MODELS PURPORTING TO SATISFY THESE REQUIREMENTS

a. The Basic D-N Model

Consider this model as providing a set of sufficient conditions for ex­planations of particular events, facts, and so on. The explanation-seeking question is of the form ‘why is it the case that p?' where p, the explanan- dum, is a sentence describing the event to be explained.

No singular sentence (or conjunction of such sentences) that entails the explanandum will appear in the explanans.^[67] Any such sentence which is an explanation-sentence that someone might utter in explaining something will itself be analyzed as a D-N explanation, i.e., as a deductive argument in which no premises that are singular sentences entail the conclusion. For example, if someone utters the singular explanation­sentence

(1) This metal's being heated explains why it expanded (caused it to expand, etc.)

in explaining why the metal expanded, a D-N theorist will restructure (1) as an argument such as this

(2) This metal was heated.

Any metal that is heated expands.

Therefore,

This metal expanded.

And he will identify the premises of (2) as the explanans of the explana­tion and the conclusion as the explanandum. The premise in (2) that is a singular sentence does not entail the conclusion.

The a priori requirement also seems to be satisfied by this model. The only empirical consideration in determining whether the explanans cor­rectly explains the explanandum is the truth of the explanans; all other considerations are a priori. What are these other considerations? They are whether the explanans (but not the conjuction of singular sentences in it) deductively entails the explanandum and whether it contains at least some sentences that are lawlike.

The D-N model as a set of sufficient conditions for particular events is very broad, and one might seek to add further restrictions. Three more limited versions will be noted.

b. The D-N Dispositional Model

In this model,^[69] the explanandum is a sentence with a form such as

(3) X manifested P when conditions of type C obtained.

And the explanans contains sentences of the form

(4) X has F, and conditions of type C obtained.

(5) Anything with F manifests P when conditions of type C obtain.

For an explanans consisting of (4) and (5) to provide a correct D-N dispo­sitional explanation of (3) the model requires that F be a disposition-term, that (5) be lawlike, that (4) and (5) entail (3), and that (4) and (5) be true. The singular sentence in the explanans is not to entail the explanandum. And the satisfaction of all the conditions of the model, save for the truth of the explanans, is determined a priori. The only condition in addition to those of the basic D-N model is that F be a disposition-term, something settleable syntactically and/or semantically.

c. The D-N Motivational Model

In this model,^{[70] [71] the explanandum is a sentence saying that some agent acted in a certain way. The explanans contains a singular sentence attributing a desire (motive, end) to that agent, a singular sentence attributing the belief to that agent that performing the act described in the explanandum is, in the circumstances, a (the best, the only) way to satisfy that desire, and a lawlike sentence relating desires, beliefs, and actions of the kind in question. For example, the explanandum might be a sentence of the form}

(6) Agent X performed act A,

and the explanans might contain sentences of the form

(7) X desired G.

(8) X believed that doing A is, in the circumstances, a (the best, the only) way to obtain G.

(9) Whenever an agent desires something G and believes that the perfor­mance of a certain act is, in the circumstances, a (etc.) way to obtain G he performs that act.¹¹

For an explanans consisting of (7)-(9) to provide a correct D-N moti­vational explanation of (6) the model requires that (9) be lawlike, that (7)-(9) entail (6), and that (7)-(9) be true. In this model, like the others, the singular sentences in the explanans are not to entail the explanandum, and the satisfaction of all the requirements of the model, save for the truth of the explanans, is settleable a priori.

d. Woodward’s Functional Interdependence Model

This model^[72] proposes adding to the basic D-N conditions the following additional necessary condition:

(10) Condition of functional interdependence: the law occurring in the explanans for the explanandum p must be stated in terms of variables or parame­ters, variations in the values of which will permit the derivation of other explananda which are appropriately different from p. (p. 46)

Suppose that the explanation-seeking question is “Why is it the case that this pendulum has a period of 2.03 seconds?” for which the explanandum is

(11) This pendulum has a period of 2.03 seconds.

Consider the following D-N argument:

(12) This pendulum is a simple pendulum.

The length of this pendulum is 100 cm.

The period T of a simple pendulum is related to the length L by the formula T = 2p(L/g)^1/2, where g = 980 cm/sec².

Therefore,

This pendulum has a period of 2.03 seconds.

The third premise in (12) is a law satisfying Woodward’s condition (10). Its variables are the period T and the length L. And variations in the values of these variables will permit the derivation of explananda which Woodward regards as appropriately different from (11). For example, if we change the explanandum (11) to

(13) This pendulum has a period of 3.14 seconds

the law in (12) allows the derivation of (13) if the value of L is changed to 245 cm.

The laws in examples [of this sort] formulate a systematic relation between... variables. They show us how a range of different changes in certain of these variables will be linked to changes in others of these variables. In con­sequence, these generalizations are such that when the variables in them as­sume one set of values (when we make certain assumptions about boundary and initial conditions) the explananda in the... explanations are derivable, and when the variables in them assume other sets of values, a range of other explananda is deriavable. (p. 46)

The satisfaction of condition (10) is settleable a priori. If this condition is the only one to be added to those of the basic D-N model, then the resulting model satisfies the a priori requirements and NES.^[73]

4.