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.

2 Singular Versus General Causation

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.Footnote 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,Footnote 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.

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

$$\displaystyle \begin{aligned} \frac{dy(t)}{dt} = k y(t)\end{aligned}$$

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 \(\frac {dy}{dt}\)’, 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).

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.’

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.Footnote 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 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 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.Footnote 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 \(42/22{,}600\cdot 0,01 \approx 0.00002\).

It is obvious that the probability for a certain event crucially depends on how we classify that event, see e.g., (Hájek, 2007).Footnote 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.

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.Footnote 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 correlationcan 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.

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 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 \(A_1,\ldots , A_n\), 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 \(A_k\), 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 \({ }^{\circ }\)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.

Fig. 5.1
A table has 6 drawings of normal and mutated Drosophila Melanogaster grown in 22, 27, and 32 degrees. M 3 at 32 degrees resembles the same as normal genes, N 1 to N 3.

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)

Full size image

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. 1.

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

  2. 2.

    The construction of the bow was too weak. (Due to the pressure from the high waves it opened up.)

  3. 3.

    Estonia had an open car deck with no partitioning. This allowed all incoming water from the opened bow to flow to one side of the ship.

  4. 4.

    The ferry company’s demand on the ferry captain to keep the time table, thus pressuring the captain to go full speed.

  5. 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 head-winds, 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.

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

  1. 1.

    Can you imagine a case where the distinction between cause and background conditions is independent of background beliefs, goals or interests on the part of the person who makes this distinction?

  2. 2.

    Could there be cases where people agree on what the cause of an undesirable state of affairs is, whereas the most efficient remedy is to do something about some factor among the background conditions?

  3. 3.

    That cause and effect must be physically connected is rather obvious when we talk about causal relations in nature. But what about historical, political or social causes; is it possible that there is no physical contact between for example two historical events, while still they could be related as cause and effect?