It is important for philosophers to be familiar with and to know the formal and technical developments by mathematicians and statisticians. It is unfortunate that there has been a tendency for philosophers to pursue their own special formalisms that do not relate well to the mainstream of work. Such formalisms tend to be, from a mathematical and conceptual standpoint, too elementary to come to grips with complex problems of applications or to offer sufficient complexity of structure to handle the main problems of interest to those pursuing technical issues. What seems to me to be the right role for philosophers in these matters is to be able to comment on and to use the concepts that are actively developed in most cases by others. I do not see as viable a special philosophical approach to probability, and my views on this matter are consonant with what I think about other issues in the philosophy of science or in philosophy generally.

Causality

Because my own approach to causality is probabilistic in character, I have included it in this section. It is hard to think of a philosophical topic that has received more attention historically than that of causality. It has already become clear to me that what I have had to say (1970a) has got to be extended, revised, and deepened, in order to meet objections that have been made by other people and to account for a variety of phenomena that I did not consider in any detail. Causality is one of those concepts that plays a major role in a variety of scientific disciplines and that can be clarified and enriched by extensive philosophical analysis. On some subjects of a probabilistic kind I find it hard to imagine how I, or another philosopher, could improve in a substantial way on what has been said with clarity and precision by probabilists and statisticians—the concept of a stochastic process is a good example. This is not true of the concept of causality. A good many statisticians use the concept in various ways in their research and writing, and the concept has been a matter of controversy both in the physical sciences and in the social sciences over the past several decades. There is a major place in these discussions for philosophical analyses of causality that join issue firmly and squarely with this extensive scientific literature.

A recent article by Woods and Walton (1977) emphasizes a point that is something of a minor scandal in philosophy. This is the absence of clear and definite elementary principles for accepting or rejecting a causal relation. The teaching of elementary logic depends upon extensive use of material implication and other truth-functional sentential connectives, in much the same way that beginning students of physics are taught Newtonian and not relativistic mechanics. We unfortunately do not at the present time have the same tradition in philosophy about a range of concepts that lie outside of formal logic. Causality is perhaps the prime example. I mention the point as a matter of pedagogy but in fact it is a matter of philosophy proper, because there has not been sufficient development or agreement about the developments that have taken place to provide a set of transparent systematic concepts that can be used in introductory teaching.

There are one or two systematic points about causality I would like to comment on here without entering into technical details The first is the objection to my characterization of causality in terms of probability. A standard remark about this characterization is that all kinds of spurious relations will satisfy the definition of prima facie cause. According to my formulation, an event A is a prima facie cause of event B if A occurs earlier than B and the conditional probability of B given A is greater than the unconditional probability of B alone. It is properly pointed out that many kinds of events are connected in the sense of this definition by a prima facie causal relation, for example, the lowering of the barometer and the rain that follows, and yet we all immediately reject the falling of the barometer as a prima face cause of the rain. I see the situation here as no different from that which applies to logical inference. The machinery is set up to be indifferent to our intuitive facts about the world, so that we can make logical inferences that seem silly. Standard examples are easy to give and are familiar to everybody. The same point is not as easily accepted about causality, but it is my claim that this is a virtue and not a defect of a general theory of causality. It should be universally applicable; intuitive counterexamples simply reflect the fact that the formal theory is indifferent as to what intuitive knowledge or substantive theory is being called upon.

Moreover, the full formal theory has appropriate devices for eliminating falling barometers as causes of rain. The standard notion to use here is that of a spurious cause. Showing that other events account for the change in conditional probability when the barometer is not present or broken provides the intuitive evidence we all accept for the absence of a causal relation between falling barometers and rainfall. The second point, related to this one, is that the notion of spurious cause itself and the closely related one of genuine cause must be relativized to a particular conceptual framework. This is made especially clear when one wants to prove a theorem about causality within the framework of a particular scientific theory. In my 1970 monograph I did not make the relativization to a particular framework an explicit part of the definitions. It is obvious how this can be done and perhaps in many cases it should be done. I do think that the insistence on relativizing the analysis of cause to a particular conceptual framework is a point on which to make a stand. Absolutists, who think they know the full truth and do not need such relativization, have the burden of providing forceful examples. I know of no interesting ones myself. I take this point as no different than the point that the systematic formal concept of truth is relative to a model and not in any sense appropriate to reality taken straight.