Remarks on explanation by covering law

Note first that the idea of providing a single analysis of explanation may be misguided. In class it was suggested that explanation is a matter of giving reasons for. Suppose that were true: it would provide a kind of uniformity (all explanation is a matter of giving reasons for something.) But on the other hand, it might not be possible to provide a uniform account of giving reasons for. Maybe there is no single way of specifying what that involves.

Hempel does aim to provide a common view as far as possible. His key idea is that explanation provides reason to believe the thing to be explained. It is that which leads – later – to some of the problems. He then ‘unpacks’ this idea by specifying 4 conditions

• • the explanation must be a valid deductive argument;

  • the explanans must contain essentially at least one general law;

  • the explanans must have empirical content;

  • the sentences constituting the explanans must be true.

which collectively set out necessary and sufficient conditions for something being an explanation.

So to test this analysis we should

a) see whether we can find cases which satisfy the conditions but – intuitively – do not seem to be explanations, and

b) see whether we can find cases which seem intuitively to be explanations but which do not fit the conditions.

Hence looking at the 4 famous counter-examples.

The flagpole and shadow case

Given the height of the flagpole and the angle of the sun and given that light travels in straight lines and shadows are caused by opaque objects – such as flagpoles – blocking the light, we can calculate the length of the shadow (using a combination of the above natural laws and basic maths) as

shadow = height of flagpole / tangent of sun’s angle

The formula gives us reason to believe that the shadow will be whatever it works out as. But this also fits the criteria for explanation. So according to Hempel’s model it is an explanation. Is it, though?

Yes it does seem to be a good explanation of why the shadow is that length.

But the same formula can be used to calculate the flagpole height from the other two factors. The formula gives us reason to believe that the height will be whatever it works out as. But this also fits the criteria for explanation. So according to Hempel’s model it is an explanation. Is it, though?

No. In normal circumstances it seems not.

Imagine: your friend is very tall but his parents are short and – rudely – you ask how come he’s so tall. He answers: I have a very long shadow. That’s no explanation of his height.

The diagnosis (of this case and the barometer and the man taking female contraceptive pills and not himself getting pregnant) seems to be that explanation has to track causal connections. Since the shadow length is not (normally) the cause of the flagpole height, it cannot be used to explain it.

(Not normally but look at this.)