What is the ‘covering law’ model of scientific explanation and what are two reasons it seems to be defective? How do these defects point to a better model of scientific explanation?

The ‘covering law’ model of scientific explanation is the view that scientific explanations consist of three elements: deductive arguments, with sound premises, which make referent to (at least) one natural law. That is, for an explanation to count as “scientific,” it must first of all be in the from of an argument, “If A is true then B is the case; A is true, therefore B is the case.” Second, the premises of the argument must be valid. In other words, “If A and B are both true, then C is the case; A and B are true, therefore C is the case” is deductively valid, but if either of the premises A or B are false, the argument is not sound and it does not serve as a scientific explanation. Finally, the explanation must refer to one or more general laws in the course of its argument. That is, in the same formulation, “If A and B are both true, then C is the case; A and B are true, therefore C is the case,” the explanation may be both deductive and sound but unscientific if neither A nor B are natural laws of some sort.

One classic example of this sort of explanation is answering why a given plant died. Given that scientists know a great many things about the necessary conditions for plants to remain alive, it is possible to construct an explanation that fits the covering law model. Such an argument might proceed as follows:

1. All living must metabolize sources of energy to stay alive [general law GL-A].
2. Plants are living things [observation O-A].
3. Plants metabolize energy via photosynthesis [general law GL-B].
4. This plant was kept in the dark [an observation O-B].
5. Therefore, this plant could not metabolize energy via photosynthesis [conclusion C-A following from GL-B and O-B].
6. Therefore, this plant died [conclusion following from C-A, O-A, and GL-A].

It would equally be possible in the absence of observations (O-A and O-B) to formulate a prediction: in place of O-B and the conclusions which follow it, we could supply this form:

4. If a plant is kept in the dark, it will not be able to metabolize energy via photosynthesis [P].
5. Therefore, a plant which is kept in the dark will die. [C-C]

Note that the two forms are symmetric, because of the rules of deductive logic. Any explanation formulated under the covering law model could also be couched as a prediction.

Although the covering law model is initially attractive, there are two serious problems with it. The first is this very point of symmetry. Explanations, it turns out, are rarely symmetric with predictions. To borrow an example from Okasha, given the rules of trigonometry, if one knows any two of the angle of the sun in the sky, the height of a flagpole, or the length of the shadow cast by the flagpole, one can predict the third element. For example, having only the length of the shadow and the height of the flagpole, one can calculate the angle of the sun in the sky. Clearly, however, the length of the shadow and the height of the flagpole have no causal relation to the position of the sun in the sky. They do not explain it, though they may be used to predict it. By contrast, the intent of the person fashioning the flagpole, and a combination of facts about the sun’s emanation of light as part of the process of fusion and the earth’s orbit around the sun do suffice to explain the length of the shadow.

This is not merely a hypothetical concern; it is precisely the distinction between ancient Babylonian and ancient Greek methods of astronomy, as J.P. Moreland comments. The Babylonian astronomers were able to predict the positions of stars in the sky, relying on careful observation and detailed tables. They did not offer any explanation of those positions, however; the Greeks did. Though the Ptolemaic model the Greeks embraced is now rejected, it was an explanatory, and therefore scientific, model. Predictions are not the same as explanations, precisely because explanations indicate the underlying causes that things are as they are.

Second, it is possible to offer explanations which satisfy the covering law model, but in which the premises are irrelevant to the conclusion. In Okasha’s example, a doctor explains why a man does not become pregnant in terms of the observation that people who regularly take oral contraceptives do not become pregnant, and the man is taking oral contraceptives. Leaving aside the question of why a man would be taking oral contraceptives, the actual explanation is quite different: the man does not become pregnant because men are biologically incapable of pregnancy. Though the argument is deductively valid, and its premises are at least potentially sound, the law actually fails as an explanation. In this case, its predictive power is actually deceptive, because the prediction is totally uncoupled from the cause.

Both of these failings share in common the same core issue: ignoring the role of causality. Scientific explanations—to be differentiated from scientific observations such as “water is two molecules of hydrogen and one of oxygen”—traffic in causes and not merely predictions. Any model of how scientific explanation actually works must therefore include the arrow of causality.