Hi. I have to say I strongly disagree with your categorical assertions that a formal theory of causality does not exist. Many readers of this list know very well the work of researchers, Simon, Pearl, Spirtes, Glymour, Scheines and many others that have developed exactly such formalisms, and I don't believe that you have presented any example below of a causal system that cannot be satisfactorily modeled by them.
Granted, the theory behind these formalisms is probably not complete, but much has been accomplished in developing a formal representation of causality. In particular: > -----Original Message----- > From: Lotfi A. Zadeh <[EMAIL PROTECTED]> > To: [EMAIL PROTECTED] > Subject: Re: [UAI] causal_or_functional models? > > The problem is that causality is not a bivalent concept-as > it is commonly assumed to be in attempts at formalization. Causality is > a matter of degree. Here are a few simple examples which illustrate the > point. > > I am a manufacturer of raincoats. To increase sales, I > increased the advertising budget by 20%. Sales went up by 10%. Was the > increase in sales caused by the increase in advertising? If so, to what > degree? The question cannot be answered because the increase in sales is > the top of an iceberg. Other events -some visible and some not- which may > have played a role were rainy weather, bankruptcy of a competitor, > improved styling, and so on ad infinitum. In this setting, how can a > degree of causality be associated with the designated events: (a) > increase in the advertising budget; and (b) increase in sales. There is > no theory which can answer this question. What you are presenting here is an example of how difficult it is to build a causal model from observations. There is no denying that the real world is complex, and any model of a complex system requires an expert which understands very well the underlying mechanisms of that system...causal models are no different in that respect from any other types of mathematical models of reality. However, there _are_ many theories that can answer that questions and they can be formalized in terms of causality, no problem. > The same problem arises in identifying the cause of death in > a death certificate. It has to be done by law, but every doctor knows > that what is done is a very crude approximation to a complex reality. Your point here is that all mathematical models are a simplification of reality. This has nothing to do with the causal nature of the models. > Causality can be treated-and has been treated rigorously-in > physics, system theory and related fields. But in human-centered > systems, this is not the case. In fact, in the realm of such systems it > is hard to find instances in which an assertion of causality is beyond > question. Example: George shot and killed John. Did George cause John's > death? At first glance, it appears that the answer is "yes." But suppose > that George was hired by Tom to kill John. Given this information, to > what degree, if any, did Tom cause John's death. Questions like this > pervade legal reasoning, but there is no theory to resolve them. Sociologists, econometricians, and psychologists are among the researchers who are most devoted to formal causal models. Your example above can easily be modeled using a directed causal graph: Tom -> George -> John. In words: "Tom caused George to kill John". George is the direct cause of John's death, Tom is an indirect cause. In this model, if George is prevented from killing John, then so is Tom, because Tom only kills John through the causal path that goes through George. That is exactly how most people would attribute the cause and effects of this situation and it is easily modeled and reasoned about using a causal diagram. Cheers, Denver.
