Critics of functional explanations in social science maintain that such explanations are illegitimate unless a mechanism is specified. Others argue that mechanisms are not necessary for causal inference and that functional explanations are a type of causal claim that raise no special difficulties for testing. I show that there is indeed a special problem that confronts testing functional explanations resulting from their connection to second-order causal claims. I explain how mechanisms can resolve this difficulty, but argue that this does not (...) provide support for methodological individualism since it is not necessary that the mechanisms be described in terms of individual interactions. (shrink)

What is exactly the emergence relation? In which sense is irreducibility associated with it besides being assumed by definition? Although in many cases the explanatory role of emergent states does not exceed the explanatory role of more basic states, this does not speak against the fact that, for some relevant explanatory contexts, emergent states are irreducible. On this basis, an epistemic concept of the emergence relation that does not depend strictly on irreducibility is here offered.

We propose an account of dynamic predicates which draws on the notion of force, eliminating reference to events in the linguistic semantics. We treat dynamic predicates as predicates of forces, represented as functions from an initial situation to a final situation that occurs ceteris paribus, that is, if nothing external intervenes. The possibility that opposing forces might intervene to prevent the transition to a given final situation leads us to a novel analysis of non-culminating accomplishment predicates in a variety of (...) languages, including the English progressive. We then apply the force-theoretic framework to the composition of basic Vendlerian eventuality types within a lexical-decomposition syntax. The difference between predicates of forces and predicates of situations is argued to underlie the dynamic/stative contrast, and also to allow for a formal treatment of the difference between be and stay. Consequences for the relationship between language and cognition are discussed. (shrink)

Causal reasoning is an aspect of learning, reasoning, and decision-making that involves the cognitive ability to discover relationships between causal relata, learn and understand these causal relationships, and make use of this causal knowledge in prediction, explanation, decision-making, and reasoning in terms of counterfactuals. Can we fully automate causal reasoning? One might feel inclined, on the basis of certain groundbreaking advances in causal epistemology, to reply in the affirmative. The aim of this paper is to demonstrate that one still has (...) good skeptical grounds for resisting any conclusions in favour of the automation of causal reasoning. If by causal reasoning is meant the entirety of the process through which we discover causal relationships and make use of this knowledge in prediction, explanation, decision-making, and reasoning in terms of counterfactuals, then one relies besides on tacit knowledge, as might be constituted by or derived from the epistemic faculty virtues and abilities of the causal reasoner, the value systems and character traits of the causal reasoner, the implicit knowledge base available to the causal reasoner, and the habits that sustain our causal reasoning practices. While certain aspects of causal reasoning may be axiomatized and formalized and algorithms may be implemented to approximate causal reasoning, one has to remain skeptical about whether causal reasoning may be fully automated. This demonstration will involve an engagement with Meno’s Paradox. (shrink)

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.

Christopher Hitchcocks discussion of my use of screening-off in analyzing the causal process of natural selection raises some interesting issues to which I am pleased to reply. The bulk of his article is devoted to some fairly general points in the theory of explanation. In particular, he questions whether or not my point that phenotype screens off genotype from reproductive success (in cases of organismic selection) supports my claim that the explanation of differential reproductive success should be in terms of (...) phenotypic differences, not genotypic differences. I will respond to this and show why the two supposed counter-examples to my position fail. (shrink)

One goal of recent philosophy of mind has been to ‘naturalize’ intentionality by showing how a purely physical system could have states that represent or are about items in the world. The project is reductionist in spirit, the aim being to explain intentional relations—to say what they really are—and to do so in terms that do not themselves utilize intentional or semantic concepts. In this vein there are attempts to explain intentional relations in terms of causal relations, informational relations, teleological (...) or functional relations, relations involving abstract similarity or isomorphism, and various combinations thereof. What makes these accounts naturalistic is the presumed objectivity and scientific respectability of the properties appelated to in the explanans. What makes them all reductive is their shared presumption that intentionality can be explained in terms that have a wider application to intentional systems as well as to systems that have no mental properties at all. (shrink)

I am very grateful to Stephan Leuenberger, Erica Shumener and Naomi Thompson for their excellent and thoughtful commentaries on Making Things Up. I have learned a lot from thinking through their replies. As it happens, they focus on pretty disparate aspects of the book: necessitation, relative fundamentality, and what builds the building facts, respectively. I will thus engage with their remarks separately.

For a long time, regularity accounts of causation have virtually vanished from the scene. Problems encountered within other theoretical frameworks have recently induced authors working on causation, laws of nature, or methodologies of causal reasoning – as e.g. May (Kausales Schliessen. Eine Untersuchung über kausale Erklärungen und Theorienbildung. Ph.D. thesis, Universität Hamburg, Hamburg, 1999), Ragin (Fuzzy-set social science. Chicago: University of Chicago Press, 2000), Graßhoff and May (Causal regularities. In W. Spohn, M. Ledwig, & M. Esfeld (Eds.), Current issues in (...) causation (pp. 85–114). Paderborn: Mentis, 2001), Swartz (The concept of physical law (2nd ed.). http://www.sfu.ca/philosophy/physical-law/, 2003), Halpin (Erkenntnis, 58, 137–168, 2003) – to direct their attention back to regularity theoretic analyses. In light of the latest proposals of regularity theories, the paper at hand therefore reassesses the criticism raised against regularity accounts since the INUS theory of causation of Mackie (The cement of the universe. A study of causation. Oxford: Clarendon Press, 1974). It is shown that most of these objections target strikingly over-simplified regularity theoretic sketches. By outlining ways to refute these objections it is argued that the prevalent conviction as to the overall failure of regularity theories has been hasty. (shrink)

The essential precondition of implementing interventionist techniques of causal reasoning is that particular variables are identified as so-called intervention variables. While the pertinent literature standardly brackets the question how this can be accomplished in concrete contexts of causal discovery, the first part of this paper shows that the interventionist nature of variables cannot, in principle, be established based only on an interventionist notion of causation. The second part then demonstrates that standard observational methods that draw on Bayesian networks identify intervention (...) variables only if they also answer the questions that can be answered by interventionist techniques—which are thus rendered dispensable. The paper concludes by suggesting a way of identifying intervention variables that allows for exploiting the whole inferential potential of interventionist techniques. (shrink)

Manipulationism holds that information about the results of interventions is of utmost importance for scientific practices such as causal assessment or explanation. Specifically, manipulation provides information about the stability, or invariance, of the relationship between X and Y: were we to wiggle the cause X, the effect Y would accordingly wiggle and, additionally, the relation between the two will not be disrupted. This sort of relationship between variables are called 'invariant empirical generalisations'. The paper focuses on questions about causal assessment (...) and analyses the status of manipulation. It is argued that manipulationism is trapped in a dilemma. If manipulationism is read as providing a conceptual analysis of causation, then it fails to provide a story about the methods for causal assessment. If, instead, manipulationism is read as providing a method for causal assessment, then it is at an impasse concerning causal assessment in areas where manipulations are not performed. Empirical generalisations are then reassessed, in such a way that manipulation is not taken as methodologically fundamental. The paper concludes that manipulation is the appropriate tool for some scientific contexts, but not for all. (shrink)

In her ‘Causality and Determination’, Anscombe argues for the strong thesis that despite centuries of philosophical assumption to the contrary, the supposition that causality and necessity have something essential to do with one another is baseless. In this paper, I assess Anscombe’s arguments and endorse her conclusion. I then attempt to argue that her arguments remain highly relevant today, despite the fact that most popular general views of causation today are firmly probabilistic in orientation and thus show no trace of (...) the assumptions Anscombe hoped to undermine. My suggestion is that Anscombe's interests in causality are distinct from those which mostly animate the modern debate about the general nature of causality and that in those specialized areas of philosophy in which those concerns still dominate, one can still see the effects of the fallacies and confusions to which she alerts us. I conclude by offering two possible complementary explanations of the tendency to suppose that causation is a variety of necessitation. (shrink)

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

Indicative conditionals and tendency causal claims are closely related (e.g., Frosch and Byrne, 2012), but despite these connections, they are usually studied separately. A unifying framework could consist in their dependence on probabilistic factors such as high conditional probability and statistical relevance (e.g., Adams, 1975; Eells, 1991; Douven, 2008, 2015). This paper presents a comparative empirical study on differences between judgments on tendency causal claims and indicative conditionals, how these judgments are driven by probabilistic factors, and how these factors differ (...) in their predictive power for both causal and conditional claims. (shrink)

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. (shrink)

In a recent article in this journal, Federica Russo and Jon Williamson argue that an analysis of causality in terms of probabilistic relationships does not do justice to the use of mechanistic evidence to support causal claims. I will present Ronald Giere's theory of probabilistic causation, and show that it can account for the use of mechanistic evidence (both in the health sciences—on which Russo and Williamson focus—and elsewhere). I also review some other probabilistic theories of causation (of Suppes, Eells, (...) and Humphreys) and show that they cannot account for the use of mechanistic evidence. I argue that these theories are also inferior to Giere's theory in other respects. (shrink)

The goal of research in social epidemiology is not simply conceptual clarification or theoretical understanding, but more importantly it is to contribute to, and enhance the health of populations (and so, too, the people who constitute those populations). Undoubtedly, understanding how various individual risk factors such as smoking and obesity affect the health of people does contribute to this goal. However, what is distinctive of much on-going work in social epidemiology is the view that analyses making use of individual-level variables (...) is not enough. In the spirit of Durkheim and Weber, S. Leonard Syme makes this point by writing that just “as bad water and food may be harmful to our health, unhealthful forces in our society may be detrimental to our capacity to make choices and to form opinions” conducive to health and well-being. Advocates of upstream (distal) causes of adverse health outcomes propose to identify the most important of these “unhealthful forces” as the fundamental causes of adverse health outcomes. However, without a clear, theoretically precise and well-grounded understanding of the characteristics of fundamental causes, there is little hope in applying the statistical tools of the health sciences to hypotheses about fundamental causes, their outcomes, and policies intended to enhance the health of populations. This paper begins the process of characterizing the social epidemiological concept of fundamental cause in a theoretically respectable and robust way. (shrink)

Nancy Cartwright begins her recent book, Hunting Causes and Using Them, by noting that while a few years ago real causal claims were in dispute, nowadays “causality is back, and with a vengeance.” In the case of the social sciences, Keith Morrison writes that “Social science asks ‘why?’. Detecting causality or its corollary—prediction—is the jewel in the crown of social science research.” With respect to the health sciences, Judea Pearl writes that the “research questions that motivate most studies in the (...) health sciences are causal in nature.” However, not all data used by people interested in making causal claims come from experiments that use random assignment to control and treatment groups. Indeed, much research in the social and health science depends on non-experimental, observational data. Thus, one of the most important problems in the social and health sciences concerns making warranted causal claims using non-experimental, observational data; viz., “Can observational data be used to make etiological inferences leading to warranted causal claims?” This paper examines one method of warranting causal claims that is especially widespread in epidemiology and the health sciences generally—the use of causal criteria. It is argued that cases of complex causation generally, and redundant causation—both causal overdetermination and causal preemption—specifically, undermine the use of such criteria to warrant causal claims. (shrink)

I argue that information is a goal-relative concept for Bayesians. More precisely, I argue that how much information is provided by a piece of evidence depends on whether the goal is to learn the truth or to rank actions by their expected utility, and that different confirmation measures should therefore be used in different contexts. I then show how information measures may reasonably be derived from confirmation measures, and I show how to derive goal-relative non-informative and informative priors given background (...) information. Finally, I argue that my arguments have important implications for both objective and subjective Bayesianism. In particular, the Uniqueness Thesis is either false or must be modified. Moreover, objective Bayesians must concede that pragmatic factors systematically influence which priors are rational, and subjective Bayesians must concede that pragmatic factors sometimes partly determine which prior distribution most accurately represents an agent's epistemic state. (shrink)

It is widely thought that there is an important argument to be made that starts with premises taken from the science of physics and ends with the conclusion of physicalism. The standard view is that this argument takes the form of a causal argument for physicalism. Roughly, physics tells us that the physical realm is causally complete, and so minds (among other entities) must be physical if they are to interact with the world as we think they do. In what (...) follows, I raise problems for this view. After an initial review of the causal argument, I begin my case by showing that the totality of physical truths do not deductively entail the causal completeness of the physical realm, using a double-prevention scenario and causation by omission to show that nonphysical causes of physical effects would not need to violate physical conservation laws. I then move on to raise problems for an inductive argument for causal completeness by drawing on the neo-Russellian view that there is no causation in fundamental physics, and so causation must itself be a realized or derived entity. I conclude by suggesting that the underlying problem is that the causal argument has fallen out of touch with the sophisticated understanding that philosophers have developed of the role of causation within physics. (shrink)

Why do people get sick? I argue that a disease explanation is best thought of as causal network instantiation, where a causal network describes the interrelations among multiple factors, and instantiation consists of observational or hypothetical assignment of factors to the patient whose disease is being explained. This paper first discusses inference from correlation to causation, integrating recent psychological discussions of causal reasoning with epidemiological approaches to understanding disease causation, particularly concerning ulcers and lung cancer. It then shows how causal (...) mechanisms represented by causal networks can contribute to reasoning involving correlation and causation. The understanding of causation and causal mechanisms provides the basis for a presentation of the causal network instantiation model of medical explanation. (shrink)

In this paper two accounts of Reichenbachian common cause systems are compared. Examples are provided which show that Hofer-Szabó and Rédei account and Hofer-Szabó et al. account is compatible, with but not equivalent, to Mazzola’s. Moreover, the difference of the two accounts with respect to their explanatory adequacy is discussed, in the light of Salmon’s statistical-relevance approach to statistical explanation.

Though common sense says that causes must temporally precede their effects, the hugely influential interventionist account of causation makes no reference to temporal precedence. Does common sense lead us astray? In this paper, I evaluate the power of the commonsense assumption from within the interventionist approach to causal modeling. I first argue that if causes temporally precede their effects, then one need not consider the outcomes of interventions in order to infer causal relevance, and that one can instead use temporal (...) and probabilistic information to infer exactly when X is causally relevant to Y in each of the senses captured by Woodward’s interventionist treatment. Then, I consider the upshot of these findings for causal decision theory, and argue that the commonsense assumption is especially powerful when an agent seeks to determine whether so-called “dominance reasoning” is applicable. (shrink)

Philosophers discussing causation take on, as one of their responsibilities, the task of specifying an ontology of causation. Both standard and non-standard accounts of that ontology make two assumptions: that the ontological category of causal relata admits a unique specification, and that cause and effect are of the same ontological type. These assumptions are rarely made explicit, but there is in fact little reason to think them true. It is argued here that, if the question has any interest, there are (...) some considerations in favor of rejecting Uniqueness and Uniformity, no good reasons in favor of them, but good reason to think that we are not in a position to make a decisive pronouncement, since some of the information needed to make a judgement on the matter is empirical in character. Philosophers have therefore made two mistakes about the relata of causation: one is to have accepted unwarranted restrictions on the categories pertinent to causation; the other is to have wrongly assumed that we are in a position to name them. (shrink)

Debates in animal cognition are frequently polarized between the romantic view that some species have human-like causal understanding and the killjoy view that human causal reasoning is unique. These apparently endless debates are often characterized by conceptual confusions and accusations of straw-men positions. What is needed is an account of causal understanding that enables researchers to investigate both similarities and differences in cognitive abilities in an incremental evolutionary framework. Here we outline the ways in which a three-dimensional model of causal (...) understanding fulfills these criteria. We describe how this approach clarifies what is at stake, illuminates recent experiments on both physical and social cognition, and plots a path for productive future research that avoids the romantic/killjoy dichotomy. (shrink)

Data from medical research are typically summarized with various types of outcome measures. We present three arguments in favor of absolute over relative outcome measures. The first argument is from cognitive bias: relative measures promote the reference class fallacy and the overestimation of treatment effectiveness. The second argument is decision-theoretic: absolute measures are superior to relative measures for making a decision between interventions. The third argument is causal: interpreted as measures of causal strength, absolute measures satisfy a set of desirable (...) properties, but relative measures do not. Absolute outcome measures outperform relative measures on all counts. (shrink)

This paper develops axiomatic foundations for a probabilistic-interventionist theory of causal strength. Transferring methods from Bayesian confirmation theory, I proceed in three steps: I develop a framework for defining and comparing measures of causal strength; I argue that no single measure can satisfy all natural constraints; I prove two representation theorems for popular measures of causal strength: Pearl's causal effect measure and Eells' difference measure. In other words, I demonstrate these two measures can be derived from a set of plausible (...) adequacy conditions. The paper concludes by sketching future research avenues. (shrink)

A system whose expected state changes with time cannot have both a forward-directed translationally invariant probabilistic law and a backward-directed translationally invariant law. When faced with this choice, science seems to favor the former. An asymmetry between cause and effect may help to explain why temporally oriented laws are usually forward-directed.

This paper proposes a game-theoretic solution of the surprise examination problem. It is argued that the game of “matching pennies” provides a useful model for the interaction of a teacher who wants her exam to be surprising and students who want to avoid being surprised. A distinction is drawn between prudential and evidential versions of the problem. In both, the teacher should not assign a probability of zero to giving the exam on the last day. This representation of the problem (...) provides a diagnosis of where the backwards induction argument, which “proves” that no surprise exam is possible, is mistaken. (shrink)

In what follows, I’ll discuss both the metaphysics and the epistemology of supervenience from a probabilistic point of view. The first half of this paper will explore how supervenience claims are related to other issues; these will include the thesis that physics is causally complete, the claim that there are emergent properties, the idea that mental properties are causally efficacious, and the notion that there are scientific laws about supervenient properties that generalize over systems that deploy different physical realizations of (...) the properties in question. The second half will examine the question of how observational evidence can lend support to supervenience claims. This problem turns out to raise some surprisingly deep issues about the nature of hypothesis testing in science. (shrink)

We argue against some of Reichenbach's claims about causal forks are incorrect. We do not see why the Second Law of Thermodynamics rules out the existence of conjunctive forks open to the past. In addition, we argue that a common effect rarely forms a conjunctive fork with its joint causes, but it sometimes does. Nevertheless, we think there is something to be said for Reichenbach's idea that forks of various kinds are relevant to explaining why we know more about the (...) past than about the future. And entropy turns out to play a role in the explanation, though not the determining role that Reichenbach envisions. (shrink)

This paper argues that the semantic facts about ‘because’ are best explained via a metaphorical treatment of metaphysical explanation that treats causal explanation as explanation par excellence. Along the way, it defends a commitment to a unified causal sense of ‘because’ and offers a proprietary explanation of grounding skepticism. With the causal metaphor account of metaphysical explanation on the table, an extended discussion of the relationship between conceptual structure and metaphysics ends with a suggestion that the semantic facts about ‘because’ (...) tell against grounding-causation unity. (shrink)

It has not been sufficiently considered in philosophical discussions of ceteris paribus (CP) laws that distinct kinds of CP-laws exist in science with rather different meanings. I distinguish between (1.) comparative CP-laws and (2.) exclusive CP-laws. There exist also mixed CP-laws, which contain a comparative and an exclusive CP-clause. Exclusive CP-laws may be either (2.1) definite, (2.2) indefinite or (2.3) normic. While CP-laws of kind (2.1) and (2.2) exhibit deductivistic behaviour, CP-laws of kind (2.3) require a probabilistic or non-monotonic reconstruction. (...) CP-laws of kind (1) may be both deductivistic or probabilistic. All these kinds of CP-laws have empirical content by which they are testable, except CP-laws of kind (2.2) which are almost vacuous. Typically, CP-laws of kind (1) express invariant correlations, CP-laws of kind (2.1) express closed system laws of physical sciences, and CP-laws of kind (2.3) express normic laws of non-physical sciences based on evolution-theoretic stability properties. (shrink)

The paper examines definitions of ‘cause’ in the epidemiological literature. Those definitions all describe causes as factors that make a difference to the distribution of disease or to individual health status. In the philosophical jargon, causes in epidemiology are difference-makers. Two claims are defended. First, it is argued that those definitions underpin an epistemology and a methodology that hinge upon the notion of variation, contra the dominant Humean paradigm according to which we infer causality from regularity. Second, despite the fact (...) that causes be defined in terms of ‘difference-making’, this cannot fixes the causal metaphysics. Causality in epidemiology ought to be interpreted according to the epistemic theory. In this approach relations are deemed causal depending on the evidence and on the available methods. Indeed, evidence to establish causal claims requires difference-making considerations; furthermore, those definitions of cause reflect the ‘variational’ epistemology and methodology of epidemiology. (shrink)

Evidential pluralists, like Federica Russo and Jon Williamson, argue that causal claims should be corroborated by establishing both the existence of a suitable correlation and a suitable mechanism complex. At first glance, this fits well with mixed method research in the social sciences, which often involves a pluralist combination of statistical and mechanistic evidence. However, statistical evidence concerns a population of cases, while mechanistic evidence is found in individual case studies. How should researchers combine such general statistical evidence and specific (...) mechanistic evidence? This article discusses a very recent answer to this question, ‘multi-method large-N qualitative analysis’ or multi-method LNQA, popular in political science and international relations studies of rare events like democratic transitions and cease-fire agreements. Multi-method LNQA combines a comprehensive study of all relevant event cases with statistical analysis, in an attempt to solve the issues of generalization faced by other types of qualitative research, such as selection bias and lack of representativeness. I will argue that the kind of general causal claim that multi-method LNQA is after, however, is crucially different from the average treatment effect found in statistical analysis and can in fact only be supported with mechanistic evidence. I conclude from this that mixed method research, and thereby evidential pluralism, may be inappropriate in this context. (shrink)

Empirical research has recently emerged as a key method for understanding the nature of causation, and our concept of causation. One thread of research aims to test intuitions about the nature of causation in a variety of classic cases. These experiments have principally been used to try to resolve certain debates within analytic philosophy, most notably that between proponents of transference and dependence views of causation. The other major thread of empirical research on our concept of causation has investigated the (...) role that normative considerations play in causal judgments. These experimental results suggest that philosophical accounts of our concept of causation should take a broader view of what might be relevant. For both lines of research, we describe some of the significant experiments and outline key philosophical morals that have been drawn, all while pointing out various limitations. We conclude by considering other kinds of empirical research that should be philosophically interesting for those studying the nature of causation and our concept of causation. In particular, we point towards the need for philosophical research about causal perception, causal reasoning, and causal learning, as well as ways in which this research could play a role in prescriptive metaphysics. (shrink)

An attempt is made to defend realism and the absence of space-like causation in quantum mechanics, by invoking indeterminism and a new necessary condition for stochastic causality, we term robustness. This condition is defended against recent critical attacks by Cartwright and Jones, and by Healey, and the violation of the robustness condition in Bell-type correlation experiments is shown to follow if an appropriate interpretation of the state vector is employed.

The explanatory role of natural selection is one of the long-term debates in evolutionary biology. Nevertheless, the consensus has been slippery because conceptual confusions and the absence of a unified, formal causal model that integrates different explanatory scopes of natural selection. In this study we attempt to examine two questions: (i) What can the theory of natural selection explain? and (ii) Is there a causal or explanatory model that integrates all natural selection explananda? For the first question, we argue that (...) five explananda have been assigned to the theory of natural selection and that four of them may be actually considered explananda of natural selection. For the second question, we claim that a probabilistic conception of causality and the statistical relevance concept of explanation are both good models for understanding the explanatory role of natural selection. We review the biological and philosophical disputes about the explanatory role of natural selection and formalize some explananda in probabilistic terms using classical results from population genetics. Most of these explananda have been discussed in philosophical terms but some of them have been mixed up and confused. We analyze and set the limits of these problems. (shrink)

Analogical reasoning addresses the question how evidence from various phenomena can be combined and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up (...) a common intuition according to which analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts. (shrink)

Objective probability, or objective chance, is the probability of some event occurring in the future independent of what anyone thinks. This paper presents and defends a theory of objective chance. I develop an informal analysis of objective chance, taking the common sense picture underlying our talk about the likelihood of future events as our starting point. A formal semantics is introduced, and I argue that the theory presented satisfies certain criteria of adequacy for a theory of probability.

Sometimes instances of perceived causation turn out to lack causal relata. The reasons may vary. Causation may display itself as prevention, or as omission, and in some cases causation occurs within such complex environments that few of the things we associate with causes and effects are true of them, etc. But even then, there may be causal explanations to be had. This suggests that the explanatory power of causal reports have other sources than the relation between cause and effect. In (...) this paper it is argued that the causal mechanisms we allude to in explanations have relevant determinables other than the traditionally acknowledged ones. The traditional but in this aspect mistaken view of causation is to be blamed. Discernability, complexity of manifestation, originality, and even stability have often been overlooked. We know, that, in fact, heat is a constant attendant of flame; but what is the connexion between them, we have no room so much as to conjecture or imagine. (Hume 1777, VII. 2, 64). (shrink)

Understanding probabilities as something other than point values has often been motivated by the need to find more realistic models for degree of belief, and in particular the idea that degree of belief should have an objective basis in “statistical knowledge of the world.” I offer here another motivation growing out of efforts to understand how chance evolves as a function of time. If the world is “chancy” in that there are non-trivial, objective, physical probabilities at the macro-level, then the (...) chance of an event e that happens at a given time is \ until it happens. But whether the chance of e goes to one continuously or not is left open. Discontinuities in such chance trajectories can have surprising and troubling consequences for probabilistic analyses of causation and accounts of how events occur in time. This, coupled with the compelling evidence for quantum discontinuities in chance’s evolution, gives rise to a “continuity bind” with respect to chance probability trajectories. I argue that a viable option for circumventing the continuity bind is to understand the probabilities “imprecisely,” that is, as intervals rather than point values. I then develop and motivate an alternative kind of continuity appropriate for interval-valued chance probability trajectories. (shrink)

Analyses of singular causation often make use of the idea that a cause increases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analysed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way, it becomes clearer that the ‘behaviour’ of probability functions in (...) small intervals about the times in question ought to be of concern. In this article, I make an extended case that causal theorists employing the ‘probability raising’ idea should pay attention to the continuity question. Specifically, if the probability functions are ‘jumping about’ in ways typical of discontinuous functions, then the stability of the relevant probability increase is called into question. The rub, however, is that sweeping requirements for either continuity or discontinuity are problematic and, as I argue, this constitutes a ‘continuity bind’. Hence more subtle considerations and constraints are needed, two of which I consider: utilizing discontinuous first derivatives of continuous probability functions, and abandoning point probability for imprecise probability. _1_ Introduction _2_ Probability Trajectories and Continuity _2.1_ Probability trajectories _2.2_ Causation as discontinuous jumps _2.3_ Against systematic discontinuity _3_ Broader Discontinuity Concerns _4_ The Continuity Bind _4.1_ Retaining continuity with discontinuous first derivatives _4.2_ Imprecise probability trajectories _5_ Concluding Remarks Appendix. (shrink)