Este artículo tiene el objetivo de responder al artículo “¿Alguien quiere mástiles? Asimetrías causales y explicativas” de James Woodward. Aquí se conjetura que, cuando la direccionalidad causal depende del diseño experimental, se debe a que las variables involucradas son capaces de producir cambios las unas en las otras. Esto se ejemplificará utilizando el caso de los gases ideales, como un escenario opuesto al de las sombras de los mástiles.
This paper aims to provide an answer to James Woodward’s article “Flagpoles anyone? Causal and explanatory asymmetries”. It will be conjectured that, when causal directionality depends on the experimental design, it is because the variables involved are capable of producing changes in each other. This will be exemplified using the case of ideal gases as opposed to the flagpole-shadow scenario.
Fernanda Samaniego*
Universidad Nacional Autónoma de México
* Correspondence to: Fernanda Samaniego. Facultad de Filosofía y Letras, Departamento de Filosofía, SUAyED. UNAM. Circuito Interior. Ciudad Universitaria, s/n (C.P. 04510. Ciudad de México) – fernandasamaniego@filos.unam.mx – https://orcid.org/0000-0002-0439-1374
How to cite: Samaniego, Fernanda (2022). «Bi-directionality in causal relationships»; Theoria. An International Journal for Theory, History and Foundations of Science, 37(1), 103-109. (https://doi.org/10.1387/theoria.22695).
Received: 2021-04-06; Final version: 2021-12-09.
ISSN 0495-4548 - eISSN 2171-679X / © 2022 UPV/EHU
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
The “Manipulability Theory” or “Interventionism” is not only a theory of causality. It is also a theory of scientific explanations since it provides insight on how causal scientific explanations work, and how good and bad explanations can be compared in terms of the number and variety of (actual or hypothetical) interventions, under which the causal relationships remain invariant.
Along this paper we will be using the general notation in Figure 1, where I is an intervention producing surgical changes in the values of the variable C via the causal relation R1. In order to study the consequent reaction on the values of E and given C is the putative cause of the effect E, both variables are connected by the relationship R2. We want to evaluate if R2 is a putative or a genuine causal relationship.
In his most recently published paper (2022), Woodward defines two notions of invariance/independence,
These two requirements are important for causal assessment, as the interventions must be performed under the best understanding of the relevant variables, the background conditions, and what specifically may be defining the values of the causal structure under study. If CSI and VRI are significant in any causal analysis, it is also pertinent to take them on account for the specific issue of causal directionality, which will be the main focus of attention here.
The aim of this paper is to discuss causal directionality, contrasting the flagpole example with the ideal gas law. This is a reaction to the paper “Flagpoles Anyone? Causal and Explanatory Asymmetries” published by Woodward in THEORIA in 2022.
Why does causal directionality matter and how is it related to invariance/independence? As it is well known, Hempel and Oppenheim’s Deductive-Nomological Model (1948) states that the phenomena explained in science can be described in a sentence (explanans), which is deduced from a set of premises (explanandum) containing laws and particular conditions. According to the model, using the laws of trigonometry and the laws of optics, the following two are perfectly valid scientific explanations:
However, explanation (i) seems far more convincing than explanation (ii) since we know that the flagpole’s specific length may be explained by budget, transport, and so on, but not by its shadow.
Along with the relevance argument, the flagpole argument is one of the most famous criticisms against the model of Hempel and Oppenheim. It shows that scientific explanations tend to be asymmetrical, in the sense that flagpoles can explain shadows, but not vice versa. Flagpoles produce shadows, but not vice versa. Relating this to causality, we are used to explaining effects by finding their causes, but not vice versa.
The scenario is radically different when we leave the flagpole example and turn to assess ideal gases. The ideal gas law states that pressure P, volume V, and temperature T are proportionally related to each other, according to the equation PV = nRT. However, in this case, none of the variables “produce” the other two. The values of any of them can be explained in terms of interventions on the values of the other two, because there is no causal hierarchy among them.
In his most recent paper on explanatory asymmetries (2022), Woodward points out that for the ideal gas law, causal directionality depends on the initial conditions. I’d like to additionally argue here that when causal directionality depends on the initial conditions, it is because we are dealing with bidirectional causal relations among variables. By bidirectional I mean that at least two of the variables can cause each other, but also that the causal structure may involve three or more variables connected by a causal arrow of this kind (see Fig. 3 below).
The case of ideal gases is particularly interesting since the variables T, P, and V are neither causally nor statistically independent of each other. However, they can be controlled in pairs, giving us the impression of causal directionality. The underlying truth, in my view, is that each pair of variables is capable of causing each other, as shown in Fig. 3.
In Woodward’s view, this case is useful to show that causal directionality is not just “in” the law considered by itself, it is not fixed or completely determined by the law, but rather has to do with the role played by the initial and boundary conditions and constraints governing the systems. I completely agree with Woodward on his claim that the relevant information about causal directionality is not only “inside” the c-generalizations or scientific laws, but also in the specific values of the initial and boundary conditions. As Woodward himself acknowledges, “this may include information about what is or is not correlated with what, what is fixed and what is not allowed to vary […] This information is relevant to causal direction since what quantities are correlated or not with others may depend […] on what is fixed and what can vary in the specific systems we are considering” (see Woodward, 2022, §8).
A consequence of this is that causal directionality is also a matter of how we approach the phenomenon under study, i.e., the experimental design and the interventions we choose to make may change how directionality is perceived. Woodward already recognizes this when he claims: “The asymmetry in the solutions arises in the same way it does in the gas in cylinder example—because of the way in which initial and boundary conditions we impose interact with the laws themselves to yield solutions that are asymmetric” (see 2022, §10).
For instance, we can decide which variable will remain fixed, which one will act as putative cause, and which one as “the effect”. This is how we define “by hand” the causal directionality in different experiments, but all this is possible because we already know the equation and we have a high degree of control over the object of study. Before the law was defined, our heroes in physics performed all kinds of interventions to deduce the equation.
But let us come back to the flagpole case. As we do now with gas boxes and pistons, we also have full control over the flagpole-shadow situation. But causal directionality does not change “at our will”. Why not? I’d like to argue that this is because—no matter how much we change the initial conditions—shadows will never cause lengths of flagpoles. Flagpoles produce shadows, not the other way around. Therefore, those variables are connected with a single causal arrow, not with a double-headed causal arrow.
Temperature produces changes in the volume and the pressure, and vice versa. Exactly the same will happen if we assess the causal relationship between a magnetic field and a flow of electrons, or gravitation forces between a couple of asteroids. In short, causal directionality is reversible only when the variables involved are already symmetrical in the sense of being able to produce changes in each other.
Why is this relevant and who would disagree? In debates about causality, people as important as Bertrand Russell (On the notion of causation, 1918
Let us assess a final case, representing Astrid Nehlig’s medical explanation of the effects of cocoa and chocolate on brain health and cognitive abilities (2012) in a causal graph (Fig. 4). The variables that will be included in the causal graph have been emphasised in the explanation and the causal graph will follow:
The causal structure represented in Fig. 4, works beautifully as an example of indubitable causal direction. No matter how we decide to set up the background conditions, or CSI and VRI invariances, the case is so neat, that the directionality of causal relations R1, R2 and R3 wont backflip, for it is clear that brain activity or brain health does not alter the amount of substances in chocolates.
Causal directionality does not rely completely on scientific laws. Woodward argued this in 2020, and here we have agreed with him. Sometimes, for a defined law or a functional relationship, a change in the initial conditions may revert causal directionality. Woodward has exemplified this point with ideal gases.
Causal directionality can also change when we work in the context of intricate relationships among variables that violate statistical independence. As it is suggested here, in those cases it is convenient to redefine the relevant variables or the functions relating them, in order to perform a “clean” causal analysis.
However, when this happens—and it will happen in a wide range of situations—we shouldn’t stop ourselves from proposing causal evaluations based on special interventions as “joint interventions”, nor conclude that interventionism is problematic for asking too much of causal systems. If I have understood Nancy Cartwright’s position in Hunting Causes and Using Them (2007), she claims that Hausman’s and Woodward’s requirements for causation
Even when causal directionality may be reversed after some changes in the initial conditions, or after some interventions on statistically dependent variables have been revaluated, there are still some strongly asymmetrical cases, as the flagpole-shadow and the chocolate-brain examples, where the variables involved have a well-defined direction that won’t change by any means.
I thank an anonymous referee and Ariel Cisneros for their comments on previous versions of this article, which was written within the Research Project “Experiencia, experimentación y explicación” reference number PROINV_21_24.
REFERENCeS Cartwright, N. (2007). Hunting causes and using them. Cambridge: Cambridge University Press. Frisch, M. (2014). Causal reasoning in physics. Cambridge: Cambridge University Press. Hausman, D., and Woodward, J. (1999). Independence, Invariance and the Causal Markov Condition. British Journal of Philosophy of Science, 50(4), 521-583. Nehlig, A. (2012). The neuroprotective effects of cocoa flavanol and its influence on cognitive performance. Brtitish Journal of Clinical Pharmacology, 75(3), 716-727. Okasha, S. (2002). Philosophy of science. A very short introduction. Oxford: Oxford University Press. Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press. Woodward, J. (2008). Invariance, modularity, and all that: Cartwright on causation. In S. Hartman, C. Hoefer, & L. Bovens (Eds.), Nancy Cartwright’s philosophy of science (pp. 198-237). New York: Taylor & Francis. Woodward, J. (2015). Interventionism and causal exclusion. Philosophy and Phenomenological Research, 91(2), 303-347. Woodward, J. (2022). Flagpoles anyone? Causal and explanatory asymmetries. THEORIA. An International Journal for Theory, History and Foundations of Science, 37(1), 7-52 (https://doi.org/10.1387/theoria.21921). FERNANDA SAMANIEGO is a Full Time Professor at the Department of Philosophy at UNAM, Mexico. She obtained her PhD at Complutense University (Madrid) and a master’s degree at LSE (UK). Her lines of research are causation in scientific explanations, the foundations of contemporary physics and the philosophy of time.ADDRESS: Facultad de Filosofía y Letras, Departamento de Filosofía, SUAyED. UNAM. Circuito Interior. Ciudad Universitaria, s/n. C.P. 04510. Ciudad de México. Email: fernandasamaniego@filos.unam.mx ORCID: 0000-0002-0439-1374
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