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)

In spacetime physics any set C of events—a causal set—is taken to be partially ordered by the relation ≤ of possible causation: for p, q ∈ C, p ≤ q means that q is in p’s future light cone. In her groundbreaking paper The internal description of a causal set: What the universe looks like from the inside, Fotini Markopoulou proposes that the causal structure of spacetime itself be represented by “sets evolving over C” —that is, (...) in essence, by the topos SetC of presheaves on Cop. To enable what she has done to be the more easily expressed within the framework presented here, I will reverse the causal ordering, that is, C will be replaced by Cop, and the latter written as P—which will, moreover, be required to be no more than a preordered set. Specifically, then: P is a set of events preordered by the relation ≤, where p ≤ q is intended to mean that p is in q’s future light cone—that q could be the cause of p, or, equally, that p could be an effect of q. In that case, for each event p, the set p↓ = {q: q ≤ p} may be identified as the causal future of p, or the set of potential effects of p. In requiring that ≤ be no more than a preordering—in dropping, that is, the antisymmetry of ≤—I am, in physical terms, allowing for the possibility that the universe is of Gödelian type, containing closed timelike lines. (shrink)

The causal set programme towards a quantum theory of gravity is situated vis-à-vis the long-standing debate between eternalism (block theory) and past-presentism or possibilism (growing block theory) in the philosophy of time. It is argued that despite 'appearances' and declarations to the contrary, the programme does not side with growing block theorists when it comes to harboring a robust notion of Becoming - at least, not more than familiar relativistic theories on continuous spacetime manifolds. The problem stems mainly from (...) the postulate of discrete general covariance - a requirement imposed upon the only fully worked out kind of dynamics for causal sets to date, a dynamics of a classical stochastic process. (shrink)

More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal set theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a (...) foil to illustrate how a mathematically informed rigorous conceptualization of structure serves to identify structures in physical theories. Furthermore, a number of technical issues infesting structuralist interpretations of physical theories such as difficulties with grounding the identity of the places of highly symmetrical physical structures in their relational profile and what may resolve these difficulties can be vividly illustrated with causal sets. (shrink)

Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied to (...) discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin’s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin’s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On the one hand, my theorems support (a): the theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b): standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin’s framework. This fact poses a challenge for the proponents of Maudlin’s theory to prove it fruitful. (shrink)

ABSTRACT Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps ‘localized’, form of ‘becoming’. The possibility of fundamental becoming is nourished by the fact that the analogue of Stein’s theorem from special relativity does not hold in CST. Despite this, we find that in many ways, the debate concerning becoming parallels the well-rehearsed lines it follows in the domain of relativity. We present, however, some new twists (...) and challenges. In particular, we show that a novel and exotic notion of becoming is compatible with causal sets. In contrast to the localized becoming considered compatible with the dynamics of CST by its advocates, our novel kind of becoming, while not answering to the typical A-theoretic demands, is global and objective. _1_ Introduction _2_ The Basics of Causal Set Theory _3_ Facing the Same Dilemma? _4_ Taking Growth Seriously _5_ Conclusion. (shrink)

Causal set theory and the theory of linear structures share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied to discrete linear structures that correspond to causal sets. Moreover, I show that (...) all topological aspects of causal sets that can be described in Maudlin’s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin’s theory. The value of this theory depends crucially on whether it is true that its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On the one hand, my theorems support : the theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine : standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin’s framework. This fact poses a challenge for the proponents of Maudlin’s theory to prove it fruitful. (shrink)

Many approaches to quantum gravity -the theory that should account for quantum and gravitational phenomena under the same theoretical umbrella- seem to point at some form of spacetime emergence, i.e., the fact that spacetime is not a fundamental entity of our physical world. This tenet has sparked many philosophical discussions: from the so-called empirical incoherence problem to different accounts of emergence and mechanisms thereof. In this contribution, I focus on the partial order relation of causal set theory and argue (...) that causation can be characterized as an a-temporal constraint over the kinematic space defined by the theory. The relation constrains the growth of a new element/event with respect to the other elements/events of a given set. Therefrom, the flow of time emerges from the collection of the possible growths of the given set, where each possibility is characterized by a classical probability assigned by the dynamics of the theory. (shrink)

Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps ‘localized’, form of ‘becoming’. The possibility of fundamental becoming is nourished by the fact that the analogue of Stein’s theorem from special relativity does not hold in causal set theory. Despite this, we find that in many ways, the debate concerning becoming parallels the well-rehearsed lines it follows in the domain of relativity. We present, however, some (...) new twists and challenges. In particular, we show that a novel and exotic notion of becoming is compatible with causal sets. In contrast to the ‘localized’ becoming considered compatible with the dynamics of causal set theory by its advocates, our novel kind of becoming, while not answering to the typical A-theoretic demands, is ‘global’ and objective. (shrink)

I present aspects of causal set theory (a research programme in quantum gravity) as being en route to achieving a reduction of Lorentzian geometry to causal sets. I take reduction in philosophers' sense; and I argue that the prospects are good for there being a reduction of the type envisaged by Nagel. (I also discuss the prospects for the stronger functionalist variant of Nagelian reduction, that was formulated by Lewis.) One main theme will be causal set (...) theory's use of a physical scale (viz. the Planck scale) to formulate how it recovers a Lorentzian manifold. This use illustrates various philosophical topics relevant to reduction, such as limiting relations between theories, and the role of analogy. I also emphasise causal set theory's probabilistic method, viz. Poisson sprinkling: which is used both for formulating the reduction and for exploring its prospects. (shrink)

A large class of the dynamical laws for causal sets described by a classical process of sequential growth yields a cyclic universe, whose cycles of expansion and contraction are punctuated by single ‘‘origin elements’’ of the causal set. We present evidence that the effective dynamics of the immediate future of one of these origin elements, within the context of the sequential growth dynamics, yields an initial period of de Sitter-like exponential expansion, and argue that the resulting picture (...) has many attractive features as a model of the early universe, with the potential to solve some of the standard model puzzles without any fine-tuning. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter introduces causal set theory and identifies and articulates a 'problem of space' in this theory.

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)

Conditionals are basic for human reasoning. In our paper, we present two experiments, which for the first time systematically compare how people reason about indicative conditionals (Experiment 1) and counterfactual conditionals (Experiment 2) in causal and non-causal task settings (N = 80). The main result of both experiments is that conditional probability is the dominant response pattern and thus a key ingredient for modeling causal, indicative, and counterfactual conditionals. In the paper, we will give an overview of (...) the main experimental results and discuss their relevance for understanding how people reason about conditionals. (shrink)

The possibility question concerns the status of possibilities: do they form an irreducible category of the external reality, or are they merely features of our cognitive framework? If fundamental physics is ever to shed light on this issue, it must be done by some future theory that unifies insights of general relativity and quantum mechanics. The paper investigates one programme of this kind, namely the causal sets programme, as it apparently considers alternative developments of a given system. To (...) evaluate this claim, we prove some algebraic facts about the sequential growth of causal sets. These facts tell against alternative developments, given that causal sets are understood as particular events. We thus interpret causal sets as multi-realisable objects, like states. This interpretation, however, is undermined by an argument for the probabilistic constraint of general covariance, as it says that multiple paths along which a causal set is produced are not physically different. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter sketches how spacetime emerges in causal set theory and demonstrates how this question is deeply entangled with genuinely philosophical concerns.

An important question for the causal modeling approach is how to integrate non‐causal dependence relations such as asymmetric supervenience into the approach. The most prominent proposal to that effect (due to Gebharter) is to treat those dependence relationships as formally analogous to causal relationships. We argue that this proposal neglects some crucial differences between causal and non‐causal dependencies, and that in the context of causal modeling non‐causal dependence relationships should be represented as mutual (...) dependence relationships. We develop a new kind of model – “hybrid models” ‐ based on this suggestion, and formulate a set of axioms for those models. Our formalism has important implications for Kim's exclusion problem: whereas Gebharter's framework vindicates Kim's causal exclusion objection against nonreductive physicalism, our framework has no such implication, and can help non‐reductive physicalists vindicate the efficacy of high‐level properties. A further benefit of our formalism is that it yields a natural and plausible way of thinking about interventions in multi‐level contexts. (shrink)

This comment discusses the suggestions made in Mahoney’s “Constructivist Set-Theoretic Analysis: An Alternative to Essentialist Social Science” (2023). Mahoney presents an approach to cases of intersectionality or confounding which produce causal results unlike those that result from traditional net effects causal modeling. He presents it as an alternative to “essentialism,” which he describes as a cognitive error. These alternatives have the same problems as those he attributes to net effects analysis, with one exception: the method does allow for (...) the identification of subpopulations with different causal mechanisms producing different outcomes for this subpopulation. (shrink)

In this paper, we attempt to explicate Salmon’s idea of a causal process, as defined in terms of the mark method, in the context of C*-dynamical systems. We prove two propositions, one establishing mark manifestation infinitely many times along a given interval of the process, and, a second one, which establishes continuous manifestation of mark with the exception of a countable number of isolated points. Furthermore, we discuss how these results can be implemented in the context of the Haag–Araki (...) theories of relativistic quantum fields on Minkowski spacetime. (shrink)

Graphical models are a powerful tool for causal model specification. Besides allowing for a hierarchical representation of variable interactions, they do not require any a priori specification of the functional dependence between variables. The construction of such graphs hence often relies on the mere testing of whether or not model variables are marginally or conditionally independent. The identification of causal relationships then solely requires some general assumptions on the relation between stochastic and causal independence, such as the (...) Causal Markov Condition and the Faithfulness Condition (Spirtes et al. 2000; Pearl 2000). However, a procedure would require further assumptions to hold. Namely those the independence tests themselves are based on. In continuous settings, Spirtes et al. (2000) suggest causal inference based on a very restrictive formulation of independence, that is, vanishing partial correlations. Such a measure does, however, limit the applicability of causal inference to linear systems. This constitutes a serious drawback especially for the social sciences where an a priori specification of the functional form proves difficult or at odds with linearity. In short: graphical models theoretically reduce specification uncertainty regarding functional dependence, but their implementation in practice deprives them of this virtue. In this paper we investigate how causal structures in continuous settings can be identified when both functional forms and probability distributions of the variables remain unspecified. We focus on tests exploiting the fact that if X and Y are conditionally independent given a set of variables Z, the two conditional densities f (X|Y, Z) and f (X|Z) must coincide. We start by estimating the conditional densities f(X|Y, Z) and f(X|Z) via nonparametric techniques (kernel methods). We proceed by testing if some metric expressing the distance between these very conditional densities is sufficiently close to zero. Out of several metrics available in the literature to express such distance we choose two, the Euclidean, and the Hellinger distance. We investigate in a Monte Carlo study how different tests involving either measure are able to detect statistical independence, conditioned on a small set of variables. One limitation may result from nonparametric density estimation being subject to the curse of dimensionality. As the number of variables increases, the estimated empirical density converges at a slower rate to its population value. To compensate this drawback we use a local bootstrap procedure which consists of resampling the data for each test. While local bootstrap strongly increases the computational time of the test, it succeeds in counterbalancing the curse of dimensionality. (shrink)

Until recently, realists and anti-realists alike have assumed that any approximations which appear in explanations and confirmations in the mathematically oriented physical and biological sciences are “mere distractions” (Laymon 1989, p. 353). When approximation techniques must be used, they are typically justified by appeals to their numerical accuracy. However, recent interest in computational complexity in the sciences has revealed that numerical accuracy is not always the only criterion which should be invoked to justify the use of approximations. Cartwright (1983), Franklin (...) (1988) and others have suggested that causal accuracy should be added as a criterion.Numerical and causal accuracy are important. However, they form a sufficient set of justificational criteria only when certain—often unstated—conditions obtain. These conditions are actually assumptions which are often not satisfied, especially in the computationally complex situations which characterize discovery and exploratory contexts. In these contexts, we need to concentrate on “delineating a justificatory set which is relevant to [the] given epistemic situation” (Duran 1988, p. 273). (shrink)

I argue that numerical and causal accuracy arguments can be successful only if: (1) the theories in use are known to be true, (2) computational difficulties do not exist, and (3) the experimental data are stable and resolved. When any one or more of these assumptions are not satisfied, additional justificational considerations must be invoked. I illustrate the need for range of validity and intelligibility claims with examples drawn from chemical kinetics. My arguments suggest that the realist and anti-realist (...) accounts of justification are incomplete. Finally, I sketch some reasons why additional justificatory criteria are needed. (shrink)

Causal and predictive learning research often employs intuitive and familiar hypothetical scenarios to facilitate learning novel relationships. The allergist task, in which participants are asked to diagnose the allergies of a fictitious patient, is one example of this. In such studies, it is common practice to ask participants to ignore their existing knowledge of the scenario and make judgments based only on the relationships presented within the experiment. Causal judgments appear to be sensitive to instructions that modify assumptions (...) about the scenario. However, the extent to which prior knowledge continues to affect competition for associative learning, even after participants are instructed to disregard it, is unknown. To answer this, we created a cue competition design that capitalized on prevailing beliefs about the allergenic properties of various foods. High and low allergenic foods were paired with foods moderately associated with allergy to create two compounds; high + moderate and low + moderate. We expected high allergenic foods to produce greater competition for associative memory than low allergenic foods. High allergenic foods may affect learning either because they generate a strong memory of allergy or because they are more salient in the context of the task. We therefore also manipulated the consistency of the high allergenic cue-outcome relationship with prior beliefs about the nature of the allergies. A high allergenic food that is paired with an inconsistent allergenic outcome should generate more prediction error and thus more competition for learning, than one that is consistent with prior beliefs. Participants were instructed to either use or ignore their knowledge of food allergies to complete the task. We found that while participants were able to set aside their prior knowledge when making causal judgments about the foods in question, associative memory was weaker for the cues paired with highly allergenic foods than cues paired with low allergenic foods regardless of instructions. The consistency manipulation had little effect on this result, suggesting that the effects in associative memory are most likely driven by selective attention to highly allergenic cues. This has implications for theories of causal learning as well as the way causal learning tasks are designed. (shrink)

This paper examines a novel notion of causality, namely, fuzzy-set-theoretic causality. Over the last decade, a number of conceptual models of causality, in the language of fuzzy-set theory, have appeared in the scientific literature and have been applied to empirical research. They have circulated widely from one scientific discipline to another, weaving a unifying thread through them. However, they have received no philosophical attention. In this paper, I will discuss the value and limitations of this type of model and will (...) read into its application several dimensions of philosophical significance. (shrink)

Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces 'spooky' hidden mechanisms. Whether one can produce a genuinely quantum framework in order to discover causal structure remains an open question. Here we introduce a new framework for quantum causal modelling that allows for the discovery of causal structure. We define quantum analogues for core features of (...) classical causal modelling techniques, including the causal Markov condition and faithfulness. Based on the process matrix formalism, this framework naturally extends to generalised structures with indefinite causal order. (shrink)

Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables LDL, HDL, and TOT that represent the level of low-density lipoprotein cholesterol, the level of lipoprotein high-density lipoprotein cholesterol, and total cholesterol level, with the relation LDL+HDL=TOT. This cannot be done in standard causal models, because we can intervene simultaneously on all three (...) variables. The goal of this paper is to extend standard causal models to allow for constraints on settings of variables. Although the extension is relatively straightforward, to make it useful we have to define a new intervention operation that disconnects a variable from a causal equation. We give examples showing the usefulness of this extension, and provide a sound and complete axiomatization for causal models with constraints. (shrink)

We model a black hole spacetime as a causal set and count, with a certain definition, the number of causal links crossing the horizon in proximity to a spacelike or null hypersurface Σ. We find that this number is proportional to the horizon's area on Σ, thus supporting the interpretation of the links as the “horizon atoms” that account for its entropy. The cases studied include not only equilibrium black holes but ones far from equilibrium.

We develop a new version of the causal theory of spacetime. Whereas traditional versions of the theory seek to identify spatiotemporal relations with causal relations, the version we develop takes causal relations to be the grounds for spatiotemporal relations. Causation is thus distinct from, and more basic than, spacetime. We argue that this non-identity theory, suitably developed, avoids the challenges facing the traditional identity theory.

Pearl opened the door to formally defining actual causation using causal models. His approach rests on two strategies: first, capturing the widespread intuition that X = x causes Y = y iff X = x is a Necessary Element of a Sufficient Set for Y = y, and second, showing that his definition gives intuitive answers on a wide set of problem cases. This inspired dozens of variations of his definition of actual causation, the most prominent of which are (...) due to Halpern & Pearl. Yet all of them ignore Pearl’s first strategy, and the second strategy taken by itself is unable to deliver a consensus. This paper offers a way out by going back to the first strategy: it offers six formal definitions of causal sufficiency and two interpretations of necessity. Combining the two gives twelve new definitions of actual causation. Several interesting results about these definitions and their relation to the various Halpern & Pearl definitions are presented. Afterwards the second strategy is evaluated as well. In order to maximize neutrality, the paper relies mostly on the examples and intuitions of Halpern & Pearl. One definition comes out as being superior to all others, and is therefore suggested as a new definition of actual causation. (shrink)

In this thesis, I give a metascientific account of causality in medicine. I begin with two historical cases of causal discovery. These are the discovery of the causation of Burkitt’s lymphoma by the Epstein-Barr virus, and of the various viral causes suggested for cervical cancer. These historical cases then support a philosophical discussion of causality in medicine. This begins with an introduction to the Russo- Williamson thesis (RWT), and discussion of a range of counter-arguments against it. Despite these, I (...) argue that the RWT is historically workable, given a small number of modifications. I then expand Russo and Williamson’s account. I first develop their suggestion that causal relationships in medicine require some kind of evidence of mechanism. I begin with a number of accounts of mechanisms and produce a range of consensus features of them. I then develop this consensus position by reference to the two historical case studies with an eye to their operational competence. In particular, I suggest that it is mechanistic models and their representations which we are concerned with in medicine, rather than the mechanism as it exists in the world. -/- I then employ these mechanistic models to give an account of the sorts of evidence used in formulating and evaluating causal claims. Again, I use the two human viral oncogenesis cases to give this account. I characterise and distinguish evidence of mechanism from evidence of difference-making, and relate this to mechanistic models. I then suggest the relationship between types of evidence presents us with a means of tackling the reference-class problem. This sets the scene for the final chapter. Here, I suggest the manner in which these two different classes of evidence become integrated is also reflected in the way that developing research programmes change as their associated causal claims develop. (shrink)

We study the selection of adjustment sets for estimating the interventional mean under an individualized treatment rule. We assume a non-parametric causal graphical model with, possibly, hidden variables and at least one adjustment set composed of observable variables. Moreover, we assume that observable variables have positive costs associated with them. We define the cost of an observable adjustment set as the sum of the costs of the variables that comprise it. We show that in this setting there exist (...) adjustment sets that are minimum cost optimal, in the sense that they yield non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that control for observable adjustment sets that have minimum cost. Our results are based on the construction of a special flow network associated with the original causal graph. We show that a minimum cost optimal adjustment set can be found by computing a maximum flow on the network, and then finding the set of vertices that are reachable from the source by augmenting paths. The optimaladj Python package implements the algorithms introduced in this article. (shrink)

Knowledge of mechanisms is critical for causal reasoning. We contrasted two possible organizations of causal knowledge—an interconnected causal network, where events are causally connected without any boundaries delineating discrete mechanisms; or a set of disparate mechanisms—causal islands—such that events in different mechanisms are not thought to be related even when they belong to the same causal chain. To distinguish these possibilities, we tested whether people make transitive judgments about causal chains by inferring, given A (...) causes B and B causes C, that A causes C. Specifically, causal chains schematized as one chunk or mechanism in semantic memory led to transitive causal judgments. On the other hand, chains schematized as multiple chunks led to intransitive judgments despite strong intermediate links. Normative accounts of causal intransitivity could not explain these intransitive judgments. (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)

Causal structure learning algorithms have focused on learning in ”batch-mode”: i.e., when a full dataset is presented. In many domains, however, it is important to learn in an online fashion from sequential or ordered data, whether because of memory storage constraints or because of potential changes in the underlying causal structure over the course of learning. In this paper, we present TDSL, a novel causal structure learning algorithm that processes data sequentially. This algorithm can track changes in (...) the generating causal structure or parameters, and requires significantly less memory in realistic settings. We show by simulation that the algorithm performs comparably to batch-mode learning when the causal structure is stationary, and significantly better in non-stationary environments. (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)

Even if one can experiment on relevant factors, learning the causal structure of a dynamical system can be quite difficult if the relevant measurement processes occur at a much slower sampling rate than the “true” underlying dynamics. This problem is exacerbated if the degree of mismatch is unknown. This paper gives a formal characterization of this learning problem, and then provides two sets of results. First, we prove a set of theorems characterizing how causal structures change under (...) undersampling. Second, we develop an algorithm for inferring aspects of the causal structure at the “true” timescale from the causal structure learned from the undersampled data. Research on causal learning in dynamical contexts has largely ignored the challenges of undersampling, but this paper provides a framework and foundation for learning causal structure from this type of complex time series data. (shrink)

One primary goal for metaphysical theories of natural kinds is to account for their epistemic fruitfulness. According to cluster theories of natural kinds, this epistemic fruitfulness is grounded in the regular and stable co- occurrence of a broad set of properties. In this paper, I defend the view that such a cluster theory is insufficient to adequately account for the epistemic fruitfulness of kinds. I argue that cluster theories can indeed account for the projectibility of natural kinds, but not for (...) several other epistemic operations that natural kinds support. Natural kinds also play a role in scientific explanations and categorizations. A theory of natural kinds can only account for these additional kind-based epistemic practices if it also analyzes their causal structure. (shrink)

Using a unique data set of causal usage drawn from research articles published between 2006–2008 in the American Journal of Sociology and American Sociological Review, this article offers an empirical assessment of causality in American sociology. Testing various aspects of what we consider the conventional wisdom on causality in the discipline, we find that “variablistic” or “covering law” models are not the dominant way of making causal claims, research methods affect but do not determine causal usage, and (...) the use of explicit causal language and the concept of “mechanisms” to make causal claims is limited. Instead, we find that metaphors and metaphoric reasoning are fundamental for causal claims-making in the discipline. On this basis, we define three dominant causal types used in sociology today, which we label the Probabilistic, Initiating and Conditioning types. We theorize this outcome as demonstrating the primary role that cognitive models play in providing inference-rich metaphors that allow sociologists to map causal relationships on to empirical processes. (shrink)

A formal theory of causal reasoning is presented that encompasses both Pearl’s approach to causality and several key formalisms of nonmonotonic reasoning in Artificial Intelligence. This theory will be derived from a single rationality principle of causal acceptance for propositions. However, this principle will also set the theory of causal reasoning apart from common representational approaches to reasoning formalisms.