# causality

Causality (from Latin causa , "cause", and causalis , "causal, causal ") is the relationship between cause and effect . It concerns the sequence of events and states that are related to one another. According to this, A is the cause of effect B when B is brought about by A.

## General

In everyday life , a distinction is often made between the concept of cause and the concepts of reason , occasion and condition ( prerequisite ) ; However, there is no agreement on the exact delimitation. Most of the time:

• the condition as a special kind of cause, namely a temporally strictly prior to the effect and in some way particularly outstanding, without which a corresponding effect does not occur;
• the occasion as a coincidental , “insignificant” trigger of an effect in addition to an “actual”, “essential” cause;
• the term reason as an element of rational considerations or justifications in contrast to natural causality .

## Monocausality, multi-causality and causal chain

In the case of monocausality , exactly one (anciently monos 'alone', 'only') event causes another event. It is also possible that this one causal event has multiple effects.

Example of an effect: A heavy stone loosens and falls (cause) onto a glass roof, causing the glass pane to shatter (effect).
Example for several effects: An explosion (cause) causes the pane of glass to shatter (effect), but also tears down the house wall (effect) and blows a hole in the front yard (effect).

In the case of multi-causality, there are several (in Latin multi , 'many') causes at play. They cause one or more events.

Example: A heavy stone loosens and falls (cause) onto a slate roof. At the same time a tree falls on the roof (cause) and the roof structure collapses (effect).
Causal chain example: dominoes: the falling of the first stone causes the falling of the second stone; this falling over in turn causes the subsequent falling of the third and so on - until the last stone has fallen.

In a causal chain , one event causes another, which in turn causes another event, and so on - until the last event in the chain has been caused. The causes are in it strictly sequentially and consistently dependent on one another .

## Causal order

The causal order is a partial order that is defined as the relation of the causal dependency within a set of events: An event A is the cause of event B (A <B) or vice versa (A> B), or the events do not influence each other ( A || B), i.e. A and B are causally independent or concurrent . In addition, most theorists view causality as transitive : if event A is a cause of B and B is a cause of C, then A is also a cause of C (if A <B and B <C, then is too A <C). Others object that at least our usual judgment practice is not transitive with regard to causality, since when looking for the cause of an event we always search for the immediately causing event.

The causal dependency and the resulting causal order are very important in various branches of science. In particular, in some areas of physics, computer science and philosophy, time itself is defined by the causal order, instead of the other way around (see Happened-Before-Relation ). The term “ simultaneity ” then loses its meaning; instead, one speaks of causally independent events. Whether two such events occur at the same time depends entirely on the observer's point of view.

## physics

In physics, the law of causality says that there is no effect without a cause. It is closely related to the requirement of determinism : if you know the state of a system in all parameters, you can use the laws of nature to calculate a future state. Max Born, on the other hand, emphasizes that causality is shaped by two properties, namely the close-up effect and the sequence. Both properties are violated in Newtonian gravity, which assumes that gravity has an instantaneous action at a distance. This is corrected by the introduction of the field term by Michael Faraday and the limit speed in Einstein's theory of relativity. In quantum mechanics, the principle of causality is maintained by a large number of measurements, which on average again behave causally.

Causality implies a strict partial order :

a) The cause of the cause of an effect is also the (indirect) cause of the effect itself (transitivity).

b) An effect must not be a direct or indirect cause of itself (irreflectivity), as otherwise contradictions can arise, such as the grandfather paradox .

### Classic mechanics

In classical mechanics , due to the assumed instantaneous action at a distance and the associated simultaneity of certain events, it is difficult to define a causal order in which the cause occurs before the effect. When Newton's third axiom speaks of “actio” and “reactio”, then both take place simultaneously. Newton did not have a causal connection in mind, but instead put as the basis of the dynamic that both forces are equal and opposite.

### theory of relativity

What Max Born means by “sequence” is easy to express in classical physics: the events that can causally influence a certain event (that is, can be the [co-] cause of this event) lie in the past of this event. Conversely, the events that can be causally influenced by a certain event lie in the future of that event.

In the theory of relativity, on the other hand, the relativity of simultaneity means that in the case of two events it depends on the reference system which event occurs sooner or later. This seems to make the introduction of a causal order more difficult. However, since effects can propagate at the maximum speed of light , the past is a cone in space-time , the so-called past light cone (one also speaks of the absolute past ); the future is also given by the future light cone.

Both the special theory of relativity and the general theory of relativity agree in the description of causality up to this point. The curvature as an additional property of spacetime in general relativity complicates the causal structure, because it can cause the future and past cones of an event to intersect. This allows closed curves to appear, along which time always moved forward. For an observer on such a closed world line , all events would occur in an orderly manner, but they were repeated after one run through the loop, whereby no beginning or end of the causal order can be determined. Only in so-called causal spacetime are past and future light cones separated .

### Quantum mechanics

The Copenhagen interpretation of quantum mechanics teaches that we can only predict the probability of later observations due to fundamentally restrictive laws of nature - what actually happens in the individual case depends on objective chance (see collapse of the wave function ). Although nature does not behave deterministically at the microscopic level, it is causal in the following sense: Only if all physically possible states B can be derived depending on state A , one can speak of causality. Results in B but also C , is A is not the cause of B . It should be noted here that determinism contains a much stronger statement than sheer causality. In addition, a situation is conceivable in which a single event can be the cause and effect of another event at the same time, even if this contradicts our everyday experiences.

The de Broglie-Bohm theory is a deterministic interpretation of quantum mechanics; the unpredictability of the future system states results in this interpretation from insufficient knowledge of the initial conditions .

The ontological chance of the Copenhagen interpretation is replaced in the De Broglie-Bohm theory by an epistemic (epistemological) indeterminacy.

The question of whether every physical event is uniquely predetermined by a set of causes, i.e. whether the universe as a whole is deterministic , does not seem to be able to be answered with a clear yes in quantum mechanics. Albert Einstein said: "God does not roll the dice". What seems to us to be a coincidence depends in reality only on unknown causes. Even human free will would be a sheer illusion. Einstein drew a parallel here to the lack of freedom of the will according to Schopenhauer . This view of Einstein led him to the view, which was falsified only years after his death , that quantum mechanics had to be supplemented by so-called " hidden variables " (see also EPR paradox and Bell's inequality ).

However, as the history of physics in the 20th century has shown, the proposition about the non-dicey god is hardly tenable. Einstein already felt the contradiction in talks with Niels Bohr in the 1920s. “'God does not roll the dice', that was a principle that Einstein held steadfastly and which he did not want to be shaken. Bohr could only answer: 'But it cannot be our job to tell God how He should rule the world.' "

Although Einstein had a great reputation as a scientist, his view remained that of a minority, and today, nearly sixty years after his death, refined experimentation has further weakened Einstein's position. "The latest quantum optical experiments should be enough to make Einstein rotate in his grave." ( Paul Davies )

### Butterfly effect

While considering a cause and an effect is called weak causality, strong causality requires that slight variations in the initial conditions cause only slight variations in the effects. However, this is not the case when the initial conditions are close to an unstable equilibrium : a small bump on a ball that is in unstable equilibrium on a mountain top can cause all possible directions in which the ball rolls. In the context of chaos theory, this leads, for example, to the question of whether the flapping of a butterfly's wing in Brazil can cause a tornado in Texas.

## Computer science

In computer science, causality plays a major role in two ways: on the one hand, as a subsequent statement about which events led to which other events. This is particularly important when communicating in distributed systems with several senders and receivers, for example to ensure that instructions are carried out in the correct order, even if messages overtake each other in the network. Logical clocks are used for this purpose , which allow the causal order of events to be determined on the basis of time stamps .

On the other hand, with computer programs it is easy to say in advance which action needs which data and from where these are provided. This results in a causal order about which operation needs the result of which other. In this way, processes can be planned accordingly and, in particular, sequentialized or parallelized .

## Systems theory

In systems theory, a system is called "causal" if its output values ​​only depend on the current and past input values. The step response or impulse response of such a system disappears for negative times. A system that is not causal is called an acausal system .

## philosophy

### Pre-Socratics

The pre-Socratic Greek philosophy asked about the "origin" of all being. However, this is not only to be understood with the search for a “cause” in today's usage of the word. Rather, they were looking for a kind of primordial substance or an all-encompassing principle, the arché or in principles such as warm, cold, fire or air.

The concept of cause ( aition or aitios , aitia , Greek: αίτιον, αἴτιος, αίτια) initially had a moral-legal meaning and denotes someone responsible or guilty. End of the 5th century BC It was used by the Hippocratic doctors to denote the causes of diseases (see also the term etiology ) and thus for the first time clearly in the causal sense. A distinction was also made between illness and symptoms or signs of illness, while a term for the effect was still missing. Democritus was one of the first philosophers to advocate the idea of ​​comprehensive causality in terms of causes and effects.

### Plato

Plato equates the effect with the becoming. Every expectant must have a cause. However, he criticizes the assumption that principles are the causes of everything. These are not necessarily related to the circumstances to be explained. One and the same cannot be the cause of opposites, and one and the same cannot result from opposing causes. So ideas must be accepted as ultimate causes. In addition, necessity is the ultimate source of the world's material conditioning.

### Aristotle

For Aristotle , knowing an explanation implies why something is important. He lists four different types of "causes" ( aitia Pl. Aitiai ) that correspond to the four ways in which why-questions can be answered:

• causa formalis : the cause of the shape (e.g. why does a saw chop wood? Because of the shape of the saw blade - the functional shape defines the essence of the saw)
• causa finalis : the ultimate cause (what is the purpose of sawing? to extract firewood)
• causa materialis : the cause of the material (Why is the saw made of metal? It must be hard enough to shred wood)
• causa efficiens : the effective cause (Why does the saw move? Because someone moves it)

According to Aristotle, form and goal are often closely related; they connect with the causal role of ideas in Plato. However, many effects are due to the material (e.g. rusting). The material and the effective cause would be neglected in Plato. But for Aristotle himself the causa finalis is in the foreground, while the causa efficiens is closer to the modern concept of causality.

This Aristotelian division into four types of causes is significant in the history of philosophy and has been taken up by many other philosophers, partially changed and further developed. In Aristotle, the term aitia means more than the current term cause. To be able to state all aitiai of a thing means to have knowledge of that thing. Natural processes are also goal-oriented and can be explained in this way. The accident , however, follow any rule.

The material cause and the causa formalis determine according to Aristotle the existence of an object: the mold penetrates the unshaped, quality and non-moving material in itself, making it a concrete, real thing (i.e., the matter..).

Example: The causa materialis of a statue is the ore of which it is made; the causa formalis, on the other hand, is the art of the sculptor who shapes it. The causa efficiens and the causa finalis , on the other hand, relate to the becoming of objects. The causa efficiens is understood in the sense of an external impulse of the movement and the causa finalis as the purpose for which something happens, a certain activity is carried out, etc.
Example: the father is the causa efficiens of the child; health is the causa finalis of sport. (cf. Aristotle, Metaphysik 1013a 24 to 1014a 25).

### Hellenism

In Hellenism the interest in causal events shifts from theoretical to practical questions. According to Epicurus , the aim of research into causes is to take away people's unrest caused by incomprehensible phenomena. In contrast to Aristotle, Zeno of Kition and the Stoa only recognize the active cause. For them, the cause is always a body that affects others. There are causes (Latin: causa continens ) that set long chains of effects in motion and can maintain them permanently.

### scholasticism

Scholasticism, here Thomism , essentially took over Aristotle's categorization of causes. However, it introduces a ranking among the causes and subordinates the less significant material and effective causes to the higher form and purpose causes . What is important is the addition of a first cause ( causa prima ), namely God , for the creation of the world and as its first mover. The complexity of the topics sometimes made further categories and subdivisions necessary.

Example: A sinner receives confession. We have: Causa formalis are the words of absolution (“Ego te absolvo a peccatis tuis in nomine Patris et Filii et Spiritus Sancti”). Causa materialis proxima , more detailed cause, are penitential acts or the resolution to do them (“pray to Our Father and a Creed ”), and the creed as such. Causa materialis remota , more distant, are the sins to be forgiven. Causa efficiens primaria , the first effective cause, is Jesus Christ in a divine and human nature. (His holy humanity is not listed as a causa instrumentalis, that would not be entirely wrong, but a little nestorianizing.) Causa efficiens secundaria , second, is the priest. Causa finalis primaria is (as always) the external glorification of God. Causa finalis secundaria is the salvation of the penitent. Causa meritoria , cause of merit, is Christ's work of redemption. Causa instrumentalis , instrumental cause, is sanctifying grace which is restored through the sacrament. Causa dispositiva , i.e. a necessary condition, is the power to confess, which the priest must have received from a legally competent superior, usually his bishop.

### Occasionalism

The occasionalism sees as actual, only true cause of all events the divine idea, while the finite, physical things only events, occasional causes ( causae occasionales should be) in which manifests the power of the divine spirit.

### David Hume

A conception of the nature of cause and causality that was widespread in modern philosophy was essentially founded by David Hume (1711–1776). Hume defines cause as

“An object followed by another, all objects similar to the first being followed by objects similar to the second. Or in other words: if the first object had not existed, the second would never have come into existence. "

Hume is resolutely opposed to the idea of ​​a necessary link between cause and effect, since in his empirical epistemology he finds no legitimate reason for such an idea. The source of our misconception of a necessary link is the habitual link between cause and effect.

“But when there are many uniform examples and the same event always follows the same object, then we begin to form the concept of cause and connection. We now feel a new feeling [...]; and this feeling is the archetype of that idea [of necessary connection] that we are looking for. "

The causality is thus defined as a reliable, regularly occurring bivariate covariation of events. From the common occurrence, no conclusions can be drawn about a previous causality. The fact that in the past an event A was always followed by an event B and we assume this to be certain does not necessarily mean that it will be the same for all future that event A would always follow event B. For this reason, according to Hume, no natural laws can be defined, because to speak of laws as a general context cannot be rationally justified. It would only be a habitually perceived, common clash of events. To speak of the objective world as such does not make much sense, according to Hume, for the world beyond our own ideas does not exist as such that we could experience. We just have sensory impressions of a world and those sensory impressions would change. We only have sensory impressions of the world and we have difficulties in forming certain assumptions and knowledge of the world as such. And we cannot even talk about ourselves as subjects, because each of us is not directly given as a subject in our own experience. We have our own thoughts, but only the impressions of them, we have an inkling of our movement, but also only our own impressions of them. Therefore we are like bundles of our own impressions of ourselves. With his work, Hume has therefore moved away from the question of what causality is and, through doubts about the existence of causality, has actually directed the focus to the question of why we claim causality as such at all.

According to Hume it is therefore problematic to want to deduce the validity of an inductive inference from several observations. What we perceive as regularity are not laws about real relationships. (see David Hume's skepticism )

In connection with a mere probability of causality, one speaks of a regularity theory of causality . According to such theories, it can only be determined by statistical studies, not by logical inferences. Accordingly, it is fundamentally impossible to make reliable forecasts . According to David Hume, the following necessary and sufficient conditions must be met in order to classify a sequence of events as a cause-effect relationship:

• e 1 is temporally immediately before e 2 .
• e 1 is spatially immediately next to e 2 .
• Whenever an e 1 incident occurs, an e 2 incident can be observed.

The view that there are no necessary causal connections in the world because only spatially adjacent events can be observed in a chronological sequence is called Humean metaphysics in modern philosophy of science .

### Materialism / Mechanicism

Materialistic and mechanistic philosophies, which were particularly widespread in France in the 18th century, ultimately attributed all causes to mechanical pressure and impact ("dance of atoms"). There were similar ideas with Democritus in antiquity . Approaches to overcoming the purely mechanical concept of cause can be found in Ludwig Feuerbach , who at least doubts that phenomena of higher forms of movement (i.e. life, thought, history) can be reduced to mechanics.

### Immanuel Kant

Immanuel Kant distinguished from the "causality according to the laws of nature " a "causality through freedom :"

“If I get up from my chair now (for example) completely free and without the necessary determining influence of the natural causes, a new series begins in this incident, including its natural consequences into infinity, although in time this incident is only a continuation of the previous row is. For this resolution and action does not lie in the sequence of mere natural effects and is not a mere continuation of them; Rather, the determining natural causes cease completely above them with regard to this event, which indeed follows the former, but does not arise from it and therefore, not in terms of time, but in terms of causality, must be called the first beginning of a series of phenomena. "

In contrast to Hume, Kant sees causality as a necessity. He argues that the causal thought belongs to the inner structure of knowledge if every particular causal rule comes from experience, because otherwise one would not be able to understand the world at all. For Kant, the proof of the necessity of causality lies in the logical and chronological sequence of time. He makes this clear in the Critique of Pure Reason using the example of the observation of a ball and an indentation in a pillow. Here there is only one logical conclusion from the ball as the cause to the indentation as the effect. The opposite conclusion would be absurd. (Example from the second analogy of experience: the principle of chronological order according to the law of causality) "The physics has largely confirmed the Kantian definition of causality and added as a postulate in its main theories." In the special theory of relativity of Einstein , although one Time dilation , but does not allow a time reversal, the causality remains in the sense of the temporal sequence. Likewise, the concept of chance in quantum theory is not violated.

On the one hand you have to have a certainty of your own thoughts that they are present in your own mind (self-confidence). On the other hand, not all concepts of one's own mind can come from pure experience, because otherwise one would not be able to categorize the impressions one receives. So you have to presuppose terms in order to be able to form ideas from sensory impressions. And to these a priori concepts, Kant also included the concept of causality. Causality is therefore not a thought content formed from impressions only constructed in retrospect, but the possibility of gaining experience at all presupposes the concept of causality, so it is necessary in order to be able to experience it in the first place. Otherwise we would only gain sensory impressions and not have the ability to construct meaningful and categorical contexts of experience. Like a toddler looking into a kaleidoscope, we would not be able to put the world together and would only look at the play of light in the kaleidoscope in amazement and remain awestruck by the play of light.

This objective world can be explored by the natural sciences, and we also assume a priori that certain regularities apply in it, which also seems to include the law of causality. The things for themselves remain hidden from us, because they lie outside of our human experience. We can only make reasonable guesses about them, since they underlie the phenomenal world in an unknowable way. According to Kant, this includes B. the idea of ​​God, the idea of ​​freedom and that of the immortal soul. There the limit of our reasonably possible knowledge is reached.

### Criticism of the concept of causality

According to Ernst Mach, there are neither real causes nor causal relationships in nature, but only functional relationships. In conditionalism , the causes are replaced by conditions. John Stuart Mill already considered the full sum of its conditions to be the cause of a thing. Max Verworn increased this view into the absolute: the concept of cause is a holdover from pre-scientific ideas; every event is not caused, but merely conditioned by the totality of an infinite number of equivalent conditions.

### Conception in dialectical materialism

In dialectical materialism in the official form of real existing socialism, internal contradictions of the objects and the new qualities appearing in the course of development are assumed. With every change, development of material things, processes, systems, etc. a. in nature and in society external and internal causes work together. External causes are called the interactions between all things, processes, and systems resulting from the universal connection; as internal causes of dialectic materialism referred to it according to all material things, processes, systems and. a. immanent contradictions that cause their movement, change and development. External and internal causes form a “dialectical unity”: the internal causes only become effective through the existence of the external, the external causes only through the mediation of the internal. The relationship between external and internal causes is relative: what is internal cause for one system can be external cause for another system and vice versa.

### Modern approaches

John Leslie Mackie introduced the INUS condition to identify causes: an event is perceived as the cause of an outcome if it is an insufficient (Necessary) part of a condition that is not itself necessary (Unnecessary) Sufficient for the result.

The Closest World concept by David Lewis is now widely accepted based on a general definition of causality. David Lewis puts the counterfactual conditional operator in the center of the considerations and he gives as an example: "If kangaroos had no tails, they would fall over".

A world with tailless kangaroos is obviously against the facts. So we have to imagine a world that deviates from reality at least in this one point. Otherwise, this “parallel world” must be largely coherent and resemble our world as much as possible. Otherwise kangaroos could also live in this world who walk on crutches and therefore do not fall over.

In Causality , Judea Pearl shows how the closest world concept can be concretized.

How are counterfactual implication and causality related? The fact that the stone was thrown as the cause of the broken pane can be expressed as follows: If I hadn't thrown the stone, the pane would not have cracked. So we have to move on to the counterfactual implication of the negations: “Don't throw a stone” counterfactually implies “The pane won't break”.

An approach that best captures what is intuitively perceived as the reason was developed by Leonard Talmy . In cognitive semantics , the category of force dynamics he introduced is used to examine linguistic expressions for the force relationships on which the situations described are based. For the first time, the theory allows a finer distinction between the various causality relationships that exist in language for example. B. through the verbs cause , help , allow , enable , prevent , prevent , depend (on) etc. are expressed. But the semantics of causality-indicating conjunctions and prepositions such as because , though , despite can be analyzed. A multitude of psychic forces, which are expressed, for example, by forcing , persuading , resisting , are also the subject of the theory. In order for there to be a reason, there must be two opposing forces, an agent (agonist) and an opponent (antagonist). The following applies to them (in the case of a basic relationship): The agonist has an intrinsic tendency to be active, the antagonist an opposite tendency to be lazy. The agonist's power is greater than that of the antagonist. It has also been suggested (Phillip Wollf) that the type of causality in the force dynamic model is determined by three dimensions, (1) the tendency of the antagonist to result, (2) the force opposition between the units involved and (3) the (non- ) Occurrence of the result.

### Determinism and Free Will

The philosophical consequences of causality are particularly interesting in connection with the philosophical line of thought of determinism . There it is assumed that each event is firmly predetermined by previous events, i.e. the universe develops as a causal chain . This applies to all levels, including the elementary particles of energy and matter . Since the human brain also consists of matter, it would also have to behave deterministically , i.e. in a way that can be theoretically calculated and predetermined.

## Biology and behavioral research

If our ancestors ascribed the black and yellow stripes (effect) flashing behind the bushes to a tiger (cause) and ran away, they were well advised. The quick decision as to what could be the cause of the observation and the resulting action were life sustaining. The causality expectation on which this behavior is based belongs to the “innate teachers” ( Konrad Lorenz ): The “hypothesis of the cause” contains the “expectation that the same thing will have the same cause. This is initially nothing more than a judgment in advance. But this prejudice proves its worth ... in such an excess of cases that it is superior to any judgment that is different in principle or the waiver of judgment "( Rupert Riedl , 1981 )

Innate teachers have a downside: they can be thought traps : “Biological knowledge contains a system of sensible hypotheses, advance judgments, which guide us with the greatest wisdom within the framework of what they have been selected for; but lead us completely and wickedly astray at its limits ”(Rupert Riedl). The expectation of causality goes back to the fact that the pilot, captain or train driver is often prematurely blamed for an accident.

## Social sciences

The extensive research on conditioning made many contributions to the understanding of the causality idea . Beginning with Thorndike's cat experiments on Pavlov's accidental discovery of classical conditioning and Skinner's operant conditioning , numerous laws were and are discovered under which conditions the idea of ​​a cause-and-effect relationship arises. The evolutionary origin of the idea of ​​causality is probably the need to identify reliable predictors for vital events.

In social science research, such as psychology , the question is often asked whether a training or a therapy has an effect or an effect. In 1979, Thomas D. Cook and Donald T. Campbell , based on John Stuart Mill, formulated three conditions that are necessary for a causal relationship:

1. Covariance : Changes in the assumed cause ( independent variable , UV) must be systematically related to changes in the assumed effect ( dependent variable , AV). So if z. B. Changes in the psychological treatment take place, it must be possible to observe these manipulations in the result, in the psychological symptoms.
2. Time sequence: The cause (UV) must take place before the effect (AV).
3. No alternative explanations: the assumed cause must be the only plausible explanation for the effect.

It is obvious that the third condition is the most difficult condition to realize. In a social science experiment / experimental design , mostly for ethical reasons, not all factors that could have an influence on the effect can be controlled, so a causal relationship can never be assumed with absolute certainty. Cross-sectional studies with third-party variable control and panel studies are helpful .

The social psychology considered phenomenal causality , the trend in social cognition , attributable to perceptible objects cause-effect relationships (so-called. Causal attribution ), which often lead together with value judgments about these objects in significant differences in the perception results.

In the therapy of learning disorders, Dieter Betz (in: Teufelskreis Lernstören, Psychologie Verlags Union, Munich-Weinheim 1987; not to be confused with the geologist of the same name) favors the effect structure as a network of very different causes, which must be made manageable if therapy has an effect as an intervention : "Anyone who works on the symptom in isolation risks a pedagogical vicious circle." Betz sees the conflict structure analysis ( KSA) as the basis for this work of the therapist .

## statistics

With the statistics Although a relationship between two can events / variables are detected, but no causality. If one can prove a connection (a correlation ) between events A and B, then there are several possible explanations:

• A could cause B.
• B could cause A.
• A and B could be caused by a third event C (see also spurious correlation ).
• The relationship in the data could be erroneous or accidental; H. in truth not even exist.

Evidence of a statistical connection ( correlation ) is often misinterpreted as causality. Causality can only be inferred from a statistical correlation through additional information that was not obtained by means of statistics . An example that is only half jokingly meant is the decline in the birth rate and the decline in the stork population in western Germany at the end of the 1960s. From the fact that both developments occurred at the same time and to about the same extent, it cannot be concluded that the storks have anything to do with the number of newborn babies.

However, causalities can be included as a prerequisite; z. B. Regression analysis looks at independent ( ) and dependent variables ( ). It is assumed that the independent variables ( ) act on the dependent variables ( ). However, whether a variable is an independent or a dependent variable is determined by definition and not derived from statistical means. ${\ displaystyle X}$${\ displaystyle Y}$${\ displaystyle X}$${\ displaystyle Y}$

A causal relationship could be formulated that cannot be read as a statistical relationship ( causality without correlation ): A random generator is switched between a switch that lights up an incandescent lamp , which can (but does not have to ) convert the switching signal into its opposite. . Knowing the circuit, it is then clear that the position of the switch has an influence on whether the lamp is on at a certain point in time or not. The effect of this influence, however, is neither predictable nor statistically demonstrable. If the circuit was not known, it would not be apparent that there is any influence at all.

## Econometrics (Granger)

In some areas of econometrics one is content with a z. B. Compared to philosophy, restricted concept of causality. In this case, the temporal order of the variables is in the foreground. The concept of causality in econometrics was decisively shaped by Clive WJ Granger . This works on the premise that the past determines the future and not the other way around. It says that a variable X for Y Granger-causality is when until the time for a given amount of information t-1 at time t , the variable Y can be better predicted than without the inclusion of the variables X . The Granger causality may apply in one direction or in both directions ( feedback - system ). The concept of causality is closely related to another theoretical concept of econometrics or time series analysis , exogeneity .

Granger causality is statistically testable. For this, consider a bivariate VAR (p) model :

${\ displaystyle {\ begin {pmatrix} Y_ {1t} \\ Y_ {2t} \ end {pmatrix}} = {\ begin {pmatrix} a_ {1} \\ a_ {2} \ end {pmatrix}} + { \ begin {pmatrix} \ phi _ {11.1} & \ phi _ {12.1} \\\ phi _ {21.1} & \ phi _ {22.1} \ end {pmatrix}} {\ begin {pmatrix} Y_ {1, t-1} \\ Y_ {2, t-1} \ end {pmatrix}} + \ dots + {\ begin {pmatrix} \ phi _ {11, p} & \ phi _ { 12, p} \\\ phi _ {21, p} & \ phi _ {22, p} \ end {pmatrix}} {\ begin {pmatrix} Y_ {1, tp} \\ Y_ {2, tp} \ end {pmatrix}} + {\ begin {pmatrix} Z_ {1t} \\ Z_ {2t} \ end {pmatrix}}}$

There is no Granger causality for on if: ${\ displaystyle Y_ {2}}$${\ displaystyle Y_ {1}}$

${\ displaystyle \ phi _ {12.1} = \ phi _ {12.2} = \ dots = \ phi _ {12, p} = 0}$

${\ displaystyle Y_ {1}}$is non-Granger-causal if: ${\ displaystyle Y_ {2}}$

${\ displaystyle \ phi _ {21.1} = \ phi _ {21.2} = \ dots = \ phi _ {21, p} = 0}$

The test for non-Granger causality thus corresponds to a test for zero restrictions for certain coefficients . The test statistic of such a test could look like this with normal white noise :

${\ displaystyle F (p, Nnp) = {\ frac {{\ text {RSS}} _ {r} - {\ text {RSS}} _ {u}} {p {\ hat {\ sigma}} _ { 11} ^ {2}}}}$

It is

• ${\ displaystyle N}$ the scope of the two time series
• ${\ displaystyle n}$the number of coefficients used in least squares estimation so that the number of degrees of freedom becomes smaller,
• ${\ displaystyle p}$the number of additional coefficients with which the variable X is included in the least squares estimation,
• ${\ displaystyle {\ text {RSS}} _ {r}}$the sum of the squared residuals of the least squares estimate of the equation with restrictions,
• ${\ displaystyle {\ text {RSS}} _ {u}}$the sum of the squared residuals of a least squares estimate of the equation without restrictions,
• ${\ displaystyle {\ hat {\ sigma}} _ {11} ^ {2} = {\ frac {{\ text {RSS}} _ {u}} {Nnp}}}$as the estimated variance of , where${\ displaystyle Z_ {1}}$
• ${\ displaystyle {\ hat {\ sigma}} _ {11}}$the standard deviation .

With the determined value of F one goes into the corresponding table of F in order to read off the probability that there is no Granger causality. It should be noted that only the (generally) lower probability of applies. The likelihood of is greater (in general) and not applicable. ${\ displaystyle F (p, Nnp)}$${\ displaystyle F (Nnp, p)}$

A cost allocation principle is a procedure for converting costs to reference values. If, for example, a product unit is selected as the reference value, the costs of this unit can be calculated depending on the allocation principle used. This gives the unit cost.

## Causality in medicine

The etiology (from ancient Greek αἰτία "cause" and λόγος "reason, doctrine") denotes the doctrine of causes in some philosophical schools in antiquity. Today the medical meaning of the term prevails.

## literature

• David M. Armstrong: A World of States of Affairs . Cambridge University Press, 1997, chap. 14th
• Mario Bunge : Causality, History and Problems . Mohr, Tübingen 1987, ISBN 3-16-944806-4
• Phil Dowe: Physical Causation . Cambridge University Press, 2000
• Dieter Hattrup : Einstein against the god who rolls the dice. At the limits of knowledge in natural science and theology Herder, Freiburg im Breisgau / Basel / Vienna 2011, ISBN 978-3-451-29785-4 .
• Geert Keil: acting and causing . Frankfurt: Klostermann, 2000
• Klowski, Joachim: The historical origin of the causal principle , in: Archive for the history of philosophy 48 (1966), pp. 225–267.
• David Lewis: "Causality" (1978), in: G. Posch (Ed.): Causality, new texts. Stuttgart: Reclam, 1981, pp. 102-126
• John L. Mackie : The Cement of the Universe - A Study of Causation . Oxford: Clarendon Press, 1980
• Uwe Meixner: Theory of causality. A guide to the concept of causation in two parts , Mentis Verlag, 2001, ISBN 3-89785-185-7
• Judea Pearl : Causality , Cambridge University Press, ISBN 0-521-77362-8
• Wolfgang Stegmüller : Problems and results of the philosophy of science and analytical philosophy. Vol. 1 Explanation, justification, causality , Springer Verlag, ISBN 3-540-11804-7
• Wolfgang Stegmüller: The Problem of Causality , 1983
• Patrick Suppes : A Probabilistic Theory of Causality . North-Holland Publishing Company, Amsterdam 1970
• Erich Steitz: causality and human freedom . Oldib, Essen 2009, ISBN 978-3-939556-08-4 .

## Videos

Wikiquote: Cause  - Quotes
Wiktionary: causality  - explanations of meanings, word origins, synonyms, translations
philosophy
physics
History of ideas
Cognitive science (mental causation)
Cognitive linguistics
Scientific conferences and congresses on the topic of causality

## Individual evidence

1. ^ Wilhelm H. Westphal: Physics - A textbook . 25./26. Edition. Springer, 1970, p. 4th f .
2. Max Born: Physics in the course of my time . Springer, 2013, ISBN 978-3-322-88794-8 ( limited preview in Google book search).
3. Lexicon of Physics. Causality. Spektrum Akademischer Verlag, Heidelberg, 1998, accessed on May 1, 2016 .
4. Ognyan Oreshkov, Fabio Costa, Časlav Brukner: Quantum correlations with no causal order . In: Nature Communications . tape 3 , 2012, p. 1092 , doi : 10.1038 / ncomms2076 .
5. Werner Heisenberg : The part and the whole. Conversations in the area of ​​atomic physics. 9th edition, Piper, Munich 2012 (first edition 1969), ISBN 978-3-492-22297-6 , page 115.
6. Paul Davies : The Immortality of Time. Modern physics between rationality and God. Scherz, Bern a. a. 1995, page 207.
7. Deterministic Chaos. Strong and weak causality. LEIFI Physik, Joachim Herz Stiftung, Hamburg, accessed on May 1, 2016 .
8. Cause / Effect , in: Historical Dictionary of Philosophy (Hist. Wb. Phil. 11), Vol. 11: UV, Basel 2001, Sp. 378–411, here: 411.
9. Plato: Phaedo 96e-101c.
10. Hist. Wb. Philos. 11, col. 379.
11. See Klowski 1966.
12. Hist. Wb. Philos. 11, col. 380 f.
13. David Hume: An Inquiry into the Human Mind . Translated by Raoul Richter, ed. by Jens Kulenkampff. 12th edition. Meiner, Hamburg 1993, p. 92f. Emphasis in the original.
14. David Hume: An Inquiry into the Human Mind . Translated by Raoul Richter, ed. by Jens Kulenkampff. 12th edition. Meiner, Hamburg 1993, p. 95. Italics in the original.
15. Andreas Bartels, Manfred Stöckler (Ed.): Wissenschaftstheorie , mentis Verlag, Paderborn 2009, Chapter 4: Causality, p. 89 ff.
16. CPR B 248-248 Academy Edition
17. ^ Quotes from: Michel Serres and Nayla Farouki (eds.), Thesaurus of the exact sciences, ZWEITAUSENDEINS, ISBN 3-86150-620-3
18. James E. Mazur: Learning and Behavior . Pearson Verlag, 6th edition. 2006, ISBN 978-3-8273-7218-5
19. ^ Cook, Thomas D., and Donald T. Campbell. Quasi-Experimentation: Design & Analysis Issues for Field Settings . Houghton Mifflin Company, Boston 1979.
20. ^ Fritz Heider : Social perception and phenomenal causality. In: Martin Irle (ed.), Together with Mario von Cranach and Hermann Vetter: Texts from experimental social psychology. Luchterhand: 1969. p. 26.
21. See also Dietrich von Engelhardt : Causality and conditionality in modern medicine. In: Heinrich Schipperges (Ed.): Pathogenesis. Basic features and perspectives of a theoretical pathology. Berlin / Heidelberg / New York / Tokyo 1985, pp. 32-58.