'Ramseyfying' Probabilistic Comparativism | Under revise & resubmit
Abstract: Comparativism is the view that the fundamental doxastic state consists in comparative probability judgments (e.g., judging p to be more likely than q), with numerical degrees of belief (e.g., believing p to some numerical degree x) seen as theoretical tools used to represent and reason about systems of comparative judgements that satisfy a minimum standard of rationality. In this paper, I develop a version of comparativism inspired by a suggestion made by Frank Ramsey in his `Probability and Partial Belief' (1929). I show how this `Ramseyan comparativism' can be used to weaken the (unrealistically strong) conditions of probabilistic coherence that comparativism traditionally relies on.
Betting Against the Zen Monk: On Preferences and Belief | Under review
Abstract: 'The degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it' (Ramsey 1931). that is, I think that the connection between partial beliefs and preferences is key to understanding what partial beliefs are, and how they're measured. But this view is not as popular as it once was: nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, or unpalatably anti-realist. Furthermore, cases like Eriksson & Hajek's (2007) preferenceless Zen monk have suggested to many philosophers that any account of partial belief that ties them too closely to preferences is hopelessly flawed. Using the Zen monk as a stalking horse, in this paper I provide a defence of preference-centric accounts of partial belief.
Comparativism and the Measurement of Partial Belief | Under review
Abstract: According to comparativism, an agent's beliefs consist fundamentally in a system of purely ordinal judgements of relative probability. (For example, the judgement that p is more probable than q, or that p and q are as probable as one another.) In this paper, I put forward three general challenges for comparativism, relating to its capacity to draw enough distinctions between doxastic states, its capacity to handle common instances of irrationality, and its capacity to handle interpersonal comparisons.
Don't Stop Believing: On the Rationality of Inquiry into the Moral Error Theory (with Jessica Isserow) | Under review; email me for a draft
Abstract: It's natural to think that there's value to improving the accuracy of one's beliefs. If beliefs are a map by which we steer our efforts to bring the world in line with our preferences, then, all else being equal, we should want a more accurate map. However, the world could be structured so as to punish learning with respect to certain topics; i.e., by coming to learn certain things, your situation as a whole may end up worse than it would have been otherwise. In this paper, we investigate whether the world is structured so as to punish learning specifically with respect to the moral error theory. We ask: If an ordinary human agent, with ordinary human preferences, had the option to learn whether the error theory is true, should she take it? We will argue that she should not.
Credal Sets and Strength of Belief | It'll be done when it's done
Abstract: I distinguish between several common ways to interpreting credal sets (i.e., sets of probability functions), which are often conflated--the supervaluational, interval, and intersectional interpretations. I discuss each in relation to the idea that the strength of a belief is a psychological quantity. I show that on the intersectional interpretation, but not on the supervaluational or interval interpretations, a number of very intuitive claims about strengths of belief become difficult to maintain, and the intersectional interpretation requires a more radical picture of the mind than is often realised by its proponents. Finally, I suggest the need for generalising the credal sets model, along with a mixed interval-supervaluational interpretation of the resulting model.
Miscellaneous bits and pieces
1. Frank P. Ramsey: Partial Belief and Subjective Probability | Stanford Encyclopedia co-authored entry
2. 'Ramseyfying' Probabilistic Comparativism | Presented at F.E.W. 2018 and the 2019 APA Eastern Division Meeting.
3. Ramsey and the Ethically Neutral Proposition | Short unpublished exposition piece for the Leeds NatRep group.
4. The Instability of Savage's Foundations: The Constant Acts Problem | Short unpublished exposition piece for the Leeds NatRep group.
2. 'Ramseyfying' Probabilistic Comparativism | Presented at F.E.W. 2018 and the 2019 APA Eastern Division Meeting.
3. Ramsey and the Ethically Neutral Proposition | Short unpublished exposition piece for the Leeds NatRep group.
4. The Instability of Savage's Foundations: The Constant Acts Problem | Short unpublished exposition piece for the Leeds NatRep group.