TWO REQUIREMENTS FOR A MODEL

The first is that no singular sentence or conjunction of such sentences in the explanans can entail the explanandum.^[63] I will call this the No-Entailment-by-Singular-Sentence requirement, or NES for short.

There are, I suggest, three reasons that modelists I have in mind support it. First, it precludes certain ‘self-explanations' and ‘partial self-explanations'. Suppose we want to explain why a particular metal expanded. Assume that the explanandum in this case is

(1) This metal expanded.

The NES requirement precludes (1) itself from being or, being part of, an explanans for (1). It also precludes from an explanans for (1) sentences such as “This metal was heated and expanded,” and “This metal expanded, and all metals that are heated expand,” which would be regarded as par­tial self-explanations of (1).

Second, modelists emphasize the importance of general laws in an explanans. Such laws provide an essential link between the singular sentences of the explanans and the singular sentence that constitutes the explanandum. Intuitively, to explain a particular event involves relating it to other particular events via a law; if the singular sentences of the explanans themselves entail the explanandum laws become unnecessary, on this view.

Third, the NES requirement in effect removes from an explanans cer­tain sentences which involve explanatory connectives such as ‘explains', ‘because', ‘on account of', ‘due to', ‘reason', and ‘causes'. Let me call sen­tences in which such terms connect phrases or other sentences explanation­sentences. Here are some examples:

(2) This metal's being heated explains why it expanded.

This metal expanded because it was heated.

This metal expanded on account of its being heated.

The reason this metal expanded is that it was heated.

This metal's expanding is due to its being heated.

The fact that this metal was heated caused it to expand.

NES precludes any of the explanation-sentences in (2) from being, or being part of, an explanans for (1), since each of them is a singular sentence that entails (1).^[64] Without a condition such as NES one could simply require, e.g., that an explanans for an explanandum p be a singular explanation-sentence of the form ‘q explains (why) p’ or ‘p because q. Any such explanans, if it were true, would correctly explain the explanandum p. Of course, any of the the six sentences in (2), if true, could be cited in correctly explaining why this metal expanded. Modelists need not deny this. Their claim is that the sentences in (2) do not correctly explain (1) in the right sort of way. They would exclude sentences in (2) from an ex­planans for (1) because they think that an adequate explanans for (1) must reconstruct the sentences in (2) so that the explanatory connectives in the latter are, in effect, analyzed in nonexplanatory terms. One of the purposes of a model of explanation is to define terms such as ‘explains', ‘because', ‘reason', and ‘cause', and not to allow them to be used as primitives within an explanans. By providing some analysis of explanation modelists want to show why it is that this metal's being heated explains why it expanded. There is little enlightenment in saying that this is so because (2) is true.

NES does not exclude all singular explanation-sentences (or all explan­atory connectives) from an explanans.^[65] But by precluding those that entail the explanandum it does eliminate ones that, from the viewpoint of the modelists, most seriously reduce the possibility of philosophical enlight­enment from the resulting explanation. (Whether such modelists would advocate a broader requirement eschewing all explanation-sentences from an explanans is a possibility I shall not discuss.)

NES also excludes certain sentences from an explanans that do not explicitly invoke explanatory connectives but are importantly like those that do which are excluded.

(3) The motion of this particle was accelerated.

Consider the explanans

(4) An electrical force accelerated the motion of this particle.

Although (4) itself contains no explicit explanatory connective such as ‘explains', ‘because', or ‘causes', it nevertheless carries a causal implication concerning the event to be explained. It is roughly equivalent to the fol­lowing explanation-sentences which do have such connectives:

(5) An electrical force caused the motion of this particle to be accelerated. The motion of this particle was accelerated because of the presence of an electrical force.

NES precludes (4) as well as (5) from an explanans for (3), since (4) is a singular sentence that entails (3). Those who support NES would empha­size that (4), no less than (5), invokes an essentially explanatory connec­tion between an explanans-event and the explanandum-event which it is the task of a model of explanation to explicate.

The second requirement, which I shall call the a priori requirement, is that the only empirical consideration in determining whether the explanans correctly explains the explanandum is the truth of the ex- planans; all other considerations are a priori. Accordingly, whether an explanans potentially explains an explanandum is a matter that can be settled by a priori means (e.g., by appeal to the meanings of words, and to deductive relationships between sentences). A model must thus im­pose conditions on potential explanations the satisfaction of which can be determined nonempirically. A condition such as this would therefore be precluded:

An explanans potentially explains an explanandum only if there is a (true) universal or statistical law relating the explanans and explanandum.

Whether there is such a law is not an a priori matter.

The idea is that a model of explanation should require that sufficient information be incorporated into the explanans that it becomes an a priori question whether the explanans, if true, would correctly explain the ex- planandum.

Often a scientist will claim that a proposition q can be proved from a proposition p, or that e is evidence that h is true, even though the sci­entist is tacitly making additional empirical background assumptions which have a bearing on the validity of the proof or on the truth of the evidence claim. If all of these assumptions are made explicit as addi­tional premises in the proof, or as additional conjuncts to the evidence, then whether such and such is a proof, or is evidence for a hypothesis, is settleable a priori. Similarly, often a scientist who claims that a certain explanans correctly explains an explanandum will be making relevant empirical background assumptions not incorporated into the explanans;

if the latter are made explicit and added to the explanans, it becomes an a priori question whether the explanans, if true, would correctly explain the explanandum.

There is an additional similarity alleged between these concepts. A sci­entist would not regard a proof as correct—i.e., as proving what it pur­ports to prove—unless its premises are true. Nor would he regard e as evidence that h (or e as confirming or supporting h) unless e is true. (That John has those spots is not evidence that he has measles unless he does have those spots.)^[66] And whether the premises of the proof, or the evi­dence report, is true is, in the empirical sciences at least, not an a priori question. Nevertheless, deductive logicians, as well as inductive logicians in the Carnapian tradition, believe that they can isolate an a priori aspect of proof and evidence such that the only empirical consideration in deter­mining whether a proof or a statement of the form ‘e is evidence that h’ is correct is the truth of the premises of the proof or of the e-statement in the evidence claim; all other considerations are a priori. What I have been calling the a priori requirement makes the corresponding claim about the concept of explanation: The only empirical consideration in determining whether an explanation is correct is the truth of the explanans.

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