Jon Williamson

This paper highlights the role of Lewis’ Principal Principle and certain auxiliary conditions on admissibility as serving to explicate normal informal standards of what is reasonable. These considerations motivate the presuppositions of the argument that the Principal Principle implies the Principle of Indifference, put forward by Hawthorne et al.. They also suggest a line of response to recent criticisms of that argument, due to Pettigrew and Titelbaum and Hart, 621–632, 2020). The paper also shows that related concerns of Hart and Titelbaum, 252–262, 2015) do not undermine the argument of Hawthorne et al..

The EBM+ programme is an attempt to improve the way in which present-day evidence-based medicine (EBM) assesses causal claims: according to EBM+, mechanistic studies should be scrutinised alongside association studies. This paper addresses two worries about EBM+: (i) that it is not feasible in practice, and (ii) that it is too malleable, i.e., its results depend on subjective choices that need to be made in order to implement the procedure. Several responses to these two worries are considered and evaluated. The paper also discusses the question of whether we should have confidence in medical interventions, in the light of Stegenga's arguments for medical nihilism.

The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain: applying it to finite sublanguages and taking the pointwise limit of the resulting probabilities as the size n of the sublanguage increases; selecting a probability function on the language as a whole whose entropy on finite sublanguages of size n is not dominated by that of any other probability function for sufficiently large n. The entropy-limit conjecture says that, where these two approaches yield determinate probabilities, the two methods yield the same probabilities. If this conjecture is found to be true, it would provide a boost to the project of seeking a single canonical inductive logic—a project which faltered when Carnap's attempts in this direction succeeded only in determining a continuum of inductive methods. The truth of the conjecture would also boost the project of providing a canonical characterisation of normal or default models of first-order theories. Hitherto, the entropy-limit conjecture has been verified for languages which contain only unary predicate symbols and also for the case in which the constraints can be captured by a categorical statement of quantifier complexity. This paper shows that the entropy-limit conjecture also holds for categorical statements of complexity, for various non-categorical constraints, and in certain other general situations.

This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some support to this version of objective Bayesianism.

While the importance of mechanisms in determining causality in medicine is currently the subject of active debate, the role of mechanistic reasoning in clinical practice has received far less attention. In this paper we look at this question in the context of the treatment of a particular individual, and argue that evidence of mechanisms is indeed key to various aspects of clinical practice, including assessing population-level research reports, diagnostic as well as therapeutic decision making, and the assessment of treatment effects. We use the pulmonary condition bronchiectasis as a source of examples of the importance of mechanistic reasoning to clinical practice.

The use of evidence in medicine is something we should continuously seek to improve. This book seeks to develop our understanding of evidence of mechanism in evaluating evidence in medicine, public health, and social care; and also offers tools to help implement improved assessment of evidence of mechanism in practice. In this way, the book offers a bridge between more theoretical and conceptual insights and worries about evidence of mechanism and practical means to fit the results into evidence assessment procedures.

The teratogenicity of the Zika virus was considered established in 2016, and is an interesting case because three different sets of causal criteria were used to assess teratogenicity. This paper appeals to the thesis of Russo and Williamson (2007) to devise an epistemological framework that can be used to compare and evaluate sets of causal criteria. The framework can also be used to decide when enough criteria are satisfied to establish causality. Arguably, the three sets of causal criteria considered here offer only a rudimentary assessment of mechanistic studies, and some suggestions are made as to alternative ways to establish causality.

The role of mechanistic evidence tends to be under-appreciated in current evidencebased medicine (EBM), which focusses on clinical studies, tending to restrict attention to randomized controlled studies (RCTs) when they are available. The EBM+ programme seeks to redress this imbalance, by suggesting methods for evaluating mechanistic studies alongside clinical studies. Drug approval is a problematic case for the view that mechanistic evidence should be taken into account, because RCTs are almost always available. Nevertheless, we argue that mechanistic evidence is central to all the key tasks in the drug approval process: in drug discovery and development; assessing pharmaceutical quality; devising dosage regimens; assessing efficacy, harms, external validity, and cost-effectiveness; evaluating adherence; and extending product licences. We recommend that, when preparing for meetings in which any aspect of drug approval is to be discussed, mechanistic evidence should be systematically analysed and presented to the committee members alongside analyses of clinical studies.

Systems medicine is a promising new paradigm for discovering associations, causal relationships and mechanisms in medicine. But it faces some tough challenges that arise from the use of big data: in particular, the problem of how to integrate evidence and the problem of how to structure the development of models. I argue that objective Bayesian models offer one way of tackling the evidence integration problem. I also offer a general methodology for structuring the development of models, within which the objective Bayesian approach fits rather naturally.

This paper presents a new argument for the Principle of Indifference. This argument can be thought of in two ways: as a pragmatic argument, justifying the principle as needing to hold if one is to minimise worst-case expected loss, or as an epistemic argument, justifying the principle as needing to hold in order to minimise worst-case expected inaccuracy. The question arises as to which interpretation is preferable. I show that the epistemic argument contradicts Evidentialism and suggest that the relative plausibility of Evidentialism provides grounds to prefer the pragmatic interpretation. If this is right, it extends to a general preference for pragmatic arguments for the Principle of Indifference, and also to a general preference for pragmatic arguments for other norms of Bayesian epistemology.

This paper presents a new argument for the Principle of Indifference. This argument can be thought of in two ways: as a pragmatic argument, justifying the principle as needing to hold if one is to minimise worst-case expected loss, or as an epistemic argument, justifying the principle as needing to hold in order to minimise worst-case expected inaccuracy. The question arises as to which interpretation is preferable. I show that the epistemic argument contradicts Evidentialism and suggest that the relative plausibility of Evidentialism provides grounds to prefer the pragmatic interpretation. If this is right, it extends to a general preference for pragmatic arguments for the Principle of Indifference, and also to a general preference for pragmatic arguments for other norms of Bayesian epistemology.

Russo and Williamson put forward the following thesis: in order to establish a causal claim in medicine, one normally needs to establish both that the putative cause and putative effect are appropriately correlated and that there is some underlying mechanism that can account for this correlation. I argue that, although the Russo-Williamson thesis conflicts with the tenets of present-day evidence-based medicine, it offers a better causal epistemology than that provided by present-day EBM because it better explains two key aspects of causal discovery. First, the thesis better explains the role of clinical studies in establishing causal claims. Second, it yields a better account of extrapolation.

We consider the use of interventions for resolving a problem of unidentified statistical models. The leading examples are from latent variable modelling, an influential statistical tool in the social sciences. We first explain the problem of statistical identifiability and contrast it with the identifiability of causal models. We then draw a parallel between the latent variable models and Bayesian networks with hidden nodes. This allows us to clarify the use of interventions for dealing with unidentified statistical models. We end by discussing the philosophical and methodological import of our result.

The Recursive Bayesian Net formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular how a simple two-level RBN can be used to model a mechanism in cancer science. The higher level of our model contains variables at the clinical level, while the lower level maps the structure of the cell's mechanism for apoptosis.

1, . . . , n | ≈ ψ ? Here 1, . . . , n, ψ are premisses of some formal language, such as a propositional language or a predicate language. | ≈ is an entailment relation: the entailment holds if all models of the premisses also satisfy the conclusion, where the logic provides some suitable notion of ‘model’ and ‘satisfy’. Proof theory is normally invoked to answer a question of this form: one tries to prove the conclusion from the premisses in a finite sequence of steps, where at each step one invokes an axiom or applies a rule of inference

How ought we learn causal relationships? While Popper advocated a hypothetico-deductive logic of causal discovery, inductive accounts are currently in vogue. Many inductive approaches depend on the causal Markov condition as a fundamental assumption. This condition, I maintain, is not universally valid, though it is justifiable as a default assumption. In which case the results of the inductive causal learning procedure must be tested before they can be accepted. This yields a synthesis of the hypothetico-deductive and inductive accounts, which forms the focus of this paper. I discuss the justification of this synthesis and draw an analogy between objective Bayesianism and the account of causal learning presented here.

Causal claims in biomedical contexts are ubiquitous albeit they are not always made explicit. This paper addresses the question of what causal claims mean in the context of disease. It is argued that in medical contexts causality ought to be interpreted according to the epistemic theory. The epistemic theory offers an alternative to traditional accounts that cash out causation either in terms of “difference-making” relations or in terms of mechanisms. According to the epistemic approach, causal claims tell us about which inferences (e.g., diagnoses and prognoses) are appropriate, rather than about the presence of some physical causal relation analogous to distance or gravitational attraction. It is shown that the epistemic theory has important consequences for medical practice, in particular with regard to evidence-based causal assessment

The need for a coherent answer to this question has become increasingly urgent in the past few years, particularly in the field of artificial intelligence. There, both logical and probabilistic techniques are routinely applied in an attempt to solve complex problems such as parsing natural language and determining the way proteins fold. The hope is that some combination of logic and probability will produce better solutions. After all, both natural language and protein molecules have some structure that admits logical representation and reasoning; yet inherent uncertainties also demand the use of probabilistic methods: this structure is only partially known and does not in any case fully determine a solution—context or environment also play a role.

this paper we argue that the formalism can also be applied to modelling the hierarchical structure of physical mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations are vital for prediction, explanation and control respectively, a recursive Bayesian net can be applied to all these tasks. We show how a Recursive Bayesian Net can be used to model mechanisms in cancer science. The highest level of the proposed model will contain variables at the clinical level, while a middle level will map the structure of the DNA damage response mechanism and the lowest level will contain information about gene expression.

Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem.