Phil. 2130, Philosophy of the Sciences

Notes, Lecture 10, November 4 2003

The nature of scientific explanation

• “To explain the phenomena in the world of our experience, to answer the question “why?” rather than only the question “what” is one of the foremost objectives of empirical science.” (Hempel, 206) There is agreement about this, but little agreement about how the “why-questions” are answered.

• Hempel wants to develop a general account of scientific explanation

• 1^st: Look at some paradigmatic examples. The thermometer example (206). The explanation involves (in part) statements of 2 kinds: (1) Antecedent conditions and (2) General laws. To say that the conjunction of these statements explain the drop and then the rise in the mercury column is according to Hempel, to say that the statement describing the occurrence of that event is entailed by the (statements of the) antecedent conditions and the laws. One explains a particular event when one “subsumes it under general laws.” (207)

• “Why questions” may be asked about general laws as well. To explain a law is to subsume it under a more general law. (Galileo’s law from Newton’s laws (and some particular facts)

• 2^nd: Abstract the essential features from the examples:

Explanandum and explanans. (These are sets of sentences that describe the

relevant phenomena)

Conditions of adequacy:

(R1) The explanandum must be logically deducible from the explanans.

(R2) The explanans must contain general laws.

(R3) The explanans must have “empirical content”.

(R4) The sentences constituting the explanans must be true.

(Is R4 really required? Why not a weaker constraint that the explanans be highly

probable?)

• (a) All copper conducts electricity.

(b) This wire is made of copper.

___________________________

(c) Therefore, this wire conducts electricity.

• Explanation vs. prediction: Merely a pragmatic difference. If the explanandum is given (i.e. what it describes has already occurred), then subsumption is explanation. If it is not given, then subsumption is prediction. (Everyday explanations are incomplete, Hempel claims.)

Problems with the account

• What are laws?

-A certain kind of true sentence.

-Having a universal conditional form. Examples: ‘All robins eggs are greenish blue’, ‘all metals are conductors of electricity’

Does this suffice? No.

(S1) Every apple in basket b at time t is red.

Does (S1) explain the fact that this apple, taken from b at t is red? Hempel says ‘no’.

What’s wrong with (S1)? Two suggestions:

(A) finite scope?

But not all universal conditionals that have finite scope appear to be non-lawlike

(S2) All the sixteen ice cubes in the freezing tray of this refrigerator have a temperature of less than ten degrees centigrade.

But (S2) can be derived from more general laws (and some particular facts), while (S1) cannot.

Derivative vs. fundamental laws. Fundamental laws must not be limited in scope.

(B) reference to a specified object? But again the restriction should be taken to apply only to fundamental laws.

The “ferple problem”.

Other problems for Hempel’s account:

Are the conditions (R1)-(R4) jointly sufficient for explanation?

(P1) Problems of relevance:

A case of complete irrelevance: Why didn’t Mr. X get pregnant? Explanation: He took the pill regularly and anyone who takes the pill regularly will fail to become pregnant. This “explanation” appears to satisfy the criteria.

A case of causal preemption: Why did Mrs. Y die when she did? Explanation: She ate a pound of arsenic, and anyone who eats a pound of arsenic dies within 24 hours. Suppose, though that, a bus ran over Mrs. Y just before her death…

A case of trivial explanation: Any old law can be derived from the conjunction of itself and some further laws. For example, Kepler's laws can be derived from the conjunction of Kepler's laws and Boyle’s laws. But we wouldn’t count this derivation as an explanation of Kepler’s laws.

(P2) Problems of symmetry

Storms and barometers: We saw earlier that, for Hempel, predictions are just explanations of an event that has yet to occur. Alternatively (and equivalently) explanations are just predictions (post dictions) of what has already occurred.

However, barometers are good predictors of storms. But barometers and their readings don’t explain the occurrence of storms. So there seems to be an asymmetry between prediction and explanation that is masked by Hempel’s account.

Flagpoles and shadows: 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.

Postdicting an eclipse: We can predict the next solar eclipse using laws and the positions of celestial bodies. But we can also postdict earlier eclipses using present positions.

Are the conditions (R1)-(R4) individually necessary for explanation?

(P3) Problems for (R1): The die.

(P4) Problems for (R2): My torn shirt, the occurrence of WW2.