Invariance is one of several dimensions of causal relationships within the interventionist account. The more invariant a relationship between two variables, the more the relationship should be considered paradigmatically causal. In this paper, I propose two formal measures to estimate invariance, illustrated by a simple example. I then discuss the notion of invariance for causal relationships between non-nominal (i.e., ordinal and quantitative) variables, for which Information theory, and hence the formalism proposed here, is not (...) well suited. Finally, I propose how invariance could be qualified for such variables. (shrink)

This essay explains what the Causal Markov Condition says and defends the condition from the many criticisms that have been launched against it. Although we are skeptical about some of the applications of the Causal Markov Condition, we argue that it is implicit in the view that causes can be used to manipulate their effects and that it cannot be surrendered without surrendering this view of causation.

In much recent work, invariance under intervention has become a hallmark of the correctness of a causal-law claim. Despite its importance this thesis generally is either simply assumed or is supported by very general arguments with heavy reliance on examples, and crucial notions involved are characterized only loosely. Yet for both philosophical analysis and practicing science, it is important to get clear about whether invariance under intervention is or is not necessary or sufficient for which kinds of (...) causal claims. Furthermore, we need to know what counts as an intervention and what invariance is. In this paper I offer explicit definitions of two different kinds for the notions intervention, invariance, and causal correctness. Then, given some natural and relatively uncontroversial assumptions, I prove two distinct sets of theorems showing that invariance is indeed a mark of causality when the concepts are appropriately interpreted. (shrink)

The most compelling extant accounts of explanation casts all explanations as causal. Yet there are sciences, theoretical population biology in particular, that explain their phenomena by appeal to statistical, non-causal properties of ensembles. I develop a generalised account of explanation. An explanation serves two functions: metaphysical and cognitive. The metaphysical function is discharged by identifying a counterfactually robust invariance relation between explanans event and explanandum. The cognitive function is discharged by providing an appropriate description of this relation. (...) I offer examples of explanations from portfolio theory and population genetics that meet this characterisation. In each case the invariance relation holds between a statistical property of an ensemble and a change in structure of the ensemble. In neither case, however, does the statistical property cause the outcome it explains. There are genuine statistical, non-causal scientific explanations. (shrink)

This paper, like its companion explores some ways in which, on the one hand, normative theorizing about causation and causal reasoning and, on the other, empirical psychological investigations into causal cognition can be mutually illuminating. The topics considered include the connection between causal claims and claims about the outcomes of interventions and the various ways that invariance claims figure in causal judgment.

Cognitive Science, Volume 46, Issue 5, May 2022.

In this paper I will present conceptions of state reduction and particle and/or system localization which render these subjects fully compatible with the general requirements of a relativistic, i.e. Lorentz invariant, quantum theory. The approach consists of a systematic generalization of the concepts of initial data assignment at definite times, initiation and completion of measurements at definite times, and dynamical evolution as time dependence, to the concepts of initial data assignment on arbitrary space-like hyperplanes, initiation and completion of measurements on (...) arbitrary space-like hyperplanes, and dynamical evolution as space-like hyperplane dependence, respectively. I also briefly discuss the superluminal propagation which emerges from the localization study and the manner in which causal anomalies are nevertheless avoided. (shrink)

Causal assessment is the problem of establishing whether a relation between (variable) X and (variable) Y is causal. This problem, to be sure, is widespread across the sciences. According to accredited positions in the philosophy of causality and in social science methodology, invariance under intervention provides the most reliable test to decide whether X causes Y. This account of invariance (under intervention) has been criticised, among other reasons, because it makes manipulations on the putative causal (...) factor fundamental for the causal methodology; consequently, the argument goes, the account is ill-suited to those contexts where manipulations are not performed, for instance, the social sciences. The article aims to extend the account of invariance (under intervention), in a way that manipulations on the putative causal factors are not methodologically fundamental, and yet invariance remains key for causal assessment both in experimental and non-experimental contexts. (shrink)

I provide a theory of causation within the causal modeling framework. In contrast to most of its predecessors, this theory is model-invariant in the following sense: if the theory says that C caused (didn't cause) E in a causal model, M, then it will continue to say that C caused (didn't cause) E once we've removed an inessential variable from M. I suggest that, if this theory is true, then we should understand a cause as something which transmits (...) deviant or non-inertial behavior to its effect. (shrink)

We report three experiments investigating whether people’s judgments about causal relationships are sensitive to the robustness or stability of such relationships across a range of background circumstances. In Experiment 1, we demonstrate that people are more willing to endorse causal and explanatory claims based on stable (as opposed to unstable) relationships, even when the overall causal strength of the relationship is held constant. In Experiment 2, we show that this effect is not driven by a causal (...) generalization’s actual scope of application. In Experiment 3, we offer evidence that stable causal relationships may be seen as better guides to action. Collectively, these experiments document a previously underappreciated factor that shapes people’s causal reasoning: the stability of the causal relationship. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found (...) already in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

The anti-causal prophecies of last century have been disproved. Causality is neither a ‘relic of a bygone’ nor ‘another fetish of modern science’; it still occupies a large part of the current debate in philosophy and the sciences. This investigation into causal modelling presents the rationale of causality, i.e. the notion that guides causal reasoning in causal modelling. It is argued that causal models are regimented by a rationale of variation, nor of regularity neither (...) class='Hi'>invariance, thus breaking down the dominant Human paradigm. The notion of variation is shown to be embedded in the scheme of reasoning behind various causal models: e.g. Rubin’s model, contingency tables, and multilevel analysis. It is also shown to be latent – yet fundamental – in many philosophical accounts. Moreover, it has significant consequences for methodological issues: the warranty of the causal interpretation of causal models, the levels of causation, the characterisation of mechanisms, and the interpretation of probability. This book offers a novel philosophical and methodological approach to causal reasoning in causal modelling and provides the reader with the tools to be up to date about various issues causality rises in social science. (shrink)

This paper is a sequel to various papers by the author devoted to the EPR correlation. The leading idea remains that the EPR correlation (either in its well-known form of nonseparability of future measurements, or in its less well-known time-reversed form of nonseparability of past preparations) displays the intrinsic time symmetry existing in almost all physical theories at the elementary level. But, as explicit Lorentz invariance has been an essential requirement in both the formalization and the conceptualization of my (...) papers, the noninvariant concept ofT symmetry has to yield in favor of the invariant concept ofPT symmetry, or even (asC symmetry is not universally valid) to that ofCPT invariance. A distinction is then drawn between “macro” special relativity, defined by invariance under the orthochronous Lorentz group and submission to the retarded causality concept, and “micro” special relativity, defined by invariance under the full Lorentz group and includingCPT symmetry. TheCPT theorem clearly implies that “micro special relativity”is relativity theory at the quantal level. It is thus of fundamental significance not only in the search of interaction Lagrangians, etc., but also in the basic interpretation of quantum mechanics, including the understanding of the EPR correlation. While the experimental existence of the EPR correlations is manifestly incompatible with macro relativity, it is fully consistent with micro relativity. Going from a retarded concept of causality to one that isCPT invariant has very radical consequences, which are briefly discussed. (shrink)

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such (...) causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams. This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a ancestral graph. We present two main results. The first result extends Pearl 's celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (shrink)

This chapter explores some issues having to do with the structure of the evidential reasoning we use to infer causal and lawful claims. It is argued that such reasoning always makes use of prior, causally, or nomologically committed information, thus undercutting various views that attempt to reduce causal and lawful claims to claims about regularities. A non-reductive account of laws and causes built around the notion of invariance is advanced as an alternative.

Knowledge of causal laws is expensive and hard to come by. But we work hard to get it because we believe that it will reduce contingency in planning policies and in building new technologies: knowledge of causal laws allows us to predict reliably what the outcomes will be when we manipulate the factors cited as causes in those laws. Or do they? This paper will argue that causal laws have no special role here. As economists from JS (...) Mill to Robert Lucas and David Hendry stress, along recently with philosophers like James Woodward and Sandra Mitchell, they can do the job only if they are invariant under the manipulations proposed. But then, I shall argue, anything that is invariant under the proposed manipulations will do this job equally well. There seems to be nothing special about causal-law knowledge in and of itself that makes it particularly valuable for policy and technology prediction. What seems to matter is invariance alone, not causality. But what guarantees invariance and how do we know when it will obtain? Here certain kinds of causal laws do have a special place – those underwritten either by what I have called ‘nomological machines’ or by what I have called ‘capacities’. Capacities and nomological machines have a double virtue that makes them invaluable for policy planning. First, the causal laws they give rise to will be invariant so long as they obtain; and second, they typically have visible markers we can come to recognize that tell us when they obtain. The markers for nomological machines are shakier than those for capacities, though, since capacities are often tied to markers by well-established empirical laws. Capacities have their own drawback however, which is the final topic of this paper: the causal laws that are guaranteed by a capacity connect the obtaining of a capacity with its exercise. But Hume argued that no distinction can be made between the obtaining of a power and its exercise. (shrink)

Knowledge of causal laws is expensive and hard to come by. But we work hard to get it because we believe that it will reduce contingency in planning policies and in building new technologies: knowledge of causal laws allows us to predict reliably what the outcomes will be when we manipulate the factors cited as causes in those laws. Or do they? This paper will argue that causal laws have no special role here. As economists from JS (...) Mill to Robert Lucas and David Hendry stress, along recently with philosophers like James Woodward and Sandra Mitchell, they can do the job only if they are invariant under the manipulations proposed. But then, I shall argue, anything that is invariant under the proposed manipulations will do this job equally well. There seems to be nothing special about causal-law knowledge in and of itself that makes it particularly valuable for policy and technology prediction. What seems to matter is invariance alone, not causality. But what guarantees invariance and how do we know when it will obtain? Here certain kinds of causal laws do have a special place – those underwritten either by what I have called ‘nomological machines’ or by what I have called ‘capacities’. Capacities and nomological machines have a double virtue that makes them invaluable for policy planning. First, the causal laws they give rise to will be invariant so long as they obtain; and second, they typically have visible markers we can come to recognize that tell us when they obtain. The markers for nomological machines are shakier than those for capacities, though, since capacities are often tied to markers by well-established empirical laws. Capacities have their own drawback however, which is the final topic of this paper: the causal laws that are guaranteed by a capacity connect the obtaining (or triggering) of a capacity with its exercise. But Hume argued (mistakenly I suggest) that no distinction can be made between the obtaining of a power and its exercise. (shrink)

Heritability is routinely interpreted causally. Yet, what such an interpretation amounts to is often unclear. Here, I provide a causal interpretation of this concept in terms of range of causal influence, one of several causal dimensions proposed within the interventionist account of causation. An information-theoretic measure of range of causal influence has recently been put forward in the literature. Starting from this formalization and relying upon Woodward’s analysis, I show that an important problem associated with interpreting (...) heritability causally, namely the locality problem, amounts, at least partly, to a low invariance and low stability between the genotype/environment and the phenotype of individuals. In light of this, I plead for a causal interpretation of heritability that takes the notions of Woodward’s invariance and stability into consideration. In doing so, I defuse naive causal interpretations of heritability. (shrink)

This paper discusses several distinct process theories of causality offered in recent years by Phil Dowe and me. It addresses problems concerning the explication of causal process, causal interaction, and causal transmission, whether given in terms of transmission of marks, transmission of invariant or conserved quantities, or mere possession of conserved quantities. Renouncing the mark-transmission and invariant quantity criteria, I accept a conserved quantity theory similar to Dowe's--differing basically with respect to causal transmission. This paper also (...) responds to several fundamental constructive criticisms contained in Christopher Hitchcock's discussion of both the mark-transmission and the conserved quantity theories. (shrink)

In a recent paper (1994) Wesley Salmon has replied to criticisms (e.g., Dowe 1992c, Kitcher 1989) of his (1984) theory of causality, and has offered a revised theory which, he argues, is not open to those criticisms. The key change concerns the characterization of causal processes, where Salmon has traded "the capacity for mark transmission" for "the transmission of an invariant quantity." Salmon argues against the view presented in Dowe (1992c), namely that the concept of "possession of a conserved (...) quantity" is sufficient to account for the difference between causal and pseudo processes. Here that view is defended, and important questions are raised about the notion of transmission and about gerrymandered aggregates. (shrink)

Epidemiological methods, which combine population thinking and group comparisons, can primarily identify causes of disease in populations. There is therefore a tension between our intuitive notion of a cause, which we want to be deterministic and invariant at the individual level, and the epidemiological notion of causes, which are invariant only at the population level. Epidemiologists have given heretofore a pragmatic solution to this tension. Causal inference in epidemiology consists in checking the logical coherence of a causality statement and (...) determining whether what has been found grossly contradicts what we think we already know: how strong is the association? Is there a dose-response relationship? Does the cause precede the effect? Is the effect biologically plausible? Etc. This approach to causal inference can be traced back to the English philosophers David Hume and John Stuart Mill. On the other hand, the mode of establishing causality, devised by Jakob Henle and Robert Koch, which has been fruitful in bacteriology, requires that in every instance the effect invariably follows the cause (e.g., inoculation of Koch bacillus and tuberculosis). This is incompatible with epidemiological causality which has to deal with probabilistic effects (e.g., smoking and lung cancer), and is therefore invariant only for the population. (shrink)

In this work we try to study theories of causation based upon causal processes and causal interactions in the context of classical and quantum physics. Our central aim is to find out whether such causal theories are compatible with the world picture suggested by contemporary theories of physics. In the first part, we review, compare and try to place among more general taxonomical schemes, the causal theories by Russell (the causal lines approach), Reichenbach (mark method, (...) probabilistic causality and the principle of common cause), Salmon (mark method, structure, invariant and conserved quantities approaches) and Dowe (conserved quantity theory). In the second part of the work, we deal with some problems that process theories of causation face whenever one tries to define, rigorously, causal concepts (e.g. “causal process” or “conjunctive common cause”) in the context of classical relativistic physical theories (van Dam – Wigner particle theory, the free Klein-Gordon field, classical electromagnetic theory) as well as quantum theories (algebraic relativistic quantum field theory). In this vein, special attention has been given to the locality problem in physical theories as it emerges from the structure of local classical the quantum theories (semantic locality), the relation between global and local conditions for physical systems (global and local determinism) as well as the problem of action at a distance, which is of central importance for the theories of causation under examination (Bell’s inequalities, EPR paradox, Reeh-Schlieder theorem and local independence conditions). We argue for three different theses: first, there are physical theories in the context of which it is impossible even to formulate the necessary physical hypotheses that allow us to define basic causal concepts and causal principles; second, there are physical theories which allow us to formulate these hypotheses only ad hoc; finally, in some cases it is necessary to revise basic causal principles and concepts bequeathed by the philosophical tradition. (shrink)

This article examines methodological individualism in terms of the theory that invariance under intervention is the signal feature of generalizations that serve as a basis for causal explanation. This theory supports the holist contention that macro-level generalizations can explain, but it also suggests a defense of methodological individualism on the grounds that greater range of invariance under intervention entails deeper explanation. Although this individualist position is not threatened by multiple-realizability, an argument for it based on rational choice (...) theory is called into question by experimental results concerning preference reversals. Key Words: methodological individualism • mechanisms • explanation • invariance • preference reversal. (shrink)

According to Woodward’s causal model of explanation, explanatory information is relevant for manipulation purposes and indicates by means of invariant causal relations how to change the value of certain target explanandum variables by intervening on others. Therefore, the depth of an explanation is evaluated through the size of the domain of invariance of the generalization involved. In this article, I argue that Woodward’s account of explanatory relevance is still unsatisfactory and claim that the depth of an explanation (...) should be explicated in terms of the size of the domain of circumstances which it designates as leaving the explanandum unchanged. (shrink)

The Buddhist philosophy of causality is primarily a theory (naya) of the human world. Its methodology, however, is objective and critical. It rejects the weight of mere authority or tradition, relies upon experience and reason, and emphasizes the critical examination and verification of all opinions. Although the Buddhist conception of knowledge and truth has a strong empirical and pragmatic bias (cf. Nyāya‐bindu 1.1), its conception of experience does not exclude introspection, rational intuition or mystical intuition (cf. Nyāya‐bindu 1.7–11). Although its (...) conception of reason creates a logical gulf between reason and experience, the gulf is bridged by a transcendental illusion (avidyā). Its employment of reason is highly analytical and it seeks to discover the ultimate elements constituting the structures of objects and experience. The constituent elements as the locus of causation are regarded as more real than their composite structures – dharma, dhātu or kṣana as contrasted with saṅghāta or santāna. At the same time, it raises dialectical questions and seriously considers the possibility of the empirical world being merely a working illusion. It discounts the apparent stability of objects, stressing their transience, finally defined as momentariness (see, for example, Ratnakīrti's Kṣaṇa‐bhaṅgasiddhi). It rejects the category of substance for that of process. Causality is thus regarded not as a dynamic interaction between substances, but as a functional, many‐one relationship of order characterized by invariance and uniformity within any given type of process. (shrink)

In this article I consider the challenges for exporting causal knowledge raised by complex biological systems. In particular, James Woodward’s interventionist approach to causality identified three types of stability in causal explanation: invariance, modularity, and insensitivity. I consider an example of robust degeneracy in genetic regulatory networks and knockout experimental practice to pose methodological and conceptual questions for our understanding of causal explanation in biology. †To contact the author, please write to: Department of History and Philosophy (...) of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected]. (shrink)

In a recent paper Wesley Salmon has replied to criticisms of his theory of causality, and has offered a revised theory which, he argues, is not open to those criticisms. The key change concerns the characterization of causal processes, where Salmon has traded “the capacity for mark transmission” for “the transmission of an invariant quantity.” Salmon argues against the view presented in Dowe, namely that the concept of “possession of a conserved quantity” is sufficient to account for the difference (...) between causal and pseudo processes. Here that view is defended, and important questions are raised about the notion of transmission and about gerrymandered aggregates. (shrink)

A formulation of probabilistic causality is given in terms of the theory of abstract dynamical systems. Causal factors are identified as invariants of motion of a system. Repetition of an experiment leads to the notion of stationarity, and causal factors yield a decomposition of the stationary probability law of the experiment into ergodic components. In these, statistical behaviour is uniform. Control of identified causal factors leads to a corresponding statistical law for the events, which is offered as (...) a notion of probabilistic causality. After a suggestion by Feller, randomization is identified as mixing, formulated in above terms. (shrink)

The principles of classical physics, including deterministic dynamics and observability of physical states, are incompatible with the existence of unobservable conscious minds that possess free will. Attempts to directly accommodate consciousness in a classical world lead to philosophical paradoxes such as causally ineffective consciousness and possibility of alternate worlds in which functional brain isomorphs behave identically but lack conscious experiences. Here, we show that because Chalmers’ principle of organizational invariance is based on a deficient nineteenth century classical physics, it (...) is inherently flawed and implies evolutionary inexplicable epiphenomenal consciousness. Consequently, if consciousness is a fundamental ingredient of physical reality, no psychophysical laws such as Chalmers’ principle of organizational invariance are needed to establish correspondence between conscious experiences and brain function. Quantum mechanics is the most successful and only modern physical theory capable of naturally accommodating consciousness without violation of physical laws. (shrink)

The problem of causality is one of the central topics of Hume’s philosophy. There are several reasons for its importance: Of all the relations it is the only one in virtue of which we can pass beyond the immediate impression of the senses or an idea of the memory and thus step outside the realm of the given. The only relation “that can be trac’d beyond our senses, and informs us of existences and objects, which we do not see or (...) feel, is causation.” It is a relation which underlies our belief in an external world. To quote another passage from the Treatise: “We readily suppose an object may continue individually the same, tho’ several times absent and present to the senses; and ascribe to it an identity, notwithstanding the interruption of the perception, whenever we conclude, that if we had kept our eye or hand constantly upon it, it would have convey’d an invariable and uninterrupted perception. (shrink)

The investigation of a method for postulating counterfactual histories of science has led to the development of a theory of science based on general units of knowledge, which are called “advances”. Advances are passed on from scientist to scientist, and may be seen as “causing” the appearance of other advances. This results in networks which may be analyzed in terms of probabilistic causal models, which are readily encodable in computer language. The probability for a set of advances to give (...) rise to another advance is taken to be invariant through history, but depends on a typical time span which is an inverse function of the degree of development of science. Examples are given from the early science of magnetism and from the 19th century physics. (shrink)

How are scientific explanations possible in ecology, given that there do not appear to be many—if any—ecological laws? To answer this question, I present and defend an account of scientific causal explanation in which ecological generalizations are explanatory if they are invariant rather than lawlike. An invariant generalization continues to hold or be valid under a special change—called an intervention—that changes the value of its variables. According to this account, causes are difference-makers that can be intervened upon to manipulate (...) or control their effects. I apply the account to ecological generalizations to show that invariance under interventions as a criterion of explanatory relevance provides interesting interpretations for the explanatory status of many ecological generalizations. Thus, I argue that there could be causal explanations in ecology by generalizations that are not, in a strict sense, laws. I also address the issue of mechanistic explanations in ecology by arguing that invariance and modularity constitute such explanations. (shrink)

In Woodward's causal model of explanation, explanatory information is information that is relevant to manipulation and control and that affords to change the value of some target explanandum variable by intervening on some other. Accordingly, the depth of an explanation is evaluated through the size of the domain of invariance of the generalization involved. In this paper, I argue that Woodward's treatment of explanatory relevance in terms of invariant causal relations is still wanting and suggest to evaluate (...) the depth of an explanation through the size of the domain of circumstances that it designates as leaving the explanandum unchanged. (shrink)

The original version of this chapter was published long before the author's conversion to a conserved or invariant theory of causality as presented in “Causality and Counterfactuals” ; nevertheless, its fundamental approach is still sound. The basic facts about causal processes and causal forks, about their interrelationships, and about the various types of forks are presented here in some detail. The only difference is that a new criterion for causal processes and interactive forks has subsequently been adopted. (...) The same processes and intersections will be classified as causal under either criterion. This chapter presents a concise but comprehensive picture of the causal structure of the world along the same lines as the author's account in his Scientific Explanation and the Causal Structure of the World. (shrink)

A shared problem across the sciences is to make sense of correlational data coming from observations and/or from experiments. Arguably, this means establishing when correlations are causal and when they are not. This is an old problem in philosophy. This paper, narrowing down the scope to quantitative causal analysis in social science, reformulates the problem in terms of the validity of statistical models. Two strategies to make sense of correlational data are presented: first, a 'structural strategy', the goal (...) of which is to model and test causal structures that explain correlational data; second, a 'manipulationist or interventionist strategy', that hinges upon the notion of invariance under intervention. It is argued that while the former can offer a solution the latter cannot. (shrink)

In their rich and intricate paper ‘Independence, Invariance, and the Causal Markov Condition’, Daniel Hausman and James Woodward ([1999]) put forward two independent theses, which they label ‘level invariance’ and ‘manipulability’, and they claim that, given a specific set of assumptions, manipulability implies the causal Markov condition. These claims are interesting and important, and this paper is devoted to commenting on them. With respect to level invariance, I argue that Hausman and Woodward's discussion is confusing (...) because, as I point out, they use different senses of ‘intervention’ and ‘invariance’ without saying so. I shall remark on these various uses and point out that the thesis is true in at least two versions. The second thesis, however, is not true. I argue that in their formulation, the manipulability thesis is patently false and that a modified version does not fare better. Furthermore, I think their proof that manipulability implies the causal Markov condition is not conclusive. In the deterministic case it is valid but vacuous, whereas it is invalid in the probabilistic case. 1 Introduction 2 Intervention, invariance and modularity 3 The causal Markov condition: CM1 and CM2 4 From MOD to the causal Markov condition and back 5 A second argument for CM2 6 The proof of the causal Markov condition for probabilistic causes 7 ‘Cartwright's objection’ defended 8 Metaphysical defenses of the causal Markov condition 9 Conclusion. (shrink)

It is claimed that the `problem of the arrow of time in classical dynamics' has been solved. Since all classical particles have a self-field (gravitational and in some cases also electromagnetic), their dynamics must include self-interaction. This fact and the observation that the domain of validity of classical physics is restricted to distances not less than of the order of a Compton wavelength (thus excluding point particles), leads to the conclusion that the fundamental classical equations of motion are not invariant (...) under time reversal: retarded self-interactions lead to different equations than advanced ones. Since causality (the time order of cause and effect) requires retarded rather than advanced self-interaction, it is causality which is ultimately responsible for the arrow of time. Classical motions described by equations with advanced self-interactions differ from retarded ones and do not occur in nature. (shrink)

The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project.The feasibility of a pure S-matrix approach are critically analyzed and their serious shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct (...) understanding about the origin of the crossing property requires the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These new concepts, which combine localization, vacuum polarization and thermal properties under the roof of modular theory, will be explained and their potential use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role but, different from Heisenberg’s and Mandelstam’s proposals, the new project is not a pure S-matrix approach. The S-matrix plays a new role as a “relative modular invariant”. (shrink)

This paper is aimed at identifying how a model’s explanatory power is constructed and identified, particularly in the practice of template-based modeling (Humphreys, Philos Sci 69:1–11, 2002; Extending ourselves: computational science, empiricism, and scientific method, 2004), and what kinds of explanations models constructed in this way can provide. In particular, this paper offers an account of non-causal structural explanation that forms an alternative to causal–mechanical accounts of model explanation that are currently popular in philosophy of biology and cognitive (...) science. Clearly, defences of non-causal explanation are far from new (e.g. Batterman, Br J Philos Sci 53:21–38, 2002a; The devil in the details: asymptotic reasoning in explanation, reduction, and emergence, 2002b; Pincock, Noûs 41:253–275, 2007; Mathematics and scientific representation 2012; Rice, Noûs. doi:10.1111/nous.12042, 2013; Biol Philos 27:685–703, 2012), so the targets here are focused on a particular type of robust phenomenon and how strong invariance to interventions can block a range of causal explanations. By focusing on a common form of model construction, the paper also ties functional or computational style explanations found in cognitive science and biology more firmly with explanatory practices across model-based science in general. (shrink)

The issue of whether there are laws in biology and the “special science”1 has been of interest owing to the debate about whether scientific explanation requires laws. A well-warn argument goes thus: no laws in social science, no explanations, or at least no scientific explanations, at most explanation-sketches. The conclusion is not just a matter of labeling. If explanations are not scientific they are not epistemically or practically reliable. There are at least three well-known diagnoses of where this argument goes (...) wrong. First, the argument that there are no laws in social science adopts an account of laws that is too stringent, one that not even the physical sciences satisfy (Cartwright 1983, Mitchell 2000). On a less stringent definition, there are plenty of laws in social science (and biology). These laws are, sensu Fodor, “non-strict,” as opposed to the “strict laws” (if any—vide Cartwright 1983) of physics. Second, scientific explanation does not require laws, and when laws do explain, they do so because they satisfy some other requirement on scientific explanation, for example unification, or the identification of causal difference-makers (Friedman 1974, Kitcher 1989, Salmon 1984, Strevens 2009). A third view, increasingly attractive among philosophers of social science and biology is due to James Woodward (2000, 2003). This view, like the second one eschews laws and identifies causes as difference makers. On this view explanations do require regularities, but these regularities need only satisfy a requirement of “invariance” under certain specified circumstances, in order to be explanatory, and.. (shrink)

This paper discusses some procedures developed in recent work in machine learning for inferring causal direction from observational data. The role of independence and invariance assumptions is emphasized. Several familiar examples including Hempel’s flagpole problem are explored in the light of these ideas. The framework is then applied to problems having to do with explanatory direction in non-causal explanation.

What caused the event we report by saying “the window shattered”? Was it the baseball, which crashed into the window? Causal exclusionists say: many, many microparticles collectively caused that event—microparticles located where common sense supposes the baseball was. Unitary large objects such as baseballs cause nothing; indeed, by Alexander’s dictum, there are no such objects. This paper argues that the false claim about causal efficacy is instead the one that attributes it to the many microparticles. Causation obtains just (...) where there is an “invariance”, a true generalization to the effect that had things been different with the putative cause, things would have been correspondingly different with the putative effect. But “correspondingly” here requires a rough metric. There must be a fact as to which alternative group events, involving many microparticles, would have departed less from the putative cause of the shattering, and which would have departed more. Surprisingly, there is no such fact. (shrink)

In Norton(2003), it was urged that the world does not conform at a fundamental level to some robust principle of causality. To defend this view, I now argue that the causal notions and principles of modern physics do not express some universal causal principle, brought to light by discoveries in physics. Rather they merely assert that, according to relativity theory, spacetime has an invariant velocity, that of light; and that theories of matter admit no propagations faster than light.

This paper deals with causal analysis in the social sciences. We first present a conceptual framework according to which causal analysis is based on a rationale of variation and invariance, and not only on regularity. We then develop a formal framework for causal analysis by means of structural modelling. Within this framework we approach causality in terms of exogeneity in a structural conditional model based which is based on (i) congruence with background knowledge, (ii) invariance (...) under a large variety of environmental changes, and (iii) model fit. We also tackle the issue of confounding and show how latent confounders can play havoc with exogeneity. This framework avoids making untestable metaphysical claims about causal relations and yet remains useful for cognitive and action-oriented goals. (shrink)

The aim of this paper is to show that the argument put forth by Bell and Hallett against Putnam's thesis regarding the invariance of meaning for quantum logical connectives is insufficient to establish their conclusion. By using an example from the causal theory of time, the paper shows how the condition they specify as relevant in cases of meaning variance in fact fails. As a result, the conclusion that negation undergoes a change of meaning in the quantum logical (...) case is left in doubt. The paper proceeds in three stages. First, a summary of Putnam's argument for the invariance of meaning in the case of quantum logical connectives is provided; this is followed by a review of the criticisms advanced against it by Bell and Hallett. Finally, it is shown how the main claim upon which their major criticism rests is unfounded. (shrink)