Jon Williamson

I put forward several desiderata that a philosophical theory of causality should satisfy: it should account for the objectivity of causality, it should underpin formalisms for causal reasoning, it should admit a viable epistemology, it should be able to cope with the great variety of causal claims that are made, and it should be ontologically parsimonious. I argue that Nancy Cartwright’s dispositional account of causality goes part way towards meeting these criteria but is lacking in important respects. I go on to argue that my epistemic account, which ties causal relationships to an agent’s knowledge and ignorance, performs well in the light of the desiderata. Such an account, I claim, is all we require from a theory of causality.

This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics.

This introduction to the volume begins with a manifesto that puts forward two theses: first, that the sciences are the best place to turn in order to understand causality; second, that scientifically-informed philosophical investigation can bring something to the sciences too. Next, the chapter goes through the various parts of the volume, drawing out relevant background and themes of the chapters in those parts. Finally, the chapter discusses the progeny of the papers and identifies some next steps for research into causality in the sciences.

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.

We argue that the health sciences make causal claims on the basis of evidence both of physical mechanisms, and of probabilistic dependencies. Consequently, an analysis of causality solely in terms of physical mechanisms or solely in terms of probabilistic relationships, does not do justice to the causal claims of these sciences. Yet there seems to be a single relation of cause in these sciences - pluralism about causality will not do either. Instead, we maintain, the health sciences require a theory of causality that unifies its mechanistic and probabilistic aspects. We argue that the epistemic theory of causality provides the required unification.

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief . One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief.

In this paper, we compare the mechanisms of protein synthesis and natural selection. We identify three core elements of mechanistic explanation: functional individuation, hierarchical nestedness or decomposition, and organization. These are now well understood elements of mechanistic explanation in fields such as protein synthesis, and widely accepted in the mechanisms literature. But Skipper and Millstein have argued that natural selection is neither decomposable nor organized. This would mean that much of the current mechanisms literature does not apply to the mechanism of natural selection.We take each element of mechanistic explanation in turn. Having appreciated the importance of functional individuation, we show how decomposition and organization should be better understood in these terms. We thereby show that mechanistic explanation by protein synthesis and natural selection are more closely analogous than they appear—both possess all three of these core elements of a mechanism widely recognized in the mechanisms literature

Mechanisms have become much-discussed, yet there is still no consensus on how to characterise them. In this paper, we start with something everyone is agreed on – that mechanisms explain – and investigate what constraints this imposes on our metaphysics of mechanisms. We examine two widely shared premises about how to understand mechanistic explanation: (1) that mechanistic explanation offers a welcome alternative to traditional laws-based explanation and (2) that there are two senses of mechanistic explanation that we call ‘epistemic explanation’ and ‘physical explanation’. We argue that mechanistic explanation requires that mechanisms are both real and local. We then go on to argue that real, local mechanisms require a broadly active metaphysics for mechanisms, such as a capacities metaphysics

According to current hierarchies of evidence for EBM, evidence of correlation is always more important than evidence of mechanisms when evaluating and establishing causal claims. We argue that evidence of mechanisms needs to be treated alongside evidence of correlation. This is for three reasons. First, correlation is always a fallible indicator of causation, subject in particular to the problem of confounding; evidence of mechanisms can in some cases be more important than evidence of correlation when assessing a causal claim. Second, evidence of mechanisms is often required in order to obtain evidence of correlation. Third, evidence of mechanisms is often required in order to generalise and apply causal claims. While the EBM movement has been enormously successful in making explicit and critically examining one aspect of our evidential practice, i.e., evidence of correlation, we wish to extend this line of work to make explicit and critically examine a second aspect of our evidential practices: evidence of mechanisms.

The theory of belief revision and merging has recently been applied to judgement aggregation. In this paper I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a threestep strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the basis of this merged evidence base, by applying objective Bayesian theory. Third, determine which judgements are appropriate given these degrees of belief by applying a decision-theoretic account of rational judgement formation

This paper addresses questions about how the levels of causality (generic and single-case causality) are related. One question is epistemological: can relationships at one level be evidence for relationships at the other level? We present three kinds of answer to this question, categorised according to whether inference is top-down, bottom-up, or the levels are independent. A second question is metaphysical: can relationships at one level be reduced to relationships at the other level? We present three kinds of answer to this second question, categorised according to whether single-case relations are reduced to generic, generic relations are reduced to single-case, or the levels are independent. We then explore causal inference in autopsy. This is an interesting case study, we argue, because it refutes all three epistemologies and all three metaphysics. We close by sketching an account of causality that survives autopsy—the epistemic theory

Causal inference is perhaps the most important form of reasoning in the sciences. A panoply of disciplines, ranging from epidemiology to biology, from econometrics to physics, make use of probability and statistics to infer causal relationships. The social and health sciences analyse population-level data using statistical methods to infer average causal relations. In diagnosis of disease, probabilistic statements are based on population-level causal knowledge combined with knowledge of a particular person’s symptoms. For the physical sciences, the Salmon-Dowe account develops an analysis of causation based on the notion of process and interaction. In artificial intelligence, the development of graphical methods has leant impetus to a probabilistic analysis of causality. The biological sciences use probabilistic methods to look for evolutionary causes of the state of a current species and to look for genetic causal factors. This variegated situation raises at least two fundamental philosophical issues: about the relation between causality and probability, and about the interpretation of probability in causal analysis. In this book we bring philosophers and scientists together to discuss the relation between causality and probability, and the applications of these concepts within the sciences.

How is probability related to logic? Should probability and logic be combined? If so, how? Bayesianism tells us we ought to reason probabilistically. In that sense, probability theory is logic. How then does probability theory relate to classical logic and the various non-classical logics that also stake a claim on normative reasoning? Is probability theory to be preferred over other logics or vice versa? Is probability theory to be used in some situations, and the other logics in other situations? Or should probability be combined with other logics?

Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to first-order logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequency-induced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.