The aim of this paper is to explicate causal generalizations such as.

Machamer, Darden, and Craver argue that causal explanations explain effects by describing the operations of the mechanisms which produce them. One of this paper’s aims is to take advantage of neglected resources of Mechanism to rethink the traditional idea that actual or counterfactual natural regularities are essential to the distinction between causal and non-causal co-occurrences, and that generalizations describing natural regularities are essential components of causal explanations. I think that causal productivity and regularity are (...) by no means the same thing, and that the Regularists are mistaken about the roles generalizations play in causal explanation. Humean, logical empiricist, and other Regularist accounts of causal explanation have had the unfortunate effect of distracting philosophers’ from important non-explanatory scientific uses of laws and lesser generalizations which purport to describe natural regularities. My second aim is to characterize some of these uses, illustrating them with examples from neuroscientific research. (shrink)

In defending the scientific legitimacy of ceteris paribus qualified causal generalizations, we situate and specify the reference of the ceteris paribus proviso within a fundamental causal framework consisting of causal agents, pathways of influence, mediators, moderators, and causal consequences. In so doing, we provide an explication of the reference and utility of the ceteris paribus proviso in terms of mediators and moderators as these constitute the range of factors that can impinge on the relation between (...) cause and effect. We argue that the conceptual causal roadmap embodied by the ceteris paribus qualification serves as a schematic template for the ongoing identification of causally relevant factors and plays an indispensable heuristic role in advancing scientific inquiry into causal relations. We then provide guidelines for differentiating between acceptable and unacceptable uses of ceteris paribus and describe how mediators and moderators conceptually encompassed by the ceteris paribus proviso can be employed in evaluating the meaning and acceptability of proposed ceteris paribus causal generalizations, as well serve as a guide to investigators in the process of designing studies to identify a causal agent, mediators, moderators, pathways of influence, and causal consequences. 2012 APA, all rights reserved). (shrink)

The issue of causal comparability in the social sciences underlies matters of both generalization and extrapolation. After critiquing two existing interpretations of comparability, due to Hitchcock and Hausman, I propose a distinction between ontological and epistemic comparability. While the former refers to whether two cases are actually comparable, the latter respects that in cases of incomplete information, we need to rely on whatever evidence we have of comparability. I argue, using a political science case study, that in those cases (...) of imperfect information, an epistemic homogeneity criterion can be an adequate justification for generalization. (shrink)

Deviant causal chain problems arise in many settings. The most famous instance of the problem is the Gettier problem, but the problem also arises in the philosophy of action and perception. Usually, attempts to tackle these problems try to solve them individually. This paper takes a different approach: I propose a general solution to the problem. I begin by providing a solution to the deviant causal chain problem for skillful performance, and I argue that the solution can be (...) extended to solve the Gettier problem and the deviant causal chain problems for perception and intentional action. As I develop my solution to these problems, I also compare it with other solutions to bring out the advantages of my approach. I then explain why the solution generalizes: my solution provides us with an analysis of disposition manifestation, which is the key to ruling out deviance. I conclude by considering objections and giving my replies. (shrink)

A central question in cognitive research concerns how new properties are generalized to categories. This article introduces a model of how generalizations involve a process of causal inference in which people estimate the likely presence of the new property in individual category exemplars and then the prevalence of the property among all category members. Evidence in favor of this causal‐based generalization (CBG) view included effects of an existing feature’s base rate (Experiment 1), the direction of the (...) class='Hi'>causal relations (Experiments 2 and 4), the number of those relations (Experiment 3), and the distribution of features among category members (Experiments 4 and 5). The results provided no support for an alternative view that generalizations are promoted by the centrality of the to‐be‐generalized feature. However, there was evidence that a minority of participants based their judgments on simpler associative reasoning processes. (shrink)

This article rebuts Ramsey's earlier theory, in 'Universals of Law and of Fact', of how laws of nature differ from other true generalisations. It argues that our laws are rules we use in judging 'if I meet an F I shall regard it as a G'. This temporal asymmetry is derived from that of cause and effect and used to distinguish what's past as what we can know about without knowing our present intentions.

How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical how-possibly (...) explanation which establishes claims of mathematical dependence. The account developed reveals how mathematical knowledge can inform claims about the world, allow ‘what-if-things-had-been-different’ inferences, and thus improve our understanding. (shrink)

A hallmark of ecological research is dealing with complexity in the systems under investigation. One strategy is to diminish this complexity by constructing models and theories that are general. Alternatively, ecologists can constrain the scope of their generalizations to particular phenomena or types of systems. However, research employing the second strategy is often met with scathing criticism. I offer a theoretical argument in support of moderate generalizations in ecological research, based on the notions of interdependence and causal (...) heterogeneity and their effect on the trade-off between generality and realism. (shrink)

I advance a new theory of causal relevance, according to which causal claims convey information about conditional probability functions. This theory is motivated by the problem of disjunctive factors, which haunts existing probabilistic theories of causation. After some introductory remarks, I present in Section 3 a sketch of Eells's (1991) probabilistic theory of causation, which provides the framework for much of the discussion. Section 4 explains how the problem of disjunctive factors arises within this framework. After rejecting three (...) proposed solutions, I offer in Section 6 a new approach to causation that avoids the problem. Decision-theoretic considerations also support the new approach. Section 8 develops the consequences of the new theory for causal explanation. The resulting theory of causal explanation incorporates the new insights while respecting important work on scientific explanation by Salmon (1971), Railton (1981), and Humphreys (1989). My conclusions are enumerated in Section 9. (shrink)

Peter Alexander: It is presumably admitted that laws, whether causal or not, are universal in form; they are appropriately stated in universal categoricals or unrestricted hypotheticals. I assume that this is not at issue in the question set. I take our question to be this: given that causal laws are universal statements, can they be said to be about, to apply to, to hold for, individual things? -/- Peter Downing: Mr. Alexander maintains that there are 'irreducibly singular' (...) class='Hi'>causal statements, and that from this it follows that causal laws need not be purely general. The view that there are irreducibly singular causal statements appears to commit Alexander to rejecting two theses: (i) that singular causal statements are analysable into statements containing specific generalizations, [...] (ii) That singular causal statements are analysable into statements containing incompletely specified generalizations [...]. Thesis (i) is, I think, clearly false. [...] Thesis (ii), however, is not easily refuted. (shrink)

This paper aims to implement Bell’s notion of local causality into a framework, called local physical theory, which is general enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will then arise as the classical case of our definition. First, we investigate what is needed for a local physical theory to be locally causal. Then we compare local causality with Reichenbach’s common cause principle and relate both to the (...) Bell inequalities. We find a nice parallelism: both local causality and the common cause principle are more general notions than captured by the Bell inequalities. Namely, Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively. (shrink)

A primary object of causal reasoning concerns what would happen to a system under certain interventions. Specifically, we are often interested in estimating the probability distribution of some random variables that would result from forcing some other variables to take certain values. The renowned do-calculus gives a set of rules that govern the identification of such post-intervention probabilities in terms of pre-intervention probabilities, assuming available a directed acyclic graph that represents the underlying causal structure. However, a DAG (...) class='Hi'>causal structure is seldom fully testable given preintervention, observational data, since many competing DAG structures are equally compatible with the data. In this paper we extend the do-calculus to cover cases where the available causal information is summarized in a so-called partial ancestral graph that represents an equivalence class of DAG structures. The causal assumptions encoded by a PAG are significantly weaker than those encoded by a full-blown DAG causal structure, and are in principle fully testable by observed conditional independence relations. (shrink)

Causal sets are a particular class of partially ordered sets, which are proposed as basic models of discrete space-time, specially in the field of quantum gravity. In this context, we show the existence of temporal foliations for any causal set, or more generally, for a causal space. Moreover, we show that automorphisms of a large class of infinite causal sets fall into two classes 1) Automorphisms of spacelike hypersurfaces in some given foliation, or 2) Translations in (...) time. More generally, we show that for any automorphism \ of a generic causal set \, there exists a partition of \ into finitely many subcausets, on each of which or above hold. These subcausets can be assumed connected if, in addition, there are enough distinct orbits under \. (shrink)

My aim in this paper is to make a case for the singularist view from the perspective of a mechanical theory of causation, and to explain what, from this perspective, causal generalizations mean, and what role they play within the mechanical theory.

In lieu of an abstract, here is a brief excerpt of the content:CAUSALITY AND GENERALITY IN THE TREATISE AND THE TRACTATUS In the Tractatus Wittgenstein cryptically rejects the existence of a causal connection (or relation or nexus) : 5.135There is no possible way of making an inference from the existence of one situation to the existence of another, entirely different situation. 5.136There is no causal nexus to justify such an inference. 5.1361 We cannot infer the events of the (...) future from those of the present. Belief stition. Belief in the causal nexus is super1 And he later proceeds to add: 6.37 There is no compulsion making one thing happen because another has happened. The only necessity that exists is logical necessity. What he is claiming can be understood in terms of the "Logical Atomism* of the Tractatus. Atomic sentences, composed of a monadic predicate or a relational predicate and a suitable number of subject terms, represent situations or possible facts. The existence of a represented situation is the ground of truth for (or condition for the truth of or explanation of the truth of) the representing atomic sentence. We can consider 2 such atomic situations or atomic facts to be composed of a monadic property or relational property and an appropriate number of particulars. (This is a matter of some debate among interpreters of the Tractatus, but that issue does not really affect the question at issue in this paper. So, I will simply treat the view in the Tractatus along the lines of Russell's more explicit version of logical atomism in his lectures of 1918.) The world, according to Wittgenstein, is made up of such facts. This is the point of: 1.11The world is the totality of facts, not of things. 1.12The facts in logical space are the world. 1.13The world divides into facts. Consider, then, the claim that a's being F is the cause of its being G. This suggests that we construe causality in terms of a relation between the situations represented by 'Fa' and 'Ga'. With 1C representing a relation or nexus of causality, we could express that situation by: (1)C(Fa, Ga). The existence of the situation represented by (1) would then ground or explain the truth of (1). But that would mean that we recognize a relation of causality and causal relations between facts or situations. I cannot here argue, but will simply assert, that Wittgenstein's logical atomism in the Tractatus is incompatible with the recognition of relations between facts. However, one point that will be relevant to the concerns of this paper is easy to see. Logical atomism involves the claim — 1.21 Each item can be the case or not the case while everything else remains the same. This is not compatible with the recognition of the relation C and a fact grounding the truth of (1), for then Fo and Ga would not be items that were "independent" in the sense of 1.21. Hence, one who holds Wittgenstein's views about the independence of atomic facts cannot recognize causal relations between such facts. Thus, no fact is represented by (1) and C cannot relate atomic facts. The same results would hold if one suggested, in place of (1), that there was a fact corresponding to (2)(X)(Fx * Gx), where we read the arrow as the "causal" arrow — anything's being F causes it to be G. For, if there were a fact corresponding to (2), it would guarantee the link between the purported atomic facts Fa and Ga, since (3)Fa + Ga would be a logical consequence of (2), and we are back to a case like (1), with the arrow replacing 'C. (2) would also be problematic in that it would be some sort of "general" fact, which Wittgenstein also rejects. Thus, as Wittgenstein sees it there is no basis in the world for the explanation of causal statements. If the sentence (4)' (x) (Fx O Gx) ' is a statement of causal law is true, it is so simply because the list of atomic facts will contain the atomic sentence 'Ga' if it contains 'Fa'. That is, (4) is true, not because of any special fact corresponding to (5)(X... (shrink)

Analysts often use data-driven approaches to supplement their knowledge when selecting covariates for effect estimation. Multiple variable selection procedures for causal effect estimation have been devised in recent years, but additional developments are still required to adequately address the needs of analysts. We propose a generalized Bayesian causal effect estimation algorithm to perform variable selection and produce double robust estimates of causal effects for binary or continuous exposures and outcomes. GBCEE employs a prior distribution that targets the (...) selection of true confounders and predictors of the outcome for the unbiased estimation of causal effects with reduced standard errors. The Bayesian machinery allows GBCEE to directly produce inferences for its estimate. In simulations, GBCEE was observed to perform similarly or to outperform DR alternatives. Its ability to directly produce inferences is also an important advantage from a computational perspective. The method is finally illustrated for the estimation of the effect of meeting physical activity recommendations on the risk of hip or upper-leg fractures among older women in the study of osteoporotic fractures. The 95% confidence interval produced by GBCEE is 61% narrower than that of a DR estimator adjusting for all potential confounders in this illustration. (shrink)

The principle of causality has traditionally been formulated in terms of the dynamic equations of classical physics. It has been believed that only stable (conservative) systems can be meaningfully studied in this way. The evolutionary systems studied by social scientists and biologists are non-conservative, and so are excluded from the traditional formulation of causality. The author argues that causal laws for non-conservative systems can be meaningfully formulated. An example based on Malthus'' population theory is given.

All accounts of causality that presuppose the propagation or transfer or some physical stuff to be an essential part of the causal relation rely for the force of their causal claims on a principle of conservation for that stuff. General Relativity does not permit the rigorous formulation of appropriate conservation principles. Consequently, in so far as General Relativity is considered and fundamental physical theory, such accounts of causality cannot be considered fundamental. The continued use of such accounts of (...) causality ought not be proscribed, but justification is due from those who would use them. (shrink)

Causation appears to present us with an interpretative difficulty. While arguably a redundant relation given fundamental physics, it is nevertheless apparently pragmatically indispensable. This chapter revisits certain arguments made previously by the author for these claims with the benefit of hindsight, starting with the role of causal models in the human sciences, and attempting to explain why it is not possible to straightforwardly ground such models in fundamental physics. This suggests that further constraints, going beyond physics, are needed to (...) legitimate such models. These supplementary constraints could be reified, but that would seem to conflict with the completeness of physics. A response is to emphasize the practical role of causal talk, and the author suggests that a fictionalist approach might be worth exploring. After clarifying fictionalism as a general approach, they carry out in some detail the project of clarifying what a fictionalist attitude to causation would involve. (shrink)

Compared to constraint-based causal discovery, causal discovery based on functional causal models is able to identify the whole causal model under appropriate assumptions [Shimizu et al. 2006; Hoyer et al. 2009; Zhang and Hyvärinen 2009b]. Functional causal models represent the effect as a function of the direct causes together with an independent noise term. Examples include the linear non-Gaussian acyclic model, nonlinear additive noise model, and post-nonlinear model. Currently, there are two ways to estimate the (...) parameters in the models: dependence minimization and maximum likelihood. In this article, we show that for any acyclic functional causal model, minimizing the mutual information between the hypothetical cause and the noise term is equivalent to maximizing the data likelihood with a flexible model for the distribution of the noise term. We then focus on estimation of the PNL causal model and propose to estimate it with the warped Gaussian process with the noise modeled by the mixture of Gaussians. As a Bayesian nonparametric approach, it outperforms the previous one based on mutual information minimization with nonlinear functions represented by multilayer perceptrons; we also show that unlike the ordinary regression, estimation results of the PNL causal model are sensitive to the assumption on the noise distribution. Experimental results on both synthetic and real data support our theoretical claims. (shrink)

The construction of causal models for research in business ethics has become fashionable in recent years. This paper explores four recent proposals, comparing and contrasting their views. The primary purpose of this paper is to expose several confusions inherent in such models and to account for these errors in terms of a failure to distinguish between models as theories and models as representing a research tradition. We conclude with a brief set of recommendations for linking two major research traditions (...) in business ethics: empiricism and ethical theory. (shrink)

Both philosophers and psychologists have argued for the existence of distinct kinds of explanations, including teleological explanations that cite functions or goals, and mechanistic explanations that cite causal mechanisms. Theories of causation, in contrast, have generally been unitary, with dominant theories focusing either on counterfactual dependence or on physical connections. This paper argues that both approaches to causation are psychologically real, with different modes of explanation promoting judgments more or less consistent with each approach. Two sets of experiments isolate (...) the contributions of counterfactual dependence and physical connections in causal ascriptions involving events with people, artifacts, or biological traits, and manipulate whether the events are construed teleologically or mechanistically. The findings suggest that when events are construed teleologically, causal ascriptions are sensitive to counterfactual dependence and relatively insensitive to the presence of physical connections, but when events are construed mechanistically, causal ascriptions are sensitive to both counterfactual dependence and physical connections. The conclusion introduces an account of causation, an "exportable dependence theory," that provides a way to understand the contributions of physical connections and teleology in terms of the functions of causal ascriptions. (shrink)

In this paper, I adopt the view that if general forces or processes can be detected in ecology, then the principles or models that represent them should provide predictions that are approximately correct and, when not, should lead to the sorts of intervening factors that usually make trouble. I argue that Lotka–Volterra principles do not meet this standard; in both their simple “strategic” and their complex “tactical” forms they are not approximately correct of the findings of the laboratory experiments and (...) historical studies most likely to confirm them; nor do they instruct ecologists where to look for likely intervening factors. Evidence drawn from long-term case studies and other available data sets suggests that the populations of predators and their prey are not regulated by an interaction between them but are controlled by transient, contingent, and accidental events that affect each animal and each population individualistically. This paper argues that the presence of general forces or processes in ecology should be determined by comparing competing models of these forces not just to each other or to a null model but also to case studies that may challenge theoretical approaches with convincing individualistic causal accounts of the phenomena. (shrink)

Two variables are usually recognised as determinants of human causal learning: the contingency between a candidate cause and effect, and the temporal and/or spatial contiguity between them. A common finding is that reductions in temporal contiguity produce concomitant decrements in causal judgement. This finding had previously (Shanks & Dickinson, 1987) been interpreted as evidence that causal induction is based on associative learning processes. Buehner and May (2002, 2003, 2004) have challenged this notion by demonstrating that the impact (...) of temporal delay depends on expectations about the timeframe between cause and effect. A corollary of this knowledge-mediation account is that in certain situations longer delays could facilitate, while shorter delays should impair, causal learning. Here we present two experiments involving a physical apparatus that demonstrate a detrimental effect of contiguity under certain conditions. In contrast to all previous studies, delays universally promoted causal learning. This evidence is clearly at variance with the notion of a bottom-up contiguity bias in causal induction. A new, more general timeframe bias is discussed. (shrink)

In this contribution, I explore the possibility of characterizing the emergence of time in causal set theory (CST) in terms of the growing block universe (GBU) metaphysics. I show that although GBU seems to be the most intuitive time metaphysics for CST, it leaves us with a number of interpretation problems, independently of which dynamics we choose to favor for the theory —here I shall consider the Classical Sequential Growth and the Covariant model. Discrete general covariance of the CSG (...) dynamics does not allow us to individuate a single history of the universe (defined by a causal history of different causal sets), thereby making the claim that ‘the past exists’ at best problematic. In addition, because the evolution of the universe in CSG dynamics leads to an outward branching causal tree, it becomes impossible to determine a proper ‘line of becoming’, thereby blurring the presentists’ claim that only the present exists. Similarly, the covariant approach runs into the same, if not even more severe problems, since each configuration of the universe would amount to a set of possible causal sets, thereby making the individuation of a single configuration of the universe —and thus the physical interpretation of the theory— implausible. (shrink)

Causal models provide a framework for precisely representing complex causal structures, where specific models can be used to efficiently predict, infer, and explain the world. At the same time, we often do not know the full causal structure a priori and so must learn it from data using a causal model search algorithm. This chapter provides a general overview of causal models and their uses, with a particular focus on causal graphical models (the most (...) commonly used causal modeling framework) and methods for learning such models from observational and experimental data. The chapter concludes with two examples of productive causal search and modeling in experimental philosophy. (shrink)

Donald Davidson brought to our attention deviant causal chains as a problem for causal theories of action. Consider Davidson's own example: " A climber might want to rid himself of the weight and danger of holding another man on a rope, and he might know that by loosening his hold on the rope he could rid himself of the weight and danger. This belief and want might so unnerve him as to cause him to loosen his hold, and (...) yet it might be the case that he never chose to loosen his hold, nor did he do it intentionally. " The loosening of the hold on the rope is an action, according to a simple causal theory of action earlier developed by Davidson , if we can describe it in a way that renders it intentional under that description. Is there a way of describing the climber's loosening of his hold of the rope as intentional? Did he intentionally loosen his hold? Well, his loosening his hold is both rationalized and explained causally with reference to the beliefs and desires held by the climber. But there seems to be something wrong with the causal chain.Is there a simple fix? Could we not say that even if the loosening of the hold on the rope is caused by a desire held by the climber it is not caused by any proximate desire of the climber ? Or, to give a new twist to this well-known argument, could we not say that the loosening of the hold on the rope is not caused in a way that is responsive to the desire? This latter idea has recently been suggested by Markus E. Schlosser as a simple solution to the …. (shrink)

It is still a matter of controversy whether the Principle of the Common Cause (PCC) can be used as a basis for sound causal inference. It is thus to be expected that its application to quantum mechanics should be a correspondingly controversial issue. Indeed the early 90’s saw a flurry of papers addressing just this issue in connection with the EPR correlations. Yet, that debate does not seem to have caught up with the most recent literature on causal (...) inference generally, which has moved on to consider the virtues of a generalised PCC-inspired condition, the so-called Causal Markov Condition (CMC). In this paper we argue that the CMC is an appropriate benchmark for debating possible causal explanations of the EPR correlations. But we go on to take issue with some pronouncements on EPR by defenders of the CMC. (shrink)

This paper provides a general introduction to the use of causal models in the metaphysics of causation, specifically structural equation models and directed acyclic graphs. It reviews the formal framework, lays out a method of interpretation capable of representing different underlying metaphysical relations, and describes the use of these models in analyzing causation.

To what extent general intelligence mechanisms are associated with causal thinking is unclear. There has been little work done experimentally to determine which developing cognitive capacities help to integrate causal knowledge into explicit systems. To investigate this neglected aspect of development, 138 children aged 5–11 studying at mainstream primary schools completed a battery of three intelligence tests: one investigating verbal ability, another looking at verbal analogical, and a third assessing non-verbal/fluid reasoning. Children were also interviewed over the course (...) of three causal tasks, with the results showing that the developmental paths exhibited uneven profiles across the three causal phenomena. Children consistently found that explaining solution, where substances disappeared toward the end of the process, was more challenging. The confirmatory factor analyses suggested that the impact of cognitive ability factor in explicitly identifying causal relations was large. The proportion of the direct effect of general intelligence was 66% and it subsumed the variances of both verbal measures. Of this, 37% was the indirect effect of age. Fluid reasoning explained a further 28% of the variance, playing a unique role in causal explanation. The results suggested that, overall, cognitive abilities are substantially related to causal reasoning, but not entirely due to developmental differences in “g” during the age periods studied. (shrink)

This work explains how different theories of causation confront causal overdetermination. Chapters clarify the problem of overdetermination and explore its fundamental aspects. It is argued that a theory of causation can account for our intuitions in overdetermination cases only by accepting that the adequacy of our claims about causation depends on the context in which they are evaluated.The author proposes arguments for causal contextualism and provides insight which is valuable for resolution of the problem. -/- These chapters enable (...) readers to quickly absorb different perspectives on overdetermination and important theories of causation, therefore it is a work that will have a broad appeal. (shrink)

Residual confounding is a common source of bias in observational studies. In this article, we build upon a series of sensitivity analyses methods for residual confounding developed by Brumback et al. and Chiba whose sensitivity parameters are constructed to quantify deviation from conditional exchangeability, given measured confounders. These sensitivity parameters are combined with the observed data to produce a “bias-corrected” estimate of the causal effect of interest. We provide important generalizations of these sensitivity analyses, by allowing for arbitrary (...) exposures and a wide range of different causal effect measures, through the specification of the target causal effect as a parameter in a generalized linear model with the arbitrary link function. We show how our generalized sensitivity analysis can be easily implemented with standard software, and how its sensitivity parameters can be calibrated against measured confounders. We demonstrate our sensitivity analysis with an application to publicly available data from a cohort study of behavior patterns and coronary heart disease. (shrink)

Einstein and Hilbert both struggled to reconcile general covariance and causality in their early work on general relativity. In Einstein’s case, this first led to his infamous “hole argument”, a stumbling block that persuaded him early on that generally covariant field equations for gravitation could never be found. After his breakthrough to general covariance in the fall of 1915, the resolution came in form of the “point-coincidence argument.” Hilbert from the beginning took a different view of the “causality problem,” though (...) he shifted his position somewhat in the light of Einstein’s breakthrough in November 1915. Nevertheless, his aim was to establish initial conditions that would lead to a well-defined Cauchy problem in general relativity. Hilbert consistently advocated the use of coordinate conditions in order to obtain solutions of the field equations that would maintain the causal ordering of events. Einstein’s “causality problem” thus differs from that of Hilbert, and the latter was never a victim of Einstein’s “hole argument.”. (shrink)

Written by pioneers in the field, this practical book presents an authoritative yet accessible overview of the methods and applications of causal inference. The text provides a thorough introduction to the basics of the theory for non-time-varying treatments and the generalization to complex longitudinal data.

Sections include: experiments and generalised causal inference; statistical conclusion validity and internal validity; construct validity and external validity; quasi-experimental designs that either lack a control group or lack pretest observations on the outcome; quasi-experimental designs that use both control groups and pretests; quasi-experiments: interrupted time-series designs; regresssion discontinuity designs; randomised experiments: rationale, designs, and conditions conducive to doing them; practical problems 1: ethics, participation recruitment and random assignment; practical problems 2: treatment implementation and attrition; generalised causal inference: a (...) grounded theory; generalised causal inference: methods for single studies; generalised causal inference: methods for multiple studies; a critical assessment of our assumptions. (shrink)