Phil

Phil. 2130, Philosophy of the Sciences

Notes, Lecture 11, November 4 2003

Hempel’s account of explanation

Hempels wants an analysis of what it is for a set of statements to count as a scientific explanation, i.e. individually necessary and jointly sufficient conditions on being an explanation.

S explains e if and only if…

(Hempelian terminology: e is the explanandum and S is the explanans.)

By looking at a few examples of what we take to be genuine explanations, Hempel concludes that explanation is a matter of “subsumption under general laws.” This is a fancy way of saying that to explain an event is to show that the occurrence of that event logically follows from certain “laws of nature” and the event’s antecedent conditions.

So,

S explains e if and only if e is deducible from S.

(This is the first “condition of adequacy”, (R1): the explanandum must be logically deducible from the explanans.)

But from the examples Hempel also thinks he can discern that S must possess certain features. It must:

(a) contain at least one statement of a law of nature. (R2)

(b) contain statements with “empirical content.” (R3)

Suppose you want to explain why this particular piece of wire conducts electricity. You might say: “It’s made of copper, and all copper wire conducts electricity.” This conforms to Hempel’s account. Or suppose--a somewhat more complicated case-- that you want to explain why when a mercury thermometer is rapidly immersed in hot water, the mercury drops for a moment and then swiftly rises. You might cite the laws of the thermic expansion for mercury and glass and the various initial conditions pertaining to the water and the thermometer. This too conforms.

So there’s evidence, from a wide range of actual cases, that Hempel is on to something with his account. To put the virtue of Hempel’s account in abstract terms we might say: It describes the way in which, for a vast number of cases, to explain e, to answer the question “Why did e occur?” is to show that e is nomically expectable; e is what we ought to expect given the laws of nature and e’s antecedent conditions.

Nevertheless, there are problems:

First: What is a law of nature? In a way, this question is easy to answer and, in another way, it’s very difficult to answer.

Clearly, there is a difference between an accidentally true universal conditional statement, like, ‘All of my shirts have coffee stains on them’ and a non-accidentally true generalization like, ‘All copper conducts electricity.’ The trouble is saying what accounts for this difference.

The proposal that Hempel adopts is problematic: the fundamental laws are those having non-finite scope and lacking reference to particulars.

But consider: ‘All gold spheres are less than a mile in diameter.’

This would count not only as a law, but as a fundamental law on Hempel’s proposal!

A way forward? Say something about the connection between F and G in ‘All F’s are Gs’. That being F necessitates being G perhaps…?

But do we, does Hempel, need an answer? Perhaps not…

Second: The problems of relevance.

Mr. X and the pill. (complete irrelevance)

1. Anyone who takes birth control pills regularly fails to get pregnant.

2. Mr. X took birth control pills regularly.

3. Therefore, Mr. X failed to get pregnant.

All of Hempel’s conditions are satisfied, but the explanans (1 + 2) does not explain the explanandum (3). So, Hempel’s conditions are not sufficient.

Mrs. Y and the bus. (preemption)

1. Anyone who eats a pound of arsenic will die within twenty four hours.

2. Mrs. Y ate a pound of arsenic at t.

3. Therefore, Mrs. Y died within twenty four hours of t.

But suppose that just before the arsenic could take its effect, Mrs. Y is run over by a bus…

Laws from themselves. (triviality)

Flagpoles and shadows (irrelevance and asymmetry)

Imagine a flagpole that casts a shadow of a definite length during some specified time of day. It’s clear that we can explain the length of the shadow by virtue of the flagpole’s height, the sun’s particular elevation, and the laws of optics. The problem arises when we consider how the length of the shadow, the elevation of the sun, etc., can be used to deduce the height of the flagpole.

Here the problem is twofold: Shadows don’t cause flagpole heights, so the “explanation” of the height of the flagpole based on the shadow’s length cites an irrelevancy. But the example also bring out the fact that some explanations are directional or asymmetrical.

Lessons of the relevance counterexamples:

1. H’s account fails to provide sufficient conditions for explanation. This is perhaps not so serious; maybe H just missed one of the necessary conditions, and that further necessary condition can just be tacked on to the theory as it stands, forming a set of conditions which, taken together, are sufficient.

2. The “missing condition” seems to be something having to do with the citation of causes in acceptable explanations. For Hempel, explanation is showing how something logically follows from something else. But what the relevance counterexamples appear to show is that the kind of relation that explanations invoke is a causal one, not a logical one.

Why does pill taking fail to explain Mr. X’s non-preganany. The pill taking doesn’t cause the non-pregnancy.

Similarly the arsenic taking doesn’t cause Mrs. Y’s death.

Isn’t it obvious that explanations cite causes? Yes, but, interestingly, Hempel’s philosophical commitments prevented him from admitting the obvious.

Hempel was an empiricist. He thought that all of our knowledge is grounded on our experience, that there is no such thing as a priori knowledge, and that any alleged phenomenon that lacks an experiential, empirical basis is suspect. This led him to follow Hume and be skeptical of the very notion of causation. For an event is supposed to cause another just in case the first forces the second to happen. But all we get in sense experience is the perception of certain events following (in a temporal sense) others. We don’t perceive this alleged causal force. We just see one billiard ball rolling over to another and the other one rolling way--a mere succession of events; we don’t see the one ball causing the second to move. So for Hempel, an unanalyzed notion of causation should not be allowed to figure crucially in an account of explanation.

3. A route to counterexamples to the necessity claim:

Consider: The impact of my knee on the desk caused the tipping over of the inkwell.