The first main qualification of the basic probability-increase idea of probabilistic causation, explained in Chapter 1, is the relativity of the causal relation to a given token population, considered to be of a given (appropriate) kind that the population exemplifies. The second main qualification of the basic probability-increase idea, to be explored in this chapter, involves the possibility of what has been called “spurious correlation.” Of course, what is meant by saying that a factor X raises the probability of a factor X is that Pr(Y/X) > Pr(Y) – equivalently, Pr(Y/X) > Pr(Y/∼X) Another way of expressing this relation is to say that Y is positively probabilistically correlated with X. It is famous that “correlation is no proof of causation,” and it is also true that causation does imply correlation. The possibility of spurious correlation is one reason why.
In this book, I will actually explore in detail three general ways in which probability increase may fail to coincide with causation, and I will show how the probability-increase idea of causation should be adjusted to accommodate these three possibilities. After briefly describing the three possibilities below, this chapter will concentrate on one of them, the one called “spurious correlation.” The other two will be dealt with in subsequent chapters.
One simple way to see that probability increase does not imply causation is to notice that the relation of positive correlation is symmetric. If X raises the probability of Y, then Y raises the probability of X.
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