EMPIRICAL MODELS

The models I shall now mention satisfy NES but overtly violate the a priori requirement. Their proponents seem to recognize that if the former requirement is to be satisfied it is not an a priori but an empirical question whether the explanans if true would correctly explain the explanandum.

a. Salmon’s Statistical-Relevance (S—R) model

This is a model for the explanation of particular events.^[77] Salmon con­strues such an explanation as answering a question of the form

(1) Why is X, which is a member of class A, a member of class B?

Although Salmon does not do so, I shall say that the explanandum in such a case has the form

(2) X, which is a member of class A, is a member of class B,

The kind of example here used against Salmon's model^[78] is similar to those raised earlier, in the following respect. In the explanans a certain fact about the wire is cited, namely, that it conducts heat, which (under the conditions of the setup) is nomologically associated, albeit indirectly, with the fact to be explained, that is, the bulb's being lit. However, it is not the explanans-fact that is the operative one in this case but the fact that the wire conducts electricity. By invoking the homogeneity condition Salmon in effect recognizes that the question of the explanatory opera­tiveness of the explanans is not an a priori matter. The problem is that his homogeneity condition is not sufficient to guarantee that the explanans- fact is operative with respect to the explanandum-fact.

b. Brody’s Essential Property Model

Brody construes this model as providing a set of sufficient conditions for explanations of particular events.^[79] These conditions are those of the basic D-N model together with the following:

Essential property condition: “The explanans contains essentially a statement attributing to a certain class of objects a property had essentially by that class of objects (even if the statement does not say that they have it es­sentially) and... at least one object involved in the event described in the explanandum is a member of the class of objects.” (p. 26)

For example, since Brody thinks that atomic numbers are essential prop­erties of the elements he would regard the following explanation as cor­rect, provided its premises are true, since the D-N conditions plus his essential property condition are satisfied:

(3) This substance is copper.

Copper has the atomic number 29.

Anything with the atomic number 29 conducts electricity.

Therefore,

This substance conducts electricity.

Brody proposes the essential property condition in order to preclude cer­tain counterexamples to the basic D-N model. Moreover, he regards the satisfaction of this condition as an empirical matter.^[80] Brody's model, in cases in which the explanans does not say explicitly that the prop­erty in question is essential, does not satisfy the a priori condition.^[81] To know whether (9) is a correct explanation if its premises are true is not an a priori matter, since we must know whether having the atomic number 29 is an essential property of copper, and this knowledge is em­pirical, according to Brody. On the other hand, the NES requirement is satisfied since the singular premises in an explanans will not entail the explanandum.

One might object to Brody's model on grounds of obscurity in the no­tion of an essential property (which, by the way, he seems to distinguish from mere properties a thing has necessarily).

Consider now the following argument which satisfies Brody's es­sential property condition plus the other requirements of the D-N model.

(4) Jones ate a pound of the substance in that jar.

The substance in that jar is arsenic.

Arsenic has the atomic number 33.

Anyone who eats a pound of substance whose atomic number is 33 dies within 24 hours.

Therefore,

Jones died within 24 hours of eating a pound of the substance in that jar.

Suppose, however, that Jones died in an unrelated car accident, and not because he ate arsenic. Although Brody's essential property condition is satisfied, as are the conditions of the D-N model, the explanans in (10) does not, even though true, correctly explain the explanandum. Brody may in effect recognize that it is not an a priori but an empirical ques­tion whether a D-N explanans if true correctly explains its explanandum. Nevertheless, the empirical requirement which his model invokes—the essential property condition—is not of the right sort to avoid the kind of problem plaguing this and previous models. Like Salmon's homogeneity condition, Brody's essential property condition is not sufficient to guaran­tee that the explanans-fact is explanatorily operative with respect to the explanandum-fact.

Both Salmon and Brody seem to recognize that if the NES require­ment is to be satisfied it is an empirical, not an a priori, question whether an explanans if true correctly explains an explanandum. Yet the empirical considerations their models deploy are not sufficient to ensure that if sat­isfied an explanation will be correct if its explanans is true. Can problems of the sort generated by these models be avoided in any way other than by abandoning NES?

6.