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112-414: In general, a process can have multiple causes, which are also said to be causal factors for it, and all lie in its past . An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future . Some writers have held that causality is metaphysically prior to notions of time and space . Causality is an abstraction that indicates how the world progresses. As such it

224-442: A n c e r | s m o k i n g ) {\displaystyle P(cancer|smoking)} , and interventional probabilities , as in P ( c a n c e r | d o ( s m o k i n g ) ) {\displaystyle P(cancer|do(smoking))} . The former reads: "the probability of finding cancer in a person known to smoke, having started, unforced by

336-503: A progression of events following one after the other as cause and effect. Incompatibilism holds that determinism is incompatible with free will, so if determinism is true, " free will " does not exist. Compatibilism , on the other hand, holds that determinism is compatible with, or even necessary for, free will. Causes may sometimes be distinguished into two types: necessary and sufficient. A third type of causation, which requires neither necessity nor sufficiency, but which contributes to

448-418: A 'substance', as distinct from an action. Since causality is a subtle metaphysical notion, considerable intellectual effort, along with exhibition of evidence, is needed to establish knowledge of it in particular empirical circumstances. According to David Hume , the human mind is unable to perceive causal relations directly. On this ground, the scholar distinguished between the regularity view of causality and

560-507: 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 only in

672-428: A cause is incorrectly identified. Counterfactual theories define causation in terms of a counterfactual relation, and can often be seen as "floating" their account of causality on top of an account of the logic of counterfactual conditionals . Counterfactual theories reduce facts about causation to facts about what would have been true under counterfactual circumstances. The idea is that causal relations can be framed in

784-441: A cause, and what kind of entity can be an effect?" One viewpoint on this question is that cause and effect are of one and the same kind of entity, causality being an asymmetric relation between them. That is to say, it would make good sense grammatically to say either " A is the cause and B the effect" or " B is the cause and A the effect", though only one of those two can be actually true. In this view, one opinion, proposed as

896-421: A certain point (the train station). Alternatively, the sentence, "He ran past us at full speed," utilizes the concept of the past to describe the position of someone ("He") that is further than the speaker. The "past" is also used to define a time that is a certain number of minute before or after a particular hour , as in "We left the party at half-past twelve." People also use "past" to refer to being beyond

1008-465: A conditional is sometimes referred to as its "if"-clause or protasis . The consequent of a conditional is sometimes referred to as a "then" -clause or as an apodosis. Counterfactuals were first discussed by Nelson Goodman as a problem for the material conditional used in classical logic . Because of these problems, early work such as that of W.V. Quine held that counterfactuals are not strictly logical, and do not make true or false claims about

1120-521: A contrary-to-fact meaning, regardless of their grammatical structure. Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey. Recently the term X-Marked has been proposed as a replacement, evoking the ex tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their o rdinary marking. The antecedent of

1232-452: A counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds. David Lewis 's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on

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1344-444: A dedicated counterfactual morphemes , while others recruit morphemes which otherwise express tense , aspect , mood , or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study. In many languages, counterfactuality is marked by past tense morphology. Since these uses of

1456-584: A definite time. Such a process can be regarded as a cause. Causality is not inherently implied in equations of motion , but postulated as an additional constraint that needs to be satisfied (i.e. a cause always precedes its effect). This constraint has mathematical implications such as the Kramers-Kronig relations . Causality is one of the most fundamental and essential notions of physics. Causal efficacy cannot 'propagate' faster than light. Otherwise, reference coordinate systems could be constructed (using

1568-520: A donkey. The counterfactual example uses the fake tense form "owned" in the "if" clause and the past-inflected modal "would" in the "then" clause. As a result, it conveys that Sally does not in fact own a donkey. English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the past perfect counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology: Another kind of conditional uses

1680-478: A formal implementation of the Ramsey test . In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision , as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising

1792-408: A known causal effect or to test a causal model than to generate causal hypotheses. For nonexperimental data, causal direction can often be inferred 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 determined by statistical time series models, for instance, or with a statistical test based on

1904-402: 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 Sewall Wright 's 1921 work on path analysis . A "recovery" algorithm

2016-443: A metaphysical account of what it is for there to be a causal relation between some pair of events. If correct, the analysis has the power to explain certain features of causation. Knowing that causation is a matter of counterfactual dependence, we may reflect on the nature of counterfactual dependence to account for the nature of causation. For example, in his paper "Counterfactual Dependence and Time's Arrow," Lewis sought to account for

2128-442: A metaphysical principle in process philosophy , is that every cause and every effect is respectively some process, event, becoming, or happening. An example is 'his tripping over the step was the cause, and his breaking his ankle the effect'. Another view is that causes and effects are 'states of affairs', with the exact natures of those entities being more loosely defined than in process philosophy. Another viewpoint on this question

2240-543: A natural language conditional, a statement of the form "if P then Q", is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether

2352-457: A particular biological age or phase of being, as in, "The boy was past the age of needing a babysitter," or, "I'm past caring about that problem." The "past" is commonly used to refer to history, either generally or with regards to specific time periods or events, as in, "Past monarchs had absolute power to determine the law in contrast to many European Kings and Queens of today." Nineteenth-century British author Charles Dickens created one of

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2464-410: 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

2576-418: A real number. One has to be careful in the use of the word cause in physics. Properly speaking, the hypothesized cause and the hypothesized effect are each temporally transient processes. For example, force is a useful concept for the explanation of acceleration, but force is not by itself a cause. More is needed. For example, a temporally transient process might be characterized by a definite change of force at

2688-399: A smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.) One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the law of excluded middle is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p

2800-446: A subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals. The terms counterfactual and subjunctive have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express

2912-401: A triangle. Nonetheless, even when interpreted counterfactually, the first statement is true. An early version of Aristotle's "four cause" theory is described as recognizing "essential cause". In this version of the theory, that the closed polygon has three sides is said to be the "essential cause" of its being a triangle. This use of the word 'cause' is of course now far obsolete. Nevertheless, it

3024-399: A wave packet travels at the phase velocity; since phase is not causal, the phase velocity of a wave packet can be faster than light. Causal notions are important in general relativity to the extent that the existence of an arrow of time demands that the universe's semi- Riemannian manifold be orientable, so that "future" and "past" are globally definable quantities. Past The past

3136-403: A window and it breaks. If Alice hadn't thrown the brick, then it still would have broken, suggesting that Alice wasn't a cause; however, intuitively, Alice did cause the window to break. The Halpern-Pearl definitions of causality take account of examples like these. The first and third Halpern-Pearl conditions are easiest to understand: AC1 requires that Alice threw the brick and the window broke in

3248-526: Is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's Counterfactuals it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did not intend

3360-469: Is a basic concept; it is more apt to be an explanation of other concepts of progression than something to be explained by other more fundamental concepts. The concept is like those of agency and efficacy . For this reason, a leap of intuition may be needed to grasp it. Accordingly, causality is implicit in the structure of ordinary language, as well as explicit in the language of scientific causal notation . In English studies of Aristotelian philosophy ,

3472-451: Is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails"

Causality - Misplaced Pages Continue

3584-553: Is a concern of the subject known as metaphysics . Kant thought that time and space were notions prior to human understanding of the progress or evolution of the world, and he also recognized the priority of causality. But he did not have the understanding that came with knowledge of Minkowski geometry and the special theory of relativity , that the notion of causality can be used as a prior foundation from which to construct notions of time and space. A general metaphysical question about cause and effect is: "what kind of entity can be

3696-439: Is a process that is varied from occasion to occasion. The occurrence or non-occurrence of subsequent bubonic plague is recorded. To establish causality, the experiment must fulfill certain criteria, only one example of which is mentioned here. For example, instances of the hypothesized cause must be set up to occur at a time when the hypothesized effect is relatively unlikely in the absence of the hypothesized cause; such unlikelihood

3808-462: Is a smoker") probabilistically causes B ("The person has now or will have cancer at some time in the future"), if the information that A occurred increases the likelihood of B s occurrence. Formally, P{ B | A }≥ P{ B } where P{ B | A } is the conditional probability that B will occur given the information that A occurred, and P{ B } is the probability that B will occur having no knowledge whether A did or did not occur. This intuitive condition

3920-421: Is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision. Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae , considering

4032-428: Is illustrated by Sobel sequences such as the following: One way of formalizing this fact is to say that the principle of Antecedent Strengthening should not hold for any connective > intended as a formalization of natural language conditionals. The most common logical accounts of counterfactuals are couched in the possible world semantics . Broadly speaking, these approaches have in common that they treat

4144-459: 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

4256-409: Is not adequate as a definition for probabilistic causation because of its being too general and thus not meeting our intuitive notion of cause and effect. For example, if A denotes the event "The person is a smoker," B denotes the event "The person now has or will have cancer at some time in the future" and C denotes the event "The person now has or will have emphysema some time in the future," then

4368-407: Is not on the action having been completed by the present moment, but rather on its having taken place actively over a time period before another moment in the past. The verb tense used in the sentence "She had been walking in the park regularly before I met her" is past perfect continuous because it describes an action ("walking") that was actively happening before a time when something else in the past

4480-425: Is not vacuously true when its antecedent is false. To see why, observe that both P {\displaystyle P} and ◻ ( P → Q ) {\displaystyle \Box (P\rightarrow Q)} will be false at w {\displaystyle w} if there is some accessible world v {\displaystyle v} where P {\displaystyle P}

4592-742: Is specifically characteristic of quantal phenomena that observations defined by incompatible variables always involve important intervention by the experimenter, as described quantitatively by the observer effect . In classical thermodynamics , processes are initiated by interventions called thermodynamic operations . In other branches of science, for example astronomy , the experimenter can often observe with negligible intervention. The theory of "causal calculus" (also known as do-calculus, Judea Pearl 's Causal Calculus, Calculus of Actions) permits one to infer interventional probabilities from conditional probabilities in causal Bayesian networks with unmeasured variables. One very practical result of this theory

Causality - Misplaced Pages Continue

4704-718: 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 X {\displaystyle X} on Y {\displaystyle Y} is any set of non-descendants of X {\displaystyle X} that d {\displaystyle d} -separate X {\displaystyle X} from Y {\displaystyle Y} after removing all arrows emanating from X {\displaystyle X} . This criterion, called "backdoor", provides

4816-477: Is the more classical one, that a cause and its effect can be of different kinds of entity. For example, in Aristotle's efficient causal explanation, an action can be a cause while an enduring object is its effect. For example, the generative actions of his parents can be regarded as the efficient cause, with Socrates being the effect, Socrates being regarded as an enduring object, in philosophical tradition called

4928-415: Is the set of all events that occurred before a given point in time. The past is contrasted with and defined by the present and the future . The concept of the past is derived from the linear fashion in which human observers experience time , and is accessed through memory and recollection . In addition, human beings have recorded the past since the advent of written language. The first known use of

5040-500: Is to be established by empirical evidence. A mere observation of a correlation is not nearly adequate to establish causality. In nearly all cases, establishment of causality relies on repetition of experiments and probabilistic reasoning. Hardly ever is causality established more firmly than as more or less probable. It is most convenient for establishment of causality if the contrasting material states of affairs are precisely matched, except for only one variable factor, perhaps measured by

5152-402: Is true and Q {\displaystyle Q} is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on

5264-406: Is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails." The causal models framework analyzes counterfactuals in terms of systems of structural equations . In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model,

5376-405: Is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example: On Stalnaker's analysis, there

5488-405: Is understood as material implication . This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic. In modern relational semantics , this means that the strict conditional is true at w iff the corresponding material conditional is true throughout the worlds accessible from w . More formally: Unlike the material conditional, the strict conditional

5600-436: Is used to describe actions that were already completed by a specific point in the past. For example, "she had walked" describes an action that took place in the past and was also completed in the past. The past perfects continuous tense refers to an action that was happening up until a particular point in the past but was completed. It is different from the past perfect tense because the emphasis of past perfect continuous verbs

5712-411: Is walking" refers to a girl who is currently walking (present tense), while "she walked" refers to a girl who was walking before now (past tense). The past continuous tense refers to actions that continued for a period of time, as in the sentence "she was walking," which describes an action that was still happening in a prior window of time to which a speaker is presently referring. The past perfect tense

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5824-497: Is within the scope of ordinary language to say that it is essential to a triangle that it has three sides. A full grasp of the concept of conditionals is important to understanding the literature on causality. In everyday language, loose conditional statements are often enough made, and need to be interpreted carefully. Fallacies of questionable cause, also known as causal fallacies, non-causa pro causa (Latin for "non-cause for cause"), or false cause, are informal fallacies where

5936-463: The Lorentz transform of special relativity ) in which an observer would see an effect precede its cause (i.e. the postulate of causality would be violated). Causal notions appear in the context of the flow of mass-energy. Any actual process has causal efficacy that can propagate no faster than light. In contrast, an abstraction has no causal efficacy. Its mathematical expression does not propagate in

6048-449: The counterfactual conditional , has a stronger connection with causality, yet even counterfactual statements are not all examples of causality. Consider the following two statements: In the first case, it would be incorrect to say that A's being a triangle caused it to have three sides, since the relationship between triangularity and three-sidedness is that of definition. The property of having three sides actually determines A's state as

6160-406: The limit and uniqueness assumptions . The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single ( unique ) one that is closest to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then

6272-415: 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 X {\displaystyle X} and Z {\displaystyle Z} have common ancestors, except that one must first condition on those ancestors. Algorithms have been developed to systematically determine

6384-511: The (mentioned above) regularity, probabilistic , counterfactual, mechanistic , and manipulationist views. The five approaches can be shown to be reductive, i.e., define causality in terms of relations of other types. According to this reading, they define causality in terms of, respectively, empirical regularities (constant conjunctions of events), changes in conditional probabilities , counterfactual conditions, mechanisms underlying causal relations, and invariance under intervention. Causality has

6496-404: The absence of firefighters. Together these are unnecessary but sufficient to the house's burning down (since many other collections of events certainly could have led to the house burning down, for example shooting the house with a flamethrower in the presence of oxygen and so forth). Within this collection, the short circuit is an insufficient (since the short circuit by itself would not have caused

6608-572: The accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence. The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates Antecedent Strengthening . To see why, observe that if P → Q {\displaystyle P\rightarrow Q} holds at every world accessible from w {\displaystyle w} ,

6720-473: The actual work. AC3 requires that Alice throwing the brick is a minimal cause (cf. blowing a kiss and throwing a brick). Taking the "updated" version of AC2(a), the basic idea is that we have to find a set of variables and settings thereof such that preventing Alice from throwing a brick also stops the window from breaking. One way to do this is to stop Bob from throwing the brick. Finally, for AC2(b), we have to hold things as per AC2(a) and show that Alice throwing

6832-433: The antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true. Counterfactuals are context dependent and vague . For example, either of the following statements can be reasonably held true, though not at the same time: Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact

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6944-472: The antecedent to precede or coincide with the consequent in time, whereas conditional statements do not require this temporal order. Confusion commonly arises since many different statements in English may be presented using "If ..., then ..." form (and, arguably, because this form is far more commonly used to make a statement of causality). The two types of statements are distinct, however. For example, all of

7056-478: 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

7168-419: 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. A subgroup of

7280-1385: The best-known fictional personifications of the "past" in his short book, " A Christmas Carol ." In the story, the Ghost of Christmas Past is an apparition that shows the main character, a cold-hearted and tight-fisted man named Ebenezer Scrooge , vignettes from his childhood and early adult life to teach him that joy does not necessarily come from wealth. The past is the object of study within such fields as time , life , history , nostalgia , archaeology , archaeoastronomy , chronology , geology , historical geology , historical linguistics , ontology , paleontology , paleobotany , paleoethnobotany , palaeogeography , paleoclimatology , etymology and physical cosmology . Counterfactual conditional Counterfactual conditionals (also contrafactual , subjunctive or X-marked ) are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives , which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of fake tense morphology , which some languages use in combination with other kinds of morphology including aspect and mood . Counterfactuals are one of

7392-434: The brick breaks the window. (The full definition is a little more involved, involving checking all subsets of variables.) 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 or emphysema . As a result, many turn to a notion of probabilistic causation. Informally, A ("The person

7504-503: The case that 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

7616-417: The chain has a limit : a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption entails the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at

7728-511: The characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely. Such conditionals are also widely referred to as subjunctive conditionals , though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch ) and many that do have it do not use it for this sort of conditional (e.g. French , Swahili , all Indo-Aryan languages that have

7840-441: The conceptual frame of the scientific method , an investigator sets up several distinct and contrasting temporally transient material processes that have the structure of experiments , and records candidate material responses, normally intending to determine causality in the physical world. For instance, one may want to know whether a high intake of carrots causes humans to develop the bubonic plague . The quantity of carrot intake

7952-695: The counterfactual notion. According to the counterfactual view , X causes Y if and only if, without X, Y would not exist. Hume interpreted the latter as an ontological view, i.e., as a description of the nature of causality but, given the limitations of the human mind, advised using the former (stating, roughly, that X causes Y if and only if the two events are spatiotemporally conjoined, and X precedes Y ) as an epistemic definition of causality. We need an epistemic concept of causality in order to distinguish between causal and noncausal relations. The contemporary philosophical literature on causality can be divided into five big approaches to causality. These include

8064-428: The derivation of a cause-and-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 theory underlying these derivations relies on the distinction between conditional probabilities , as in P ( c

8176-433: The effect, is called a "contributory cause". J. L. Mackie argues that usual talk of "cause" in fact refers to INUS conditions ( i nsufficient but n on-redundant parts of a condition which is itself u nnecessary but s ufficient for the occurrence of the effect). An example is a short circuit as a cause for a house burning down. Consider the collection of events: the short circuit, the proximity of flammable material, and

8288-455: The experimenter, to do so at an unspecified time in the past", while the latter reads: "the probability of finding cancer in a person forced by the experimenter to smoke at a specified time in the past". The former is a statistical notion that can be estimated by observation with negligible intervention by the experimenter, while the latter is a causal notion which is estimated in an experiment with an important controlled randomized intervention. It

8400-423: The fire) but non-redundant (because the fire would not have happened without it, everything else being equal) part of a condition which is itself unnecessary but sufficient for the occurrence of the effect. So, the short circuit is an INUS condition for the occurrence of the house burning down. Conditional statements are not statements of causality. An important distinction is that statements of causality require

8512-508: The following definition of the notion of causal dependence : Causation is then analyzed in terms of counterfactual dependence. That is, C causes E if and only if there exists a sequence of events C, D 1 , D 2 , ... D k , E such that each event in the sequence counterfactually depends on the previous. This chain of causal dependence may be called a mechanism . Note that the analysis does not purport to explain how we make causal judgements or how we reason about causation, but rather to give

8624-417: The following statements are true when interpreting "If ..., then ..." as the material conditional: The first is true since both the antecedent and the consequent are true. The second is true in sentential logic and indeterminate in natural language, regardless of the consequent statement that follows, because the antecedent is false. The ordinary indicative conditional has somewhat more structure than

8736-410: The following three relationships hold: P{ B | A } ≥ P{ B }, P{ C | A } ≥ P{ C } and P{ B | C } ≥ P{ B }. The last relationship states that knowing that the person has emphysema increases the likelihood that he will have cancer. The reason for this is that having the information that the person has emphysema increases the likelihood that the person is a smoker, thus indirectly increasing the likelihood that

8848-422: The form "were", generally referred to as the irrealis or subjunctive form. Past perfect and irrealis counterfactuals can undergo conditional inversion : The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has

8960-493: The form of "Had C not occurred, E would not have occurred." This approach can be traced back to David Hume 's definition of the causal relation as that "where, if the first object had not been, the second never had existed." More full-fledged analysis of causation in terms of counterfactual conditionals only came in the 20th century after development of the possible world semantics for the evaluation of counterfactual conditionals. In his 1973 paper "Causation," David Lewis proposed

9072-497: The idea of Granger causality , or by direct experimental manipulation. The use of temporal data can permit statistical tests of 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 cross-correlations , ARIMA models, or cross-spectral analysis using vector time series data than by cross-sectional data . Nobel laureate Herbert A. Simon and philosopher Nicholas Rescher claim that

9184-405: The literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well. In the variably strict approach, the semantics of a conditional A > B is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other. On Lewis's account, A > C

9296-497: The market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis. The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula ◻ ( P → Q ) {\displaystyle \Box (P\rightarrow Q)} . In this formula, ◻ {\displaystyle \Box } expresses necessity and → {\displaystyle \rightarrow }

9408-410: The material conditional. For instance, although the first is the closest, neither of the preceding two statements seems true as an ordinary indicative reading. But the sentence: intuitively 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,

9520-430: The maximal sets of these formulae that are consistent with A , and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets. Languages use different strategies for expressing counterfactuality. Some have

9632-473: The metric of 'closeness' to be simply our ordinary notion of overall similarity . Example: On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am. Stalnaker's account differs from Lewis's most notably in his acceptance of

9744-465: The monotonicity of the material conditional guarantees that P ∧ R → Q {\displaystyle P\land R\rightarrow Q} will be too. Thus, we will have that ◻ ( P → Q ) ⊨ ◻ ( P ∧ R → Q ) {\displaystyle \Box (P\rightarrow Q)\models \Box (P\land R\rightarrow Q)} . This fact led to widespread abandonment of

9856-689: The most studied phenomena in philosophical logic , formal semantics , and philosophy of language . They were first discussed as a problem for the material conditional analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic possible world approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as causal models and dynamic semantics . Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of

9968-434: The natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by Judea Pearl (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems. In the belief revision framework, counterfactuals are treated using

10080-430: The notion of causality is metaphysically prior to the notions of time and space. In practical terms, this is because use of the relation of causality is necessary for the interpretation of empirical experiments. Interpretation of experiments is needed to establish the physical and geometrical notions of time and space. The deterministic world-view holds that the history of the universe can be exhaustively represented as

10192-414: The offices of those who have previously served in an organization, group, or event such as, "past president," or, "past champions." "Past" can also refer to something or someone being at or in a position that is further than a particular point. For instance, in the sentence, "I live on Fielding Road, just past the train station," the word "past" is used to describe a location (the speaker's residence) beyond

10304-440: The one nearest to the concerns of the present article is the "efficient" one. David Hume , as part of his opposition to rationalism , argued that pure reason alone cannot prove the reality of efficient causality; instead, he appealed to custom and mental habit, observing that all human knowledge derives solely from experience . The topic of causality remains a staple in contemporary philosophy . The nature of cause and effect

10416-426: The ordinary sense of the word, though it may refer to virtual or nominal 'velocities' with magnitudes greater than that of light. For example, wave packets are mathematical objects that have group velocity and phase velocity . The energy of a wave packet travels at the group velocity (under normal circumstances); since energy has causal efficacy, the group velocity cannot be faster than the speed of light. The phase of

10528-459: The past tense do not convey their typical temporal meaning, they are called fake past or fake tense . English is one language which uses fake past to mark counterfactuality, as shown in the following minimal pair . In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with

10640-414: The person will have cancer. However, we would not want to conclude that having emphysema causes cancer. Thus, we need additional conditions such as temporal relationship of A to B and a rational explanation as to the mechanism of action. It is hard to quantify this last requirement and thus different authors prefer somewhat different definitions. When experimental interventions are infeasible or illegal,

10752-440: The process theories is the mechanistic view on causality. It states that causal relations supervene on mechanisms. While the notion of mechanism is understood differently, the definition put forward by the group of philosophers referred to as the 'New Mechanists' dominate the literature. For the scientific investigation of efficient causality, the cause and effect are each best conceived of as temporally transient processes. Within

10864-473: The properties of antecedence and contiguity. These are topological, and are ingredients for space-time geometry. As developed by Alfred Robb , these properties allow the derivation of the notions of time and space. Max Jammer writes "the Einstein postulate ... opens the way to a straightforward construction of the causal topology ... of Minkowski space." Causal efficacy propagates no faster than light. Thus,

10976-407: The resultant insights to fields including history, marketing, and epidemiology. An example of the difference between indicative and counterfactual conditionals is the following English minimal pair : These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "owns" and therefore conveys that the speaker is agnostic about whether Sally in fact owns

11088-413: The sentence " Y would be y had X been x " (formally, X = x > Y = y ) is defined as the assertion: If we replace the equation currently determining X with a constant X = x , and solve the set of equations for variable Y , the solution obtained will be Y = y . This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in

11200-488: The sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea

11312-403: The single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup

11424-660: 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 analyzing time series data or, preferably, designing appropriately controlled experiments . In contrast with Bayesian Networks, path analysis (and its generalization, structural equation modeling ), serve better to estimate

11536-443: The strict conditional comes from Irene Heim's observation that Sobel Sequences are generally infelicitous (i.e. sound strange) in reverse. Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in

11648-416: The strict conditional, in particular in favor of Lewis's variably strict analysis . However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that Sobel sequences do not demand a non-monotonic logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as

11760-427: The time-directedness of counterfactual dependence in terms of the semantics of the counterfactual conditional. If correct, this theory can serve to explain a fundamental part of our experience, which is that we can causally affect the future but not the past. One challenge for the counterfactual account is overdetermination , whereby an effect has multiple causes. For instance, suppose Alice and Bob both throw bricks at

11872-486: The word "cause" is used as a specialized technical term, the translation of Aristotle 's term αἰτία, by which Aristotle meant "explanation" or "answer to a 'why' question". Aristotle categorized the four types of answers as material, formal, efficient, and final "causes". In this case, the "cause" is the explanans for the explanandum , and failure to recognize that different kinds of "cause" are being considered can lead to futile debate. Of Aristotle's four explanatory modes,

11984-663: The word "past" was in the fourteenth century; it developed as the past participle of the Middle English verb passen meaning "to pass." In English grammar , actions are classified according to one of the following twelve verb tenses: past (past, uses of English verb forms , past perfect , or past perfect continuous ), present ( present , present continuous , present perfect , or present perfect continuous ), or future ( future , future continuous , future perfect , or future perfect continuous ). The past tense refers to actions that have already happened. For example, "she

12096-451: The world. Some attempts to defend manipulability theories are recent accounts that do not claim to reduce causality to manipulation. These accounts 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

12208-426: The world. However, in the 1960s and 1970s, work by Robert Stalnaker and David Lewis showed that these problems are surmountable given an appropriate intensional logical framework. Work since then in formal semantics , philosophical logic , philosophy of language , and cognitive science has built on this insight, taking it in a variety of different directions. According to the material conditional analysis,

12320-711: Was developed by Rebane and Pearl (1987) which rests on Wright's 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., X {\displaystyle X} and Z {\displaystyle Z} are independent given Y {\displaystyle Y} ) and are, therefore, indistinguishable within purely cross-sectional data . Type 3, however, can be uniquely identified, since X {\displaystyle X} and Z {\displaystyle Z} are marginally independent and all other pairs are dependent. Thus, while

12432-474: Was happening (when "I met her"). Depending on its usage in a sentence, "past" can be described using a variety of terms. Synonyms for "past" as an adjective include, "former," "bygone," "earlier," "preceding," and "previous." Synonyms for "past" as a noun include, "history, "background," "life story," and "biography." Synonyms of "past" as a preposition include, "in front of," "beyond," "by," and "in excess of." The word "past" can also be used to describe

12544-503: Was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality. Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of dynamic semantics , and given a number of linguistic arguments in favor. One argument is that conditional antecedents license negative polarity items , which are thought to be licensed only by monotonic operators. Another argument in favor of

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