# Three Remarks on the Deductive-Nomological Model

I wanted to pull together and restate precisely some of the points concerning the deductive-nomological model that have come out of the last two weeks of discussion. These are certainly not the last things we shall want to say about the model, but they are, I hope, worth restating.

1. What almost everybody takes to *be* the deductive-nomological model consists of what Hempel and Oppenheim listed as "conditions of adequacy" on the model. Their hope was to formulate a set of precise and empirically respectable (meaningful) syntactic and semantic conditions that would be necessary and sufficient for anything to count as a non-statistical scientific explanation. So the model could not rely on the notion of causation or even on the notion of a law, because these notions were either not empirically respectable or redundant (because specifiable in terms of empirically respectable concepts such as universality). So in the formal presentation of the original model, they require that the explanans contain sentences that are purely universal and that contain only purely qualitative predicates -- even though they already had serious doubts about whether these conditions could discriminate the sheep (laws) from the goats (accidental generalizations). From this perspective formal criticism such as that by Eberle, Kaplan, and Montague (1961) was very serious. But from our perspective these formal issues are, I think, of very little interest, because *there is no hope of offering a semi-formal analysis of explanation that employs no concepts that would appear suspicious to an empiricist* (or so I believe). As I read "Aspects," Hempel has implicitly abandoned this hope -- though without fully recognizing the consequences of doing so.

2. The so-called symmetry thesis consists of two sub-theses. To simplify the exposition, take P to be a sentence describing some event to be explained or predicted. What is predicted is that P. What is explained is why P. The two sub-thesis of the symmetry thesis can then be stated:

- Every scientifically adequate prediction that P could serve as an adequate scientific explanation why P, if the truth of P were already known.
- Every adequate scientific explanation why P could serve as a scientifically adequate prediction that P if its explanans were already known and the truth of its explanandum were not already known.

Hempel firmly defends (2) but (in "Aspects") is ambiguous and ambivalent about (1), sometimes questioning it, sometimes regarding its truth as still open. Scriven is dismissive concerning both parts of the symmetry thesis. In part this is because Scriven takes a prediction to be simply a statement about the future. Since it is obvious that the statement P does not explain why P, (1) is obviously false. Since explananda are not always about the future and, in the case of the explanation of laws, do not concern events, (2) is just as obviously false.

But these objections are nit-picking. Let us limit ourselves to explanations of events, and take P to express a prediction if its truth is not yet known. Furthermore, let us take the prediction that P to include the basis upon which it is made.

Consider then the following (contestable) theses:

- (a) Every adequate non-statistical explanation satisfies the conditions of the D-N model.
- (b) Everything that satisfies the conditions of the D-N model is an adequate scientific explanation.
- (c) Every deduction of a statement P whose truth is not known from a set of statements known to satisfy the conditions Hempel imposes on the explanans of a D-N argument is a scientifically adequate prediction that P.
- (d) Every scientifically adequate prediction that P is a deduction of P from a set of statements known to satisfy the conditions Hempel imposes on the explanans of a D-N argument.

(b) and (d) imply the first half of the symmetry thesis, while (a) and (c) imply the second half. Since (c) is virtually undeniable, it is virtually undeniable that D-N explanations could be used to predict their explananda if their explananda had not been known and their explanans had been known. It does not follow that it is virtually undeniable that every adequate non-statistical explanation could have been used to predict its explananda, because (a) is controversial.

Turning to the first half of the symmetry thesis, (d) is obviously false. Not only can one base predictions on statistical generalizations, but it seems obvious that scientifically adequate prediction requires only a *reliable* basis, not a basis in truth or genuine laws. Ptolemaic astronomy (which places the Earth in the center of the universe) is a good basis for making many predictions concerning astronomy and locations; and until recently it was still in use for the purposes of navigation. Yet it offers no adequate scientific explanation of the appearances of the heavens at different locations and times. So this half of the symmetry thesis would be false *even if* (b) were correct -- that is, even if satisfying the conditions of the D-N model were sufficient for an argument to count as a scientific explanation.

The truth of (a), on the other hand, the claim that satisfying the conditions of the D-N model is *necessary* for a non-statistical account to be an adequate scientific explanation, stands or falls with the other half of the symmetry thesis. If Hempel is right and all non-statistical explanations satisfy the D-N model, then it must be the case that such explanations could have served as predictions. If, on the other hand, there are adequate non-statistical explanations that could not have served as predictions (if their explanans had been known and their explananda unknown), then Hempel must be wrong and there must be adequate non-statistical explanations that do not satisfy the conditions of the D-N model. Consider the syphilis-paresis example. If one can explain why somebody got paresis by pointing out that he/she had untreated syphilis, even though only a small percentage of those who have untreated syphilis get paresis, then there are explanations that could not have been used to make predictions and there are explanations that do not satisfy the D-N model.

3. As Hempel recognizes, few of those things that scientists recognize as explanations satisfy all the conditions of the deductive-nomological model. Actual scientific explanations -- including Hempel's own examples of paradigm scientific explanations -- are typically "elliptical" and, given Hempel's terminology, not explanations at all. Although there are occasions in which one wants to say of a purported explanation that "it is no explanation at all," let's be much looser for the moment at least, and take lots of things that don't satisfy the D-N model to be explanations, while interpreting Hempel to be making the claim that something is a completely adequate non-statistical explanation if and only if it satisfies the conditions of the D-N model. So elliptical explanations would count as genuine explanations, though they would not be completely adequate.

Why should an explanation that does not specify the laws linking the factors it cites to the phenomenon explained (like the example in class of the decline and then rise of the mercury level in a thermometer immersed in hot water) not be completely adequate? If both the person asking for the explanation and the person giving the explanation know the relevant laws, then surely the job of explaining has been fully and correctly accomplished.

I think that Hempel would agree that the explanatory task has been fully and correctly accomplished when the relevant laws are known but not mentioned. There is nothing to fault, and indeed to mention the laws and carry out the derivation might be a waste of time and resources and thus scientifically inferior. If it were acceptable to make reference to the explanatory context, to what the parties asking for the explanation and offering the explanation know, then one could say that this explanation was completely adequate. Hempel could say (for example) that the statements S constituting a purported explanation of an explanandum E in a context C constitute a completely adequate explanation of E, if both those asking for an explanation of E and those giving the explanation of E could construct a derivation of E employing S that satisfies the conditions of the D-N model.

Hempel would not be happy with this emendation of his views, because he wants to give an account of explanation that does not make reference to such pragmatic features. But if this were the only modification needed, the D-N model would be basically correct. The really serious criticisms Scriven and others make are not that explanations do not need to specify explicitly everything required by the D-N model. The really serious criticisms are (a) that satisfying the conditions does not suffice and (b) that there are completely adequate non-statistical explanations even when the parties are incapable of formulating explanatory arguments satisfying the conditions of the D-N model.