Online research in philosophy

Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.

I offer one possible explanation of why inertial and gravitational mass are equal in Newtonian gravitation. I then argue that the explanation given is an example of a kind of explanation that is not captured by standard philosophical accounts of scientific explanation. Moreover, this form of explanation is particularly important, at least in physics, because demands for this kind of explanation are used to motivate and shape research into the next generation of physical theories.

Recent discussions in the philosophy of science have devoted considerable attention to the analysis of conceptual issues relating to the methodology of explanation and prediction in the sciences. Part of this literature has been devoted to clarifying the very ideas of explanation and prediction. But the discussion has also ranged over various related topics, including the status of laws to be used for explanatory and predictive purposes, the logical interrelationships between explanatory and predictive reasonings, the differences in the strategy of explanatory argumentation in different branches of science, the nature and possibility of teleological explanation, etc. The aim of the present article is to examine the issues involved in such questions from the specialized perspective afforded by one particular kind of physical systems--namely, systems, here to be characterized as discrete state systems, whose behavior has been studied extensively in the scientific literature under the general heading of Markov chains. These systems have been chosen as our focus because their behavior over time can be analyzed at once with great ease and with extraordinary precision.

For the case of statistical theories, the criteria of explanation, prediction, and testability can all be viewed as particular instances of a more general evaluation scheme. Using the ideas of a gain matrix and expected gain from statistical decision theory, these three criteria can be compared in terms of the elements in their associated gain matrices. This analysis leads to (1) further understanding of the interrelationship between the current criteria, (2) the proposal of an ordering for the criteria, and (3) the suggestion of a new criterion.

Scientific explanation in terms of laws and initial conditions (or better, in terms of objects with powers and liabilities) is contrasted with personal explanation in terms of agents with powers and purposes. In each case the factors involved in explanation may themselves be explained, and infinite regress of explanation is logically possible. There can be no absolute explanation of phenomena, which is explanation in terms of the logically necessary; but there can be ultimate explanation which is explanation in terms of factors which themselves have no explanation. Our normal criteria of explanation suggest that the explanation of the universe lies in the action of God.

We present a logically detailed case-study of explanation and prediction in Newtonian mechanics. The case in question is that of a planet’s elliptical orbit in the Sun’s gravitational field. Care is taken to distinguish the respective contributions of the mathematics that is being applied, and of the empirical hypotheses that receive a mathematical formulation. This enables one to appreciate how in this case the overall logical structure of scientific explanation and prediction is exactly in accordance with the hypotheticodeductive model.

The paper has two main aims. The first is to reformulate Hempel's version of the thesis of the symmetry of explanation and prediction, as regards the deductive covering-law model, so as to generalise it and make it no longer subject to some of the criticisms which have been directed at it (Section II). The second aim is to consider, with special critical reference to Hempel's recent treatment in Aspects of Scientific Explanation (New York and London, 1965), some central criticisms of both the constituent parts of the above symmetry thesis, viz. that adequate explanations are potentially predictive (Section III), and that adequate predictive arguments are potentially explanatory (Section IV).

The distinction between explanation and prediction has received much attention in recent literature, but the equally important distinction between explanation and description (or between prediction and description) remains blurred. This latter distinction is particularly important in the social sciences, where probabilistic models (or theories) often play dual roles as explanatory and descriptive devices. The distinction between explanation (or prediction) and description is explicated in the present paper in terms of information theory. The explanatory (or predictive) power of a probabilistic model is identified with information taken from (or transmitted by) the environment (e.g., the independent, experimentally manipulated variables), while the descriptive power of a model reflects additional information taken from (or transmitted by) the data. Although information is usually transmitted by the data in the process of estimating parameters, it turns out that the number of free parameters is not a reliable index of transmitted information. Thus, the common practice of treating parameters as degrees-of-freedom in testing probabilistic models is questionable. Finally, this information-theoretic analysis of explanation, prediction, and description suggests ways of resolving some recent controversies surrounding the pragmatic aspects of explanation and the so-called structural identity thesis.

The three cardinal aims of science are prediction, control, and explanation; but the greatest of these is explanation. Also the most inscrutable: prediction aims at truth, and control at happiness, and insofar as we have some independent grasp of these notions, we can evaluate science’s strategies of prediction and control from the outside. Explanation, by contrast, aims at scientific understanding, a good intrinsic to science and therefore something that it seems we can only look to science itself to explicate.

Perhaps because both explanation and prediction are key components to understanding, philosophers and psychologists often portray these two abilities as though they arise from the same competence, and sometimes they are taken to be the same competence. When explanation and prediction are associated in this way, they are taken to be two expressions of a single cognitive capacity that differ from one another only pragmatically. If the difference between prediction and explanation of human behavior is merely pragmatic, then anytime I predict someone’s future behavior, I would at that moment also have an explanation of the behavior. I argue that advocates of both the theory theory and the simulation theory accept the symmetry of psychological prediction and explanation. However, there is very good reason to believe that this hypothesis is false. Just as we can predict the occurrence of some physical phenomena that we have no explanation for, we are also able to make accurate predictions of intentional behavior without having an explanation. Rather than requiring mental state attribution, I argue that the prediction of human behavior is most often accomplished by statistical induction rather than through an appeal to mental states. However, explanations are not given in these terms.