Jon Williamson

I present a formalism that combines two methodologies: objective Bayesianism and Bayesian nets. According to objective Bayesianism, an agent’s degrees of belief (i) ought to satisfy the axioms of probability, (ii) ought to satisfy constraints imposed by background knowledge, and (iii) should otherwise be as non-committal as possible (i.e. have maximum entropy). Bayesian nets offer an efficient way of representing and updating probability functions. An objective Bayesian net is a Bayesian net representation of the maximum entropy probability function.

In this paper, we examine what is to be said in defence of Machamer, Darden and Craver’s (MDC) controversial dualism about activities and entities (Machamer, Darden and Craver’s in Philos Sci 67:1–25, 2000). We explain why we believe the notion of an activity to be a novel, valuable one, and set about clearing away some initial objections that can lead to its being brushed aside unexamined. We argue that substantive debate about ontology can only be effective when desiderata for an ontology are explicitly articulated. We distinguish three such desiderata. The first is a more permissive descriptive ontology of science, the second a more reductive ontology prioritising understanding, and the third a more reductive ontology prioritising minimalism. We compare MDC’s entities-activities ontology to its closest rival, the entities-capacities ontology, and argue that the entities-activities ontology does better on all three desiderata

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

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.

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

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.

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

Practical reasoning requires decision—making in the face of uncertainty. Xenelda has just left to go to work when she hears a burglar alarm. She doesn’t know whether it is hers but remembers that she left a window slightly open. Should she be worried? Her house may not be being burgled, since the wind or a power cut may have set the burglar alarm off, and even if it isn’t her alarm sounding she might conceivably be being burgled. Thus Xenelda can not be certain that her house is being burgled, and the decision that she takes must be based on her degree of certainty, together with the possible outcomes of that decision.

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.

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.

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

Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief ½ to the next raven being black, however many other black ravens have been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used to capture the Johnson-Carnap continuum of inductive methods, as well as the Nix-Paris continuum, and show how inductive influence can be measured

Subjective Probability: The Real Thing is the last book written by the late Richard Jeffrey, a key proponent of the Bayesian interpretation of probability.Bayesians hold that probability is a mental notion: saying that the probability of rain is 0.7 is just saying that you believe it will rain to degree 0.7. Degrees of belief are themselves cashed out in terms of bets—in this case you consider 7:3 to be fair odds for a bet on rain. There are two extreme Bayesian positions. Strict subjectivists think that an agent can adopt whatever degrees of belief she likes, as long as they satisfy the axioms of probability. Thus your degree of belief in rain and degree of belief in no rain must sum to one but are otherwise unconstrained. At the other extreme, objectivists claim that an agent's background knowledge considerably narrows down the choice of appropriate degrees of belief. In particular, if you know only that the frequency of rain is 0.7 then you should believe it will rain to degree 0.7; if you know absolutely nothing about the weather then you should set your degree of belief in rain to be 0.5; in neither of these cases is there room for subjective choice of degree of belief. In this book, Jeffrey advocates what is sometimes called empirically-based subjectivism, a position that lies between the two extremes of strict subjectivism and objectivism. According to this position, knowledge of frequencies constrains degree of belief, but lack of knowledge does not impose any constraints, so that if you know nothing about the weather you may adopt any degree of belief in rain you like.1The aim of the book is not so much to justify this point of view as to provide a comprehensive exposition of probability theory from the …

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.

:A normative Bayesian theory of deliberation and judgement requires a procedure for merging the evidence of a collection of agents. In order to provide such a procedure, one needs to ask what the evidence is that grounds Bayesian probabilities. After finding fault with several views on the nature of evidence, it is argued that evidence is whatever is rationally taken for granted. This view is shown to have consequences for an account of merging evidence, and it is argued that standard axioms for merging need to be altered somewhat.

Cancer treatment decisions should be based on all available evidence. But this evidence is complex and varied: it includes not only the patient’s symptoms and expert knowledge of the relevant causal processes, but also clinical databases relating to past patients, databases of observations made at the molecular level, and evidence encapsulated in scientific papers and medical informatics systems. Objective Bayesian nets offer a principled path to knowledge integration, and we show in this chapter how they can be applied to integrate various kinds of evidence in the cancer domain. This is important from the systems biology perspective, which needs to integrate data that concern different levels of analysis, and is also important from the point of view of medical informatics.