Causality is a fascinating topic and one I hope to learn more about, perhaps via the Pearl book Tim mentioned or another that someone might recommend. Here are some very random and disorganized thoughts on the topic.
Googling on "causality" led to a brief web page that summarized 2000 years of philosophical thought in a few paragraphs, http://www.helsinki.fi/~mqsalo/documents/causalit.htm. Generally there seem to be two schools of thought; one is that causality is an artifact of our minds' efforts to understand and interpret the world; the other is that causality has objective reality. The modern philosopher's definition of causality has always struck me as somewhat backwards: "The cause of any event is a preceding event without which the event in question would not have occurred." This means that "A causes B" is equivalent to A happening before B, plus the logical proposition, "if B then A". You'd think that A causes B would mean "if A then B". But philosophers interpret it to mean "if not-A then not-B", as stated above (I've read this elsewhere also), which is equivalent to "if B then A". So if we say "heavy rains cause flooding" we mean that if there were no heavy rains then there would be no flooding; or equivalently, if there is flooding then there must have been heavy rains. This is consistent with there being heavy rains and no flooding. It really doesn't make sense to me. The problem with judging causality is the well known cautionary rule that "correlation is not causation". Just because A and B always occur together, and A comes before B, that doesn't mean that A causes B. This is a common danger that scientific researchers have to guard against. It's easy to observe correlation but hard to determine what is the true cause. This is a reason to view causality as just a matter of our perceptions. A strange aspect of causality is that to a large degree our laws of physics appear to be time symmetric. This means that you can reverse the time sequence of events and get a physically valid (although possibly unlikely) scenario. If that is so, then if A causes B in the forward direction, can we with equal validity say that B causes A when we look at things backwards? In that case the causal roles are fundamentally arbitrary. Of course in most situations we have a strong arrow of time based on the growth of entropy which allows us to break this apparent symmetry. But this is not always the case. Systems in thermodynamic equilibrium, if considered in isolation, have no arrow of time. We can look at a microscopic part of such a system and see fluctuations which appear to be describable in causal terms. For example, a temporary void forms randomly, causing matter at the edges to move towards the center. Or in reverse we say that matter moved away from the center, causing a void to form. Both are equally valid ways of describing the situation, indicating that there is no true causality. The real mystery is why our physical laws are time symmetric. A priori it does not seem to be absolutely necessary for life to evolve. I mean, of all sets of physical laws that allow life to evolve, will most be time symmetric? I'm not aware of any reason why this should be the case. One final point regarding causality. Although it seems to be more a matter of metaphysics than physics, there are some places where people take causality to be a fundamental part of physical reality. Specifically, this is done in some theories of consciousness. Functionalists adopt essentially the view that Bruno calls COMP, that consciousness is a computational phenomenon and any system which implements the corresponding computation will be conscious. This is the foundation for ideas of "uploading", that is, brain simulation by computer. Functionalists believe such simulations are conscious in the same way that the brain was, provided that the simulation is performing the same computation that the brain did. This then raises the question of whether a particular physical system (like a computer) is implementing a particular computation (which is an abstract program, perhaps expressed in some computing language). Surprisingly, this is a difficult and yet unsolved question in philosophy. No one has ever come up with a widely accepted, hard and fast rule or procedure to decide whether a physical system is implementing a given computation. Broadly speaking, the basic approach is to set up a mapping or correspondence between aspects of the physical system and aspects of the abstract computation. For example, with today's computers the registers and memory elements work by holding electrical charge. One could map these charge concentrations to values of variables in the abstract representation of the computation and there would be a good correspondence. This works well in this case, but there are two problems. The first is that it does not capture the causal nature of the program. A computer which was not actually computing, but just playing back a recorded pattern of charge distributions, would successfully satisfy the mapping. I'll say more about this in a moment. The second problem is that by making the mapping more elaborate, one can show that simple, even trivial systems are implementing complex computations; essentially you do all the work in the mapping. It's hard to set up a concrete rule for how complex the mapping can be, and I don't believe anyone has succeeded in this yet. But the more relevant problem for now is the issue of causality. Most functionalist philosophers believe that for a physical system to be truly implementing a computation, it must include all of the causality of that computation and not just "passively" reproduce the patterns. When we apply this rule to the functionalist model of consciousness, it works out like this: if a system has the right causality, it is conscious; if it is only passive, it is not conscious. This elevates causality to having a functional role in the physical world! It makes the difference between a system having a mind and just being an elaborate tape recorder. It means that we cannot view causality as just an artifact of our perceptions, it must be a true element of reality. That would put significant constraints on how philosophers treat the concept of causality. Anyway, these are some of the issues and musings which make causality of great interest to me. I hope to learn more about it in the next few years. Hal Finney