Jon Williamson

The epistemic theory of causality views causality as a tool that helps us to predict, explain and control our world, rather than as a relation that exists independently of our epistemic practices. In this chapter, we first provide an introduction to the epistemic theory of causality. We then outline four considerations that motivate the epistemic theory: the failure of standard theories of causality; parsimony; the epistemology of causality; and neutrality. We illustrate these four considerations in the contexts of the social sciences and the cognitive sciences. We argue that the epistemic theory provides a very natural account of causality across these contexts.

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time.

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time.

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time.

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time.

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time.

The epistemic theory of causality is analogous to epistemic theories of probability. Most proponents of epistemic probability would argue that one's degrees of belief should be calibrated to chances, insofar as one has evidence of chances. The question arises as to whether causal beliefs should satisfy an analogous calibration norm. In this paper, I formulate a particular version of a norm requiring calibration to chances and argue that this norm is the most fundamental evidential norm for epistemic probability. I then develop an analogous calibration norm for epistemic causality, argue that it is the *only* evidential norm required for epistemic causality, and show how an epistemic account of causality that incorporates this norm can be used to analyse objective causal relationships.

According to the objective Bayesian approach to inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy the premisses, satisfies the conclusion. When premisses and conclusion are constraints on probabilities of sentences of a first-order predicate language, however, it is by no means obvious how to determine these maximal entropy functions. This paper makes progress on the problem in the following ways. Firstly, we introduce the concept of a limit in entropy and show that, if the set of probability functions satisfying the premisses contains a limit in entropy, then this limit point is unique and is the maximal entropy probability function. Next, we turn to the special case in which the premisses are categorical sentences of the logical language. We show that if the uniform probability function gives the premisses positive probability, then the maximal entropy function can be found by simply conditionalising this uniform prior on the premisses. We generalise our results to demonstrate agreement between the maximal entropy approach and Jeffrey conditionalisation in the case in which there is a single premiss that specifies the probability of a sentence of the language. We show that, after learning such a premiss, certain inferences are preserved, namely inferences to inductive tautologies. Finally, we consider potential pathologies of the approach: we explore the extent to which the maximal entropy approach is invariant under permutations of the constants of the language, and we discuss some cases in which there is no maximal entropy probability function.

Cognitive theorists routinely disagree about the evidence supporting claims in cognitive science. Here, we first argue that some disagreements about evidence in cognitive science are about the evidence available to be drawn upon by cognitive theorists. Then, we show that one’s explanation of why this first kind of disagreement obtains will cohere with one’s theory of evidence. We argue that the best explanation for why cognitive theorists disagree in this way is because their evidence is what they rationally grant. Finally, we explain why our view does not lead to a pernicious kind of relativism in cognitive science.

Social scientists often draw on a variety of evidence for their causal inferences. There is also a call to use a greater variety of evidence in social science research. This topical collection examines the philosophical foundations and implications of evidential diversity in the social sciences. It assesses the application of Evidential Pluralism in the context of the social sciences, especially its application to economics and political science. It also discusses the concept of causation in cognitive science and the implications of evidential diversity for the social sciences.

This paper addresses a data integration problem: given several mutually consistent datasets each of which measures a subset of the variables of interest, how can one construct a probabilistic model that fits the data and gives reasonable answers to questions which are under-determined by the data? Here we show how to obtain a Bayesian network model which represents the unique probability function that agrees with the probability distributions measured by the datasets and otherwise has maximum entropy. We provide a general algorithm, OBN-cDS, which offers substantial efficiency savings over the standard brute-force approach to determining the maximum entropy probability function. Furthermore, we develop modifications to the general algorithm which enable further efficiency savings but which are only applicable in particular situations. We show that there are circumstances in which one can obtain the model directly from the data; by solving algebraic problems; and by solving relatively simple independent optimisation problems.

That one person's modus ponens is another's modus tollens is the bane of philosophy because it strips many philosophical arguments of their persuasive force. The problem is that philosophical arguments become mere pantomemes: arguments that are reasonable to resist simply by denying the conclusion. Appeals to proof, intuition, evidence, and truth fail to alleviate the problem. Two broad strategies, however, do help in certain circumstances: an appeal to normal informal standards of what is reasonable (nisowir) and argument by interpretation. The method of explication features prominently in both strategies, and the paper extends this method to apply to nisowir, introducing the concept of canonical explication. The paper illustrates the two strategies with examples of arguments from formal epistemology and suggests that an appeal to nisowir might help to defend against philosophical scepticism by shifting the burden of proof to the sceptic.

Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is also hard to reconcile with standard probabilism. So, I argue, standard probabilistic approaches cannot appeal to direct inference to explicate the logic of induction. However, I go on to defend a non-standard objective Bayesian account of induction: I argue that this approach can both accommodate direct inference and provide a viable account of the logic of induction. I then defend this account against Schurz’ criticisms.

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.

Evidential Pluralism maintains that in order to establish a causal claim one normally needs to establish the existence of an appropriate conditional correlation and the existence of an appropriate mechanism complex, so when assessing a causal claim one ought to consider both association studies and mechanistic studies. Hitherto, Evidential Pluralism has been applied to medicine, leading to the EBM+ programme, which recommends that evidence-based medicine should systematically evaluate mechanistic studies alongside clinical studies. This paper argues that Evidential Pluralism can also be fruitfully applied to the social sciences. In particular, Evidential Pluralism provides (i) a new approach to evidence-based policy; (ii) an account of the evidential relationships in more theoretical research; and (iii) new philosophical motivation for mixed methods research. The application of Evidential Pluralism to the social sciences is also defended against two objections.

In this chapter we explore the process of extrapolating causal claims from model organisms to humans in pharmacology. We describe and compare four strategies of extrapolation: enumerative induction, comparative process tracing, phylogenetic reasoning, and robustness reasoning. We argue that evidence of mechanisms plays a crucial role in several strategies for extrapolation and in the underlying logic of extrapolation: the more directly a strategy establishes mechanistic similarities between a model and humans, the more reliable the extrapolation. We present case studies from the research on atherosclerosis and the development of statins, that illustrate these strategies and the role of mechanistic evidence in extrapolation.

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.

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.