While this informal understanding will suffice in everyday usage, the philosophical analysis of causality or causation has proved exceedingly difficult. The work of philosophers to understand causality and how best to characterize it extends over millennia. In the western philosophical tradition explicit discussion stretches back at least as far as Aristotle, and the topic remains a staple in contemporary philosophy journals. Though cause and effect are typically related to events, other candidates include processes, properties, variables, facts, and states of affairs; which of these comprise the correct causal relata, and how best to characterize the nature of the relationship between them, has as yet no universally accepted answer, and remains under discussion.
- "Causality postulates that there are laws by which the occurrence of an entity B of a certain class depends on the occurrence of an entity A of another class, where the word entity means any physical object, phenomenon, situation, or event. A is called the cause, B the effect.
- "Antecedence postulates that the cause must be prior to, or at least simultaneous with, the effect.
- "Contiguity postulates that cause and effect must be in spatial contact or connected by a chain of intermediate things in contact." (Born, 1949, as cited in Sowa, 2000)
However, according to Sowa (2000), "relativity and quantum mechanics have forced physicists to abandon these assumptions as exact statements of what happens at the most fundamental levels, but they remain valid at the level of human experience."
It should be noted here, however, that physicists themselves never denied causality or stated that causality is violated in quantum mechanics or relativity. Vice versa, any experiment designed to show violation of causality so far failed to do so.
In his Posterior Analytics and Metaphysics, Aristotle wrote, "All causes are beginnings...", "... we have scientific knowledge when we know the cause...", and "... to know a thing's nature is to know the reason why it is..." This formulation set the guidelines for subsequent causal theories by specifying the number, nature, principles, elements, varieties, order of causes as well as the modes of causation. Aristotle's account of the causes of things is a comprehensive model.
Aristotle's theory enumerates the possible causes which fall into several wide groups, amounting to the ways the question "why" may be answered; namely, by reference to the material worked upon (as by an artisan) or what might be called the substratum; to the essence, i.e., the pattern, the form, or the structure by reference to which the "matter" or "substratum" is to be worked; to the primary moving agent of change or the agent and its action; and to the goal, the plan, the end, or the good that the figurative artisan intended to obtain. As a result, the major kinds of causes come under the following divisions:
- The material cause is that "raw material" from which a thing is produced as from its parts, constituents, substratum, or materials. This rubric limits the explanation of cause to the parts (the factors, elements, constituents, ingredients) forming the whole (the system, structure, compound, complex, composite, or combination) (the part-whole causation).
- The formal cause tells us what, by analogy to the plans of an artisan, a thing is intended and planned to be. Any thing is thought to be determined by its definition, form (mold), pattern, essence, whole, synthesis, or archetype. This analysis embraces the account of causes in terms of fundamental principles or general laws, as the intended whole (macrostructure) is the cause that explains the production of its parts (the whole-part causation).
- The efficient cause is that external entity from which the change or the ending of the change first starts. It identifies 'what makes of what is made and what causes change of what is changed' and so suggests all sorts of agents, nonliving or living, acting as the sources of change or movement or rest. Representing the current understanding of causality as the relation of cause and effect, this analysis covers the modern definitions of "cause" as either the agent, agency, particular causal events, or the relevant causal states of affairs.
- The final cause is that for the sake of which a thing exists, or is done - including both purposeful and instrumental actions. The final cause, or telos, is the purpose, or end, that something is supposed to serve; or it is that from which, and that to which, the change is. This analysis also covers modern ideas of mental causation involving such psychological causes as volition, need, motivation, or motives; rational, irrational, ethical - all that gives purpose to behavior.
Additionally, things can be causes of one another, reciprocally causing each other, as hard work causes fitness, and vice versa - although not in the same way or by means of the same function: the one is as the beginning of change, the other is as its goal. (Thus Aristotle first suggested a reciprocal or circular causality - as a relation of mutual dependence, action, or influence of cause and effect.) Also; Aristotle indicated that the same thing can be the cause of contrary effects - as its presence and absence may result in different outcomes. In speaking thus he formulated what currently is ordinarily termed a "causal factor," e.g., atmospheric pressure as it affects chemical or physical reactions.
Aristotle marked two modes of causation: proper (prior) causation and accidental (chance) causation. All causes, proper and incidental, can be spoken as potential or as actual, particular or generic. The same language refers to the effects of causes; so that generic effects assigned to generic causes, particular effects to particular causes, and operating causes to actual effects. It is also essential that ontological causality does not suggest the temporal relation of before and after - between the cause and the effect; that spontaneity (in nature) and chance (in the sphere of moral actions) are among the causes of effects belonging to the efficient causation, and that no incidental, spontaneous, or chance cause can be prior to a proper, real, or underlying cause per se.
All investigations of causality coming later in history will consist in imposing a favorite hierarchy on the order (priority) of causes; such as "final > efficient > material > formal" (Aquinas), or in restricting all causality to the material and efficient causes or, to the efficient causality (deterministic or chance), or just to regular sequences and correlations of natural phenomena (the natural sciences describing how things happen rather than asking why they happen).
Causality, determinism, and existentialism
The deterministic world-view is one in which the universe is no more than a chain of events following one after another according to the law of cause and effect. To hold this worldview, as an incompatibilist, there is no such thing as "free will". However, compatibilists argue that determinism is compatible with, or even necessary for, free will.
Learning to bear the burden of a meaningless universe, and justify one's own existence, is the first step toward becoming the "Übermensch" (English: "overman" or "superman") that Nietzsche speaks of extensively in his philosophical writings.
Existentialists have suggested that people have the courage to accept that while no meaning has been designed in the universe, we each can provide a meaning for ourselves.
Though philosophers have pointed out the difficulties in establishing theories of the validity of causal relations, there is yet the plausible example of causation afforded daily which is our own ability to be the cause of events. This concept of causation does not prevent seeing ourselves as moral agents.
Theories of causality in Indian philosophy focus mainly on the relationship between cause and effect. The various philosophical schools (darsanas) provide different theories.
The doctrine of satkaryavada affirms that the effect inheres in the cause in some way. The effect is thus either a real or apparent modification of the cause.
The doctrine of asatkaryavada affirms that the effect does not inhere in the cause, but is a new arising.
Among the Buddhist thinkers, Nagarjuna uses a variety of arguments to deny the validity of the cause and effect relationship.
See Nyaya for some details of the theory of causation in the Nyaya school.
Necessary and sufficient causes
- A similar concept occurs in logic, for this see Necessary and sufficient conditions
Causes are often distinguished into two types: Necessary and sufficient. 
If x is a necessary cause of y, then the presence of y necessarily implies the presence of x. The presence of x, however, does not imply that y will occur.
If x is a sufficient cause of y, then the presence of x necessarily implies the presence of y. However, another cause z may alternatively cause y. Thus the presence of y does not imply the presence of x.
J. L. Mackie argues that usual talk of "cause", in fact, refers to INUS conditions (insufficient and non-redundant parts of unnecessary but sufficient causes). For example; consider the short circuit as a cause of the house burning down. Consider the collection of events, the short circuit, the proximity of flammable material, and the absence of firefighters. Considered together these are unnecessary but sufficient to the house's destruction (since many other collection of events certainly could have destroyed the house). Within this collection; the short circuit is an insufficient but non-redundant part (since the short circuit by itself would not cause the fire, but the fire will not happen without it with everything else being equal). So the short circuit is an INUS cause of the house burning down.
Causality contrasted with conditionals
Conditional statements are not statements of causality. Perhaps the most important distinction is that statements of causality require the antecedent to precede the consequent in time, whereas this temporal order is not required by a conditional statement. Since many different statements may be presented using "If...then..." in English (and, arguably, because this form is far more commonly used to make a statement of causality), they are commonly confused; they are distinct, however.
For example all of the following statements are true interpreting "If... then..." as the material conditional:
- If George Bush was president of the United States in 2004, then Germany is in Europe.
- If George Washington was president of the United States in 2004, then Germany is in Europe.
- If George Washington was president of the United States in 2004, then Germany is not in Europe.
The first is true since both the antecedent and the consequent are true. The second is true because the antecedent is false and the consequent is true. The third is true because both the consequent and antecedent are both false. These statement are trivial examples. Of course, none of these statements express a causal connection between the antecedent and consequent, but they are true because they do not have the combination of having both true antecedent and false consequent.
The ordinary indicative conditional seems to have some more structure than the material conditional - for instance, none of the three statements above seem to be correct under an ordinary indicative reading, though the first is closest. But the sentence
- If Shakespeare of Stratford on Avon didn't write Macbeth then someone else did.
seems to be true, even though there is no straightforward causal relation (in this hypothetical situation) between Shakespeare's not writing Macbeth and someone else's actually writing it.
Another sort of conditional, known as the counterfactual conditional has a stronger connection with causality. However, not even all counterfactual statements count as examples of causality. Consider the following two statements:
- If A were a triangle, then A would have three sides.
- If switch S were thrown, then bulb B would light.
In the first case it would not be correct to say that A's being a triangle caused it to have three sides, since the relationship between triangularity and three-sidedness is one of definition. It is actually the three sides that determine A's state as a triangle. Nonetheless, even interpreted counterfactually, the first statement is true.
It is probably important to fully grasp the concept of conditionals before the literature on causality can be understood. A crucial stumbling block is that, in everyday usage, conditionals are usually used to describe a general situation. For example "if I drop my coffee, then my shoe gets wet" relates an infinite number of possible events; it is shorthand for "for any fact that would count as 'dropping my coffee', some fact that counts as 'my shoe gets wet' will be true". This general statement will be strictly false if there is any circumstance where I drop my coffee and my shoe doesn't get wet. However, an "if... then..." statement in logic typically relates two specific events or facts - a specific coffee-dropping did or did not occur, and a specific shoe-wetting did or did not follow. Thus, with explicit events in mind, if I drop my coffee and wet my shoe then it is true that "if I dropped my coffee then I wet my shoe", regardless of the fact that yesterday I dropped a coffee in the trash for the opposite effect - the conditional relates to specific facts. More counter-intuitively, if I didn't drop my coffee at all then it is also true that "if I drop my coffee then I wet my shoe", or "dropping my coffee implies I wet my shoe", regardless of whether I wet my shoe or not by any means. This usage would not be counter-intuitive if it weren't for the everyday usage. Briefly, "if X then Y" is equivalent to the first-order logic statement "A implies B" or "not B-and-not-A", where A and B are predicates, but the more familiar usage of an "if A then B" statement would need to be written symbolically using a higher order logic using quantifiers ("for all" and "there exists").
The philosopher David Lewis notably suggested that all statements about causality can be understood as counterfactual statements. So, for instance, the statement that John's smoking caused his premature death is equivalent to saying that had John not smoked he would not have prematurely died. (In addition, it need also be true that John did smoke and did prematurely die, although this requirement is not unique to Lewis' theory.) However, simple logics prove this to be false: the proposition p → q (John smoked, therefore he died prematurely) is logically equivalent to ¬q → ¬p (John did not die prematurely, therefore he did not smoke) (We can also say that p → q <=> ¬q → ¬p, meaning that p → q is logically equivalent to ¬q → ¬p, is a tautology). Saying that John didn't smoke, and therefore didn't die prematurely (¬p → ¬q) is a proposition that cannot be deduced from p → q without extra information.
Translating causal into counterfactual statements would only be beneficial if the latter were less problematic than the former. This is indeed the case, as is demonstrated by the structural account of counterfactual conditionals devised by the computer scientist Judea Pearl (2000). This account provides clear semantics and effective algorithms for computing counterfactuals which, in contrast to Lewis' closest world semantics does not rely on the ambiguous notion of similarity among worlds. For instance, one can compute unambiguously the probability that John would be alive had he not smoked given that, in reality, John did smoke and did die. The quest for a counterfactual interpretation of causal statements is therefore justified.
One problem Lewis' theory confronts is causal preemption. Suppose that John did smoke and did in fact die as a result of that smoking. However, there was a murderer who was bent on killing John, and would have killed him a second later had he not first died from smoking. Here we still want to say that smoking caused John's death. This presents a problem for Lewis' theory since, had John not smoked, he still would have died prematurely. Lewis himself discusses this example, and it has received substantial discussion (cf.). A structural solution to this problem has been given in [Halpern and Pearl, 2005].
Interpreting causation as a deterministic relation means that if A causes B, then A must always be followed by B. In this sense, war does not cause deaths, nor does smoking cause cancer. As a result, many turn to a notion of probabilistic causation. Informally, A probabilistically causes B if A's occurrence increases the probability of B. This is sometimes interpreted to reflect imperfect knowledge of a deterministic system but other times interpreted to mean that the causal system under study has an inherently chancy nature.
When experiments are infeasible or illegal, the derivation of cause effect relationship from observational studies must rest on some qualitative theoretical assumptions, for example, that symptoms do not cause diseases, usually expressed in the form of missing arrows in causal graphs such as Bayesian Networks or path diagrams. The mathematical theory underlying these derivations relies on the distinction between conditional probabilities, as in , and interventional probabilities, as in . The former reads: "the probability of finding cancer in a person known to smoke" while the latter reads: "the probability of finding cancer in a person forced to smoke". The former is a statistical notion that can be estimated directly in observational studies, while the latter is a causal notion (also called "causal effect") which is what we estimate in a controlled randomized experiment.
The theory of "causal calculus" permits one to infer interventional probabilities from conditional probabilities in causal Bayesian Networks with unmeasured variables. One very practical result of this theory is the characterization of confounding variables, namely, a sufficient set of variables that, if adjusted for, would yield the correct causal effect between variables of interest. It can be shown that a sufficient set for estimating the causal effect of on is any set of non-descendants of that -separate from after removing all arrows emanating from . This criterion, called "backdoor", provides a mathematical definition of "confounding" and helps researchers identify accessible sets of variables worthy of measurement.
While derivations in Causal Calculus rely on the structure of the causal graph, parts of the causal structure can, under certain assumptions, be learned from statistical data. The basic idea goes back to a recovery algorithm developed by Rebane and Pearl (1987) and rests on the distinction between the three possible types of causal substructures allowed in a directed acyclic graph (DAG):
Type 1 and type 2 represent the same statistical dependencies (i.e., and are independent given ) and are, therefore, indistinguishable. Type 3, however, can be uniquely identified, since and are marginally independent and all other pairs are dependent. Thus, while the skeletons (the graphs stripped of arrows) of these three triplets are identical, the directionality of the arrows is partially identifiable. The same distinction applies when and have common ancestors, except that one must first condition on those ancestors. Algorithms have been developed to systematically determine the skeleton of the underlying graph and, then, orient all arrows whose directionality is dictated by the conditional independencies observed   .
Alternative methods of structure learning search through the many possible causal structures among the variables, and remove ones which are strongly incompatible with the observed correlations. In general this leaves a set of possible causal relations, which should then be tested by designing appropriate experiments. If experimental data is already available, the algorithms can take advantage of that as well. In contrast with Bayesian Networks, path analysis and its generalization, structural equation modeling, serve better to estimate a known causal effect or test a causal model than to generate causal hypotheses.
For nonexperimental data, causal direction can be hinted if information about time is available. This is because (according to many, though not all, theories) causes must precede their effects temporally. This can be set up by simple linear regression models, for instance, with an analysis of covariance in which baseline and follow up values are known for a theorized cause and effect. The addition of time as a variable, though not proving causality, is a big help in supporting a pre-existing theory of causal direction. For instance, our degree of confidence in the direction and nature of causality is much greater when supported by data from a longitudinal study than by data from a cross-sectional study.
The Nobel Prize holder Herbert Simon and Philosopher Nicholas Rescher claim that the asymmetry of the causal relation is unrelated to the asymmetry of any mode of implication that contraposes. Rather, a causal relation is not a relation between values of variables, but a function of one variable (the cause) on to another (the effect). So, given a system of equations, and a set of variables appearing in these equations, we can introduce an asymmetric relation among individual equations and variables that corresponds perfectly to our commonsense notion of a causal ordering. The system of equations must have certain properties, most importantly, if some values are chosen arbitrarily, the remaining values will be determined uniquely through a path of serial discovery that is perfectly causal. They postulate the inherent serialization of such a system of equations may correctly capture causation in all empirical fields, including physics and economics.
Some theorists have equated causality with manipulability. Under these theories, x causes y just in case one can change x in order to change y. This coincides with commonsense notions of causations, since often we ask causal questions in order to change some feature of the world. For instance, we are interested in knowing the causes of crime so that we might find ways of reducing it.
These theories have been criticized on two primary grounds. First, theorists complain that these accounts are circular. Attempting to reduce causal claims to manipulation requires that manipulation is more basic than causal interaction. But describing manipulations in non-causal terms has provided a substantial difficulty.
The second criticism centers around concerns of anthropocentrism. It seems to many people that causality is some existing relationship in the world that we can harness for our desires. If causality is identified with our manipulation, then this intuition is lost. In this sense, it makes humans overly central to interactions in the world.
Some attempts to save manipulability theories are recent accounts that don't claim to reduce causality to manipulation. These account use manipulation as a sign or feature in causation without claiming that manipulation is more fundamental than causation.
Some theorists are interested in distinguishing between causal processes and non-causal processes (Russell 1948; Salmon 1984). These theorists often want to distinguish between a process and a pseudo-process. As an example, a ball moving through the air (a process) is contrasted with the motion of a shadow (a pseudo-process). The former is causal in nature while the latter is not.
Salmon (1984) claims that causal processes can be identified by their ability to transmit an alteration over space and time. An alteration of the ball (a mark by a pen, perhaps) is carried with it as the ball goes through the air. On the other hand an alteration of the shadow (insofar as it is possible) will not be transmitted by the shadow as it moves along.
These theorists claim that the important concept for understanding causality is not causal relationships or causal interactions, but rather identifying causal processes. The former notions can then be defined in terms of causal processes.
In addition, many scientists in a variety of fieldsTemplate:Specify disagree that experiments are necessary to determine causality. For example, the link between smoking and lung cancer is considered proven by health agencies of the United States government, but experimental methods (for example, randomized controlled trials) were not used to establish that link. This view has been controversial. In addition, many philosophers are beginning to turn to more relativized notions of causality. Rather than providing a theory of causality in toto, they opt to provide a theory of causality in biology or causality in physics.
Physicists conclude that certain elemental forces: gravity, the strong and weak nuclear forces, and electromagnetism are said to be the four fundamental forces which are the causes of all other events in the universe. Causality is hard to interpret to ordinary language from many different physical theories. One problem is typified by the moon's gravity. It isn't accurate to say, "the moon exerts a gravitic pull and then the tides rise." In Newtonian mechanics gravity, rather, is a law expressing a constant observable relationship among masses, and the movement of the tides is an example of that relationship. There are no discrete events or "pulls" that can be said to precede the rising of tides. Interpreting gravity causally is even more complicated in general relativity. Another important implication of Causality in physics is its intimate connection to the Second Law of Thermodynamics (see the fluctuation theorem). Quantum mechanics is yet another branch of physics in which the nature of causality is somewhat unclear.
The treatment of the concept of causality within the Second Law of Thermodynamics yields a loss in the translation. The statistical basis of the maintenance of the exchange of entropy confines the subject to an extent such that the observer loses perspective. The 2nd Law states that "in a closed system, disorder increases". This is a corollary of the concept that an effect cannot be greater than the cause. Consider information content. Applying the 2nd Law, the information content in a closed system cannot increase. If the boundaries of the system are penetrated then a system can increase in information content but the loss is felt elsewhere. Strict adherence to the principles of the second law preclude boundary violation. However, this is not to say a closed system cannot increase in order locally. Take AI for example. The 2nd law does not preclude the existence of an artificial intelligence capable of growing greater than its creator since energy must constantly be supplied to the system. In physics matter and energy are considered forms of information. Thus, the AI could grow in order and comlexity, but only at the expense of an equal or greater increase in entropy in the form of dissipated energy, allowing the system to increase in disorder globally.
A causal system is a system with output and internal states that depends only on the current and previous input values. A system that has some dependence on input values from the future (in addition to possible past or current input values) is termed an acausal system, and a system that depends solely on future input values is an anticausal system. Acausal filters, for example, can only exist as digital filters, because these filters can extract future values from a memory buffer or a file.
Biology and medicine
A. B. Hill built upon the work of Hume and Popper and suggested that the following aspects of an association be considered in attempting to distinguish causal from noncausal associations: 1) strength, 2) consistency, 3) specificity, 4) temporality, 5) biological gradient, 6) plausibility, 7) coherence, 8) experimental evidence, and 9) analogy.
The above theories are attempts to define a reflectively stable notion of causality. This process uses our standard causal intuitions to develop a theory that we would find satisfactory in identifying causes. Another avenue of research is to empirically investigate how people (and non-human animals) learn and reason about causal relations in the world. This approach is taken by work in psychology. It also is possible to tackle causalities in surveys with a technique of elaboration. Given a relationship between two variables, what can be learned by introducing a third variable into the analysis (Rosenberg, 1968, xiii)? So elaboration is a device of the analysis that results in different kinds of relationships between variables e.g. suppression, extraneous, and distorter relations.
Attribution theory is the theory concerning how people explain individual occurrences of causation. Attribution can be external (assigning causality to an outside agent or force - claiming that some outside thing motivated the event) or internal (assigning causality to factors within the person - taking personal responsibility or accountability for one's actions and claiming that the person was directly responsible for the event). Taking causation one step further, the type of attribution a person provides influences their future behavior.
Whereas David Hume argued that causes are inferred from non-causal observations, Immanuel Kant claimed that people have innate assumptions about causes. Within psychology, Patricia Cheng (1997) attempted to reconcile the Humean and Kantian views. According to her power PC theory, people filter observations of events through a basic belief that causes have the power to generate (or prevent) their effects, thereby inferring specific cause-effect relations. The theory assumes probabilistic causation. Pearl (2000) has shown that Cheng's causal power can be given a counterfactual interpretation, (i.e., the probability that, absent and , would be true if were true) and is computable therefore using structural models.
Causation and salience
Our view of causation depends on what we consider to be the relevant events. Another way to view the statement, "Lightning causes thunder" is to see both lightning and thunder as two perceptions of the same event, viz., an electric discharge that we perceive first visually and then aurally.
Naming and causality
While the names we give objects often refer to their appearance, they can also refer to an object's causal powers - what that object can do, the effects it has on other objects or people. David Sobel and Alison Gopnik from the Psychology Department of UC Berkeley designed a device known as the blicket detector which suggests that "when causal property and perceptual features are equally evident, children are equally as likely to use causal powers as they are to use perceptual properties when naming objects".
In the discussion of history, events are often considered as if in some way being agents that can then bring about other historical events. Thus, the combination of poor harvests, the hardships of the peasants, high taxes, lack of representation of the people, and kingly ineptitude are among the causes of the French Revolution. This is a somewhat Platonic and Hegelian view that reifies causes as ontological entities. In Aristotelian terminology, this use approximates to the case of the efficient cause.
- Main article: causation (law)
According to law and jurisprudence, legal cause must be demonstrated in order to hold a defendant liable for a crime or a tort (ie. a civil wrong such as negligence or trespass). It must be proven that causality, or a 'sufficient causal link' relates the defendant's actions to the criminal event or damage in question.
Religion and theology
One of the classic arguments for the existence of God is known as the "Cosmological argument" or "First cause" argument. It works from the premise that every natural event is the effect of a cause. If this is so, then the events that caused today's events must have had causes themselves, which must have had causes, and so forth. If the chain never ends, then one must uphold the hypothesis of an "actual infinite", which is often regarded as problematic, see Hilbert's paradox of the Grand Hotel. If the chain does end, it must end with a non-natural or supernatural cause at the start of the natural world -- e.g. a creation by God.
Two questions that can help to focus the argument are:
- What is an event without cause?
- How does an event without a cause occur?
Critics of this argument point out problems with it.
A question related to this argument is which came first, the chicken or the egg?
For example, if a person always does good deeds then it is believed that he or she will be "rewarded" for his or her behavior with fortunate events such as avoiding fatal accident or winning the lottery. If he or she always commits antagonistic behaviors, then it is believed that he will be punished with unfortunate events.
In Buddhist philosophy, especially Zen, the word karma simply means the law of cause and effect, ie. causality.
Destiny might be considered reverse causality in that a cause is predated by an effect; e.g., "I found a twenty dollar bill on the ground because later I would need it."
and that causality does not proceed inward, from external random causes toward effects on a perceiving individual, but rather outward, from a perceiving individual's causative mental requests toward responsive external physical effects that only seem to be independent causes. Such thought gives rise to new causality principles such as the doctrine of responsibility assumption.
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- The Metaphysics of Causation
- Dictionary of the History of Ideas: Causation
- Dictionary of the History of Ideas: Causation in Law
- Dictionary of the History of Ideas: Causation in History
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