Lots of people have raised objections. Some of them Hempel discusses himself.

 

I. Laws

Some may think that the idea of a law, as required by condition (R2), just isn’t all that clear.

Laws are universal generalizations. (Ignore statistical laws for now.) But not all universal generalizations are laws.

 

First, if something is a law, then it has empirical content. This eliminates nonsense and things true by definition (analytic statements). Since an explanation must contain a law, this classifies some things as non-explanations. [Bachelor example from last time.]

 

Second, something is a law only if it is true. [Note: given this, Hempel’s 4 conditions can be reduced to 2, since his R3 and R4 follow from R2.] This is all a terminological point. [We can say that some statements are “lawlike” when they are like laws, but not true.]

 

Third, a generalization is a law only if it is non-accidental. We saw examples of this last time. But it would be good to say more about this. One way it is explained is in terms of counterfactual conditionals. A law, but not an accidental generalization, supports the corresponding counterfactual. R. discusses this on p. 34. Some different examples may help. Consider:

 

1. All students in this room are UR students or faculty.

2. All people taking this course for credit are students.

3. All bodies not subject to external forces maintain constant velocity.

 

Next consider some corresponding counterfactuals:

 

4. If Hilary Clinton were in this room, then she’d be a UR student or faculty

5. If HC were taking this course for credit, she would be a student

6. If HC were not subject to external forces, she would maintain constant velocity. [Maybe this one is confusing. If so, replace HC by some inanimate object.]

 

You should be inclined to accept (5) and (6), but reject (4). So (1) is ruled out as a law, but (3) is ruled in. (2) is ruled out - it passes this condition, but not the empirical content condition.

 

So the suggestion is that laws are true, non-analytic, generalizations, that support counterfactuals.

 

A complication: you cannot tell by the form of the sentence which sort of generalization it is. In fact, the sentences are ambiguous. Each one can be used in either way. But, given background information, the most likely interpretations of the sentences differ in this way. That is, if a person said (1), the person would mean just the accidental generalization and not the thing that implies the counterfactual, whereas, if a person were to assert (3), the person would mean the stronger claim that does support the counterfactual. But a person could use the sentences in the opposite ways.

 

So, a law is is a non-analytic universal generalization interpreted in such a way that it is non-accidental, i.e., supports counterfactuals. Any such generalization that is not true is still lawlike.

 

A few more examples. Which of the following are, on their likely intended interpretations, laws? 1) All US presidents are male. 2) All people sitting in this room are mortal. 3) All pennies are made (partly) of copper. 4) All copper expands when heated.

 

R. says that supporting counterfactuals is a symptom, not an explanation, of something being a law. Why does (3) but not (1) support the counterfactual? He mentions the idea of physical necessity. But this is not so helpful.

 

Let’s proceed as if we understand this well enough

 

II. Some Proposed Objections

 

A. Objection 1: Good explanations do not need laws

 

Example 1: See R. p. 37.

Example 2: Knocking the pen off the table.

 

Reply: These are “explanation sketches” - incomplete statements of full explanations. They could be filled out. Strictly, then, it is false that they are explanations, and thus they are not counterexamples.

 

B. Objection 2: Teleological explanations

 

(See Hempel, p. 213) We sometimes explain human behavior by citing the goals people have. Thus:

 

Example 3:

Q) Why did Sara go to the library?
A) Sara went to the library in order to get a book for her research project.

(A) constitutes an explanation of the behavior. It does not look like it fits the model. Note also: the explanation can be correct even if she failed to get a book. So the general idea is that the model fails for purposive behavior. This involves goals or ends, not prior causes. This is supposed to show that there are good explanations that do not fit the model.

But Hempel thinks that this does fit the model. For the stated explanation can be put into different words, where it does fit the model: 

C1: Sara wanted a book for her research project; C2: Sara believed that she could get such a book at the library.
L: Whenever a person wants something, and believes that she can get it by going to a certain place, then she goes to that place.
________
E: Sara went to the library

 

This fits the model. It’s clearly too crude: (L) is not even close to true. State counterexamples. But the general idea seems ok. So - the explanation in Example 3 is not a counterexample because it is not really an explanation, but rather a reformulated version of an explanation sketch.

            This connects to big issues: freedom and determinism. Are there laws governing human behavior? If so, can we still be free and responsible? We won’t discuss them now. It also connects to questions about purposive explanations in other areas. We will return to this next week, and beyond.

 

So these first two objections don’t refute Hempel’s view. He would say that all explanations either fit the model or can be rephrased and filled out as explanations that fit the model.

 

III. Are Hempel’s Conditions Sufficient for Explanations?

 

A. The Barometer

 

Suppose that someone asks why there was a storm, and it is explained in terms of a prior the reading of a barometer:

 

C: The reading on the barometer dropped at t1.
L: Whenever the reading on the barometer drops, there is a storm a little later.
E. There will be a storm at t2.

 

(Obviously, this is rough. L is surely not quite right. But the details don’t affect the main point. It could be filled out.)

 

The objection is that this satisfies all the conditions, but it is not a good explanation. (Go through the conditions.) This seems to be a good counterexample. In this case, what seems to matter is that there is some common factor - a drop in pressure, perhaps, - that leads to both the change in the barometer and the storm. But neither of these results explains the occurrence of the other.

 

B. The Flagpole

 

The flag pole example in the text (p. 38) raises a related point. First, suppose we asked why the shadow of the flag pole is, say, 50ft long. A good explanation might cite the height of the pole, the position of the sun, a law about light traveling in a straight line, and the relevant math. Display this as an explanation, using the sentences from the text. This seems pretty good. But notice that you can reverse things. From the length of the shadow and the laws you can deduce the height of the flagpole. But the shadow does not explain the height. So this is an other counterexample.

 

This example turns on the following idea: in certain cases, there is a kind of symmetry that enables the argument to go in either direction: you can deduce the height of the pole from the shadow length and the background conditions or v.v. But the explanation relation is not similarly symmetric.

 

C. Men Not Getting Pregnant

 

Suppose Mr. Jones explains why he didn’t get pregnant by citing the fact that he took birth control pills.

 

            C: Mr. Jones took birth control pills from t₁-t₂

L: All people who take birth controls during some time period do not get pregnant during that time period.

            E: Mr. Jones did not get pregnant from t₁-t₂.

 

This also fits the conditions. But it is not an explanation.

 

One conclusion to draw from these examples: Hempel’s conditions are not sufficient for explanation.

 

Second, somewhat more speculative conclusions: explanation involves causation in a way that the D/N model ignored. There can be arguments following the D/N pattern that do not identify the causes of particular things. Merely fitting something under a law is not sufficient. You might think that a causal concept should be added. We will discuss that idea next time.