The fresh ideas canvassed in this point every build the essential suggestion that triggers improve the likelihood of their outcomes. This type of concepts was indeed one of several best concepts out-of causation when you look at the last half of one’s 20 th century. Now, he’s got largely already been supplanted by causal modeling tactics chatted about inside Point 3.
2.1 Likelihood-increasing and you will Conditional Possibilities
The new central indisputable fact that 
reasons enhance the odds of its consequences is indicated formally playing with conditional likelihood. C enhances the likelihood of Age of course, if:
Into the conditions, the probability one to Elizabeth happens, given that C happens, is higher than brand new unconditional likelihood you to Age occurs. Alternately, we would point out that C enhances the probability of Age just however, if:
your chances that Age happen, given that C happen, is higher than the probability that Elizabeth happen, as the C does not exist. These preparations grow to be equivalent in the same manner one inequality \(\PR_1\) often keep whenever \(\PR_2\) holds. Some article writers (age.grams., Reichenbach 1956, Suppes 1970, Cartwright 1979) have invented probabilistic ideas out of causation using inequalities eg \(\PR_1\), other people (elizabeth.grams., Skyrms 1980, Eells 1991) used inequalities particularly \(\PR_2\). This change is certainly caused by immaterial, but for consistency we’ll stay glued to (\(\PR_2)\). Thus a primary stab during the good probabilistic concept from causation perform be:
PR has some advantages over the simplest version of a regularity theory of causation (discussed in Section 1.1 above). PR is compatible with imperfect regularities: C may raise the probability of E even though instances of C are not invariably followed by instances of E. Moreover, PR addresses the problem of relevance: if C is a cause of E, then C makes a difference for the probability of E. But as it stands, PR does not address either the problem of asymmetry, or the problem of spurious correlations. PR does not address the problem of asymmetry because probability-raising turns out to be symmetric: \(\PP(E \mid C) \gt \PP(E \mid <\nsim>C)\), if and only if \(\PP(C \mid E) \gt \PP(C \mid <\nsim>E)\). Thus PR by itself cannot determine whether C is the cause of E or vice versa. PR also has trouble with spurious correlations. If C and E are both caused by some third factor, A, then it may be that \(\PP(E \mid C) \gt \PP(E \mid <\nsim>C)\) even though C does not cause E. This is the situation shown in Figure 1 above. Here, C is the drop in the level of mercury in a barometer, and E is the occurrence of a storm. Then we would expect that \(\PP(E \mid C) \gt \PP(E \mid <\nsim>C)\). In this case, atmospheric pressure is referred to as a confounding factor.
dos.2 Evaluation of
Hans Reichenbachs New Guidance of energy is composed posthumously in the 1956. With it, Reichenbach is worried into roots from temporally asymmetric phenomena, particularly the boost in entropy determined of the second laws of thermodynamics. Within works, he merchandise the first completely arranged probabilistic theory regarding causation, while some of the suggestions shall be traced to an prior to report off 1925 (Reichenbach 1925).
In the event that \(\PP(Age \middle A great \amplifier C) = \PP(Age \middle C)\), following C is considered so you’re able to screen Good off from Elizabeth. Whenever \(\PP(A good \amp C) \gt 0\), it equivalence is the same as \(\PP(A \amplifier E \mid C) = \PP(A good \middle C) \minutes \PP(Age \middle C)\); i.elizabeth., Good and you will Elizabeth was probabilistically separate conditional upon C.
Reichenbach acknowledged there had been two categories of causal framework inside the and therefore C tend to typically display An excellent off from Elizabeth. The first occurs when A power C, which causes Elizabeth, and there’s hardly any other channel otherwise processes which An excellent outcomes Elizabeth. It is shown for the Profile dos.