Causality: A Deep Exploration of Cause and Effect

This summary explains the nature of causality and how it is understood and applied across various academic disciplines. In particular, it emphasizes the concept of causality from philosophical perspectives, the distinction between necessary and sufficient causes, and the importance of counterfactual and probabilistic theories of causation. It also covers in detail how causality is addressed in physics, biology, medicine, statistics, economics, history, law, and Eastern philosophy, providing a comprehensive understanding of this complex concept.

1. Definition and Basic Concepts of Causality

Causality refers to the relationship in which an event, process, state, or object (the cause) contributes to producing another event, process, state, or object (the effect), where the cause is at least partially responsible for the effect, and the effect is at least partially dependent on the cause. In simple terms, it can be described as the "reason" why something happened.

Generally, a single effect can have multiple causes, which are called causal factors. All causes exist prior to the occurrence of the effect. Conversely, an effect can be the cause of many other effects, all of which occur in the future. Therefore, the distinction between cause and effect either presupposes or provides the distinction between past and future. In physics, the former perspective is more common, though some scholars argue that causality is metaphysically prior to the concepts of time and space.

Causality is an abstract concept that shows how the world unfolds. As a fundamental concept, it is better suited for explaining other advanced concepts and is difficult to explain through more basic ideas. Similar to concepts like agency and efficacy, fully understanding it may require intuition. Thus, causality is not only implicitly embedded in the structure of everyday language but is also explicitly used in scientific causal notation.

2. Aristotle's Four Causes

In English-language studies of Aristotelian philosophy, the word "cause" is used as a translation of Aristotle's term "aitia," which he meant as "explanation" or "an answer to a why question." He classified four types of answers to this "why" question:

Material Cause: The material from which a thing is made. For example, the "bronze" of a statue or the "silver" of a cup.
Formal Cause: The form or structure of a thing that determines its properties and functions. Just as the form of a human differs from the form of a statue.
Efficient Cause: That which provides the initial movement causing change. For example, a person lifting a stone or erecting a statue. This concept is closest to what we generally think of as a "cause" today.
Final Cause: The standard or purpose for the completion of a thing. For example, explaining the ultimate reason for an action, such as walking for health.

Among Aristotle's four modes of explanation, the one closest to what we currently consider causality is the efficient cause. The other three may be better understood as material composition, structure and mechanics, and standards of completion.

3. David Hume's and Kant's Perspectives on Causality

3.1. David Hume's Empiricist Perspective

David Hume opposed rationalism, arguing that pure reason alone cannot prove the reality of efficient causation. Instead, he emphasized that all human knowledge derives solely from experience, appealing to habit and mental custom. He held that the human mind cannot directly perceive causal relationships.

"If the first object had not been, the second never had existed."

Along with this claim, Hume distinguished causality into a regularity view and a counterfactual concept.

Counterfactual view: To say X is the cause of Y means that if X had not existed, Y would not have existed either. Hume interpreted this as an ontological view of the essence of causation.
Regularity view: To say X is the cause of Y means that the two events are conjoined in space and time, and X occurs before Y. Considering the limitations of the human mind, Hume recommended using the regularity view as an epistemological definition of causation.

3.2. Kant and Minkowski Geometry

Kant considered time and space to be concepts that exist prior to human understanding of the world's progress or evolution, and he also recognized the priority of causality. However, because he lacked knowledge of Minkowski geometry and special relativity, he did not understand that the concept of causality could be used as a prior foundation for constructing the concepts of time and space. In modern times, there is a view that causality can serve as a more fundamental foundation for constructing the concepts of time and space.

4. The Nature of Cause and Effect Entities

There is an important metaphysical question about what kinds of entities causes and effects can be.

4.1. Entities of the Same Kind

One view is that cause and effect are entities of the same kind, and causation is an asymmetric relation between them. For example, one can say "his tripping was the cause, and his ankle breaking was the effect." In process philosophy, it is argued that all causes and effects are respectively some process, event, becoming, or occurrence. Another view holds that causes and effects are "situations," with the exact nature of these entities defined more loosely than in process philosophy.

4.2. Entities of Different Kinds

Another view is the classical position that cause and effect can be entities of different kinds. For example, in Aristotle's efficient cause explanation, an action can be the cause and a long-lasting object the effect. The productive action of parents can be considered the cause of the "enduring object" that is Socrates.

5. Establishing Knowledge of Causation and Modern Approaches

Because causation is a subtle metaphysical concept, establishing knowledge of causation in specific empirical situations requires considerable intellectual effort and evidence. Given Hume's argument that the human mind cannot directly perceive causation, epistemological concepts are needed to distinguish causal from non-causal relationships.

In modern philosophy, there are five major approaches to addressing causation:

Regularity view: Defines causation through the empirical regularity of constant conjunction of events.
Probabilistic view: Explains causation through changes in conditional probability.
Counterfactual view: Defines causation through counterfactual conditionals.
Mechanistic view: Explains causation through the mechanisms underlying causal relations.
Manipulationist view: Defines causation through invariance under intervention.

All five approaches share the characteristic of defining causation by reducing it to other types of relations.

6. Spacetime Geometry and Causality

6.1. The Priority Relationship Between Causality and Spacetime

Causality possesses the properties of precedence and contiguity, which are topological and important elements of spacetime geometry. As developed by Alfred Robb, these properties can be used to derive the concepts of time and space. Max Jammer stated, "Einstein's hypothesis opens the way to an intuitive construction of the causal topology of Minkowski space."

"Einstein's hypothesis opens the way to an intuitive construction of the causal topology of Minkowski space."

Causal efficacy cannot propagate faster than light. If it could, one could use the Lorentz transformations of special relativity to construct a reference frame in which an observer would see effects preceding causes, thereby violating the hypothesis of causality.

Therefore, the concept of causality is metaphysically prior to the concepts of time and space. From a practical standpoint, this is because the use of causality is essential for interpreting empirical experiments. Interpreting experiments is necessary for establishing the physical and geometric concepts of time and space.

6.2. Determinism, Free Will, and Spacetime

A deterministic worldview holds that the history of the universe can be thoroughly expressed as a progression of events connected by cause and effect. Incompatibilism argues that determinism is incompatible with free will, so if determinism is true, "free will" does not exist. Conversely, compatibilism argues that determinism is compatible with free will, or even essential to it.

7. Necessary Causes, Sufficient Causes, and Contributory Causes

Causes can sometimes be distinguished into two types: necessary causes and sufficient causes. A third type that does not require both but contributes to the effect is called a contributory cause.

7.1. Necessary Cause

If X is a necessary cause of Y, then the existence of Y necessarily implies the prior occurrence of X. However, the existence of X does not imply the occurrence of Y.

7.2. Sufficient Cause

If X is a sufficient cause of Y, then the existence of X necessarily implies the subsequent occurrence of Y. However, since another cause Z could also produce Y, the existence of Y does not imply the prior occurrence of X.

7.3. Contributory Cause

For a specific effect, a factor that is a contributory cause in a single instance is one of several co-occurring causes. Implicitly, all of these causes are considered contributory. Generally, a contributory cause is not necessary, though sometimes it may be. Generally, a contributory cause is not sufficient, because by definition it co-occurs with other causes -- if it were sufficient, the other causes would not be considered causes.

J. L. Mackie argued that general references to "cause" actually refer to INUS conditions (insufficient but non-redundant parts of an unnecessary but sufficient condition). For example, consider a short circuit as the cause of a house fire. Taking together the short circuit, proximity of combustible materials, and absence of firefighters, these constitute an unnecessary but sufficient condition for a house fire (since many other events could also lead to a fire). Within this collection, the short circuit is an insufficient (the short circuit alone would not cause a fire) but non-redundant (all other conditions being equal, the fire would not have occurred without the short circuit) part of an unnecessary but sufficient condition. Therefore, the short circuit is an INUS condition for the occurrence of the house fire.

However, Mackie's INUS account faces the problem of joint effects of a common cause -- it is criticized for incorrectly identifying one effect of a common cause as an instantiated INUS condition of the other effect.

8. Difference from Conditionals

Conditionals are not statements that indicate causation. An important distinction is that causal statements require the antecedent event to temporally precede or be simultaneous with the consequent event, whereas conditionals do not require this temporal ordering. In English, many statements can be presented using the "if...then..." form, and because this form is more commonly used to indicate causation, confusion frequently arises. However, these two types of statements are clearly different.

For example, all of the following statements are true when interpreting "if...then..." as a material conditional:

"If Barack Obama was the President of the United States in 2011, then Germany is in Europe." (True because both antecedent and consequent are true)
"If George Washington was the President of the United States in 2011, then any arbitrary statement." (True because the antecedent is false, making the conditional true regardless of the consequent)

However, when viewed as ordinary indicative conditionals, the above statements may not feel true. But the following statement seems intuitively true:

"If Shakespeare of Stratford-upon-Avon did not write Macbeth, then someone else did."

In this hypothetical situation, there is no direct causal relationship between Shakespeare not writing Macbeth and someone else actually writing it.

Counterfactual conditionals have a stronger connection to causation, but not all counterfactual statements are instances of causation. Consider the following two statements:

"If A were a triangle, then A would have three sides."
"If switch S had been turned on, then light bulb B would have been on."

In the first case, it is wrong to say that A being a triangle caused A to have three sides, because the relationship between being a triangle and having three sides is one of definition. The property of having three sides actually determines A's status as a triangle. Nevertheless, the first statement is true even when interpreted counterfactually.

Fully understanding the concept of conditionals is important for understanding the causation literature. Since loose conditionals are frequently used in everyday language, careful interpretation is required. Additionally, the questionable cause fallacy -- non causa pro causa -- is an informal fallacy where the cause is incorrectly identified.

9. Various Theoretical Approaches to Causation

9.1. Counterfactual Theories

Counterfactual theories define causation as a counterfactual relation, often based on the logic of counterfactual conditionals. These theories reduce facts about causation to facts about what would have been true in counterfactual situations. The core idea is to construct causation in the form "If C had not occurred, E would not have occurred either." This approach can be traced back to David Hume's definition of causation.

"If the first object had not been, the second never had existed."

David Lewis defined the concept of causal dependence in his 1973 paper "Causation":

Event E is causally dependent on C if and only if (i) if C had occurred then E would have occurred, and (ii) if C had not occurred then E would not have occurred.

Causation is analyzed through such counterfactual dependence. That is, C causes E when there exists a chain of events C, D1, D2, ... Dk, E, where each event in the chain counterfactually depends on the previous event. Such a chain of causal dependence can be called a mechanism.

This analysis aims to provide a metaphysical account of what it means for causation to exist between particular pairs of events, rather than explaining how we make causal judgments or reason about causation. If this analysis is correct, it has the power to explain certain features of causation. For example, in his paper "Counterfactual Dependence and Time's Arrow," Lewis attempted to explain the temporal directionality of counterfactual dependence in terms of the semantics of counterfactual conditionals. If this theory is correct, it could explain the fundamental aspect of our experience that we can causally influence the future but not the past.

One challenge for the counterfactual account is the problem of overdetermination. For example, suppose both Alice and Bob throw bricks at a window, breaking it. Even if Alice had not thrown her brick, the window would still have broken, leading to the conclusion that Alice was not a cause -- yet intuitively, Alice did contribute to breaking the window. The Halpern-Pearl definition of causation takes such cases into consideration.

9.2. Probabilistic Causation

If causation is interpreted as a deterministic relation, then if A causes B, A must always entail B. In this sense, war does not always cause death, nor does smoking always cause cancer or emphysema. As a result, many people have turned to the concept of probabilistic causation. Informally, the statement that A ("this person is a smoker") probabilistically causes B ("this person has cancer now or will develop cancer in the future") means that the information that A has occurred increases the probability of B occurring.

Formally, this is expressed as P{B|A} >= P{B}, where P{B|A} is the conditional probability of B occurring given that A has occurred, and P{B} is the probability of B occurring without knowing whether A has occurred. However, this intuitive condition alone is not sufficient as a definition of probabilistic causation. For example, while smoking can be a cause of both emphysema and cancer, one cannot conclude that emphysema causes cancer. Therefore, additional conditions such as a reasonable account of the mechanism of causation and temporal relationships are needed.

When experimental intervention is impossible or illegal, deriving cause-effect relationships from observational studies requires reliance on specific qualitative theoretical hypotheses. For example, the hypothesis that symptoms do not cause diseases is represented as the absence of arrows in causal graphs such as Bayesian networks or path diagrams.

The theory of causal calculus enables inferring interventional probabilities from conditional probabilities in causal Bayesian networks with unmeasured variables. One highly practical result of this theory is the characterization of confounding variables -- identifying a sufficient set of variables that must be adjusted to obtain the correct causal effect between variables of interest.

9.3. Derivation Theory

Nobel laureate Herbert A. Simon and philosopher Nicholas Rescher argue that the asymmetry of causation is unrelated to the asymmetry of the implication of contrapositives. Rather, they view causation not as a relationship between variable values but as a function from one variable (cause) to another variable (effect). They argue that the essential serialization of systems of equations can correctly capture causation in all empirical fields, including physics and economics.

9.4. Manipulation Theory

Some theorists have equated causation with manipulability. According to these theories, X causes Y only when one can change Y by changing X. This aligns with the commonsense notion of causation where we ask causal questions in order to change some feature of the world. For example, knowing the causes of crime can help find ways to reduce crime.

These theories have faced two main criticisms. First, the attempt to reduce causal claims to manipulation requires that manipulation is more fundamental than causal interaction, but explaining manipulation in non-causal terms proves considerably difficult. Second, there is a concern about anthropocentrism. If causation is equated with our manipulation, the intuition that causation is some relationship existing in the world disappears, and humans are criticized for playing an excessively central role in worldly interactions.

Recently, there have been attempts to defend manipulability theories without claiming to reduce causation to manipulation. These accounts use manipulation as a sign or feature of causation while not claiming that manipulation is more fundamental than causation.

10. Understanding Causality Across Disciplines

10.1. Physics and Engineering

Care must be taken in using the word "cause" in physics. Properly speaking, hypothetical causes and effects are each temporally transient processes. For example, force is a useful concept for explaining acceleration, but force itself is not a cause. More is needed. For example, a temporally transient process characterized by a definite change of force at a particular time can be considered a cause.

Causation is not inherently implied in equations of motion but is rather assumed as an additional constraint that must be satisfied (i.e., causes must always precede effects). This constraint has mathematical implications such as the Kramers-Kronig relations.

Causation is one of the most fundamental and essential concepts in physics. Causal efficacy cannot "propagate faster than light." Otherwise, a reference frame could be constructed where an observer sees effects preceding causes (i.e., the hypothesis of causality would be violated).

Regarding energy flow, causal concepts appear. No real process can have causal efficacy that propagates faster than light. In contrast, abstract concepts have no causal efficacy. Great care must be taken when dealing with causation in physics and engineering. Cellier, Elmqvist, and Otter explain that the causation underlying physics is a misunderstanding. According to their argument, physics is inherently non-causal.

"The relationship between voltage and current across an electrical resistor can be described by Ohm's law, V=IR, but whether the current flowing through the resistor causes the voltage drop, or whether the potential difference between two wires causes the current to flow, is a meaningless question from a physical standpoint."

In practice, if using the law to describe cause-effect, two explanations would be needed for an electrical resistor: "voltage drop causer" or "current flow causer." No physical experiment in the world can distinguish action from reaction.

10.2. Biology, Medicine, and Epidemiology

A mediator is an element of a causal chain (top), while a confounder is a spurious factor that falsely suggests causation (bottom).

Austin Bradford Hill, building on the work of Hume and Popper, proposed that when attempting to distinguish causal from non-causal associations in epidemiological situations, aspects of association such as strength, consistency, specificity, and temporality should be considered (see Bradford Hill criteria). However, he did not mention that temporality is the only necessary criterion among these aspects. Directed acyclic graphs (DAGs) are increasingly used in epidemiology to clarify causal thinking.

10.3. Psychology

Psychologists take an empirical approach, investigating how people and non-human animals detect or infer causation from sensory information, prior experience, and innate knowledge.

Attribution: Attribution theory concerns how people explain individual causal occurrences. Attributions can be external (assigning causality to outside agents or forces) or internal (assigning causality to factors within the individual).
Causal powers: While Hume argued causation is inferred from non-causal observations, Kant argued people have innate assumptions about causes. Patricia Cheng attempted to reconcile these views. Her power PC theory proposes that people filter event observations through the intuition that causes possess the power to produce (or prevent) their effects, inferring specific cause-effect relationships.
Causality and salience: Our views on causation depend on which events we consider relevant. The statement "lightning causes thunder" can also be viewed as both lightning and thunder being two perceptions of the same event -- an electrical discharge perceived visually first and auditorily later.
Naming and causality: David Sobel and Alison Gopnik of UC Berkeley psychology devised a "blicket detector" that lights up when an object is placed on it. Their research suggests "young children learn readily and quickly about novel causal powers and spontaneously use that information in classifying and naming objects."
Perception of launching events: Some researchers, including Anjan Chatterjee of the University of Pennsylvania and Jonathan Fugelsang of the University of Waterloo, use neuroscience techniques to investigate the neurological and psychological foundations of causal launching events -- where one object causes the movement of another.

10.4. Statistics and Economics

Statistics and economics generally use existing or experimental data to infer causation through regression methods. A linear relationship is typically assumed:

Where $y_{i}$ is the ith observation of the dependent variable (assumed to be the effect), $x_{j,i}$ is the ith observation of the jth independent variable (assumed to be a cause) for j=1,...,k, and $e_{i}$ is the error term for the ith observation (including the combined effect of all other causal variables that must be uncorrelated with the included independent variables).

This approach to testing causation presupposes the belief that there is no reverse causation where Y causes Xj. This belief can be established in several ways:

Non-economic variables: For example, when assuming rainfall affects agricultural futures prices, it is impossible for futures prices to affect rainfall.
Instrumental variable technique: Introducing other variables (instruments) known to be unaffected by the dependent variable can eliminate reverse causation.
Effects cannot precede causes: The principle of including only variables that temporally precede the dependent variable on the right side of the regression equation. This is used in Granger causality tests and vector autoregressive models.

Regression analysis controls for other relevant variables by including them as regressors. This helps avoid false causal inferences arising from third underlying variables that affect both potential cause and potential effect variables.

An Ishikawa diagram used in management and engineering shows factors that cause an effect. Small arrows connect sub-causes to major causes.

In the 1960s, for manufacturing quality control, Kaoru Ishikawa developed a cause-and-effect diagram known as the Ishikawa diagram or fishbone diagram. This diagram classifies causes into six major categories, which are further subdivided. Ishikawa diagrams are used beyond quality control in other areas of management and engineering.

10.5. History

In history, events are sometimes treated as if they were agents that cause other historical events. For example, crop failures, peasant suffering, high taxes, absence of popular representation, and incompetent monarchy are cited as causes of the French Revolution. This is similar to a Platonic, Hegelian view that objectifies causes as ontological entities. In Aristotelian terms, this is closest to the efficient cause.

John Gaddis distinguished exceptional causes from general causes and distinguished between "routine" and "unique" connections in causation. He also identified direct, intermediate, and distant causes. Christopher Lloyd proposed four "general causal concepts" used in history: metaphysical idealist, empiricist (Humean) regularity, functional/teleological/consequentialist, and realist/structuralist/dispositional approaches.

10.6. Law and Jurisprudence

In law and jurisprudence, legal cause must be established for a defendant to be held liable for a crime or tort (e.g., negligence or trespass). It must be proven that there is a causal relationship or "sufficient causal connection" between the defendant's actions and the criminal case or damage. Causation is also an essential legal element that must be proved to qualify for remedies under international trade law.

10.7. Indian Philosophy

Vedic period (c. 1750-500 BCE) texts contain early discussions of karma. Karma is a concept in Hinduism and other Indian religions that a person's actions cause specific positive or negative consequences in their current or future life. In the Brahma Samhita, Brahma describes Krishna as the primordial cause of all causes.

Bhagavad Gita 18:14 identifies five causes for all actions (the body, the individual soul, the senses, effort, and the transcendental soul).

According to Monier-Williams, the Nyaya theory of causation from Vaisheshika philosophy states that "absence of effect follows from absence of cause, but absence of cause does not follow from absence of effect." That is, the cause precedes the effect. Using the thread and cloth metaphor, three types of causes are explained:

Co-inherence cause: A "substantial cause" arising from substantial contact, corresponding to Aristotle's material cause.
Non-substantial cause: The method of making thread into cloth, corresponding to Aristotle's formal cause.
Instrumental cause: The tools for making cloth, corresponding to Aristotle's efficient cause.

10.8. Buddhist Philosophy

In Buddhist philosophy, karma is the principle of causality, focusing on 1) cause, 2) action, and 3) result. Here, mental phenomena guide actions performed by the agent. Buddhism trains the agent's actions toward continuous, unintentional virtuous outcomes that aim to reduce suffering.

The general or universal definition of pratityasamutpada (also "dependent origination," "dependent arising," "interdependent co-arising") is that everything arises depending on multiple causes and conditions, and nothing exists as a single, independent entity. The traditional example from Buddhist scriptures is three sticks leaning against each other, supporting one another. If one stick is removed, the other two fall to the ground.

The Chittamatrin school's approach to causation, Asanga's mind-only Buddhist school, argues that objects cause consciousness from the image of the mind.

The Vaibhashika (c. 500 BCE), an early Buddhist school, favors direct object contact and accepts simultaneous cause and effect. This is based on the example of consciousness, where intention and emotion are mutually entailing mental factors supporting each other like a tripod. Conversely, those who reject simultaneous cause and effect argue that if the effect already exists, it cannot be influenced again in the same way.

All classical Buddhist schools teach karma. "The law of karma is a special case of the law of causality, where all our actions of body, speech, and mind are causes, and all our experiences are their effects."

11. Changes in the Concept of Causality Since the Medieval Period

Before Aquinas, in Aristotelian philosophy the word "cause" had the broad meaning of an answer to a "why" question or an "explanation," and Aristotelian scholars recognized four kinds of answers. As the Middle Ages ended, the meaning of "cause" in many philosophical usages narrowed. It lost its broad sense and was often restricted to one of the four kinds. For authors like Niccolo Machiavelli and Francis Bacon, Aristotle's efficient cause was the primary concern.

David Hume assumed a widely used modern definition of causation in this newly narrowed sense. He conducted epistemological and metaphysical investigations of the concept of efficient cause. Hume denied that we can ever perceive cause and effect. Rather, he argued that we can only cognize cause and effect through developing a habit or mental custom of associating two types of objects or events that always occur adjacently and in succession.

In his book A Treatise of Human Nature, Part III, Section 15, Hume presented eight methods for judging whether two things can be cause and effect:

"The cause and effect must be contiguous in space and time."
"The cause must be prior to the effect."
"There must be a constant union betwixt the cause and effect. 'Tis chiefly this quality, that constitutes the relation."

And three additional related criteria derived from our experience, which are "the source of most of our philosophical reasonings":

"The same cause always produces the same effect, and the same effect never arises but from the same cause."
Based on the above principle, Hume states "where several different objects produce the same effect, it must be by means of some quality, which we discover to be common amongst them."
And "based on the same reason": "The difference in the effects of two resembling objects must proceed from that particular, in which they differ."

Two additional criteria also exist:

"An object, which exists for any time in its full perfection without any effect, is not the sole cause of that effect, but requires to be assisted by some other principle, which may forward its influence and operation."
"Where an object increases or diminishes with the increase or diminution of its cause, 'tis to be regarded as a compounded effect, deriv'd from the union of the several different effects, that arise from the several different parts of the cause."

In 1949, physicist Max Born distinguished determination from causality. For him, determination meant that actual events are connected by laws of nature, enabling reliable prediction and reconstruction from sufficient present data. He described two kinds of causation: nomic or generic causation and singular causation. Nomic causation means cause and effect are connected by more or less certain or probabilistic general laws covering many possible or potential instances. This can be recognized as a probabilized version of Hume's third criterion. Singular causation is a specific occurrence of a distinct composite event, physically connected by precedence and contiguity. This can be recognized as Hume's first and second criteria.

Conclusion

Causality extends far beyond simple cause-and-effect connections, being a complex and multifaceted concept that has been deeply explored across all academic fields -- from philosophy, science, and society to even religion. From Aristotle's four causes to Hume's empiricist view and modern probabilistic and counterfactual theories, human effort to understand causality has continued through the ages.

In physics, it connects to the fundamental constraints of spacetime; in biology and medicine, it becomes an important tool for uncovering disease causes. Statistics and economics infer causal relationships through data analysis, and psychology studies how humans perceive and reason about causation. History analyzes the complex causes of past events, and law requires causal connections to determine liability. Eastern philosophy explains cosmic causation through concepts like karma and dependent origination.

The exploration of causality provides an essential foundation for understanding the world, predicting the future, and intervening to create desirable outcomes. Understanding this constantly evolving concept will play an important role in navigating the complexity of the world we live in.