# **SpringerBriefs in Philosophy**

**Lars-Göran Johansson · Thomas Banitz · Volker Grimm · Tilman Hertz · Emilie Lindkvist · Rodrigo Martínez Peña · Sonja Radosavljevic · Petri Ylikoski · Maja Schlüter**

# **A Primer to Causal Reasoning About a**

**Complex World**

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Lars-Göran Johansson • Thomas Banitz • Volker Grimm • Tilman Hertz • Emilie Lindkvist • Rodrigo Martínez Peña • Sonja Radosavljevic • Petri Ylikoski • Maja Schlüter

# A Primer to Causal Reasoning About a Complex World

Lars-Göran Johansson Department of Philosophy Uppsala University Uppsala, Sweden

Volker Grimm Department of Ecological Modelling Helmholtz Centre for Environmental Research - UFZ Leipzig, Germany

Emilie Lindkvist Stockholm Resilience Centre Stockholm University Stockholm, Sweden

Sonja Radosavljevic Stockholm Resilience Centre Stockholm University Stockholm, Sweden

Maja Schlüter Stockholm Resilence Centre Stockholm University Stockholm, Sweden

Thomas Banitz Department of Ecological Modelling Helmholtz Centre for Environmental Research - UFZ Leipzig, Germany

Tilman Hertz Stockholm Resilience Centre Stockholm University Stockholm, Sweden

Rodrigo Martínez Peña Institute of Analytical Sociology Linköping University Norrköping, Sweden

Petri Ylikoski Department of Sociology University of Helsinki Helsinki, Finland

ISSN 2211-4548 ISSN 2211-4556 (electronic) SpringerBriefs in Philosophy ISBN 978-3-031-59134-1 ISBN 978-3-031-59135-8 (eBook) https://doi.org/10.1007/978-3-031-59135-8

This work was supported by Stockholms Universitet.

© The Editor(s) (if applicable) and The Author(s) 2024. This book is an open access publication.

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*The development of Western science is based on two great achievements; the invention of the formal logical system (in Euclidian geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiments (during the Renaissance). A. Einstein (1953)*

*No causes in, no causes out. N. Cartwright (1989)*

# **Preface**

This book is meant as an introduction to students and researchers in the multidisciplinary field of sustainability science who are interested in a better understanding of what 'causation' means, and how it can be explored in a more systematic way. It introduces fundamental ideas about causation from philosophy, particularly those that underlie studies of causation that are based on quantitative data and statistical methods of causal inference. Chapter 9 then takes a broader view to present the diversity of causal reasoning found in Social Ecological Systems, SES for short research and discuss how to disclose and navigate it. While we are focusing on application to, SES, where such better understanding is badly needed, readers from virtually all disciplines will benefit, because in most disciplines assumptions about causation are usually implicit, which often will limit progress. Thus, this book should serve as an introductory textbook to be used for classes and seminars, but also for self-studying. To support this, each chapter ends with a list of questions that guide to further literature, stimulate discussions, or to be used for homework assignments.

This book is one result of an interdisciplinary project at Stockholm Resilience Centre at Stockholm University, 'Approaches to causation in the social and natural sciences and their implications for theory building in sustainability science— CauSES', whose goal was to investigate causal thinking in research on SES. This is a relatively new interdisciplinary field, attracting researchers with different backgrounds and different presuppositions about causal relations. Observing the vast differences between ecologists, physicists, economists, political scientists, sociologists, anthropologists, statisticians and others regarding causation, one might wonder whether there is any common idea about causation at all.

Philosophers have discussed both epistemological and a metaphysical aspects of causation since antiquity. The debate has been more lively than ever the last decades. There is some convergence about some aspects of causation, but universal agreement about the concept of causation is still not in sight.

Our approach is more empirical than most philosophical contributions to the causation debate. We have two starting points: the first is exploring how we use the terms 'cause', 'effect' and related words in ordinary discourse without any explicit justification. These uses together make up an implicit characterisation of the basic meaning of causal terms. The second is investigating how scientists in different disciplines make inferences using the causal vocabulary.

A fairly coherent conception of causal relations has been achieved in the natural sciences. The extension of this conception to parts of social sciences has been difficult, for reasons to be discussed in this book.

We, the nine members of the research group, have had many meetings where outlines of papers and chapters of this book have been thoroughly discussed. It was decided that Lars-Göran Johansson should take the main responsibility for writing this book by writing drafts of the chapters, which then have been discussed several rounds in the entire group. Chapter 9 is an exception; here Maja Schlüter, Emilie Lindkvist, Tilman Hertz, Rodrigo Martínez Peña and Thomas Banitz wrote the first drafts.

This work was funded by the Swedish Research Council, grant No 2018-06139.

Uppsala, Sweden Leipzig, Germany Leipzig, Germany Stockholm, Sweden Stockholm, Sweden Norrköping, Sweden Stockholm, Sweden Helsinki, Finland Stockholm, Sweden

Lars-Göran Johansson Thomas Banitz Volker Grimm Tilman Hertz Emilie Lindkvist Rodrigo Martínez Peña Sonja Radosavljevic Petri Ylikoski Maja Schlüter

# **Contents**

# Contents xi

# **Part III Causation in Complex SES**

# **Chapter 1 Introduction: Causation in Social-Ecological Systems**

**Abstract** In this chapter we start the discussion about causal idiom by giving excerpts from three papers, each discussing the dynamics of a social-ecological system. There is plenty of talk about causes in these papers, but, interestingly, the authors talk about causes and effects without much reflection on the criteria for something being a cause of something else, nor about the required evidence for such claims.

This book is about causal thinking and use of causal idiom in general, with the aim to provide the basic understanding required to explore the diversity of causal reasoning about social-ecological systems (SES) in particular.1 Three questions stand in focus: (i) What are the meanings of different causal expressions, (ii) what is sufficient evidence for inferences from observations to causal relations, and (iii) how to handle the diversity of causal relations in SES?

As a starter, let's have a brief look at three excerpts from SES research. The first is from (Hruska, 2017):

A social–ecological system (SES) is a combination of social and ecological actors and processes that influence each other in profound ways. The SES framework is not a research methodology or a checklist to identify problems. It is a conceptual framework designed to keep both the social and ecological components of a system in focus so that the interactions between them can be scrutinised for drivers of change and causes of specific outcomes. Resilience, adaptability, and transformability have been identified as the three related attributes of SESs that determine their future trajectories. Identifying feedbacks between social and ecological components of the system at multiple scales is a key to SES-based analysis.

...[T]he SES framework facilitates identification of cross-system feedbacks to explain otherwise puzzling outcomes. While information intensive and logistically challenging in the management context, the SES framework can help overcome intractable challenges to working rangelands such as rangeland conversion and climate change. The primary benefit

1 Illari and Russo (2014) and Norton et al. (2014) are two other books discussing scientific practice and philosophical theories about causation.

L.-G. Johansson et al., *A Primer to Causal Reasoning About a Complex World*, SpringerBriefs in Philosophy, https://doi.org/10.1007/978-3-031-59135-8\_1

of the SES framework is the improved ability to prevent or correct social policies that cause negative ecological outcomes, and to achieve ecological objectives in ways that support, rather than hurt, rangeland users. (op. cit. p. 263)

Several expressions indicating causal relations are here used: 'interactions', 'drivers of change', 'causes', 'feedbacks', 'prevent', 'correct' and 'achieve objectives'. The authors do not give any precise definitions of these expressions, apparently thinking that they are sufficiently common and well understood in ordinary language use or within the SES community.

Later in the chapter we find a diagram showing the components of rangeland social-ecological systems, but it is no diagram in the ordinary sense of this word; It is no more than a display of a number of concepts ordered in five or six groups. It does not suggest anything about causal relations.

The caption says a lot more, but almost nothing of what is said in that text is displayed in any way in the figure (Fig. 1.1).

**Fig. 1.1** Generalized diagram of a rangeland social–ecological system. Humans and the environment interact in countless ways outside of natural resource management, but the interactions are most directly planned, manipulated, and monitored in natural resource management activities. Local, regional, and global social processes can all shape natural resource use and management activities. While resource policy may be set at large geographical scales (e.g., national), management activities occur within a single ecosystem. Livestock grazing differs from other types of natural resource use in that it is indirect; rather than directly manipulating a rangeland ecosystem, livestock operators devote their primary attention to managing livestock, and the livestock interact directly with the rangeland (adapted from Hruska, 2017, 266)

The second excerpt is a case study of green turtle fisheries in Nicaragua. Here is the summary:

*2.3 Robustness Summary*. The Nicaraguan green turtle fishery does not represent a robust system of CPR governance. Persistent poverty, lack of alternative employment opportunities, and a high population growth rate (initially within communities, but more recently through in-migration) continue to be the main drivers for the commercialization of this fishery under a domestic subsistence use exception to endangered species protection of green turtles. Instead of protecting the species from exploitation, the ratification of the Convention on International Trade in Endangered Species (CITES) in 1977 by the national government, and subsequent closure of the legal international market for green turtle meat, has merely led to a shift in focus by turtle fishers from responding to international market demands to creating and satisfying a domestic demand for green turtles. Although de jure rules limiting the harvesting of green turtles exist at all government levels, including at the territorial, municipal, and community level in the RAAS and the RAAN, there is no overarching coordination of those rules, and no monitoring or enforcement, but for the collection of harvesting data that is being conducted by a researcher formerly involved with an international NGO. In essence, the fishery is de facto operated year-round without any restrictions. Prior limiting factors, such as the special skills required to navigate sailing dories and harpoon turtles, have been eliminated through the increased use of motor boats and turtle nets. The literature mentions three factors that provide evidence of the long-term unsustainability of the fishery: (1) actual capture rates are believed to be significantly higher than reported; (2) a majority of the animals captured are large, sexually immature juveniles and adult turtles from the Tortuguero natal nesting site, which effectively removes the base for a future breeding population; and (3) recent declines in capture rates in regions with previous turtle abundance (Lagueux et al. 2014). Given many Miskitos reliance on green turtles as a sole source of cash revenues, a turtle population collapse could have significant social-ecological consequences (Brady et al., 2015).

The core causal claim is that there are 'three factors that provide evidence of the long-term unsustainability of the fishery'. This formulation tells us that plausibly there are three *causes* of unsustainability, although the word 'cause' is not used. It is followed by a short account of the causal mechanisms.

The third excerpt is the abstract of a paper about the governance of coastal fisheries in Chile:

Here we explore social, political, and ecological aspects of a transformation in governance of Chile's coastal marine resources, from 1980 to today. Critical elements in the initial preparatory phase of the transformation were (i) recognition of the depletion of resource stocks, (ii) scientific knowledge on the ecology and resilience of targeted species and their role in ecosystem dynamics, and (iii) demonstration-scale experimental trials, building on smaller-scale scientific experiments, which identified new management pathways. The trials improved cooperation among scientists and fishers, integrating knowledge and establishing trust. Political turbulence and resource stock collapse provided a window of opportunity that triggered the transformation, supported by new enabling legislation. Essential elements to navigate this transformation were the ability to network knowledge from the local level to influence the decision-making processes at the national level, and a preexisting social network of fishers that provided political leverage through a national confederation of artisanal fishing collectives. The resultant governance scheme includes a revolutionary national system of marine tenure that allocates user rights and responsibilities to fisher collectives. Although fine tuning is necessary to build resilience of this new regime, this transformation has improved the sustainability of the interconnected social–ecological system. Our analysis of how this transformation unfolded provides insights into how the Chilean system could be further developed and identifies generalised pathways for improved governance of marine resources around the world (Gelcich et al., 2010).

In all three examples it is clear that a main goal of the research is to arrive at knowledge about system's dynamics and what to do to change things, in the first case to improve management of rangelands, in the second case to arrive at a more sustainable turtle fishery and in the third case to explain the change in governance of coastal fisheries. In order to know what to do one needs causal knowledge, reliable knowledge of the form, 'If we do X, then Y will probably occur'.

Causal knowledge is thus often wanted because one wants to understand why and how SES change and to obtain guidance for future actions. However, in neither case is the reported research particularly illuminating about the criteria for counting something as a cause of something else. And with one exception, there is no indication of what kind of evidence the authors require for inferences to causes of observed states of affairs.

This, we believe, is a rather common feature of much empirical science; causal notions are often used without much reflection and questions about evidence for causal relations are often not discussed. The intense discussion among philosophers about the concept of causation has had little influence on empirical scientists. This we will try to remedy to some extent.

Broadly speaking there are three types of questions addressed by SES researchers:

Answers to questions 1 and 2 are causal explanations, while answers to the third one are *constitutive explanations*, i.e., explanations that consist of descriptions of the parts making up the system. This distinction will be elaborated upon in Chap. 8.

The rest of this book is divided into three parts. The Part I, Chaps. 2, 3, and 4, is a general analysis and discussion of the use of causal idiom in ordinary language. It does not result in an explicit definition of the terms 'cause' and 'effect', but it gives their meaning in particular contexts. This is a necessary prerequisite for a discussion about causal inference in science, which is the topic of the Part II, Chaps. 5–8. The Part III, Chap. 9, is about the diversity of causal reasoning in SES research. It discusses how this diversity results from the diverse backgrounds, interests, epistemological stances and scientific norms of researchers and practitioners in this multi-disciplinary field and where and how during a research process it manifests. It also provides suggestions about how to navigate this often confusing diversity.

While the chapters do have, of course, a sequence, and although we suggest to follow this sequence while reading, there is not necessarily a strict linear flow from simple to complex, or basic to advance, as a textbook on, e.g., statistics would be organised. Rather, there are multiple aspects to consider, when trying to understand what 'causation' can mean, and what the challenges are when trying to understand causation. Therefore, to some degree, each chapter has its own main focus, which is relevant but also strongly connected to most of the topics of the other chapters. To make this very clear, we added, after each chapter's abstract, a bullet point list summarising the main lessons to be learned in this chapter, plus a brief summary why and how the chapter's topics are relevant regarding the overall purpose of this book, which is being better prepared to ask and answer questions about causation, both in general and for SES in particular.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Part I Semantics of Causal Expressions**

# **Chapter 2 Causal Talk Permeates Ordinary Language**

**Abstract** This chapter gives an overview of causal idiom in ordinary language and introduces some fundamental semantic distinctions. The main points are:

# **2.1 Introduction**

There is a great variety of causal expressions and even a very brief overview of ordinary language reveals how common expressions for causal relations are; some examples are 'bring about', 'make happen', 'produce', 'do', 'perform' 'result in' 'effect of', and 'leads to'. Two questions immediately come to the fore: (i) is there any common meaning of these expressions, a core meaning of respectively 'cause' and 'effect', and (ii) what evidence is required as justification for causal claims?

Many different things have been related as cause and effect in ordinary as well as in philosophical and scientific discourse: events, states of affairs, properties, categories, quantities, processes, desires, beliefs and actions. This list is not complete and one may reasonably wonder if there is any core meaning at all for all the diverse uses of the terms 'cause', effect' and other terms with a causal connotation. We believe there is, there are some necessary conditions for the correctness of sentences of the form 'x causes y', and its converse 'y is the effect of x', but in any particular context more conditions are needed and these differ in different contexts. There is a wide diversity of causal notions, which will be surveyed and analysed in this book.

Causal idiom and causal thinking is a basic trait of humans. Already in the second verse of Iliad (circa 800 BC), the first work of western literature, We are given a seemingly causal explanation of the hostility between Agamemnon and Achilles:

And which of the gods was it that set them on to quarrel? It was the son of Jove and Leto; for he was angry with the king and sent a pestilence upon the host to plague the people, because the son of Atreus had dishonoured Chryses his priest. (Transl. S. Butler).

Thus, the conflict between Agamemnon and Achilles is said to have been caused, indirectly, by the god Apollo ('the son of Jove an Leto') who is attributed a typical human psychology: Apollo was angry with the king and acted accordingly. The cause of the quarrel is an action of a sentient being.

In the epilogue to his book *Causality: Models, Reasoning and Inference* Judea Pearl does not mention this passage, but noticed that in ancient times questions about causes were questions about agents, their motives and desires:

The agents of the causal forces in the ancient world were either deities, who cause things to happen for a purpose, or human beings and animals, who possess free will for which they are punished and rewarded. This notion of causation was naive but clear and unproblematic.

The problem began, as usual, with engineering; when machines had to be constructed to do useful jobs. [....] And once people began to build multistage systems, an interesting thing happened to causality - *physical objects began acquiring causal character.* (Pearl, 2000, 333)

One might say that in ancient times the prototypical cause is an agent who acts for a purpose, whereas from the scientific revolution onwards the prototypical case is a ball colliding with another ball and changing the latter's motion.

The ancient notion of causation—a cause is an action of an agent—is still very common in ordinary thinking and language, less so in scientific discourse, except perhaps in some social sciences. The latter are concerned with human actions, individual and collective, so in these disciplines there is plenty of talk about causal agents driven by beliefs and desires.

Having analysed the different aspects of causal discourse in both ordinary and several scientific contexts, we will at the end of the book focus on causal reasoning in complex SES. Analysing causal relations in such systems is particularly demanding because of the diversity of kinds of entities, properties and relations and the complex dynamics they generate.1

1 A book that focuses on our habits and cognitive abilities to understand causal connections is (Grotzer, 2012).

# **2.2 Causal Phrases**

As an illustration of the variety of expressions used for making causal claims, we may have a look at the beginning of (Lindegren et al., 2009):

Atlantic cod (Gadus morhua) is among the commercially most important fish species of the European waters. Many of the stocks have declined dramatically and still remain at historically low levels (1, 2). These collapses have largely resulted from overfishing (3, 4) and climate-driven declines in productivity (5, 6). The climate effect generally works through changes in the physical environment (e.g., temperature and salinity), but also through altered food supply for early life-history stages, eventually affecting recruitment (5, 6). In accordance with this effect, recruitment failure of Eastern Baltic cod was caused mainly by high egg and larval mortalities as a result of climate-induced hydrographic change (7, 8). In several areas the collapses of cod stocks were part or major drivers of large-scale reorganisations of ecosystems (9). These so-called regime shifts are frequently caused by climatic changes (9, 10) and/or over-exploitation resulting in cascading trophic interactions (11, 12). Similarly to other areas, the Baltic Sea underwent both regime shifts and trophic cascades (8, 13). Such alterations in ecosystem structure typically affect species interactions, eventually influencing food-web dynamics through both positive and negative feedback loops (14).

In this introduction we observe at least seven expressions indicating causal relations:

All these sentences convey information having the form that someone or something makes something else happen. In neither case could the researchers directly have observed these events, so one immediately wonders how the authors know that the relations expressed by 'cause', 'make happen', 'drives', 'affect', etc, really obtain, i.e. what evidence they have collected. This question in turn triggers the question what these expressions really mean, for we cannot decide what evidence we require for a certain statement if we do not know what it means. Questions about evidence for causal claims and questions about the meaning of these claims are thus deeply and intimately related; the meaning of an expression determines what kinds of evidence there might be for a sentence containing this expression.

The diversity of ideas about causation is not only a matter of methods, there are also different ideas of what causation is and what it entails. For instance, people

disagree about (i) generalisability of singular causal relations, (ii) origins of causal powers, and (iii) which causes are more important than others.

# **2.3 Some Remarks on the Semantics of 'Cause', 'Effect' and Their Cognates**

# *2.3.1 Causal Relations Between Events/States of Affairs*

Our most basic use of causal idiom consists in relating *particular* events or states of affairs by a two-place predicate 'x caused y', 'x was the effect of y', 'x leads to y', or some other expression with clear causal meaning.2 In other words, things causally related to each other are singular events or states of affairs that occur at particular times and places. This is the fundamental use of causal idiom. But use of words for causal relations is wider: with the development of modern science, causal talk has been extended to cover also relations between categories and quantities.3 By abstracting from individual cases, we simply say that one attribute is the cause of another attribute. For example, overweight is said to be a cause (not the only one!) of high blood pressure.

# *2.3.2 Causal Relations Between Categories*

The pandemic Covid-19 was caused by the virus SARS-CoV-2. This is a relation between two categories: the cause is a virus of a certain type or category, and the effect is a disease of another category; being exposed to particles belonging to this virus type increases the probability of getting the disease Covid-19.

A necessary condition for this causal relation to occur is that the conditional probability to attract Covid-19 when exposed to the virus is higher than the marginal probability to get the disease. In mathematical notation:

*prob(*|Covid-19 | being exposed to SARS-CoV-2*) > prob(*Covid-19*).* (2.1)

2 In logic, the term 'predicate' has a more general meaning than in ordinary grammar. Predicates are what is left of a sentence when you remove the noun phrase and direct objects. If you only remove the noun phrase, you have a one-place predicate, if you remove more terms you get twoplace, three-place predicates, etc.

3 Collected data must be organised in some way. This is done using variables. The basic distinction among variables is between category variables, such as sex, or ethnic group, and quantitative variables such as biomass, weight or age. Hence, categories are basically sets of objects identified by a common attribute, whereas quantities are quantitative attributes of things, see further Sect. 5.2.

This means that Covid-19 and SARS-CoV-2 are correlated. Still, this statistical relation is not sufficient evidence for there being a causal relation; more evidence is needed, see Sect. 2.4 and Chap. 6. In this case we know that the virus is the cause of the infection based on experimental evidence, not just on statistical correlations. More carefully expressed: we know that in any individual case of someone having the Covid-19 infection, this event was caused by him being infected by the SARS-CoV-2 virus. So we generalise and say that the virus causes this disease, thus saying that one category causes another category. We have thus extended the possible relata of the relation *... causes....* to include categories. (In this case the disease is identified by its cause, so the probability of getting the disease without being exposed to SARS-CoV-2 is zero.)

From a purely grammatical point of view, the terms 'SARS-CoV-2' and 'Covid-19' are singular terms (see textbox below). That does not conflict with their referents being categories, i.e., classes of things. A category, when given a name, is treated, grammatically and from a logical point of view, as an entity, a particular thing. (Whether this should be understood as that there exists categories, i.e., properties and relations, over and above the individual cases, is a perennial dispute in metaphysics. Luckily, for the purpose of this book, we need not take any stance in this debate.)

### **Singular and General Terms**

From a logical point of view, the simplest cases of complete declarative sentences consist of a general term, (a predicate phrase) and one or several singular terms. Singular terms are proper names, personal pronouns, definite descriptions, or variables standing for such things.

A singular term cannot function as predicate, while general terms can occur both as nouns and predicates.

An example with one singular term is

#1. The oldest person in Sweden is more than 100 years.

Here, 'The oldest person in Sweden' is the singular term, it is a definite description of one distinct entity. The rest of the sentence is the predicate phrase 'is more than 100 years'; this is a general term, which means that it can be predicated about many things.

A sentence with two singular terms is

#2. Sweden has a smaller population than Germany.

Here, 'Sweden' and 'Germany' are the two singular terms, they are each a name of a political and geographical entity. (Thus in predicate logic we do not distinguish between noun and direct object.)

(continued)

A sentence with three singular terms is

#3. The judge in a civil case determines whether the plaintiff or the defendant wins the case.

Here, 'The judge in a civil case', 'the plaintiff' and 'the defendant' are the three singular terms.

So singular and general terms are the logical constituents of the simplest complete declarative sentences. Singular terms *may* refer to things, objects, events, etc., i.e., entities that can be identified as individuals, i.e., thought of as *one*.

A singular term need not refer to anything. 'The king of France' is a singular term, but there is no king of France.

Things referred to by singular terms, i.e., individuals, need not be individuals in any ordinary sense. In the sentence 'Manchester United won The Premier League 2012–2013', the name 'Manchester United', is a name for an individual entity, a football club. When talking about Manchester United we *treat it as one object*, disregarding whether or not it consists of a number of players and other members.

# *2.3.3 Causal Relations Between Quantitative Variables*

A common scientific question is whether a certain variable is the cause of another variable and huge efforts are often made in order to answer such questions. The starting point when asking about a possible causal relation between two variables is to see whether they are correlated or not. Suppose the answer is yes. That is not sufficient for inferring that they are causally related, since a correlation can occur without there being a causal connection. But if there is a causal relation between two variables, they are correlated, when other variables are controlled for. So observing a correlation is a reason for further inquiry to see whether there is a causal relation or not.

As a starter, we observe that an expression of the form 'variable X is a cause of variable Y' means that a change in the value of variable X attributed to some object causes a change in the value of variable Y attributed to the same or another object. In other words, causal relations between variables are based on causal relations between ordered pairs of individual events. But neither in ordinary nor in scientific contexts is this explicitly stated; the common expression is that a certain variable causes another one.

Relations between two quantitative variables are often expressed as functions of the form *y* = *f (x)*. Such an expression does not contain any information about any causal relation, because a function by itself does not express any relation between

events in the real world. But even if we add an interpretation to the effect that variable values represent events in the world that are causally related, the form of this expression does not distinguish between cause and effect. The reason is that the causal relation is asymmetric, it is 'directed' from the cause to the effect, while a mathematical function only expresses a numerical relation between the values of the two variables.

In many cases, when the function *y* = *f (x)* has an inverse, this is immediately clear, since the equations *y* = *f (x)* and *x* = *f* −1*(y)* are logically equivalent, they are two different expressions for the same fact of the matter. Thus, the mere syntactic form of the equation *y* = *f (x)* does not tell us anything about which is the cause and which is the effect, or whether there is any causal relation at all between these variables. We will discuss this more thoroughly in the next section. The formalism of *structural equations* is another matter, to be discussed in Chap. 7.

Most often a causal interpretation of an equation comes from an intuitive and tacit judgement about which variable we naturally, or most easily, can manipulate. Hence, the causal interpretation of a mathematical relation between two variables comes from our *agency perspective*, to be discussed in Chap. 3. An equation by itself does not say anything at all about causal relations.

# *2.3.4 Common Causes*

The fact that a correlation between two variables is very strong does not by itself say anything about the probability for there being a causal connection. There are many well-known cases of correlations between two variables that no one would think of as causally related. The correlation is in such a case explained by being produced by a *common cause*, often called a confounder. If variable A is a cause of variable B via one causal mechanism and a cause of another variable C via another causal mechanism, we may observe a correlation between B and C without there being any causal link between them. Here is one example of a strong correlation which most plausibly, given even a very limited background knowledge, is the outcome of a common cause. Tyler Vigen, from whose home page tylervigen.com/spurious/correlation the figure is taken, discusses some possibilities (Fig. 2.1).

The expression 'confounding cause' is often used when referring to a common cause. This term is a bit misleading since it suggests that the confounding cause is not a real cause, while in fact it *is* the cause of the correlation. What the confounder can do is to mislead us into thinking that there is a causal link between two observed and correlated variables, while there is not.

How to decide, by empirical means, whether two observed variables really are causally related or whether there is a common cause will be discussed in Chap. 6.

**Fig. 2.1** The number of bachelor's degrees in physical science strongly correlates with the distance between Saturn and the moon during the period 2012–2021, see Tyler Vigen, Spurious Correlations, available at https://tylervigen.com/spurious-correlations

# **2.4 Causal Powers**

When we talk about the cause of a certain effect, we are inclined to describe the situation as that some entity, a person, a physical object or a machine, has a certain *causal power*, which under certain conditions is manifested by bringing about the effect. It is, for example, common to say that the Earth has the power to attract bodies and that this explains why a stone falls to the ground. This causal power is the Earth's gravitation and this explanation appears to most people satisfying.

Another example: some persons are charming, which is a dispositional property of having the ability to charm other persons, thus sometimes causing certain behaviours in other persons. For example, one might explain a person's foolish behaviour by saying that he/she was charmed by another person, and the latter is well-known for their charming capacity. Thus, the terms 'dispositional property' and 'capacity' are often believed to express causal powers attributed to things.

One may first observe that a causal power is not the same as the cause of a particular event or action. The cause of a particular event is another event. But when we observe a regular connection between two types of events, for example that ponderable bodies fall to the ground when the support is removed, or that many people are charmed by a certain person, we are inclined to explain such a regularity by postulating a causal power in the entity thought to be the cause of this regularity. Thus, causal powers are invoked in causal *explanations* of recurring features and behaviour, although strictly speaking the causal power is not the direct cause of a singular effect.

Saying that a certain thing has a certain power is to ascribe to this thing a dispositional property, i.e., a property that only under certain conditions is manifested as an event that can be observed; but causal powers themselves are not observable, although thought to be permanent properties of things.

Postulating that an object has a certain causal power may be regarded as the proper explanation of our observations of some regular and recurrent behaviours, but it does not increase our ability to manipulate things or predict the future. This is so because any inference to future events is based on observed regularities, and these observed regularities are exactly the very reasons we have for inferring a causal power. Postulating a causal power does not increase the probability for a certain future event to occur. Hence, philosophers with an empiricist mind-set are sceptical about causal powers. The argument is Ockham's razor: 'do not without necessity postulate an entity.' (There are several formulations of this principle; the Latin version is 'Entia praeter necessitatem non esse multiplicanda.') We can make exactly the same inferences, with the same degree of certainty, to future events without causal powers.

Reflecting on Ockham's razor, one might ask 'necessary for what?' and it is pretty obvious that the tacit assumption is that the goal is to make predictions about events and states of affairs not observed when the utterance is made.

But causal powers are often held to have explanatory force, they give us understanding of recurrent events, and one might be tempted to infer that understanding is a prerequisite for successful predictions about the future.

The validity of this line of thought depends crucially on the criteria for understanding a phenomenon. A prediction either succeeds or fails and that can be determined by observations. But what are the criteria for understanding? They seem to be crucially dependent on background knowledge had by those being given the explanation. We will discuss this topic further in Chap. 8.

Causal powers are unobservable, but that is not the relevant epistemological point. There are, for certain, many cases in the history of science where unobserved entities are postulated in order to explain observed phenomena. The crucial point is that such a postulated entity is accepted as real only when there is independent evidence for its existence. In the case of causal powers, there cannot be any such independent evidence; a causal power only manifests itself as a certain observed regularity, which is exactly the same as what is needed as the empirical basis for inferences about unobserved events.

Summarising, there is no empirical evidence for causal powers being responsible for the observed events in nature or for human behaviour. Nevertheless, many people hold that causal powers explain observable events. Whether that is so depends on our criteria for causal explanations.

# **2.5 Summary**

Causal idiom is a basic feature of natural language, just as words for e.g., animals, colours, people, activities and events. The difference between on the one side words for these things, and on the other hand causal expressions, is that the latter concern relations between pairs of entities, while the former are talk about singular entities. In the second case, one observes *two* events and under certain conditions infers that they are related as cause and effect. Children learn causal expressions directly, in interactions with parents and other care-takers, not by being taught verbal definitions.

The notion of cause (and effect) can be expressed by quite a number of different words and expressions, for example, 'bring about', 'make happen', 'produce' and 'do'. None is more fundamental than the other.

When we ask for a cause, we have tacitly a certain event in mind, we ask for the cause of a particular event. The question has the form 'What is the cause of E?' Hence, the terms 'cause' and 'effect' are relational words; the effect (or the cause, if the effect is asked about) is often not mentioned as being obvious in the context at hand.

Questions about causes and effects are basically questions about relations between events and, secondarily, relations between types of events and their representations, quantitative and category variables. Casual relations between quantitative and category variables depend on causal relations between individual instances of these relations.

### *Discussion Questions*

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Chapter 3 Causal Talk Is Fundamental**

**Abstract** The terms 'cause' and 'effect' are very common in both ordinary and scientific discourse. Since they have a number of synonyms (or near synonyms), there is no point in trying to define 'cause' or 'effect' using any of these synonyms; 'cause' and 'effect' belong to the most fundamental level of language learnt in childhood. The way to give their meaning is to display a number of contexts in which causal expressions are used without any justification. The chapter ends with a presentation and discussion of Hume's criteria for the use of the term 'cause'. The main points are:

# **3.1 Introduction: The Pervasiveness of Causal Talk**

The words 'cause', 'effect' and their synonyms are used mainly for two purposes: to explain things and to help us decide what to do in order to achieve a certain desired state of affairs. Therefore, it is important to have a deeper understanding of their meaning. One may view the meaning of a term as the rules for its correct use. This is not to say that there is anything like a well defined meaning of the term 'cause' (and its converse 'effect') that is the same in all contexts; as with very many expressions, the meaning depends to some extent on context.

As observed in the previous chapter, relating events or states of affairs as cause and effect is a basic feature of our thinking, acting and use of language. This fact strongly suggests that it is not possible to define the term 'cause' (or its converse 'effect') using more primitive vocabulary; we learn to use the words 'cause' and 'effect' when we learn to talk, without being given any verbal explanations. We do not first learn a basic vocabulary that later is used in an explicit definition of 'cause'. What we instead can do is to state a number of conditions for the correct use of 'cause', for example, that in a singular case a cause never happens later than its effect.

Causal claims are often made without any scientific backing. As an illustration, look at the following list of quotes, randomly selected, from New York Times 2020- 08-17, where 'cause' and 'effect' are italicised by us, not by NYT:

'But when the pandemic *caused* demand for bikes to jump, Giant needed to reverse course.'

'Gov. Gavin Newsom of California called for an investigation into what he described as a major utility failure that was even more alarming set against the backdrop of the pandemic, when people, many largely confined inside, may be more dependent than ever on electricity: rolling blackouts over the weekend, *caused* by a record-shattering heat wave.'

'Problems with coronavirus data reporting *cause* confusion in Iowa and beyond.'

'Uncertain still was what *effect*, if any, the event would have on the spread of the virus.'

'The Interstate Highway System was justified in part with dubious claims about national security, but it had the *effect* of reinforcing national unity.'

'Dr. Kimberly Manning, an internal medicine doctor at Grady Memorial Hospital in Atlanta, recalled countless micro-aggressions in clinical settings. "People might not realise you're offended, but it's like death by a thousand paper cuts," Dr. Manning said. "It can *cause* you to shrink."'

These causal claims (understandably, several relating to the Covid-19 pandemic!) are not explicitly backed by any profound scientific analysis; the NYT journalists and the persons' referred to take the readers to understand and accept the causal claims as correct against a background of common knowledge.

The scientific literature is no less filled with the words 'cause' and 'effect'. In a paper discussing Bertrand Russell's thesis that there are no causal laws (Russell, 1913), the authors started to look for the prevalence of the words 'cause' and 'effect' in a leading scientific journal:

A search for articles in which the word 'cause' appeared in the on-line archives of *Science*  between October 1995 and June 2003 returned a list of results containing 8288 documents, averaging around 90 documents per month, in which the word 'cause' occurred. 'Effect' was more popular - 10456 documents for the same period, around 112 per month. (Ross and Spurrett, 2007, 60)

But we use not only the words 'cause' and 'effect' for talking about causation; expressions such as 'bring about', 'lead to', 'make happen', 'produce', 'result in', do', etc., also express causal relations. And we have also the negative counterparts to these, such as 'stop', 'prevent' and 'hinder', expressions that suggest causal actions performed in order to bring an end to some undesirable state.

The same is true of 'effect', which in many contexts can be replaced by 'result', 'outcome', 'final state', 'impact', etc. So we submit that if the authors of the paper had included these other causal expressions indicated above, the figures would have been still higher. It is safe to say that causal thinking is deeply ingrained in our thinking, it belongs to our nature.

That causal thinking is a fundamental aspect of our being as humans was a point already made by Kant in his *Critique of Pure Reason* (Kant et al., 2003, (A80/B106)). He argued that our mind has certain structural features that determine the forms of our judgements. Thus, Kant identified 12 fundamental concepts, called *categories*1 among which *cause* is one. These categories make up the conceptual basis for all judgements, according to Kant.

His arguments are convoluted and much debated, but one may arrive at a similar conclusion, at least in the case of causal judgements, without taking any stance about his transcendental arguments. One may, as was done above, observe ordinary language use, instead of speculating about our minds. Doing that, we realise how common and basic the use of causal expressions are in ordinary discourse.

# **3.2 Attempts to Define 'Cause'**

In science we are required to define central terms. Giving a verbal definition of a term is to give its meaning in terms of more common and well known expressions. This is hardly possible when it comes to such a basic term as 'cause'.

At the online Merriam-Webster dictionary we are given the following list of synonyms for 'cause' used as verb: 'beget', 'breed', 'bring', 'bring about', 'bring on', 'catalyse', 'create', 'do', 'draw on', 'effect', 'effectuate', 'engender', 'generate', 'induce', 'invoke', 'make', 'occasion', 'produce', 'prompt', 'result (in)', 'spawn', 'translate (into)', 'work' and 'yield'.

If we attempt to define 'cause' in terms of e.g., 'bring about', we might further ask about the meaning of 'bring about'. Then a natural response would be to say that it means 'cause'. In common language, none of these terms is more basic and informative than the others.

In Nancy Cartwright's *How the Laws of Physics Lie* we read:

Causes make their effects happen. We begin with a phenomenon which, relative to our other general beliefs, we think would not occur unless something peculiar brought it about. (Cartwright, 1983, p. 76)

Here Cartwright gives the meaning of 'cause' in two ways: first as synonymous to 'make happen', then using a counterfactual, a sentence of the form 'If A had not occurred, B would not have happened.' The first would suffice if the defined term is less well understood than the defining term, but that is hardly the case with 'cause' and 'make happen', as earlier pointed out. Why not reverse and explain the meaning of 'make happen' in terms of causation? The term 'cause' is one of the most common and basic words in natural language. So maybe that is why she immediately moves to a counterfactual explanation.

1 Kant's use of the term 'category' is quite different from our modern term, see the glossary item 'category variable'.

Cartwright is not alone in explaining the meaning of the term 'cause' by a counterfactual expression, it is quite common in philosophy. But how do we know that a counterfactual statement is true? Obviously it can never be justified by an observation. This will be further discussed in Chap. 4.

The notion that we somehow could define 'cause' and its converse 'effect' using a more basic and clearer vocabulary seems indeed dubious. The meanings of 'cause' and 'effect' and their synonyms are determined by the rules we automatically and without any conscious justification apply when we use these terms in concrete communication situations. We talk about causes and effects mainly for two purposes; to explain things and to decide what to do in order to achieve our goals; successful doing is causing a desired event to happen. Causal thinking and causal talk is a basic trait of humans, which, by the way, also was Kant's conclusion.

We have in ordinary language no explicit criteria of application for the terms 'cause' and 'effect'. But when they are used in a scientific context, one must state criteria in order to know what can be inferred from causal statements. Thus Cartwright writes:

Like Machamer et al. (2000) I too have long followed Anscombe's view that the ordinary concept of 'cause' is highly general. It is what, following Otto Neurath, I call a 'Ballung' concept. A Ballung concept is a concept with rough, shifting, porous boundaries, a congestion of different ideas and implications that can in various combinations be brought into focus for different purposes and in different contexts. Many of our ordinary concepts of everyday life are just like this. Ballung concepts also can, and often do, play a central role in science and especially in social science. But they cannot do so in their original form. To function properly in a scientific context they need to be made more precise. This will be done in different ways in different scientific sub-disciplines, serving different ends and to fit with the different concepts, methods, assumptions, and standards operating in these disciplines. The more precise scientific concepts that result will in general then be very different from each other and different yet again from the original Ballung concept. (Cartwright, 2017, 136)

We basically agree with Cartwright that in scientific contexts we need to clearly state the conditions for the legitimate use of 'cause', 'effect' and their near synonyms.

# **3.3 Are Causal Connections Observable?**

Given the omnipresence of the term 'cause' (and 'effect') in everyday life and in science, what, then, are the criteria for it and its synonyms? Can one directly observe a causal connection between two events?

Some philosophers (for example G.E.M. Anscombe (1971)) argue that we can, in certain cases, observe causation. We are not convinced. One may reasonably be doubtful on the ground that 'cause' and 'effect' are relational terms; the basic syntax is 'x is the cause of y' and 'y is the effect of x', where the placeholders 'x' and 'y' represent events, states of affairs, or aggregates of such things described by categories or quantitative variables. We observe events and states of affairs, but do

we observe their causal connection? Do we really *see* or *hear* the cause propagating its impact to the effect? Can one really say that we directly observe any kind of connection of any two things? We think not. Perception is primarily perception of objects and, derivatively, of their changes.

Empiricists are prone to say the same, they restrict the use of the term 'direct observation' to things we discern with our sense organs.

But how to draw the line between a direct observation and an inference from such an observation? Consider the following situation: you enter a new hotel room and want to turn on the light. You push the first button you see and the bathroom, not the room, is lit. Then you push another button and the room is lit. Can one say that you observed that pressing the first button caused the bathroom to be lit, pressing the second one caused the room to be lit? Would a person who never before has been in a modern building with electric lights, for example, a person belonging to a hunter-gatherer culture in the Amazon rainforest, say that they saw the causing? We think not.

When people are prone to say that they observed these two events being causally connected, they rely on previous experience and tacit inferences made from such experiences, and some knowledge about electricity. In general, inferences to causal relations between events are based on experiences from experimentation; if we manipulate one object in certain ways and observe changes in some other object so that one can control the states of the second object by doing things with the first, we apply the cause-effect relation. And this is an inference, not a direct perception.

If we, on the contrary, describe this situation as a direct observation of a cause-effect relation, we have in fact made the well known fallacy *post hoc, ergo propter hoc*. 2 We distinguish between mere succession and causation and that cannot be done by mere observations; ultimately, we must perform experiments by manipulating one variable and observing the other. A statement about a causal relation is the result of an explicit or implicit inference from such experiments.

# **3.4 Hume's Criteria for the Use of 'Cause'**

David Hume discussed the observational basis for talk about causation (Hume, 1986/1739). His proposal was that there are basically two directly observable features of a pair of events that trigger (i.e., *cause*!) us to say that they are related as cause and effect:

But this is obviously not sufficient. There are many cases of pairs of events/states of affairs being in physical contact and one of them preceding the other, without us

2 'After this, hence because of this.'

saying that the first one is the cause of the other. Hume therefore added the *regularity condition*, popularly stated as 'same cause, same effect'. Expressed more carefully: A is the cause of B if and only if A belongs to a type of events/states of affairs that regularly is followed by another type to which B belongs, and if A and B satisfy the other two conditions.

Thus Hume's analysis of the use of 'cause' and 'effect' may be summarised as that each of the three conditions: (1) the cause precedes its effect, (2) cause and effect are contiguous and (3) the same type of cause is regularly followed by the same type of effect, are necessary and that they are jointly sufficient for the correct use of sentences of the form 'x causes y'.

Each of the conditions has been doubted and Hume in fact discussed caveats to all three (Hume, 1986/1739). Regarding timing, he accepted that cause and effect sometimes could be simultaneous. Regarding contiguity he realised that there could be intermediate events/states of affairs so that cause and effect may be indirectly connected via a chain of intermediate events/states of affairs. The causal relation is transitive. Finally, about regularity, he accepted the possibility of several causes for a particular effect, in which case we must say that a particular cause is not always followed by its effect, for other causes may also be needed. So a particular cause only increases the probability for the effect to occur.

Many philosophers have been critical towards Hume's regularity theory, the main argument being that it does not really explain what a cause is. Many people ask for explanations of regularities, usually in terms of causal powers. For an empiricist this is reversing the order of explanation; if there are any such things as causal powers, these must be explained in terms of observations, i.e., observed regularities, see Sect. 2.5.

But there is another problem with the regularity view: there are many regularities that we do not count as instances of causation. It is a well established piece of knowledge that correlation is not causation. How to distinguish cases of correlation that indicates causation from those that do not?

The first step is to use Hume's condition 2; individual instances of causes and effects must be in contact, provided we can give a clear meaning to the notion of contact. The problem is that events, states of affairs, properties, or other kinds of entities being related as cause and effect hardly can be said to be in contact, since they are not bodies.

It is easy to grasp the underlying idea that there must be a process, some kind of physical, chemical or biological link between cause and effect, when these are two individual events in space and time. But how to apply that to, e.g., a causal relation between two attributes?

One hint may be found by reflecting on how we distinguish between correlations and causal relations. An observed correlation between two variables, i.e., events/states of affairs of types A and B respectively, is a causal relation only if there is a mechanism, a chain of events/states of affairs connected by physical signals (remember: 'physical' here includes chemical and biological events) transferring information from any particular A-event to a particular B-event. And how do we know that there was a transfer from an A-event to a B-event and not the opposite?

There are two factors determining this: timing and deliberate manipulation of the A-event.

The contact requirement is a *necessary condition*. This is illustrated by the fact that we do not believe in extra-sensory perception (ESP). Some people claim that they can acquire information about things from which no physical, chemical or biological signals could have reached their mind, but no evidence has been produced. Several well-conducted experiments performed with persons claiming to have extra-sensory capacities have been made and they have all failed; there is simply no empirical evidence for ESP. Perception requires physical signals triggering our sense organs, so if there is no physical signal from an individual A-event to an individual B-event, the A-event cannot be a cause of the B-event.3

These reflections indicate, again, that experiments where one variable is manipulated and another is observed are crucial for establishing a causal relation. If we observe a variation in an observed variable following variations in a variable being manipulated, we infer that there is a causal link connecting the two variables. And we take it for granted that there is a physical, chemical or biological mechanism making up the connection between pairs of singular events.

So causal relations between variables, quantities and other abstract things are grounded on causal relations between those individual events making up these abstract entities; physical signals transferring information between individual events or states of affairs make perfect sense and has been discussed by several philosophers, e.g. Reichenbach and Reichenbach (1999), Salmon (1984), Salmon (1997), Salmon (2001), and Collier (1999).

This is not to say that physical links between cause and effect always is a salient aspect of a causal explanation. Talking about causes of historical events, wars for example, the physical connections between power centres, (letters or telegrams sent between presidents and prime ministers before a war) are rarely of any relevance for our questions about causes in history. But there must be such links.

The fundamental method to obtain information about physical links is to perform experiments, to be further discussed in Chap. 7. But it all depends on our ability to keep factors other than the hypothesised cause under control. How do we ascertain that, when we do not know which other factors there might be? That is often our problem when trying to decide which causal connections there are between parts of a complex social, ecological or social-ecological system.

Another way to decide whether a correlation between A and B is due to a causal link or not is to use earlier established scientific theory to describe causal mechanisms, to be discussed in Chap. 8. But this earlier established theory must in turn be based on experimental evidence for causal links.

3 In particle physics there is a phenomenon called 'entanglement' which seems to show that information without signals is transferred between distant objects. This is however a misrepresentation of the facts, see e.g. Johansson (2007).

# **3.5 Summary**

Our fundamental causal terms, ('cause', 'effect', 'make happen', 'bring about', etc.) belong to our basic vocabulary, learnt as part of learning ones mother tongue. This means that one cannot define 'cause', 'effect', etc., in some more basic vocabulary. The meaning of such words are learnt by learning their application to a number of concrete situations as experienced by the child.

Cause and effect are relational terms, they are predicates of the form '.... is the cause of....' and '.... is the effect of.....'. We cannot directly observe causal relations; we observe physical objects and events, and under certain conditions two such observed events satisfy the predicate '...is the cause of......'

The conditions for saying that an event is a cause of another event was first formulated by Hume. They are (1) cause precedes its effect (or is practically simultaneous), (2) cause and effect are in contact (directly of indirectly) and (3) same types of causes are regularly followed by same type of effects. All three conditions have been extensively discussed by philosophers. We hold that Hume was almost correct. The only improvement needed is that the regularity condition should be restricted, namely, that the correlation ('regularity') is observed in experiments where the cause is manipulated and the effect varies accordingly. Hume's three conditions might have been a correct description of common use of the term 'cause' in his days, but we have later learnt to be more restrictive.

### *Discussion Questions*

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# **Chapter 4 Causation, Counterfactual Dependence and Potential Outcomes**

**Abstract** When talking about causes we often think of an imagined contrast to the real sequence of events: we use a counterfactual, asking what *would* have happened if the cause had not occurred. But one might be doubtful about the explanatory force of this analysis. The basic problem is that the truth or falsity of a counterfactual statement cannot be determined by empirical means. In some cases, notably in physics, we can apply a strict law when justifying claims about alternative scenarios. In most cases, however, we have at best regularities and in such cases it is difficult to have any confidence in the corresponding counterfactual. An account of causation in terms of the more restricted concept of potential outcomes is much more useful. It is closer to empirical practice and is more reliable. The main points are:

# **4.1 Introduction**

The concept of cause (as used in sentences of the form 'A caused B', or its converse 'B is an effect of A') is quite often explained as 'If A had not been the case (or occurred), then B would not have been the case (or happened)'. It is a counterfactual (or contrary-to-fact) statement since A and B in fact both occurred.

How, then, do we know what *would* have happened if A had in fact not happened? It is obvious that our justification for saying what would have happened, if the stream of events had differed from what actually occurred, must be based on some inference from actually occurring and observed regularities to unobserved events. How do we ascertain that?

This is an instance of the problem of induction, the problem to state under what conditions an inductive inference can be relied upon.1 If we have a trustworthy and exception-less law at our hand, the problem is solved. Instead of using observed states as initial conditions in calculating future states of affairs, we can put in nonactual values and use the strict law to calculate what would have happened in such a non-actual case. But in most situations we have no strict law at our disposal. We will further discuss the connections between laws and causation in Chap. 7.

This will not work if we use non-strict laws, i.e., laws with so called ceteris paribus clauses ('All else being the same'). This is so because when we imagine a non-actual initial condition we do not know whether other relevant circumstances also would differ from the actual observed situation. When we suspect that our law is not strict we add the clause 'ceteris paribus' just because we do not know which factors we need to take into account or not.

Can one say something about counterfactuals and causation without using strict laws? Empiricists are sceptical. Stating truth conditions for counterfactuals has proven to be a deep problem and there is no agreement about its solution. It appears, if anything, more difficult than stating truth conditions for statements about causal relations.

# **4.2 Goodman on Counterfactuals**

The seminal paper in the discussion about counterfactuals was Nelson Goodman's *The Problem of Counterfactual Conditionals* (Goodman, 1946). In that paper Goodman observed that there is a profound semantic difference between counterfactual and indicative conditionals.

Counterfactual and indicative conditionals differ in verb form; counterfactuals are expressed using the subjunctive mood, whereas indicative conditionals are expressed in indicative mood, and this difference indicates a semantic difference. The following example may illustrate:

*Indicative conditional*: If it is raining right now, then Sally is inside.

*Counterfactual conditional*: If it were raining right now, then Sally would be inside.

1 This is the modern conception of the problem of induction, emanating from Goodman. The traditional problem was to give a general justification of inductive reasoning, which proved impossible.

These two sentences differ in meaning, hence there is a difference in their truth conditions. In order to analyse this difference, we start with the truth table for the indicative conditional (also called the material conditional):

We can formulate the content of this table as that an indicative conditional is true whenever the antecedent is false or the consequent is true.2

If we apply this truth table to the counterfactual conditional it will come out true, since the verb form 'were' means that what follows is in fact not the case. Hence 'were' tells us that the antecedent is false, it is not raining. So far, so good. But according to the truth table it doesn't matter whether Sally is inside or not, both #1 and #2 come out true:

#1. If it were raining right now, then Sally would be inside.

#2. If it were raining right now, then Sally would not be inside.

That cannot be correct, they contradict each other. Hence, the truth conditional analysis where antecedent and consequent are evaluated separately must be wrong in the case of counterfactual statements. No truth table can account for the semantics of counterfactual sentences.

As Goodman observed, it is some sort of connection between the events described in the antecedent and the consequent that determines the truth value of a counterfactual statement. This connection is not, and cannot be, reflected in any *merely logical* connection between antecedent and consequent, since logic concerns the *forms of sentences* and *formal relations* between sentences.

Goodman next observed that the difference between true and false counterfactuals is that true counterfactuals are connected to laws, while false are connected to true, *accidental generalisations*. Here is one example of a contrast between a law and an accidental generalisation (not discussed by Goodman, but by several later philosophers):

# 3. All spheres of gold are less than 1 km in diameter.

# 4. All spheres of U-235 are less than 1 km in diameter.

#3 and #4 have the same logical form and presumably are they both true. (If one would find somewhere in the universe a really big lump of gold, we could have a

2 Indicative conditionals are used for making conditional claims: the consequence is claimed to be true under the condition that the antecedent is true. If the antecedent is false, no claim about the consequent is made, it may be true or false.

longer diameter.) But there is a difference; #4 is a consequence of fundamental laws of nuclear physics, and therefore itself a law, which means that it is not merely true but necessarily so; it is impossible to assemble an amount of U-235 bigger than the critical mass (52 kg, a sphere with diameter = 17 cm) of this radioactive isotope.3 By contrast, #3 is accidentally true; it just happens to be no big lumps of gold in the universe.

Based on #3 and #4 we can now construct two counterfactuals, one true and one false:

#5. If x were a sphere of gold, it would be less than 1 km i diameter.

#6. If x were a sphere of U-235, it would be less than 1 km in diameter.

As far as we know, #5 is false while #6 is certainly true. So it seems reasonable to say that true counterfactuals are based on laws whereas false counterfactuals are based on accidental generalisations.

This would be a real step forward, if we had a clear explanation of the difference between laws and accidental generalisations. But we have not; many people have strong intuitions about the difference, but so far no generally accepted analysis is in sight.4

Goodman concluded his paper by admitting that he had no solution to the problem with counterfactual conditionals, since he had no suggestion of how to distinguish between laws and accidental generalisations.

The discussion about causation and counterfactuals has been intense and one may discern two main strategies: either to analyse causation in terms of counterfactuals, or the other way round. This choice is guided by ones metaphysical views: David Lewis (1973) and many others think that a semantics of counterfactuals in terms of possible worlds is satisfactory and taking that as a firm ground one can then define causation in terms of counterfactuals. Those sceptical about the existence of possible worlds, or even the intelligibility of this notion, (How do you identify a possible but not actual world?) hold that the explanation should go from causation to counterfactuals.

We belong to this latter camp. Counterfactual statements belong both to our vernacular and to scientific discourse; they are widely used and there is no reason to assume that users of this idiom tacitly or explicitly delve into deep metaphysics concerning possible worlds and our access to them. Hence, we think counterfactuals should be explained in terms of more basic concepts such as causes or perhaps laws. As we showed in Chap. 3, causal talk belongs to our very basic vocabulary, learned already when first learning to talk our mother tongue. This means that explanations of the meanings of less basic expressions should be done in terms of the basic vocabulary.

3 This impossibility is a consequence of fundamental properties of U-235 nuclei, which can be derived from quantum theory.

4 But see Johansson (2019) for an empiricist account of strict laws not built upon counterfactuals or necessity.

In 1940s, when Goodman's paper was published, there were little discussion about the concept of a law of nature. The received view was that when a hypothetical general statement was supported by a sufficient number of observations and no counter instances were observed, one had reason to believe that the general conclusion was correct, and it was then elevated to being a law. Those who elaborated the details of this line of thought argued that probability arguments could be used. But this idea met, justifiably, devastating criticism. Having high probability is not the same as certainty, and strict laws are certain. Furthermore, as Goodman pointed out, there is a profound difference between laws, which are necessary, and other true general statements of the same logical form, which are not necessary, and this difference could not be analysed using only empirical arguments.

What does this mean for the counterfactual analysis of causation? Our view is that in so far as we are unclear about the meaning of 'cause', giving this concept a definition in terms of counterfactuals is no step forward; counterfactuals are strongly related to laws, and both the notions of *counterfactual* and *law* are less clear than that of *cause*. So what to do? James Woodward has suggested a way out.

# **4.3 Woodward's Account of Causation**

James Woodward has discussed the counterfactual analysis of causation in several papers (Woodward, 1997, 2002, 2003, 2008, 2016). One might guess that Woodward was inspired by Goodman's observation of the strong connection between true counterfactuals and laws, although he made no references to Goodman's paper. Taking into account that the concept of a law of nature is as much in dispute as are counterfactuals, Woodward's step forward was to base true counterfactuals on what he called 'invariances'.

An invariance is an observed regularity, although not one elevated to the status of being a law. Thus Woodward was able to avoid the metaphysical jungle of necessities. Neither is an invariance merely an accidental generalisation. Woodward's idea is that an observed regularity which has been used in several successful predictions may be labelled an *invariance*, which tells us that it is a weaker concept than that of a natural law. But what, more precisely, is the difference?

Woodward intended 'invariances' to refer to regularly occurring phenomena restricted to some region in space and time. One could for example say that it is an invariance (or 'restricted regularity') that almost all people who has spent 10 years or more in Sweden understand, to some degree, Swedish, while hesitating to call this regularity a 'law'. But it depends on what we mean by 'law'.

In any case, if we accept this regularity we are prone to accept as true the counterfactual 'If NN had been living in Sweden for 15 years, she would understand Swedish', said about a certain person that only understands her mother tongue, say Swahili, and has never been in Sweden.

This type of local and restricted invariances differ from laws in that they are not exception-less. Observing such an exception we are prone to ask for an explanation, i.e., a causal explanation. We are back to causes.

One further difference between laws and invariances is that laws properly so called are integrated into a theory consisting of a number of laws logically related to each other.

The question is: can one refer to an invariance as evidence for a counterfactual? It seems that the answer is no, unless we know the causal mechanism producing the invariance. For how could an invariance observed in a number of cases be known to be valid also in a non-observed case? Invariances may have exceptions, they are not strict laws, and how do we know that an unobserved case is not an exception?

It seems that an 'explanation' of the concept of cause in terms of counterfactual dependence is no step forward. It is much more reasonable to say that we can explain 'counterfactual dependence' in terms of causes. The word 'cause' and it's synonyms ('bring about', 'lead to', 'produce', etc.) belong to common language and is much easier to understand than any technical term.

# **4.4 Potential Outcomes Instead of Counterfactuals?**

Instead of analysing causation in terms of counterfactuals, Rubin, following Neyman (1923) and Fisher (1925), uses the concept of *potential outcomes*. Here is how he motivates it:

Some authors (e.g. Greenland et al., 1999; Dawid, 2000) call the potential outcomes "counterfactuals", borrowing the term from philosophy (e.g. Lewis, 1973). I much prefer Neyman's implied term 'potential outcomes' because these values are not counterfactual until after treatments are assigned, and calling all potential outcomes 'counterfactuals' certainly confuses quantities that can never be observed (e.g. your height at the age of 3 if you were born in the Arctic) and so are truly a priori counterfactual, with unobserved potential outcomes that are not a priori counterfactual (see Frangakis and Rubin (2002), Rubin (2004); and the discussion and reply for more on this point.) (Rubin, 2005, 325)

Here is a simple illustration of how to use the concept of potential outcomes. Suppose we have randomly divided a test sample, taken from some population, into two groups, one consisting of those being treated in some way, the rest is the control group. For each unit in the treatment group one can only observe its actual state after the treatment and similarly for the control group; in this group one can only observe the state of a unit after not being treated during the experiment. Both the actual state and the non-actual possible state of a unit are *observable*, although only one state is actually observed. Hence the term 'potential outcome'. We can now compare the observed outcomes in the two groups. We can calculate the conditional probability for the outcome B, conditioned on the intervention A, p(B|A) and compare with the marginal probability p(B). If prob(B |A) > prob(B), we have strong reason to believe that A is a cause of B. (N.B. the indefinite 'a cause'; there may be more causes!) The intervention A may be a intentional manipulation or an intervention not planned by the experimenter, i.e., a so called 'natural experiment'.

Replacing the concept of potential outcome for counterfactual in discussions about causation is a significant step towards a more empirical approach. Moreover, it connects to the manipulability account of causation, see Sects. 3.4 and 6.1. It is useful when making inferences about causation from observed results of experiments, and also in making inferences from so called 'natural experiments', see Sect. 6.2.

From a philosophical point of view this is a significant improvement as compared with the counterfactual analysis. The semantics of counterfactuals in terms of possible worlds faces two obstacles: (1) how do we identify a possible world and (2) *which* possible worlds should we take into account when describing the semantics of causation? One needs to impose restrictions on what to count as a possible world, which is usually made in terms of similarity to our actual world. This can be made formally stringent, but it is not helpful for the empirical researcher, since it leaves the notion of similarity with the actual world undefined. The crucial question is 'Similar in what respect?'

The terminology of potential outcomes is, in comparison, applicable to actual experiments and observations. The set of potential outcomes are defined in the experimental design. We perform an experiment and explicitly state the set of possible outcomes, of which one is actualised. For further discussion see e.g., (Menzies and Beebee, 2020) and (Rubin, 2005).

# **4.5 Summary**

In ordinary parlance we take it for granted that the sentence 'A is the cause of B' is more or less synonymous with 'If A had not occurred, B would not have occurred.' This assumption is then used for explaining causation in terms of counterfactuals. But on second thoughts one may reasonably conclude that this is not of much value as an explanation; the meaning of counterfactuals is much more foggy than the meaning of 'cause'. How do we know what would have happened if the course of events had been different from what actually happened?

It seems that only if we have a strict scientific law at our disposal can we know with some certainty what would have happened, if the conditions had been different from what they actually were. But in very many cases we know no strict laws, so an analysis of causation in terms of counterfactuals is no step forward.

Woodward has suggested to use term 'invariance' instead of laws for explaining causation; Invariances are inferred from observed regularities in some local setting and believed to be true also in unobserved cases in the same type of settings, while not being elevated to the status of law and not integrated into a theoretical structure of laws related to each other.

A somewhat similar approach is taken by e.g. Rubin, who has suggested replacing the concept of *potential outcome* for *counterfactual*. Given a dynamical equation we can calculate what would be the outcome for any chosen initial condition, actual or not. This equation guides the time evolution from the initial situation and we can map the set of selected initial conditions onto the set of potential outcomes. The dynamics may be strict (mapping one initial state onto one final state), or probabilistic, mapping a set of possible outcomes from each initial state). The list of alternative outcomes are clearly stated and all are observable; but only one will be observed, that which is actualised.

# *Discussion Questions*

# **References**

Dawid AP (2000) Causal inference without counterfactuals. J Am Stat Assoc 95:407–448

Fisher RA (1925) Statistical methods for research workers. Oliver and Boyd, Edinburgh

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# **Part II Causation in Science**

# **Chapter 5 Causal Relations and Causal Relata in Science**

**Abstract** There is no such class of things as *causes*. The terms 'cause' and 'effect' are relational terms, in other words, our concern is the *causal relation* 'x causes y'. This relation is applied to pairs of singular events and states of affairs, to pairs of types of events/and states of affairs and to pairs of variables. In science we are mostly interested in generalities, so the focus is usually how to infer causal relations between types of events/states of affairs and between variables.

The main points in this chapter are:

# **5.1 Introduction**

Implicit in all talk about causes is the prior identification of an event, or a type of events, called 'the effect'. When we for example ask about the cause of the global warming, it is the global warming that is the effect. This remark may seem utterly trivial, but the point is that causes do not make up a distinct category of things, events or states of affairs. Discussions about causes are discussions about *causal relations*.

Statements about relations between two entities have the canonical form 'xRy', where 'R' is short for a two-place predicate. The things related are called 'relata'. In the case of causal relations it is 'x is a cause of y', or 'y is an effect of x'.

Relations relate things, objects, events, states of affairs, properties, variables and perhaps other things as well. From both an ontological and an epistemological point of view it is important to distinguish between singular and general causation.

# **5.2 Singular Versus General Causation**

# *5.2.1 Causal Relations Between Singular Events/States of Affairs*

The basic use of causal expressions relates, singular events; one event is said to cause another event. One might be uncertain which particular event was the cause of some identified event; still the basic idea is that a certain event, called 'the effect', is caused by another event and the effect in turn causes one or several other events. Thus, causal relations are transitive.1

An illustration from the present pandemic: when a particular individual *A* is infected by Covid-virus, we know that the cause is that he/she had been in too short a distance from another infected person *B*; this event, *A* and *B* coming into close vicinity to each other, is the immediate cause of *A* being infected. Hence the first and most obvious measure for diminishing the spread of Covid is that people keep distance.

It is also part of ordinary and scientific language to express causal relations between states of affairs. The state of affairs that the temperature in Stockholm was below zero for some weeks in January 2021 caused the lakes in this area to be frozen. These frozen lakes were for some time a state of affairs and it was the effect of the low temperature.

Perhaps there is no sharp distinction between events and states of affairs, and for the purpose of analysing causation it doesn't matter. For the present purpose it suffices to observe that events and states of affairs are individual things, i.e. entities referred to by singular terms,2 which may be related as cause and effect. This is the basic form of application of the two-place predicate '... causes...'.

But more things than individual events and states of affairs have since long been said to be related as cause and effect. The first extension is to *types* of events and states of affairs.

1 Some authors, e.g., Menzies (2012), hold that causation is not always transitive. The purported examples of non-transitive causation have been criticised, in our view successfully, in (Cartwright, 2017, sec. 5).

2 Singular terms often occur as noun phrases, but school grammar is not useful for semantic analysis. The most obvious difference is that from a logical point of view, in expressions for relations, as in 'Carl is taller than Ann' both names are singular terms, but in school grammar are they treated as different grammatical parts, 'Carl' is the noun and 'Ann' is the direct object.

# *5.2.2 Generalised Causal Relations*

In science one usually wants generalisable knowledge, one wants to be able to make inferences from particular phenomena to general states of affairs. In doing so one must organise data about individual cases using classifications of some sort. When making such classifications we use *variables*, categorical or quantitative. A number of individual cases belonging to the same category or quantity constitute the values of the chosen variable.

So for example, a differential equation of the form

$$\frac{d\mathbf{y}(t)}{dt} = k\mathbf{y}(t)$$

states a generality: for each time point *t* in a given interval, the value of the state variable *y(t)* is proportional to its own time derivative. This statement has the logical form 'For all times *t* in an interval, the function *y(t)* is proportional to the derivative *dy dt* ', which is a statement about pairs of properties attributable to some systems or perhaps only to one particular system. Even in the latter case it is a general statement, since it is a generalisation over a system's states during a certain time period.

By spelling out the full expression for a functional relation we directly see that it does not contain any causal information. But such equations are often unconsciously given a causal interpretation. Such a causal interpretation requires additional information.

Correlation reports are similarly general statements, because the correlation is a relation between two variables. And it is well known that a correlation by itself is not enough for inferring a cause-effect relation.

Sometimes such extra information is at hand, in which case we say that one variable is the cause of another variable. (This topic will be further discussed in Sects. 7.1–7.3, and 8.5.1) Thus we causally relate *abstract things*, i.e., *types* of events and states of affairs, universals, as they are called in philosophy. A trivial example is 'repeated exercise increases fitness'. The meaning of this is that a person can increase his/her fitness, i.e., he/she can cause increase of fitness, if he/she performs regular exercise. This statement is not about any particular exercising event, but about all instances of exercise; it is a general statement, and empirical research has given us solid evidence for this causal relation between two attributes of persons.

Some functional relations in science are called 'laws', 'regularities' or 'equations'. These are often interpreted as expressing causal relations. So for example, most people take for granted that Newton's second law, *f* = *ma*, says that the force *f* on a body with mass *m* is *the cause* of that body's acceleration *a*. This reading is however not mandatory and can in fact be strongly criticised. In any case, the validity of inferences using Newton's second law depends only on the fact that the equation *f* = *ma* is an identity; whatever the letters *f* , *m* and *a* refer to, Newton's

law tells us that the left and the right hand side in any particular application of this formula are different expressions for the same number. Nothing in the equation says anything about causes and effects.

But we use laws when calculating what to do in order to achieve our goals. In such reasoning it is the action or intervention that is the cause of the desired outcome. More about this in Sect. 6.7.

If a causal conclusion is drawn from a particular equation, be it a law or not, it is based on tacit causal assumptions, not expressed by that equation. From a mere mathematical relation between values of variables, no causal conclusion can legitimately be drawn. Nancy Cartwright formulated this as 'No causes in, no causes out' (Cartwright, 1983).

# **5.3 Causation in Qualitative Studies**

A few philosophers hold that one can, in some cases, directly observe a causal relation between two individual events. In Sect. 3.3 we have argued against that view, we hold that one cannot observe any relations at all; what we observe are objects and singular events, and in some cases we can tell the time ordering of a sequence of events/states of affairs. But this is obviously not sufficient for inferring any causal relations between such events/states of affairs; hence causal relations cannot be inferred *only* from singular case studies, irrespective of whether one collects quantitative or qualitative data.

Some researchers, such as Guba and Lincoln (1989) conclude that causation has no place in qualitative studies, whereas others, notably Joseph Maxwell (Maxwell, 2004, 2012, 2021) are of the opposite view.

The argument that causation has no place in qualitative research is based on two premises: (1) experiments with control groups are necessary for valid inferences to cause-effect relations and such experiments are not done in qualitative research, and (2) valid generalisations from singular case studies are not possible, unless background assumptions are invoked.

Data from a qualitative study concerns a very limited number of informants not being randomly selected from a population. So even if we obtain information about sequences of events from what the informants are saying, how do we know that the observations can be generalised? And even if one can, given some reasons for generalising the findings to other cases, how do we know that events are causally related? These sceptical reflections have led many qualitative researchers to hold that causation has no place in qualitative studies; qualitative studies aim at descriptions of individual phenomena only. However, when using ordinary language for these descriptions it is hard to completely avoid causal idiom. Maxwell writes:

Becker described how it led qualitative researchers to use evasive circumlocutions for causal statements, "hinting at what we would like, but don't dare, to say" (Becker, 1986, 8). However, Hammersley argued that "in practice, virtually all qualitative researchers implicitly make causal claims, for example about what factors have 'influenced', 'shaped',

'formed', 'brought about', etc., some outcome" (Hammersley, 2012, 72). (Maxwell, 2021, 379)

Hammersley's observation is similar to the general observation we made in Sect. 2.2 that causal relations are indicated by quite a number of different expressions, e.g., 'bring about', 'produce','make happen', 'lead to' etc.

Successive cause-effect relations make up causal mechanisms, see Sect. 8.4. Those defending inferences to causal relations using qualitative data do so by referring to such causal mechanisms known in advance. The core idea is that a detailed description of the sequence of events in one or a few individual cases enables us not only to tell the time order of events, but also that we sometimes, using previous theory as background, can infer that they are causally related. Thus Miles and Huberman (1994, 147) writes:

Qualitative analysis, with its close-up look, can identify *mechanisms*, going beyond sheer association. It is unrelentingly *local* and deals well with the *complex* network of events and processes in a situation. It can sort out the *temporal* dimension, showing clearly what preceded what, either through direct observation or *retrospection*.(emphasis in original).

Another researcher writes:

Causal arguments are usually framed in terms of the effects of variables on each other. However, developmental, mechanical, processual, and comparative arguments all imply something about why and how social phenomena or processes occur or operate, and in this sense qualitative research does deal with questions of causality, although very often it wishes to think and speak of it in a different way. In fact, many have argued that qualitative research is particularly good at understanding causality, again precisely because of its attention to detail, complexity and contextuality, and because it does not expect to find a cause and an effect in any straightforward fashion. (Mason, 2018, 222)

The claim is thus that attention to 'detail, complexity and contextuality' may provide information about causal relations. It may do, but it requires background knowledge. Just as in quantitative studies, inferring a cause-effect relation requires more information than mere observations of one or a few individual cases. Cartwright (1983) concluded: 'No causes in, no causes out.'

# **5.4 Causation and Feedback Loops**

Feedback loops might seem to contradict the condition that causes precede their effects. That is a mistaken conclusion.

An individual cause precedes its effect. In the limit, cause and effect may, for all practical purposes, be simultaneous, but it is not possible that the effect precedes its cause. The reason is simple: if we know, or have strong reason to believe, that two events or states of affairs are related as cause and effect, we label them 'cause' and 'effect' according to their timing; the first occurring is the cause of the other one, the effect. A component of the meaning of the word 'cause' is that it is followed in time by its effect. This is merely another way of stating the point made at the

beginning of this chapter, namely, that '....causes...' is an asymmetric relational term. This asymmetry is based on the fact that all transmission of signals takes time and causation requires signals.

The time order of cause and effect follows from two facts: (1) the cause must do something in order to bring about its effect, i.e., sending a signal of some sort, and (2) signals travel with at most the velocity of light.

In physics it is uncontroversial that a cause and its effect are connected by a signal carrying a conserved quantity, for example energy, being transmitted between cause and effect. There is an upper limit for the velocity of such signals, the velocity of light in vacuum; this is a consequence of relativity theory. This means that if two events occur at times and places such that no signal could have been transmitted between them, they cannot be causally related.3

Cause and effect must be connected by a physical signal also when we discuss causal relations in biology, psychology, sociology or history. It is for example often said that the cause of the First World War was the assassination of archduke Franz Ferdinand in Sarajevo on June 28, 1914. The physical signals, such as telegrams sent from Sarajevo to Vienna, Berlin and other power centres, are not salient in discussions about the causes of the First World War. But without any such transmission of information via physical links there would not be any causal link between the assassination and the outbreak of that war. So the physical link is a *necessary condition* for a causal relation between two events, but such links are often not *salient* in discussions about causes in history. The topic will be further discussed in Sect. 5.6.

The time order of cause and effect might appear to conflict with the idea of feedback loops, but that is not so; in fact feedback loops presuppose that each individual cause precedes its effect in time.

A feedback is usually described as that a cause *A* brings about its effect *B*, which in turn causes *A*. This is confusing. What is meant by a feedback loop should properly be described by talking about individual events. Event 1 causes Event 2, which in turn causes Event 3, which in turn causes Event 4, etc. This may be described as a feedback loop if for example Event 1, Event 3, Event 5, etc., are individual cases of the same *type* of events, let's say A, and if Event 2, Event 4, Event 6, etc., all belong to another *type* of events, B. A system may change from a particular state *s*1 to another state *s*2 at a certain time interval and that state change causes another system to change its state at a somewhat later time, and this in turn causes the first system to return to its initial state *s*1. The process may continue in many loops.

The point is that saying that a system is in the same state at several different times, we are talking about the same *type* of state. Around ten o'clock every day

3 There occur in quantum physics so called non-local correlations in which two seemingly distinct events are strictly correlated without there being any common cause and which can be proven to occur within a time interval too short for a signal to pass from one event to the other. This seems to contradict the idea that causation can be transmitted by at most the velocity of light. That is however a false conclusion, see e.g. (Johansson, 2021, ch. 14).

I want coffee; I am in the same *type* of state every day, but each day my state of wanting to drink coffee is distinct from all the other instances of the same state type; they occur at different times.

When talking about types of states and events we have no timing in the descriptions, since types of events and states are not individual things, they are abstract entities not occurring in space and time.

The statement that a type of events/state of affairs causes another type of events/state of affairs is to be interpreted as that each individual cause precede its particular effect in time. Hence, feedback loops do not contradict the idea that an individual cause precedes its effect in time. In fact, feedback loops *presupposes* just that.

# **5.5 Causation and Probability**

We often talk about probable causes of events and there is a connection between conditional probability and causation. The basic idea is that if a type of events *A* causes another type of events *B*, then *p(B*|*A) > p(B)*, i.e., the probability of *B* conditional on *A* is higher than the unconditional, or so called *marginal probability*, *p(B)*. (But the converse need not be the case!)

When we attribute probabilities to singular events, the latter must be described in some way. One and the same event may be identified by different descriptions and this affects its probability. Here is an illustration.

According to the records from WHO, circa 1% of all those who has had Covid died of this disease. So one may say that the probability that a certain Covid-infected person N will die is circa 1%.

But suppose we know the age of N, he is 20 years old. We may then use data of Covid deaths by age groups.4 According to these figures the risk of dying of Covid in that age group is much, much smaller; only 42 deaths of 22,600 belong to his age group.(These are figures from Sweden, but the general trend is general, young persons have a much lower risk of dying of Covid than older people.) In other words, the probability of N dying of Covid, given that he is infected and belongs to the age group 20–29 years of age is 42*/*22*,*600 · 0*,* 01 ≈ 0*.*00002.

It is obvious that the probability for a certain event crucially depends on how we classify that event, see e.g., (Hájek, 2007).5 It seems reasonable to conclude that if we had a complete description of an event (and of the individual(s) involved), its probability would be either zero or one.

4 https://www.statista.com/statistics/1107913/number-of-coronavirus-deaths-in-sweden-by-agegroups.

5 This fact very strongly indicates that probabilities should not be thought of as attributes of events per se, but of events as described in specific ways.

This dependence on classification of events is called the *reference class problem*. It has been called a 'problem' since it is a problem for those who think that probabilities are objective properties of events per se. In our view, this is in most cases wrong; probability attributions depends on our knowledge.6 It is no problem that probabilities of events depend on how we classify them.

So far the discussion about probabilities has been based on the frequency interpretation of probabilities. There are other meanings of probability, though. One alternative is probability as degree of belief. Consider for example a conversation about politics held at the end of 2022 where one person asks another how probable she thinks it is that the war in Ukraine will end before the end of 2023. Whatever the answer, the probability is naturally interpreted as a degree of belief in the mind of the respondent, not on any observed frequencies of the lengths of wars. Thus the probability assignment is to a person's mental state. Another person may have another degree of belief. Differences between different person's degrees of belief need not be based on different reference classes, they might be subjective estimates based on all sorts of information, or perhaps none at all.

Such subjective probabilities are however not very often used in scientific discourse; the great majority of talk about probabilities in science is based on relative frequencies. Briefly: the probability for a type of event A, is the relative frequency of individual events of type A in an infinite series of trials/tests/observations of this event type. Since we cannot perform an infinite number of observations we need a method to calculate probabilities from observed frequencies in observed samples. This is presented in the next chapter and in Appendix C.

To repeat, if A causes B, then *p(B*|*A) > p(B)*, if the probabilities are interpreted as relative frequencies in populations. But the converse is not true; from *p(B*|*A) > p(B)* we cannot infer that A is a cause of B. The reason is that this inequality shows no more than that A and B are correlated, and a correlation can occur without there being any causal link between the correlated events; there might be a common cause, in medicine and other fields usually called a confounder. More about that in the next chapter.

Summarising, talk about the probability of an event in scientific contexts presupposes in most cases that event is classified as belonging to a reference class. This is so since the probability of an event is defined as the relative frequency of this *type* of events in the reference class.

# **5.6 Many Causes: INUS-Conditions**

The statement 'A caused B' does not entail that A was the only cause of B. Almost any event, state of affairs or variable may have several causes. One way to bring some order among these is to investigate their time order. This may enable us to

6 There is one exception, namely, transition probabilities in quantum theory, see (Railton, 1981).

discern causal chains, which is possible since causal relations are transitive; if A is a cause of B and B is a cause of C, then A is a cause of C. If need be, we explicitly say that A is an indirect cause of C.

Another way of bringing some order is to separate between causes and background conditions. This is a pragmatic distinction. Suppose we have good reason to say that all of *A*1*,...,An*, are causes to a certain event or state of affairs B. But what to do with this information? When we want to do something about B, to make an intervention, it is good to know what is the easiest, or most effective intervention to do. When such information is at hand and one has selected one cause, say *Ak*, as the cause (the most important cause, or the most effective cause etc.), one may, for all practical purposes, treat the other factors as background conditions.

A very illuminating illustration can be found in (Hesslow, 1984), see Fig. 5.1. We see that some fruit flies have shortened wings and when asking for the cause of this fact, the answer depends on which comparison one makes. If we take the temperature at 22 ◦C as a fixed background condition, one explains the shortened wings as being caused by the mutation. But if we compare the wing lengths at different temperatures we naturally say that the cause was the low temperature.

We may conclude that there are at least two necessary conditions for fruit flies to have shortened wings: (1) a mutation, and (2) being bred at room temperature. Which one of these conditions one selects as *the cause* depends on which comparison one makes. Hesslow's conclusion was that the distinction between genetic and environmental causes of diseases and other aberrant states depends on contrast, it is no real difference.

This example fits nicely into John Mackie's definition of cause as an INUS-condition (Mackie, 1965):

**Def.** A CAUSE is an Insufficient but Necessary part of a complex of conditions, which together, as a complex, is Unnecessary but Sufficient for the effect.

One may observe the indefinite 'A cause'; it follows from the definition that a particular effect may have several causes all satisfying the definition.

Many, following Mackie, have distinguished between causes and background conditions, the latter also satisfying the definition given above, but not labelled 'causes' in specific contexts. It is rather obvious that the distinction between cause and background conditions is a pragmatic affair; one chooses one INUS-condition as the cause depending on ones particular interests, background assumptions or perceived contrast.

### **Illustration: The Discussion About the Causes of the Estonia Disaster**

M.S. Estonia, a cruise-ferry built 1980, sailed on Estline's Tallinn–Stockholm route. The ship sank in stormy weather on 28 September 1994 in the Baltic Sea between Sweden, Finland and Estonia. It was one of the worst maritime disasters of the twentieth century, claiming 852 lives. A heated debate about the cause followed this disaster. A number of factors were mentioned:

1. The captain's decision to go full speed in the strong head-wind. (it was nearly full storm.)

**Fig. 5.1** Two breeds of Drosophila Melanogaster, one with normal genes and with a mutation. The two breeds have been grown in three different temperatures. Figure adapted from Hesslow (1984)

5. The decision made by the maritime classification society (Norske Veritas) to register this ship for traffic between Tallinn and Stockholm; its construction was not appropriate for this duty.

All these factors are clearly INUS-conditions for the disaster. An INUS-condition which never has been mentioned as the cause is the weather (!), the strong headwinds, producing waves of 10 m or more. Why was this condition never mentioned?

It is apparent that different agents chose different factors as being the main cause and that the different views depend on different perspectives and goals. Some agents wanted to pick who was legally and morally responsible; others were more interested in learning from this disaster and changing the construction of car ferries, the rules for car ferries, security prescriptions etc.

One cannot really blame the weather, nor do anything about it, so no one mentioned the weather as the cause. This is clearly a difference from the views of our ancestors; similar disasters, ships going down during storms and causing many deaths, have in most cases in history been explained by stormy weather.

The selection of 'the cause' or 'the main cause' among these factors is clearly made from an agency perspective. People want to know the cause, or the most important cause, or the salient cause, because they want to take action. Some relatives to the diseased wanted to know who is responsible in order to start a court trial, shipping authorities wanted to know what could be done in order to prevent similar catastrophes in the future, etc.

# **5.7 Summary**

Causation is primarily a relation between individual events or states of affairs. Secondly it may obtain between types of events, states of affairs and variables. If the latter is the case, there must be causal relations between individual events/states of affairs making up these types and variable values.

A merely functional relation between two variables is not sufficient for concluding that these variables are causally related; one need more information in order to interpret an equation as being based on a causal relation.

If a type of events or state of affairs is a cause of another type of event or state of affairs, that cause increases the probability of the effect; prob(effect|cause) >prob(effect).

Most events have many INUS-conditions. In any particular case one or few of these are labelled 'cause', the rest is treated as background conditions. This distinction is based on pragmatic considerations.

# *Discussion Questions*

# **References**

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Cartwright N (1983) How the laws of physics lie. Oxford University Press, Oxford

Cartwright N (2017) Can structural equations explain how mechanisms explain? In: Beebee H, Hitchcock C, Price H (eds) Making a difference: essays on the philosophy of causation. Oxford University Press, Oxford, Chap. 8

Guba EG, Lincoln YS (1989) Fourth generation evaluation. Sage Publications, Newbury Park

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Hammersley M (2012) Qualitative causal analysis: grounded theorizing and the qualitative survey. In: Cooper B, Glaesser J, Goom R, Hammersley M (eds) Challenging the qualitativequantitative divide. Explorations in case-focused causal analysis. Continuum, London, pp 72–95

Hesslow G (1984) What is a genetic disease? On the relative importance of causes. Nordenfelt L, Lindahl BIB (eds) Health, disease and causal explanations in medicine. Reidel, Dordrecht, pp 183–193

Miles MB, Huberman AM (1994) Qualitative data analysis: an expanded sourcebook. Sage Publications, Thousand Oaks

Railton P (1981) Probability, explanation, and information. Synthese 48(2):233–256

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# **Chapter 6 Causation, Laws and Regularities**

**Abstract** In this chapter we explore the connections between on the one hand causal relations and on the other hand strict and less strict laws, i.e., regularities, expressed as correlations and regressions.

It is tempting to think that laws and regularities describe general causal relations. They do not. Neither laws nor regularities distinguish between cause and effect, they state relations between quantities only; the causal aspect is connected to the manipulation and this aspect is not represented in formulations of laws and regularities.

Non-strict laws, often called 'regularities', differ from strict laws in that they are conditioned on ceteris paribus clauses, i.e., unspecified clauses of the form 'all else the same'. This makes generalisations, i.e., inferences to unobserved situations, difficult.

The main points of this chapter are:

# **6.1 Laws and Causation**

Many scientists and philosophers have assumed that general causal relations are expressed by causal laws. That is wrong, which was first realised by Bertrand Russell:

'The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm. (Russell, 1913).

It is not obvious what Russell meant by 'the law of causality', although it had been a standard phrase for a long time in philosophy. In any case, we take it that he held that there are no such things as causal laws in science. If so, he was basically right. Physics and chemistry do not contain anything that rightly could be called a 'causal law' and it is doubtful if there are any laws whatsoever outside physics and chemistry.

But we use laws (or weaker connections, *regularities*, to be discussed in Sect. 6.3) when making inferences about cause-effect relations. Physical and chemical laws connect variables to each other, or state invariance principles, and these laws are used in derivations.

The point is that several criteria must be satisfied for establishing a general causeeffect relation. The mathematical connection between the variables is only one of these conditions. A law, expressed as an equation, (or a regularity expressed as an equation including a random variable) is a *necessary* but not sufficient condition for there being a causal relation between the variables. In order to see this more clearly we may consider an episode in the history of science, Boyle's discovery of the law named after him.

Robert Boyle (1627–1691) studied the connection between pressure and volume of gases using a J-formed tube filled with mercury, as in Fig. 6.1. By adding mercury in the open end of the tube he changed the pressure on the air in the closed end of the tube. The volume of the air was measured by the scale on the left leg of the tube. He found that the product of pressure and volume is a constant, abbreviated as *pV* = *constant*, which is Boyle's law.

This simple mathematical relation between two quantities does not say which is the cause and which is the effect. This distinction is made first when identifying what is *manipulated* in a particular concrete case. In the experiments Boyle reported in (Boyle, 1662) that he *changed* the pressure by increasing the amount of mercury and passively *observed* the volume of the air; hence the pressure change is the cause and the volume change is the effect in this experiment. In another experiment it could be the converse.

It is obvious from the mere form of Boyle's law that it doesn't say anything about cause and effect. But the law is needed for establishing cause-effect relations involving changes of pressure and volume of gases.

This is a general trait of laws; mathematical relations between quantities only tell us that a change in any of the variables *logically entails* changes of at least one of the other variables. But mathematical-logical relations are not the same as causal relations.

**Fig. 6.1** Boyle's experiment, figure adapted from https://chemed.chem.purdue.edu/genchem/ topicreview/bp/ch4/gaslaws3.html

# **6.2 Laws, Regularities and Ceteris Paribus Clauses**

# *6.2.1 The Form of Laws*

Boyle's law is one among a number of laws in physics and chemistry. These laws have the common feature of being general statements relating a number of quantities to each other, see (Johansson, 2019). But the generality is never explicit; usually only the numerical relations between quantities are explicit in law statements, while it is tacitly understood that these quantities are attributes of real objects of some kind. Here are some examples of physical laws expressing relations between quantitative variables:

1. Newton's second law:

$$f = ma\tag{6.1}$$

### 60 6 Causation, Laws and Regularities

2. Coulomb's law:

$$f = k \frac{q\_1 q\_2}{r^2} \tag{6.2}$$

3. Maxwell's equations:

$$
\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon} \tag{6.3}
$$

$$
\nabla \cdot \mathbf{B} = 0\tag{6.4}
$$

$$
\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} \tag{6.5}
$$

$$
\nabla \times \mathbf{B} = \frac{4\pi k}{c^2} \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t} \tag{6.6}
$$

These equations, stating relations between quantities, are to be understood as abbreviations for full law statements. The quantities are in any particular application attributed to physical objects, i.e., bodies or fields. So the full verbal formulation of a physical law always contains a generalisation over all objects that can be attributed such quantities. So for example, Newton's second law is the following more complete statement:

**Newton's second law**: For any body with mass *m*, acceleration *a* and upon which a total force *f* acts, it holds that *f* = *ma*.

Thus, the logical form of scientific laws is that of *universally generalised conditionals*, UGCs for short. They do not tell us anything about causal relations; they merely inform us about numerical relations between some quantities attributed to a set of objects. They are general statements since they are true of all objects in a domain.

### **UGCs: Universally Generalised Conditionals**

A conditional is a sentence of the form 'if A, then B', where A and B are complete sentences. (The word 'then' is often omitted.)

Example: If it is raining, then the ground is wet.

A universally generalised conditional is a sentence of the form

'For all x, if x is A, then x is B'.

Example: For all x: if x is a human, x has a heart.

In logic, the expression 'For all' is called 'the universal quantifier'; hence a sentence of the form shown above may be called a universally generalised conditional.

(continued)

A conditional is true if and only if either the antecedent is false or the consequent is true. The conditional doesn't say anything about what *makes*  it true; whether it follows from mathematical or logical axioms, or if the meaning of B is included in the meaning of A, or whether A causes B. The same goes for UGCs.

One may now ask whether there are any tacit conditions for such general statements? In the case of Boyle's law, several researchers, the first was Amontons (1663–1705), discovered that the pressure of a gas depends on its temperature if the volume is constant. So a tacit assumption in Boyle's law is that temperature is constant. By combining these two relations and introducing the amount of matter, the number of moles, n, we arrive at the general law of gases, *pV* = *nRT* .

Is this the final truth about gases? No. In extreme conditions, for example at very high pressure or high temperature, one must take into account quantum effects, which entails some adjustments, resulting in van der Waals' law.

# *6.2.2 Strict and Not-So-Strict Laws*