Jon Williamson

Russo and Williamson (Int Stud Philos Sci 21(2):157–170, 2007) put forward the thesis that, at least in the health sciences, to establish the claim that C is a cause of E, one normally needs evidence of an underlying mechanism linking C and E as well as evidence that C makes a difference to E. This epistemological thesis poses a problem for most current analyses of causality which, in virtue of analysing causality in terms of just one of mechanisms or difference making, cannot account for the need for the other kind of evidence. Weber (Int Stud Philos Sci 23(2):277–295, 2009) has suggested to the contrary that Giere’s probabilistic analysis of causality survives this criticism. In this paper, we look in detail at the case of medical imaging technology, which, we argue, supports the thesis of Russo and Williamson, and we respond to Weber’s suggestion, arguing that Giere’s account does not survive the criticism

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

This volume arose out of an international, interdisciplinary academic network on Probabilistic Logic and Probabilistic Networks involving four of us (Haenni, Romeijn, Wheeler and Williamson), called Progicnet and funded by the Leverhulme Trust from 2006–8. Many of the papers in this volume were presented at an associated conference, the Third Workshop on Combining Probability and Logic (Progic 2007), held at the University of Kent on 5–7 September 2007. The papers in this volume concern either the special focus on the connection between probabilistic logic and probabilistic networks or the more general question of the links between probability and logic. Here we introduce probabilistic logic, probabilistic networks, current and future directions of research and also the themes of the papers that follow.

The paper considers the legal tools that have been developed in German pharmaceutical regulation as a result of the precautionary attitude inaugurated by the Contergan decision. These tools are the notion of “well-founded suspicion”, which attenuates the requirements for safety intervention by relaxing the requirement of a proved causal connection between danger and source, and the introduction of the reversal of proof burden in liability norms. The paper focuses on the first and proposes seeing the precautionary principle as an instance of the requirement that one should maximise expected utility. In order to maximise expected utility certain probabilities are required and it is argued that objective Bayesianism offers the most plausible means to determine the optimal decision in cases where evidence supports diverging choices.

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.

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.

Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premises of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this work, Jon Williamson embarks on a quest to find a general, reasonable, applicable inductive logic (GRAIL), all the while examining why pioneers such as Ludwig Wittgenstein and Rudolf Carnap did not entirely succeed in this task.

In this chapter I discuss connections between machine learning and the philosophy of science. First I consider the relationship between the two disciplines. There is a clear analogy between hypothesis choice in science and model selection in machine learning. While this analogy has been invoked to argue that the two disciplines are essentially doing the same thing and should merge, I maintain that the disciplines are distinct but related and that there is a dynamic interaction operating between the two: a series of mutually beneficial interactions that changes over time. I will introduce some particularly fruitful interactions, in particular the consequences of automated scientific discovery for the debate on inductivism versus falsificationism in the philosophy of science, and the importance of philosophical work on Bayesian epistemology and causality for contemporary machine learning. I will close by suggesting the locus of a possible future interaction: evidence integration.

According to Russo and Williamson (Int Stud Philos Sci 21(2):157–170, 2007, Hist Philos Life Sci 33:389–396, 2011a, Philos Sci 1(1):47–69, 2011b ), in order to establish a causal claim of the form, ‘_C_ is a cause of _E_’, one typically needs evidence that there is an underlying mechanism between _C_ and _E_ as well as evidence that _C_ makes a difference to _E_. This thesis has been used to argue that hierarchies of evidence, as championed by evidence-based movements, tend to give primacy to evidence of difference making over evidence of mechanisms and are flawed because the two sorts of evidence are required and they should be treated on a par. An alternative approach gives primacy to evidence of mechanism over evidence of difference making. In this paper, we argue that this alternative approach is equally flawed, again because both sorts of evidence need to be treated on a par. As an illustration of this parity, we explain how scientists working in the ‘EnviroGenomarkers’ project constantly make use of the two evidential components in a dynamic and intertwined way. We argue that such an interplay is needed not only for causal assessment but also for policy purposes.

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.

Evidence-based medicine (EBM) makes use of explicit procedures for grading evidence for causal claims. Normally, these procedures categorise evidence of correlation produced by statistical trials as better evidence for a causal claim than evidence of mechanisms produced by other methods. We argue, in contrast, that evidence of mechanisms needs to be viewed as complementary to, rather than inferior to, evidence of correlation. In this paper we first set out the case for treating evidence of mechanisms alongside evidence of correlation in explicit protocols for evaluating evidence. Next we provide case studies which exemplify the ways in which evidence of mechanisms complements evidence of correlation in practice. Finally, we put forward some general considerations as to how the two sorts of evidence can be more closely integrated by EBM.

The mechanistic and causal accounts of explanation are often conflated to yield a ‘causal-mechanical’ account. This paper prizes them apart and asks: if the mechanistic account is correct, how can causal explanations be explanatory? The answer to this question varies according to how causality itself is understood. It is argued that difference-making, mechanistic, dualist and inferentialist accounts of causality all struggle to yield explanatory causal explanations, but that an epistemic account of causality is more promising in this regard.