VIOLATION OF THE A PRIORI REQUIREMENT

Despite the claims of these models the a priori requirement is not really satisfied (or else we will have to call certain explanations correct which are clearly not so). In order to show this I shall make use of some of the many counterexamples that have been employed against the D-N model.

Consider this example:

(a) Jones ate a pound of arsenic at time t.

Anyone who eats a pound of arsenic dies within 24 hours.

Therefore,

Jones died within 24 hours of t.

Assume that the premises of (a) are true. Then it is supposed to be set­tleable a priori whether these premises correctly explain the conclusion. According to the D-N model all we need to determine is whether the second premise is lawlike (let us assume that it is), and whether the conjunction of premises (but not the first premise alone) entails the con­clusion (it does). Since these D-N conditions are satisfied, the explan­ans should correctly explain the explanandum; and assuming the truth of the explanans, this matter is settleable on a priori grounds alone, no matter what other empirical propositions are true. However, the matter is not settleable a priori, since Jones could have died within 24 hours of t for some unrelated reason. For example, he might have died in a car accident not brought on by his arsenic feast, which, given the informa­tion in the explanans, could only be determined empirically. Suppose he did die from being hit by a car. Then the explanans in (a) does not correctly explain the explanandum, even though all the conditions of the D-N model are satisfied. Assuming the truth of the premises in (a) it is not settleable a priori whether these premises correctly explain the explanandum.

A similar problem besets all the more specialized versions of the D-N model cited above. Thus consider these D-N arguments:

(b) Disposition example

That bar is magnetic, and a small piece of iron was placed near it.

Any magnetic bar is such that when a small piece of iron is placed near it the iron moves toward the bar.

Therefore,

This small piece of iron moved toward the bar.

Suppose, however, that a much more powerful contact force had been ex­erted on the small piece of iron, and that it moved toward the bar because of this force, not because the bar is magnetic. (Assume that the magnetic force is negligible by comparison with the mechanical force.)

(c) Motivational example

Smith desired to buy eggs and he believed that going to the store is the only way to buy eggs.

Whenever, etc. (law relating beliefs and desires to actions)

Therefore,

Smith went to the store.

But suppose Smith went to the store because he wanted to see his girl­friend who works in the store, not because he wanted to buy eggs.

(d) Functional interdependence example

This pendulum is a simple pendulum.

The period of this pendulum is 2.03 seconds.

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

Therefore,

This pendulum has a length of 100 cm.

A pendulum has the period it has because of its length, but not vice versa. (This type of counterexample is like the others insofar as it invokes an explanans-fact that is inoperative with respect to the explanandum-fact but the case is also different because there is no intervening cause here, although there is in the others.)

With each of the D-N models considered, whether a particular ex­ample satisfies the requirements of the model (with the exception of the truth-requirement for the explanans) is a settleable a priori. Yet in all of these cases, given the truth of the explanans, whether the latter correctly explains the explanandum is not settleable a priori.

(1) Smith went to the store because he desired to buy eggs and believed that going to the store is the only way to buy eggs.

The explanans of (c) correctly explains the explanandum only if (1) is true. Yet given the truth of the explanans of (c) it is not settleable a priori, but only empirically, whether (1) is true.

We could, of course, see to it that the matter is settleable a priori by changing the motivational model so as to incorporate (1) into the explan- ans of (c). Assuming that this enlarged explanans is true, whether the latter correctly explains the explanandum is a priori—indeed trivially so. But now, of course, the NES requirement is violated, since (1) is a singular sentence that entails the explanandum of (c).

In example (d), even if the explanans is true and Woodward's condi­tion of functional interdependence is satisfied, it does not follow that

(2) This pendulum has a length of 100 cm because it is a simple pendulum with a period of 2.03 seconds and the law of the simple pendulum holds.^[74]

The explanans of (d) correctly explains the explanandum only if (2) is true. Yet assuming the truth of the explanans of (d), the truth-value of

(2) is not settleable a priori, but only empirically. Assuming that there is a lawlike connection between the period and length of a simple pendulum, whether the pendulum has the period it does because of its length, or whether it has the length it does because of its period, or whether neither of these is true, is not knowable a priori.^[75]

More generally, in the explanans in each of these models some factors are cited, together with a lawlike sentence relating these factors to the type of event to be explained. But given that the factors were present and that the lawlike sentence is true, there is no a priori guarantee that the event in question occurred because of those factors.

It might be replied that we should tighten the conditions on the law­like sentence in the explanans by requiring not simply that it relate the factors cited in the explanans to the type of event in the explanandum, but that it do so in an explicitly explanatory way. Thus in (a) we might require the lawlike sentence not to be simply “Anyone who eats a pound of arsenic dies within 24 hours” but

(3) Anyone who eats a pound of arsenic dies within 24 hours because he had done so.

It is settleable a priori whether an explanans consisting of (3) together with “Jones ate a pound of arsenic” is such that, if true, it would correctly explain the explanandum in (a).

This solution, however, would not be an attractive one for D-N the­orists, since (3) is just a generalized explanation-sentence containing an explanatory connective that such theorists are trying to analyze by means of their model. Moreover, tightening the lawlike sentence in this way will produce many false explanations, since such tightened sentences will often be false even though their looser counterparts are true. For example,

(3), construed as lawlike, is false since people who eat a pound of arsenic can die from unrelated causes. And if we weaken (3)—still keeping the explanatory clause—by writing

(4) Anyone who eats a pound of arsenic can die within 24 hours because he has done so,

we obtain a sentence that is true but not powerful enough for the job. It is not settleable a priori whether an explanans consisting of (4) together with “Jones ate a pound of arsenic at t,” if true, would correctly explain why Jones died within t + 24, since he could have died for a different reason even though this explanans is true.

Another possible way of tightening the conditions on the lawlike sen­tence in the explanans is to require that it relate spatio-temporally contig­uous events. (This would mean that the explanans would have to describe an event—or chain of events—that is spatio-temporally contiguous with the explanandum-event.) Jaegwon Kim has discussed laws of this sort, and he provides schemas for them which are roughly equivalent to the following:

(5) (x) (t) (t3 (x has P at t, and loc(x, t) is spatially contiguous with loc(x, t'),

and t is temporally contiguous with t' x has Q at t')

(6) (x) (y) (t) (t3 (x has P at t, and loc(x, t) is spatially contiguous with loc(y, 13, and t is temporally contiguous with t' y has Q at t^z).^[76]

‘loc(x, t)’ means the location of x at time t. Kim does not specify a pre­cise meaning for the arrow in (5) and (6), except that it is to convey the idea of “causal or nomological implication” (p. 229, note 19). Under the present proposal, the arsenic explanation (a) would be precluded, since the only law invoked in (a) is not of forms (5) or (6). It does not express a relationship between types of events that are spatio-temporally con­tiguous. And, indeed, the explanans-event in (a) is not spatio-temporally contiguous with the explanandum-event.

This solution, like the previous one, may succeed in excluding inter­vening cause counterexamples such as (a). But it would not, I think, be welcomed by D-N theorists. If the arrow in (5) and (6) is to be construed causally as meaning (something like) “causes it to be the case that,” then, as with (3), the laws in D-N explanations will be generalized explanation­sentences containing an explanatory connective that D-N theorists seek to define by means of their model. Furthermore, requiring laws of forms (5) or (6) in an explanans will disallow explanations that D-N theorists, and many others, find perfectly acceptable. For example, it will not per­mit an explanation of a particle’s acceleration due to the gravitational or electrical force of another body acting over a spatial distance.

(x)(t)( 13 (x is a simple pendulum with a period T at time t, and loc(x, t) is spatially contiguous with loc(x, t'), and t is temporally contiguous with t' x has a length L at t' which is related to Tby the formula T = 2p(L/g)^1/2).

This, being of form (5), can be used in the explanans in (d), which, when suitably modified, will permit an explanation of the pendulum’s length by reference to its period. For these reasons the present proposal does not seem promising.

Our observations regarding the various D-N models can be general­ized. Assume that the explanans satisfies the NES requirement. In the explanans we can describe an event of a type always associated with an event of the sort described in the explanandum. We can include a law saying that such events are invariably and necessarily associated. The truth of the explanans event-description and of the law is no guarantee that the explanandum-event occurred because of the explanans-event. It could have occurred because some event unrelated to the one in the explanans was operative whereas the explanans-event was not. And this cannot be known a priori from the explanans. We can make it a priori by including in the explanans an appropriate singular sentence that entails the explanandum (e.g., an explanation-sentence that says in effect that the explanandum is true because the explanans is, or that the explanans- event caused the explanandum-event). But then the NES requirement would be violated. Or, we can make it a priori by using a generalized explanation-sentence. But since this is contrary to the philosophical spirit of such models and will, in any case, tend to produce false explanations, it will not be considered a viable solution. We can also make it a priori by requiring laws of form (5) or (6) and construing the arrow causally. But this too does not satisfy the intent of such models, and, in addition, will not permit wanted explanations. On the other hand, if the arrow is understood nomologically but not causally, then whether the explanans, if true, correctly explains the explanandum is, in general, not knowable a priori.

To avoid the kind of problem in question we can say that it is an empir­ical, not an a priori, question whether an explanans describing events and containing laws relating these types of events to the explanandum-event correctly explains the latter. Or we can include in the explanans some singular sentence—either an explanation-sentence or something like it (e.g., (4) in section 2)—that entails the explanandum. In the first case the a priori requirement is violated, in the second, NES. For this reason, I suggest, D-N models which attempt to provide sufficient conditions for correct explanations in such a way as to satisfy both these requirements will not be successful.

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