Jon Williamson

Inductive logic admits a variety of semantics (Haenni et al., 2011, Part 1). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010, Chapter 7). §1 introduces the semantics and then, in §2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008). §3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising

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.

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

It is tempting to analyse causality in terms of just one of the indicators of causal relationships, e.g., mechanisms, probabilistic dependencies or independencies, counterfactual conditionals or agency considerations. While such an analysis will surely shed light on some aspect of our concept of cause, it will fail to capture the whole, rather multifarious, notion. So one might instead plump for pluralism: a different analysis for a different occasion. But we do not seem to have lots of different concepts of cause – just one eclectic notion. The resolution of this conundrum, I think, requires us to accept that our causal beliefs are generated by a wide variety of indicators, but to deny that this variety of indicators yields a variety of concepts of cause. This focus on the relation between evidence and causal beliefs leads to what I call epistemic causality. Under this view, certain causal beliefs are appropriate or rational on the basis of observed evidence; our notion of cause can be understood purely in terms of these rational beliefs. Causality, then, is a feature of our epistemic representation of the world, rather than of the world itself. This yields one, multifaceted notion of cause

Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way.

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

Metabolism is a set of chemical reactions, used by living organisms to process chemical compounds in order to take energy and eliminate toxic compounds, for example. Its processes are referred as metabolic pathways. Understanding metabolism is imperative to biology, toxicology and medicine, but the number and complexity of metabolic pathways makes this a difficult task. In our paper, we investigate the use of causal Bayesian networks to model the pathways of yeast saccharomyces cerevisiae metabolism: such a network can be used to draw predictions about the levels of metabolites and enzymes in a particular specimen. We propose a two-stage methodology for causal networks, as follows. First construct a causal network from the network of metabolic pathways. The viability of this causal network depends on the validity of the causal Markov condition. If this condition fails, however, the principle of the common cause motivates the addition of a new causal arrow or a new `hidden' common cause to the network (stage 2 of the model formation process). Algorithms for adding arrows or hidden nodes have been developed separately in a number of papers, and in this paper we combine them, showing how the resulting procedure can be applied to the metabolic pathway problem. Our general approach was tested on neural cell morphology data and demonstrated noticeable improvements in both prediction and network accuracy.

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.

Expert probability forecasts can be useful for decision making . But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty . Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language . But Bayesian epistemology comes in three main varieties. Strictly subjective Bayesianism and empirically-based subjective Bayesianism have difficulty in justifying the use of a forecaster’s probabilities for decision making . On the other hand, objective Bayesianism can justify the use of these probabilities, at least when the probabilities are consistent with the agent’s evidence . Hence objective Bayesianism offers the most promise overall for explaining how testimony of uncertainty can be useful for decision making. Interestingly, the objective Bayesian analysis provided in Sect. 5 can also be used to justify a version of the Principle of Reflection.

Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a first-order predicate language, with a view to applying the resulting formalism to inductive logic. We show that the maximum entropy principle can be motivated largely in terms of minimising worst-case expected loss.

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.

We present a new framework for combining logic with probability, and demonstrate the application of this framework to breast cancer prognosis. Background knowledge concerning breast cancer prognosis is represented using logical arguments. This background knowledge and a database are used to build a Bayesian net that captures the probabilistic relationships amongst the variables. Causal hypotheses gleaned from the Bayesian net in turn generate new arguments. The Bayesian net can be queried to help decide when one argument attacks another. The Bayesian net is used to perform the prognosis, while the argumentation framework is used to provide a qualitative explanation of the prognosis.

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 objective Bayesianism, an agent’s degrees of belief should be determined by a probability function, out of all those that satisfy constraints imposed by background knowledge, that maximises entropy. A Bayesian net offers a way of efficiently representing a probability function and efficiently drawing inferences from that function. An objective Bayesian net is a Bayesian net representation of the maximum entropy probability function. In this paper we apply the machinery of objective Bayesian nets to breast cancer prognosis. Background knowledge is diverse and comes from several different sources: a database of clinical data, a database of molecular data, and quantitative data from the literature. We show how an objective Bayesian net can be constructed from this background knowledge and how it can be applied to yield prognoses and aid translation of clinical knowledge to genomics research

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

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 (the views that evidence is knowledge; that evidence is whatever is fully believed; that evidence is observationally set credence; that evidence is information), 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.

According to current hierarchies of evidence for EBM, evidence of correlation (e.g., from RCTs) 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 (for example, in order to set up and evaluate RCTs). 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.