A Model-Invariant Theory of Causation

2021. The Philosophical Review 130 (1): 45–96

I provide a theory of causation within the causal modeling framework. In contrast to most of its predecessors, this theory is model-invariant in the following sense: if the theory says that C caused (didn’t cause) E in a causal model, M, then it will continue to say that C caused (didn’t cause) E once we’ve removed an inessential variable from M. I suggest that, if this theory is true, then we should understand a cause as something which transmits deviant or non-inertial behavior to its effect.

A Theory of Structural Determination

2016. Philosophical Studies 173 (1): 159–186.

While structural equations modeling is increasingly used in philosophical theorizing about causation, it remains unclear what it takes for a particular structural equations model to be correct. To the extent that this issue has been addressed, the consensus appears to be that it takes a certain family of causal counterfactuals being true. I argue that this account faces difficulties in securing the independent manipulability of the structural determination relations represented in a correct structural equations model. I then offer an alternate understanding of structural determination, and I demonstrate that this theory guarantees that structural determination relations are independently manipulable. The account provides a straightforward way of understanding hypothetical interventions, as well as a criterion for distinguishing hypothetical changes in the values of variables which constitute interventions from those which do not. It additionally affords a semantics for causal counterfactual conditionals which is able to yield a clean solution to a problem case for the standard ‘closest possible world’ semantics.

The Emergence of Causation

2015. The Journal of Philosophy 112 (6): 261–-308.

Several philosophers have embraced the view that high-level events—events like Zimbabwe’s monetary policy and its hyper-inflation—are causally related if their corresponding low-level, fundamental physical events are causally related. I dub the view which denies this without denying that high-level events are ever causally related causal emergentism. Several extant philosophical theories of causality entail causal emergentism, while others are inconsistent with the thesis. I illustrate this with David Lewis’s two theories of causation, one of which entails causal emergentism, the other of which entails its negation. I then argue for causal emergentism on the grounds that it provides the only adequate means of squaring the apparent plenitude of causal relations between low-level events with the apparent scarcity of causal relations between high-level events. This tension between the apparent abundance of low-level causation and the apparent scarcity of high-level causation has been noted before. However, it has been thought that various theses about the semantics or the pragmatics of causal claims could be used to ameliorate the tension without going in for causal emergentism. I argue that none of the suggested semantic or pragmatic strategies meet with success, and recommend emergentist theories of causality in their stead. As Lewis’s 1973 account illustrates, causal emergentism is consistent with the thesis that all facts reduce to microphysical facts.


A Subjectivist’s Guide to Deterministic Chance

2021. Synthese 198: 4339–4372.

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.


Escaping the Cycle

To appear in Mind.

I present a decision problem in which causal decision theory appears to violate the independence of irrelevant alternatives (IIA) and normal-form extensive-form equivalence (NEE). I show that these violations lead to exploitable behavior and long-run poverty. These consequences appear damning, but I urge caution. Causalists can dispute the charge that they violate IIA and NEE in this case by carefully specifying when options in different decision problems are similar enough to be counted as the same.

Riches and Rationality

2021. The Australasian Journal of Philosophy 99 (1): 114–129.

A one-boxer, Erica, and a two-boxer, Chloe, engage in a familiar debate. The debate begins with Erica asking Chloe: ‘If you’re so smart, then why ain’cha rich?’. As the debate progresses, Chloe is led to endorse a novel causalist theory of rational choice. This new theory allows Chloe to forge a connection between rational choice and long-run riches. In brief: Chloe concludes that it is not long-run wealth but rather long-run wealth creation which is symptomatic of rationality.

The Causal Decision Theorist’s Guide to Managing the News

2020. The Journal of Philosophy 117 (3): 117–149.

According to orthodox causal decision theory, performing an action can give you information about factors outside of your control, but you should not take this information into account when deciding what to do. Causal decision theorists caution against an irrational policy of ‘managing the news’. But, by providing information about factors outside of your control, performing an act can give you two, importantly different, kinds of good news. It can tell you that the world in which you find yourself is good in ways you can’t control, and it can also tell you that the act itself is in a position to make the world better. While the first kind of news does not speak in favor of performing an act, I believe that the second kind of news does. I present a revision of causal decision theory which advises you to manage the news about the good you stand to promote, while ignoring news about the good the world has provided for you.

Review of Newcomb’s Problem, edited by Arif Ahmed

2020. Economics & Philosophy 36 (1), 171–176.


Updating for Externalists

To Appear in Noûs.

The externalist says that your evidence could fail to tell you what evidence you do or not do have. In that case, it could be rational for you to be uncertain about what your evidence is. This is a kind of uncertainty which orthodox Bayesian epistemology has difficulty modeling. For, if externalism is correct, then the orthodox Bayesian learning norms of conditionalization and reflection are inconsistent with each other. I recommend that an externalist Bayesian reject conditionalization. In its stead, I provide a new theory of rational learning for the externalist. I defend this theory by arguing that its advice will be followed by anyone whose learning dispositions maximize expected accuracy. I then explore some of this theory’s consequences for the rationality of epistemic akrasia, peer disagreement, undercutting defeat, and uncertain evidence.

Learning and Value Change

2019. Philosophers’ Imprint 19 (29): 1–22.

Accuracy-first accounts of rational learning attempt to vindicate the intuitive idea that, while rationally-formed belief need not be true, it is nevertheless likely to be true. To this end, they attempt to show that the Bayesian’s rational learning norms are a consequence of the rational pursuit of accuracy. Existing accounts fall short of this goal, for they presuppose evidential norms which are not and cannot be vindicated in terms of the single-minded pursuit of accuracy. I propose an alternative account, according to which learning experiences rationalize changes in the way you value accuracy, which in turn rationalize changes in belief. I show that this account is capable of vindicating the Bayesian’s rational learning norms in terms of the single-minded pursuit of accuracy, so long as accuracy is rationally valued.

Diachronic Dutch Books and Evidential Import

2019. Philosophy and Phenomenological Research 99 (1): 49–80.

A handful of well-known arguments (the ‘diachronic Dutch book arguments’) rely upon theorems establishing that, in certain circumstances, you are immune from sure monetary loss (you are not ‘diachronically Dutch bookable’) if and only if you adopt the strategy of conditionalizing (or Jeffrey conditionalizing) on whatever evidence you happen to receive. These theorems require non-trivial assumptions about which evidence you might acquire—in the case of conditionalization, the assumption is that, if you might learn that e, then it is not the case that you might learn something else that is consistent with e. These assumptions may not be relaxed. When they are, not only will non-(Jeffrey) conditionalizers be immune from diachronic Dutch bookability, but (Jeffrey) conditionalizers will themselves be diachronically Dutch bookable. I argue: 1) that there are epistemic situations in which these assumptions are violated; 2) that this reveals a conflict between the premise that susceptibility to sure monetary loss is irrational, on the one hand, and the view that rational belief revision is a function of your prior beliefs and the acquired evidence alone, on the other; and 3) that this inconsistency demonstrates that diachronic Dutch book arguments for (Jeffrey) conditionalization are invalid.

No One Can Serve Two Epistemic Masters

2016. Philosophical Studies 175 (10): 2389–2398..

Consider two epistemic experts–for concreteness, let them be two weather forecasters. Suppose that you aren’t certain that they will issue identical forecasts, and you would like to proportion your degrees of belief to theirs in the following way: first, conditional on either’s forecast of rain being x, you’d like your own degree of belief in rain to be x. Secondly, conditional on them issuing different forecasts of rain, you’d like your own degree of belief in rain to be some weighted average of the forecast of each. Finally, you’d like your degrees of belief to be given by an orthodox probability measure. Moderate ambitions, all. But you can’t always get what you want.

How to Learn from Theory-Dependent Evidence

2014. The British Journal for the Philosophy of Science 65 (3): 493–519.

Weisberg provides an argument that neither conditionalization nor Jeffrey conditionalization is capable of accommodating the holist’s claim that beliefs acquired directly from experience can suffer undercutting defeat. I diagnose this failure as stemming from the fact that neither conditionalization nor Jeffrey conditionalization give any advice about how to rationally respond to theory-dependent evidence, and I propose a novel updating procedure that does tell us how to respond to evidence like this. This holistic updating rule yields conditionalization as a special case in which our evidence is entirely theory independent. Note: I revise and further generalize this theory in Updating for Externalists.


These papers are still being revised. Feedback is very much appreciated.

Causal Counterfactuals without Miracles or Backtracking

If the laws are deterministic, then standard theories of counterfactuals are forced to reject at least one of the following conditionals: 1) had you chosen differently, there would not have been a violation of the laws of nature; and 2) had you chosen differently, the initial conditions of the universe would not have been different. On the relevant readings—where we hold fixed factors causally independent of your choice—both of these conditionals appear true. And rejecting either one leads to trouble for philosophical theories which rely upon counterfactual conditionals—like, for instance, causal decision theory. Here, I outline a semantics for counterfactual conditionals which allows us to accept both (1) and (2). And I discuss how this semantics deals with objections to causal decision theory from Arif Ahmed.

Decision and Foreknowledge

My topic is how to make decisions when you possess foreknowledge of the consequences of your choice. Many have thought that these kinds of decisions pose a distinctive and novel problem for causal decision theory (CDT). My thesis is that foreknowledge poses no new problems for CDT. Some of the purported problems are not problems. Others are problems, but they are not problems for CDT. Rather, they are problems for our theories of subjunctive supposition. Others are problems, but they are not new problems. They are old problems transposed into a new key. Nonetheless, decisions made with foreknowledge teach us important lessons about the instrumental value of our choices. Once we’ve appreciated these lessons, we are left with a version of CDT which faces no novel threats from foreknowledge.

Video of a talk on this material is available here

Dependence, Defaults, and Needs

We are sometimes inclined to deny that c caused e on the grounds that c “didn’t make any difference” to whether e, or that e was “bound to happen anyway”, whether or not c. Though this justification is incredibly natural, the philosophical study of causation has taught many of us to regard it with suspicion. For we’ve been taught to equate c’s “making a difference” to whether e with e counterfactually depending upon whether c. And we’ve been taught to equate being “bound to happen anyway” with a lack of counterfactual dependence. Since causation doesn’t imply counterfactual dependence, this reason for denying that c caused e looks suspect. Here, I provide a different way of understanding what it takes for c to make a difference to whether e, and what it takes for e to be bound to happen anyway, whether or not c. I then integrate this notion into a theory of causation. According to this theory, if e was bound to happen whether or not c, then e was not caused by c.

Expert Deference De Se

Principles of expert deference say that you should align your credences with those of an expert. This expert could be your doctor, the objective chances, or your future self, after you’ve learnt something new. These kinds of principles face difficulties in cases in which you are uncertain of the truth-conditions of the thoughts in which you invest credence, as well as cases in which the thoughts have different truth-conditions for you and the expert. For instance, you shouldn’t defer to your doctor by aligning your credence in the de se thought ‘I am sick’ with the doctor’s credence in that same de se thought. Here, I generalise principles of expert deference to handle these kinds of problem cases.

Chance Deference De Se

Principles of chance deference face two kinds of problems. In the first place, they face difficulties with a priori knowable contingencies. In the second place, they face difficulties in cases where you’ve lost track of the time. I provide a generalisation of these principles which handles these problem cases. The generalisation has surprising consequences for Adam Elga’s Sleeping Beauty puzzle.

Video of a talk I gave on this material is available here

It Can Be Irrational to Knowingly Choose the Best

‘Prediction-insensitive’ causalists say that which choice is rational does not depend upon how likely you think you are to choose any of your available options. Jack Spencer presents an argument against prediction-insensitive causalists. He points out that they are forced to deny this principle: ‘‘If you know that you will choose an option, x, and you know that x is better than every other option available to you, then it is permissible for you to choose x.’’ Spencer is correct that prediction-insensitive causalists must reject this principle. However, he is incorrect insofar as he suggests that he and orthodox causalists are free to accept it. Both orthodox CDT and Spencer’s own theory of rational choice are incompatible with the principle as well. It may be surprising to realise, but all are agreed: it can be irrational to knowingly choose the best.

The Principle of Indifference and the Principal Principle are Incompatible

The Principle of Indifference (POI) says that, in the absence of evidence, you should distribute your credences evenly. The Principal Principle (PP) says that, in the absence of evidence, you should align your credences with the chances. Richard Pettigrew (2016) appears to accept both the PP and the POI. However, the POI and the PP are incompatible. Abiding the POI means violating the PP. So Bayesians cannot accept both principles; they must choose which, if either, to endorse.