Christopher Hitchcock

Probability theory is a key tool of the physical, mathematical, and social sciences. It has also been playing an increasingly significant role in philosophy: in epistemology, philosophy of science, ethics, social philosophy, philosophy of religion, and elsewhere. This Handbook encapsulates and furthers the influence of philosophy on probability, and of probability on philosophy. Nearly forty articles summarise the state of play and present new insights in various areas of research at the intersection of these two fields. The articles will be of special interest to practitioners of probability who seek a greater understanding of its mathematical and conceptual foundations, and to philosophers who want to get up to speed on the cutting edge of research in this area. The volume begins with a primer on those parts of probability theory that we believe are most important for philosophers to know, and the rest is divided into seven main sections: History; Formalism; Alternatives to Standard Probability Theory; Interpretations and Interpretive Issues; Probabilistic Judgment and Its Applications; Applications of Probability: Science; and Applications of Probability: Philosophy.

Concerning any object of philosophical analysis, we can ask several questions, including the two posed in the title of this paper. Despite difficulties in formulating a precise criterion to distinguish causal processes from pseudoprocesses, and causal interactions from mere spatiotemporal intersections, I argue that Salmon answered the first of these questions with extraordinary clarity. The second question, by contrast, has received very little attention. I will present two problems: in the first, it seems that Salmon has provided exactly the conceptual resources needed to solve the problem; in the second, it is difficult to see how causal processes and interactions may be used to shed any light. In general, the way to carry Salmon's program forward will be to demonstrate that these resources can be made to do real philosophical work.

Larry Wright and others have advanced causal accounts of functional explanation, designed to alleviate fears about the legitimacy of such explanations. These analyses take functional explanations to describe second order causal relations. These second order relations are conceptually puzzling. I present an account of second order causation from within the framework of Eells' probabilistic theory of causation; the account makes use of the population-relativity of causation that is built into this theory.

It is a commonplace that in philosophy, intuitions supply evidence for and against philosophical theories. Recent work in experimental philosophy has brought to bear the intuitions of philosophically naïve subjects in a number of different ways. One line of response to this work has been to claim that philosophers have expertise that privileges their intuitive judgments, and allows them to disregard the judgments of non-experts. This expertise is supposed to be analogous to the expertise of the mathematician or the physicist. This paper critically evaluates this appeal to philosophical expertise.

We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values to be reconciled? We show that only the first argument is valid for a standard, countably additive probability distribution. However, both lines of reasoning are legitimate if probabilities are non-standard. The subjective probability of death rises from 1/36 to 0.9 by conditionalizing on an event that is not measurable, or whose probability is zero. Thus we can sometimes meaningfully ascribe conditional probabilities even when the event conditionalized upon is not of positive finite (or even infinitesimal) measure.

an observation to formulate a theory, it is no surprise that the resulting theory accurately captures that observation. However, when the theory makes a novel prediction—when it predicts an observation that was not used in its formulation—this seems to provide more substantial confirmation of the theory. This paper presents a new approach to the vexed problem of understanding the epistemic difference between prediction and accommodation. In fact, there are several problems that need to be disentangled; in all of them, the key is the concept of overfitting. We float the hypothesis that accommodation is a defective methodology only when the methods used to accommodate the data fail to guard against the risk of overfitting. We connect our analysis with the proposals that other philosophers have made. We also discuss its bearing on the conflict between instrumentalism and scientific realism. Introduction Predictivisms—a taxonomy Observations Formulating the problem What might Annie be doing wrong? Solutions Observations explained Mayo on severe tests The miracle argument and scientific realism Concluding comments.

Much of the philosophical literature on causation has focused on the concept of actual causation, sometimes called token causation. In particular, it is this notion of actual causation that many philosophical theories of causation have attempted to capture.2 In this paper, we address the question: what purpose does this concept serve? As we shall see in the next section, one does not need this concept for purposes of prediction or rational deliberation. What then could the purpose be? We will argue that one can gain an important clue here by looking at the ways in which causal judgments are shaped by people‘s understanding of norms.

Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. A number of philosophers and computer scientists have also suggested that an appeal to such factors can help deal with problems facing existing accounts of actual causation. This article develops a flexible formal framework for incorporating defaults, typicality, and normality into an account of actual causation. The resulting account takes actual causation to be both graded and comparative. We then show how our account would handle a number of standard cases. 1 Introduction2 Causal Models3 The HP Definition of Actual Causation4 The Problem of Isomorphism5 Defaults, Typicality, and Normality6 Extended Causal Models7 Examples7.1 Omissions7.2 Knobe effects7.3 Causes versus background conditions7.4 Bogus prevention7.5 Causal chains7.6 Legal doctrines of intervening causes7.7 Pre-emption and short circuits8 Conclusion

This article describes research pursued by members of the McDonnell Collaborative on Causal Learning. A number of members independently converged on a similar idea: one of the central functions served by claims of actual causation is to highlight patterns of dependence that are highly portable into novel contexts. I describe in detail how this idea emerged in my own work and also in that of the psychologist Tania Lombrozo. In addition, I use the occasion to reflect on the nature of interdisciplinary collaboration in general and on the interaction between philosophy and psychology in particular.

It it tempting to think that if an outcome had some probability of not occurring, then we cannot explain why that outcome in fact occurred. Despite this intuition, most philosophers of science have come to admit the possibility of indeterministic explanation. Yet some of them continue to hold that if an outcome was not determined, it cannot be explained why that outcome rather than some other occurred. I argue that this is an untenable compromise: if indeterministic explanation is possible, then indeterministic contrastive explanation is possible too. In order to defend this conclusion, I develop an account of contrastive explanation.

Causation is a central topic in many areas of philosophy. In metaphysics, philosophers want to know what causation is, and how it is related to laws of nature, probability, action, and freedom of the will. In epistemology, philosophers investigate how causal claims can be inferred from statistical data, and how causation is related to perception, knowledge and explanation. In the philosophy of mind, philosophers want to know whether and how the mind can be said to have causal efficacy, and in ethics, whether there is a moral distinction between acts and omissions and whether the moral value of an act can be judged according to its consequences. And causation is a contested concept in other fields of enquiry, such as biology, physics, and the law. This book provides an in-depth and comprehensive overview of these and other topics, as well as the history of the causation debate from the ancient Greeks to the logical empiricists. The chapters provide surveys of contemporary debates, while often also advancing novel and controversial claims; and each includes a comprehensive bibliography and suggestions for further reading. The book is thus the most comprehensive source of information about causation currently available, and will be invaluable for upper-level undergraduates through to professional philosophers.

Causes often influence their effects via multiple routes. Moderate alcohol consumption can raise the level of HDL ('good') cholesterol, which in tum reduces the risk of heart disease. Unfortunately, moderate alcohol consumption can also increase the level of homocysteine, which in tum increases the risk of heart disease. The net or overall effect of alcohol consumption on heart disease will depend upon both of these routes, and no doubt upon many others as well. This is a familiar fact of life for engineers and policy makers, one that often gives rise to unintended consequences. Suppose, for example, that the American Federal Aviation Administration were to institute new regulations requiring that aeroplanes be equipped with some expensive new safety feature. Would this regulation save lives? Not necessarily. Every dollar (or pound, or euro, or yen ... ) that an airline spends to upgrade its fleet is a dollar that must be recouped in some way, most likely through higher fares. Higher fares may, in tum, persuade some travellers to drive instead of fly- especially on shorter routes. But it is inherently more dangerous to drive a given route than to fly it, so the net effect of the new regulation may cost lives, rather than saving them (Glassner 1999: 188).

A simple counterfactual theory of causation fails because of problems with cases of preemption. This might lead us to expect that preemption will raise problems for counterfactual theories of other concepts that have a causal dimension. Indeed, examples are easy to find. But there is one case where we do not find this. Several versions of causal decision theory are formulated using counterfactuals. This might lead us to expect that these theories will yield the wrong recommendations in cases of preemption. But they do not. The explanation, I argue, is that the ‘cause’ that has been the target of counterfactual analyses is a specific relation, ‘actual causation’, that is not needed for prospective deliberation. A simple counterfactual theory of causation seems to capture the notion of cause needed for causal decision theory. This shows, in opposition to some critics, that counterfactual theories of causation are not barking up the wrong tree.

Despite the platitude that analytic philosophy is deeply concerned with language, philosophers of science have paid little attention to methodological issues that arise within historical linguistics. I broach this topic by arguing that many inferences in historical linguistics conform to Reichenbach's common cause principle (CCP). Although the scope of CCP is narrower than many have thought, inferences about the genealogies of languages are particularly apt for reconstruction using CCP. Quantitative approaches to language comparison are readily understood as methods for detecting the correlations that serve as premises for common cause inferences, and potential sources of error in historical linguistics correspond to well-known limitations of CCP