Peter Spirtes. Discovering Causal Relations Among Latent Variables in Directed Acyclical Graphical Models.

Many philosophers now regard causal approaches to explanation as highly promising, even in physics. This is due in large part to James Woodward's influential argument that a wide variety of scientific explanations are causal, based on his interventionist approach to causation. This article argues that some derivations describing causal relations and satisfying Woodward's criteria for causal explanation fail to be explanatory. Further, causal relations are unnecessary for a range of explanations, widespread in physics, involving highly (...) idealized models. These constitute significant limitations on the scope of causal explanation. We have good reason to doubt that causal explanation is as widespread or important in physics as Woodward and other proponents maintain. (shrink)

There is no doubt that spatial relations aid us in pairing up causes and effects. But when we consider the possibility of qualitatively indiscernible things, it might seem that spatial relations are more than a mere aid – they might seem positively required. The belief that spatial relations are required for causal relations is behind an important objection to Cartesian Dualism, the pairing problem. I argue that the Cartesian can answer this objection by appeal to the possibility of primitive (...) causal relations, a possibility I defend. This topic is of importance beyond the philosophy of mind; the possibility that causal relations might sometimes hold brutely is of general metaphysical importance. I close with a discussion of what Cartesians should say about embodiment, and how that bears on issues of mental causation. (shrink)

The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities (...) for the observable input-output relations. In this paper, I investigate the relation between the classical notion of reality and quantum superpositions by identifying the conditions under which the intermediate states can have real external effects, as expressed by measurement operators inserted into the inner product. It is shown that classical reality emerges at the macroscopic level, where the relevant limit of the measurement resolution is given by the variance of the action around the classical solution. It is thus possible to demonstrate that the classical notion of objective reality emerges only at the macroscopic level, where observations are limited to low resolutions by a lack of sufficiently strong intermediate interactions. This result indicates that causality is more fundamental to physics than the notion of an objective reality, which means that the apparent contradictions between quantum physics and classical physics may be resolved by carefully distinguishing between observable causality and unobservable sequences of hypothetical realities “out there”. (shrink)

The semantic relations between and within utterances are marked by the use of connectors and adverbials. One type of semantic relations is causal relations expressed by causal markers such as because, therefore, so, for, etc. Some of these markers cover different types of causal relations such as causality, explanation and justification. In certain types of discourse, causal relations also imply an intentional element. This paper describes the way in which the semantic and pragmatic functions of (...) class='Hi'>causal markers can be accounted for in terms of linguistic and rhetorical theories of argumentation. (shrink)

Studies with humans have failed to produce evidence that any direct causal relation exists between the asymmetry of one function in an individual and the asymmetry of a different function in that individual. Without such evidence, factors external to an individual's nervous system, such as social interactions, may play crucial roles in explaining the directions of all asymmetries at all levels.

Abraham’s Dilemma is the conjunction of three jointly inconsistent propositions: God’s commands are never morally wrong, God has commanded Abraham to kill his innocent son, and killing innocent people is morally wrong. Drawing on an overlooked point from the Qur’an regarding the content of the command as well as a conceptual analysis of intentional action, this paper proposes a novel solution to the dilemma by discarding proposition in a new way. Current approaches to rejecting proposition tend to appeal to epistemic (...) failure on the side of Abraham. In my approach, which draws on the so-called accordion effect in intentional action, God’s command is interpreted in such a way that God has not commanded Abraham to kill his son nor has Abraham tried to do so, although the challenging and difficult nature of the test and thus Abraham’s status as the ‘father of faith’ are retained. (shrink)

The semantic relations between and within utterances are marked by the use of connectors and adverbials. One type of semantic relations is causal relations expressed by causal markers such as because, therefore, so, for, etc. Some of these markers cover different types of causal relations such as causality, explanation and justification. In certain types of discourse, causal relations also imply an intentional element. This paper describes the way in which the semantic and pragmatic functions of (...) class='Hi'>causal markers can be accounted for in terms of linguistic and rhetorical theories of argumentation. (shrink)

nature of modern data collection and storage techniques, and the increases in the speed and storage capacities of computers. Statistics books from 30 years ago often presented examples with fewer than 10 variables, in domains where some background knowledge was plausible. In contrast, in new domains, such as climate research where satellite data now provide daily quantities of data unthinkable a few decades ago, fMRI brain imaging, and microarray measurements of gene expression, the number of variables can range into the (...) tens of thousands, and there is often limited background knowledge to reduce the space of alternative causal hypotheses. In such domains, non-automated causal discovery techniques appear to be hopeless, while the availability of faster computers with larger memories and disc space allow for the practical implementation of computationally intensive automated search algorithms over large search spaces. Contemporary science is not your grandfather’s science, or Karl Popper’s. Causal inference without experimental controls has long seemed as if it must somehow be capable of being cast as a kind of statistical inference involving estimators with some kind of convergence and accuracy properties under some kind of assumptions. Until recently, the statistical literature said not. While parameter estimation and experimental design for the effective use of data developed throughout the 20th century, as recently as 20 years ago the methodology of causal inference without experimental controls remained relatively primitive. Besides a cessation of hostilities from the majority of the statistical and philosophical communities (which has still only partially happened), several things were needed for theories of causal estimation to appear and to flower: well defined mathematical objects to represent causal relations; well defined connections between aspects of these objects and sample data; and a way to compute those connections. A sequence of studies beginning with Dempster’s work on the factorization of probability distributions [Dempster 1972] and culminating with Kiiveri and Speed’s [Kiiveri & Speed 1982] study of linear structural equation models, provided the first, in the form of directed acyclic graphs, and the second, in the form of the “local” Markov condition.. (shrink)

A model of causation is presented which shares the advantages of Reichenbach's definition in terms of the screening-off relation, but which has the added advantage of distinguishing cause and effect without reference to temporal directionality. This model is defined in terms of the masking relation, which in turn is defined in terms of the equivocation relation of communication theory.

Why do we represent the world around us using causal generalizations, rather than, say, purely statistical generalizations? Do causal representations contain useful additional information, or are they merely more efficient for inferential purposes? This paper considers the second kind of answer: it investigates some ways in which causal cognition might aid us not because of its expressive power, but because of its organizational power. Three styles of explanation are considered. The first, building on the work of Reichenbach (...) in "The Direction of Time", points to causal representation as especially efficient for predictive purposes in a world containing certain pervasive patterns of conditional independence. The second, inspired by work of Woodward and others, finds causal representation to be an excellent vehicle for representing all-important relations of manipulability. The third, based in part on my own work, locates the importance of causal cognition in the special role it reserves for information about underlying mechanisms. All three varieties of explanation show promise, but particular emphasis is placed on the third. (shrink)

Mary Shepherd and the Causal Relation - Part One -/- Part One gives context to the life and work of Lady Mary Shepherd. It weaves together the stories of her ancestors, her own stories and the wider social, historical and philosophical context. The aim is to evoke a world from which to mark the emergence of Mary Shepherd, Scotland’s first female philosopher.

How are causal relations between particular states of affairs related to causal laws? There appear to be three main answers to this question, and the choice among those three alternatives would seem to be crucial for any account of causation. In spite of this fact, the question of which view is correct has been all but totally neglected in present-day discussions. Indeed, since the time of Hume, one answer has more or less dominated philosophical thinking about causation. This (...) is the view that causal relations between events/states of affairs logically supervene upon causal laws plus non-causal states of affairs. In this paper, I shall attempt to show that the view in question is exposed to decisive objections,. (shrink)

The need to find an intrinsic characterization of what makes a relation between events causal arises not only in local theories of causation like Salmon's process theory but also in global approaches like Lewis' counterfactual theory. According to the localist intuition, whether a process connecting two events is causal should depend only on what goes on between the events, not on conditions that hold elsewhere in the world. If such intrinsic characterizations could be found, an identification of (...) the causal relation in the actual world (though not in other possible worlds) with physical processes may be feasible (the a posteriori identification). I consider recent proposals made for intrinsic characterizations of causality and conclude that none of them is able to deliver the intended result. (shrink)

This contribution claims that the two fundamental notions of causation at work in the health sciences are manipulative and mechanistic, and investigates what kinds of evidence matter for the assessment of causal relations. This article is a development of our 2007 article, ‘Plurality of Causality’, where we argue for a pluralistic account of causation with an eye to econometrics and a single medical example. The present contribution has a wider focus, and considers the notion of evidence within a whole (...) range of disciplines belonging to the health sciences. Section 1 addresses the relations between kinds of evidence and causal accounts, and it is shown how different notions of causation can be employed in various medical cases. Section 2 calls attention to issues crucial for any adequate epistemological theory of causation, such as the distinctions between types and tokens, observational and experimental regimes, explanation and prediction. Lastly, the notion of context is articulated, highlighted in its role in the assessment of causal links. All these issues are tackled in the framework of what we label a ‘bottom–up’ epistemology. (shrink)

In his recent article, ``Self-Consciousness'’, George Bealer has set outa novel and interesting argument against functionalism in the philosophyof mind. I shall attempt to show, however, that Bealer's argument cannotbe sustained.In arguing for this conclusion, I shall be defending three main theses.The first is connected with the problem of defining theoreticalpredicates that occur in theories where the following two features arepresent: first, the theoretical predicate in question occurswithin both extensional and non-extensional contexts; secondly, thetheory in question asserts that the relevant (...) theoretical states enterinto causal relations. What I shall argue is that a Ramsey-styleapproach to the definition of such theoretical terms requires twodistinct quantifiers: one which ranges over concepts, and theother which ranges over properties in the world.My second thesis is a corollary: since the theories on whichBealer is focusing have both of the features just mentioned, and sincethe method that he employs to define theoretical terms in his argumentagainst functionalism does not involve both quantifiers that range overproperties and quantifiers that range over concepts, that method isunsound.My final thesis is that when a sound method is used, Bealer's argumentagainst functionalism no longer goes through.The structure of my discussion is as follows. I begin by setting out twoarguments – the one, a condensed version of Bealer's argument, andthe other, an argument that parallels Bealer's argument very closely.The parallel argument leads to a conclusion, however, that, rather thanbeing merely somewhat surprising, seems very implausible indeed. Forwhat the second argument establishes, if sound, is that there can betheoretical terms that apply to objects by virtue of their first-orderphysical properties, but whose meaning cannot be defined via aRamsey-style approach.Having set out the two parallel arguments, I then go on to focus uponthe second, to determine what is wrong with it. My diagnosis will bethat the problem with the argument arises from the fact that it involvesdefining a theoretical term that occurs both inside and outside ofopaque contexts, for the method employed fails to take into account thefact that the types of entities that are involved in the relevanttruthmakers are different when a sentence occurs within an extensionalcontext from those involved when a sentence occurs within anon-extensional context.I then go on to discuss how one should define a theoretical term thatoccurs within such theories, and I argue that in such a case one needstwo quantifiers, ranging over different types of entities – on theone hand, over properties and relations, and the other, over concepts. Ithen show that, when such an approach is followed, the argument inquestion collapses.I then turn to Bealer's argument against functionalism, and I show,first, that precisely the same method of defining theoretical terms canbe applied there, and, secondly, that, when this is done, it turns outthat that argument is also unsound.Next, I consider two responses that Bealer might make to my argument,and I argue that those responses would not succeed.Finally, I conclude by asking exactly where the problem lies in the caseof Bealer's argument. My answer will be that it is not simply the factthat one is dealing with a theoretical term that occurs in bothextensional and non-extensional contexts. It is rather the combinationof that feature together with the fact that the theory in questionasserts that the relevant type of theoretical state enters into causalrelations. For the first of these features means that the Ramseysentence for the theory must involve quantification over concepts, whilethe presence of the second feature means that the Ramsey sentence mustinvolve quantification over properties in the world, and so no attemptto offer a Ramsey-style account of the meaning of the relevanttheoretical term can succeed unless one employs both quantification overconcepts and quantification over properties. Bealer, however, in hisargument against functionalism, uses a method of defining theoreticalterms that does not involve both types of quantification, and it isprecisely because of this that his argument does not in the end succeed. (shrink)

Can the persistence of a human being's soul at death and prior to the bodily resurrection be sufficient to guarantee that the resurrected human being is numerically identical to the human being who died? According to Thomas Aquinas, it can. Yet, given that Aquinas holds that the human being is identical to the composite of soul and body and ceases to exist at death, it's difficult to see how he can maintain this view. In this paper, I address Aquinas's response (...) to this objection . After making a crucial clarification concerning the nature of the non-repeatability principle on which the objection relies, I argue that the contemporary notion of immanent causal relations provides us with a way of understanding Aquinas's defence that renders it both highly interesting and philosophically plausible. (shrink)

The learning of immediate causation within a dynamic environment was examined. Participants encountered seven decision points in which they needed to choose which of three possible candidates was the cause of explosions in the environment. Each candidate was firing a weapon at random every few seconds, but only one of them produced an immediate effect. Some participants showed little learning, but most demonstrated increases in accuracy across time. On average, men showed higher accuracy and shorter latencies that were not explained (...) by differences in self-reported prior video game experience. This result suggests that prior reports of sex differences in causal choice in the game are not specific to situations involving delayed or probabilistic causal relations. (shrink)

This paper makes explicit and takes issue with the bizarre view, which is unfortunately prevalent among social scientists, that causal relations are features of models only. There are some good reasons to represent causal factors with independent variables. But the association between causes and independent variables is only a desideratum in model construction. It is not a criterion for judging which things are causes and which are effects.

Armstrong holds that a law of nature is a certain sort of structural universal which, in turn, fixes causal relations between particular states of affairs. His claim that these nomic structural universals explain causal relations commits him to saying that such universals are irreducible, not supervenient upon the particular causal relations they fix. However, Armstrong also wants to avoid Plato’s view that a universal can exist without being instantiated, a view which he regards as incompatible with naturalism. (...) This construal of naturalism forces Armstrong to say that universals are abstractions from a certain class of particulars; they are abstractions from first-order states of affairs, to be more precise. It is here argued that these two tendencies in Armstrong cannot be reconciled: To say that universals are abstractions from first-order states of affairs is not compatible with saying that universals fix causal relations between particulars. Causal relations are themselves states of affairs of a sort, and Armstrong’s claim that a law is a kind of structural universal is best understood as the view that any given law logically supervenes on its corresponding causal relations. The result is an inconsistency, Armstrong having to say that laws do not supervene on particular causal relations while also being committed to the view that they do so supervene. The inconsistency is perhaps best resolved by denying that universals are abstractions from states of affairs. (shrink)

Recent approaches to causal modelling rely upon the causal Markov condition, which specifies which probability distributions are compatible with a directed acyclic graph. Further principles are required in order to choose among the large number of DAGs compatible with a given probability distribution. Here we present a principle that we call frugality. This principle tells one to choose the DAG with the fewest causal arrows. We argue that frugality has several desirable properties compared to the other principles (...) that have been suggested, including the well-known causal faithfulness condition. _1_ Introduction _2_ The Causal Markov Condition _3_ Faithfulness _4_ Frugality _4.1_ Basic independences and frugality _4.2_ General properties of directed acyclic graphs satisfying frugality _4.3_ Connection to minimality assumptions _5_ Frugality as a Parsimony Principle _6_ Conclusion Appendix. (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.

Reasoning is not just following logical rules, but a large part of human reasoning depends on our expectations about the world. To some extent, non-monotonic logic has been developed to account for the role of expectations. In this article, the focus is on expectations based on actions and their consequences. The analysis is based on a two-vector model of events where an event is represented in terms of two main components – the force of an action that drives the event, (...) and the result of its application. Actions are modelled in terms of the force domain and the results are modelled with the aid of different domains for locations or properties of objects. As a consequence, the assumption that reasoning about causal relations should be made in terms of propositional structures becomes very unnatural. Instead, the reasoning will be based on the geometric and topological properties of causes and effects modelled in conceptual spaces. (shrink)

This article explores the question of what character relations must have before the orthodox law of obligations will describe them as ‘causal’ relations. The article does not purport to identify the metaphysical nature of ‘causation’. Instead it provides a non-reductive account of what is essential before the law has described the relation between a specific factor and the existence of a particular indivisible phenomenon as ‘causal’. Section 1 presents a simple test for this relation—an ‘extended but-for (...) test’—that can be deployed in a straightforward way without engaging with theoretically complex and often problematic accounts of causation based on the notion of sufficient sets, such as Wright’s NESS account. Section 2 demonstrates how important principles relating to the separateness of a legal entity and to legal responsibility can resolve theoretical puzzles and in turn illuminate why the orthodox law of obligations does not choose to describe as ‘causal’ a relation wider than the one identified in this article. (shrink)

A large number of legal rules create an obligation to prevent, repair or otherwise mitigate damage to human health or the environment. Many of these rules require that a legally relevant causal relation between human behaviour and the damage at issue is established, and in the establishment of causal relations of this kind scientific information is often pressed into service. This thesis examines this specifically legal use of scientific information. It shows that many legally relevant causal (...) relations cannot be established in this way. It also shows that the legal strategy for dealing with epistemic difficulties by relaxing the standard of proof is of limited value in tackling this problem. Consequently, the legal rules focused upon are less efficient tools for combating damage to human health and the environment than their appearances suggest. Other legal means to achieve this aim should therefore be considered. The thesis begins by presenting a framework which can be used to solve some important problems with communication and the division of labour that arise when scientific information is used to answer legal questions. This framework recognizes both epistemological and ontological differences between law and science. The latter are differences between the kinds of entity which are relevant in distinct theoretical contexts; the former, by contrast, are differences between applicable standards of proof. In subsequent parts of the thesis this framework shapes the discussion of the question: To what extent can legally relevant causal relations, involving legally significant entities, be established through the application of scientific information about other, scientifically relevant entities and legal standards of proof. The thesis concludes with a discussion of some of the ways in which the legal regulation could, potentially, be adapted, so as to counteract damage to human health and the environment more efficiently. (shrink)

Shepherd argues that we can know that there exists a universe external to the mind because that universe is the only possible cause of our sensations. As a part of that argument, Shepherd eliminates the possibility that sensations might be caused by other sensations on the grounds that sensations are merely momentary existences and so not capable of standing in causal relations with each other. And yet she claims that sensations do stand in causal relations to other objects, (...) both as the effects of the combination of the external world, our organs of sense, and our minds, and as the partial causes of other sensations. These claims together generate a puzzle. If sensations are too fleeting to stand in causal relations with each other, how are they nonetheless capable of standing in causal relations to other objects? I suggest that because sensations exist only for a moment, to stand in synchronous causal relations with other sensations would require that the two sensations exist at precisely the same moment. But since cause and effect are identical during the moment in which they are combined, any two sensations that exist for only the moment of their combination are identical. Nothing can be its own cause, so sensations cannot be the sole cause of other sensations. Sensations can be the partial cause or effect of other objects, though, so long as those objects endure for more than a single moment. For example, external objects, organs of sense, and the mind, all exist both before and after the moments in which they combine to form a sensation. So, while their combination is identical to that sensation in that moment, all of these other objects exist outside of that moment, and that combination as well. (shrink)

We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log2(N ) + 1 experiments are sufficient and in the worst case necessary to determine the causal relations among N ≥ 2 variables when no latent variables, no sample selection bias and no feedback cycles are present. For all K, 0 < K <.