Probabilistic causality
This is post7 in a sequence exploring formalisations of causality entitled “Reasoning with causality”.
Many of the posts on this blog in relation to causality have a hidden assumption: Namely, that causality is inherently probabilistic (though many of the posts are still just as relevant whether this is accepted or not). However, this goes against the mainstream view. This post will summarise part of the paper Varieties of Causal Intervention which argues against the mainstream.
Deterministic causality
Judea Pearl, one of the principle researchers in the area of causality, has argued that causality should be interpreted deterministically for the following reasons:
 The deterministic interpretation is the more intuitive one.
 Deterministic interpretations are more general as any indeterministic interpretation can be modelled as a deterministic one.
 A deterministic causality is needed to make sense of counterfactuals and causal explanation.
This post is going to ignore the first point (intuitive doesn’t mean right) and will explore possible responses to the other two.
Deterministic causality as the more general theory
Imagine a system where both A and B have a causal influence on C. We can model that as the following equation:
C = dA + eB + U
This says that C is influenced to degree d by A and degree e by B. It also says that C isn’t entirely determined by A and B but there is some degree of variation. By adding U in, a case that was originally indeterministic has become deterministic. However, that doesn’t mean the causal system being modelled is in fact deterministic unless U is a part of the system. Given that, in practice, U is normally defined as that which is left over, claiming this as part of the system seems to be reasonable only if we presume from the start that the system is deterministic.
Given that indeterminstic worlds are consistent, it seems to be an a posteriori question to determine whether causality should be deterministic or indeterministic and hence such an a priori assumption seems unwarranted.
Even if you don’t buy all that, there’s a further point: This process can be applied two ways. This means that any indeterminstic system can be modelled as a deterministic one but any deterministic one can also be modelled as an indeterministic one.
Neither way is more general.
Indeterministic causality and causal explanation
In a previous post I discussed an approach by the same author to type and token causality that claims to present an indeterministic account of causal explanation. As such, the third of the problems listed above seems to be solved.
The next post is Categories and types of intervention

December 24, 2010 at 12:56 amUses of Bayes Nets in causality: Modeling type and token causal relevance « Formalised Thinking