Sign up. Publications Pages Publications Pages. Recently viewed 0 Save Search. Users without a subscription are not able to see the full content. Causality and Explanation. Find in Worldcat. Go to page:. Your current browser may not support copying via this button. Search within book. Find in Worldcat. Go to page:.
Your current browser may not support copying via this button. Search within book. Subscriber sign in You could not be signed in, please check and try again. Username Please enter your Username. Password Please enter your Password. Forgot password? You could not be signed in, please check and try again. Sign in with your library card Please enter your library card number. Don't have an account? Signup here. Probabilistic Causation.
The essence of probabilistic causation is not that one factor causes another to happen, but rather one factor increases the likelihood of another event happening, all else being equal. Probabilistic Causation is often confused with general a deterministic relationship.
We may define a cause to be an object, followed by another, and where all the objects similar to the first, are followed by objects similar to the second. There are a number of well-known problems facing regularity theories, at least in their simplest forms, and these may be used to motivate probabilistic approaches to causation. Moreover, an overview of these difficulties will help to give a sense of the kinds of problem that any adequate theory of causation would have to solve.
The first difficulty is that most causes are not invariably followed by their effects. For example, smoking is a cause of lung cancer, even though some smokers do not develop lung cancer. Imperfect regularities may arise for two different reasons. First, they may arise because of the heterogeneity of circumstances in which the cause arises.
For example, some smokers may have a genetic susceptibility to lung cancer, while others do not; some non-smokers may be exposed to other carcinogens such as asbestos , while others are not. Second, imperfect regularities may also arise because of a failure of physical determinism. If an event is not determined to occur, then no other event can be or be a part of a sufficient condition for that event.
The success of quantum mechanics—and to a lesser extent, other theories employing probability—has shaken our faith in determinism. Thus it has struck many philosophers as desirable to develop a theory of causation that does not presuppose determinism. The central idea behind probabilistic theories of causation is that causes change the probability of their effects; an effect may still occur in the absence of a cause or fail to occur in its presence.
Thus smoking is a cause of lung cancer, not because all smokers develop lung cancer, but because smokers are more likely to develop lung cancer than non-smokers.
This is entirely consistent with there being some smokers who avoid lung cancer, and some non-smokers who succumb to it. A condition that is invariably followed by some outcome may nonetheless be irrelevant to that outcome. Salt that has been hexed by a sorcerer invariably dissolves when placed in water Kyburg , but hexing does not cause the salt to dissolve.
Hexing does not make a difference for dissolution. Probabilistic theories of causation capture this notion of making a difference by requiring that a cause make a difference for the probability of its effect.
If A causes B , then, typically, B will not also cause A. Smoking causes lung cancer, but lung cancer does not cause one to smoke.
One way of enforcing the asymmetry of causation is to stipulate that causes precede their effects in time. But it would be nice if a theory of causation could provide some explanation of the directionality of causation, rather than merely stipulate it. Some proponents of probabilistic theories of causation have attempted to use the resources of probability theory to articulate a substantive account of the asymmetry of causation.
Suppose that a cause is regularly followed by two effects. Here is an example from Jeffrey : Suppose that whenever the barometric pressure in a certain region drops below a certain level, two things happen. First, the height of the column of mercury in a particular barometer drops below a certain level.
Shortly afterwards, a storm occurs. This situation is shown schematically in Figure 1. Then, it may well also be the case that whenever the column of mercury drops, there will be a storm. If so, a simple regularity theory would seem to rule that the drop of the mercury column causes the storm. In fact, however, the regularity relating these two events is spurious. The ability to handle such spurious correlations is probably the greatest source of attraction for probabilistic theories of causation.
In this sub-section, we will review some of the basics of the mathematical theory of probability, and introduce some notation. Readers already familiar the mathematics of probability may wish to skip this section. Probability is a function, P, that assigns values between zero and one, inclusive. Usually the arguments of the function are taken to be sets, or propositions in a formal language.
Sometimes when there is a long conjunction, this is abbreviated by using commas instead of ampersands. The domain of a probability function has the structure of a field or a Boolean algebra. This means that the domain is closed under complementation and the taking of finite unions or intersections for sets , or under negation, conjunction, and disjunction for propositions. In addition to probability theory, the entry will use basic notation from set theory and logic.
Sets will appear in boldface. We will ignore this problem here. As a convenient shorthand, a probabilistic statement that contains only a variable or set of variables, but no values, will be understood as a universal quantification over all possible values of the variable s. Causal relations are normally thought to be objective features of the world.
If they are to be captured in terms of probability theory, then probability assignments should represent some objective feature of the world. There are a number of attempts to interpret probabilities objectively, the most prominent being frequency interpretations and propensity interpretations.
Most proponents of probabilistic theories of causation have understood probabilities in one of these two ways. Notable exceptions are Suppes , who takes probability to be a feature of a model of a scientific theory; and Skyrms , who understands the relevant probabilities to be the subjective probabilities of a certain kind of rational agent.
It is common to distinguish between general , or type-level causation, on the one hand, and singular , token-level or actual causation, on the other. This entry adopts the terms general causation and actual causation. C and E are the relata of the causal claim; we will discuss causal relata in more detail in the next section. General causation and actual causation are often distinguished by their relata.
This is an imperfect guide, however; for example, some theories of general causation to be discussed below take their causal relata to be time-indexed. A related distinction is that general causation is concerned with a full range of possibilities, whereas actual causation is concerned with how events actually play out in a specific case.
The theories to be discussed in Sections 2 and 3 below primarily concern general causation, while Section 4 discusses theories of actual causation.
A number of different candidates have been proposed for the relata of causal relations. The relata of actual causal relations are often taken to be events not to be confused with events in the purely technical sense , although some authors e. The relata of general causal relations are often taken to be properties or event-types.
For purposes of definiteness, events will refer to the relata of actual causation, and factors will refer to the relata of general causation. These terms are not intended to imply a commitment to any particular view on the nature of the causal relata. In probabilistic approaches to causation, causal relata are represented by events or random variables in a probability space.
Since the formalism requires us to make use of negation, conjunction, and disjunction, the relata must be entities or be accurately represented by entities to which these operations can be meaningfully applied. In some theories, the time at which an event occurs or a property is instantiated plays an important role. In such cases, it will be useful to include a subscript indicating the relevant time. If the relata are particular events, this subscript is just a reminder; it adds no further information.
In the case of properties or event-types, however, such subscripts do add further information. The time index need not refer to a date or absolute time. It could refer to a stage in the development of a particular kind of system.
For example, exposure to lead paint in children can cause learning disabilities. Here the time index would indicate that it is exposure in children , that is, in the early stages of human life, that causes the effect in question. The time indices may also indicate relative times.
Exposure to the measles virus causes the appearance of a rash approximately two weeks later. It is standard to assume that causes and effects must be distinct from one another. This means that they must not stand in logical relations or part-whole relations to one another.
Lewis a contains a detailed discussion of the relevant notion of distinctness. We will typically leave this restriction tacit. Psillos provides an overview of regularity theories of causation. Lewis contains a brief but clear and forceful overview of problems with regularity theories. The entry for scientific explanation contains discussions of some of these problems. Billingsley and Feller are two standard texts on probability theory.
The entry for interpretations of probability includes a brief introduction to the formalism of probability theory, and discusses the various interpretations of probability.
Galavotti and Gillies are good surveys of philosophical theories of probability. The Introduction of Eells provides a good overview of the distinction between general and actual causation. Bennett is an excellent discussion of facts and events in the context of causation. Ehring is a survey of views about causal relata. See also the entries for the metaphysics of causation , events , facts , and properties. The theories canvassed in this section all develop the basic idea that causes raise the probability of their effects.
These theories were among the leading theories of causation during the second half of the 20 th century. Today, they have largely been supplanted by the causal modeling approaches discussed in Section 3. The central idea that causes raise the probability of their effects can be expressed formally using conditional probability. C raises the probability of E just in case:. In words, the probability that E occurs, given that C occurs, is higher than the unconditional probability that E occurs.
Alternately, we might say that C raises the probability of E just in case:. Some authors e. Thus a first stab at a probabilistic theory of causation would be:. PR has some advantages over the simplest version of a regularity theory of causation discussed in Section 1.
0コメント