## Published & Accepted Papers

**Impossible Worlds and Partial Belief**

**|***Forthcoming in Synthese*

**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.

**A Representation Theorem for Frequently Irrational Agents |**

**2017,**

*Journal of Philosophical Logic 46 (5): 467-506*

The published version is available at Springer, http://link.springer.com/article/10.1007%2Fs10992-016-9408-8

**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 at Springer, http://dx.doi.org/DOI:10.1007/s10670-016-9824-8

**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.

**Ramsey Without Ethical Neutrality: A New Representation Theorem |**2016,

*Mind 126 (501): 1-51*

The published version is available at the Oxford Journals site, http://mind.oxfordjournals.org/content/early/2016/10/13/mind.fzv180.full.pdf?keytype=ref&ijkey=y2Dzzq2PeqPKP1v

**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.

**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 at http://www.tandfonline.com/doi/abs/10.1080/00048402.2012.693112

**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.

## Works in Progress

**Unawareness, Possible Worlds, and the Informational Content of Belief |**

*Under Review*

**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. I argue that at least one of these conditions is implausible when applied to a model of belief. The plausibility of the two others rests on further questions regarding the scope and granularity of mental content; however, I also show that it's possible to strengthen these conditions while retaining non-trivial unawareness.

**Comparativism and the Measurement of Partial Belief |**

*Under Review*

**Abstract:**Comparativism is the view that comparative beliefs (e.g., believing p to be more likely than q) are more fundamental than partial beliefs (e.g., believing p to some degree x). In this paper, I first provide an account of how comparativism can make sense of quantitative comparisons (e.g., believing p twice as much as q), which generalises and improves upon the standard comparativist approach. This is achieved by means of a simple 'Ramseyan' representation theorem, with axioms demonstratively weaker than those to which comparativists usually appeal. I then provide a number of arguments against comparativism. Ultimately, there are too many things that we ought to be able to say about partial beliefs that we cannot say under any version of comparativism. Moreover, there are alternative ways to account for the measurement of belief that need not face the same limitations.

## Exposition Pieces

Below are three short-ish exposition pieces on different varieties of decision-theoretic representation theorem:

1. Ramsey and the Ethically Neutral Proposition

2. The Instability of Savage's Foundations: The Constant Acts Problem

3. Monoset Representation Theorems1. Ramsey and the Ethically Neutral Proposition

2. The Instability of Savage's Foundations: The Constant Acts Problem

3. Monoset Representation Theorems

## Doctoral Thesis

**Representation Theorems and the Grounds of Intentionality |**

*Australian National University*; submitted August 2015

**Abstract:**This work evaluates and defends the idea that decision-theoretic representation theorems can play an important role in showing how credences and utilities can be characterized, at least in large part, in terms of their connection with preferences (i.e.,

*characterizational representationism*). Roughly, a

*decision-theoretic representation theorem*tells us that if an agent’s preferences satisfy constraints, then that agent can be represented as maximising her expected utility under a unique set of credences (modelled by a credence function) and utilities (modelled by a utility function). Such theorems have been thought by many to not only show how credences and utilities can be understood

*via*their relation to preferences, but also to show how credences and utilities can be

*naturalized*—that is, characterized in wholly non-mental, non-intentional, and non-normative terms.

There are two broad questions that are addressed. The first (and more specific) question is whether any version of characterizational representationism, based on one of the representation theorems that are currently available to us, will be of much use in directly advancing the long-standing project of showing how representational mental states can exist within the natural world. I argue that there is no current representation theorem which lends itself to a naturalistic interpretation suitable for the goal of reducing facts about credences and utilities to a naturalistic base. A naturalistic variety of characterizational representationism will have to await a new kind of representation theorem, quite different from any which have yet been developed.

The second question is whether characterizational representationism in any form (naturalistic or otherwise) is a viable position—whether, in particular, there is any value to developing representation theorems with the goal of characterizing what it is to have credences and utilities. Of this I am less skeptical. In particular, I defend a weak version of characterizational representationism against a number of philosophical critiques. With that in mind, I also argue that there are serious drawbacks with the particular theorems that decision theorists have developed thus far; particularly those which have been developed within the four basic formal frameworks developed by Savage, Anscombe and Aumann, Jeffrey, and Ramsey.

In the final part of the work, however, I develop a new representation theorem, which I argue goes some of the way towards resolving the most troubling issues associated with earlier theorems. I first show how to construct a theorem which is ontologically similar to Jeffrey’s, but formally more similar to Ramsey’s— but which does not suffer from the infamous problems associated with Ramsey’s notion of ethical neutrality, and which has stronger uniqueness results than Jeffrey’s theorem. Furthermore, it is argued that the new theorem’s preference conditions are descriptively reasonable, even for ordinary agents, and that the credence and utility functions associated with this theorem are capable of representing a wide range of non-ideal agents—including those who: (i) might have credences and utilities only towards non-specific propositions, (ii) are probabilistically incoherent, (iii) are deductively fallible, and (iv) have distinct credences and utilities towards logically equivalent propositions