Hempel and the flagpole

Robert Marchand is not only a good cyclist at his age of 105, he is also a good scientist. For before his ride by which he set up the new world record in one-hour track cycling in the over-105 age group he said: “I am here to prove that at 105 years old you can still ride a bike.” So, he organised an experiment with a 105 years old person (himself) that he seated on a bike and let him make a ride of an hour. And so he proved his hypothesis that a 105 years old person can ride a bike. Okay, it’s not exactly correct that he proved that at 105 any person can ride a bike, but that there is at least one such a person who can, namely Robert Marchand. Let us forgive him for this slip up in view of his splendid performance.

We wouldn’t have forgiven him if he were not only a cyclist with an established name but also a methodologist with an earned reputation. And since it is always interesting to look at old cases, I want to return to Carl G. Hempel, one of the most important methodologists of the last century. Despite his merits – and I want to say that, although I have never been a fan of his approach – Hempel sometimes made weird mistakes, as we have seen a few weeks ago, when I discussed the raven paradox. We saw there that Hempel thought that the fact that an apple is red – if it is – can confirm that ravens are black. It’s not the only mistake Hempel by made and nor is it his most important one. One of the basic characteristics of Hempel’s methodology – called “covering law theory” – is that explaining the occurrence of a phenomenon and predicting that a phenomenon will occur are two sides of the same coin. Explanation and prediction are symmetric in his view, or, as he calls it, “structural identical”. This thesis is the conjunction of two sub-theses, so Hempel (p. 367): (i) “every adequate explanation is potentially a prediction” and (ii) “every adequate prediction is potentially an explanation”. Although sub-thesis (i) is correct, the weird thing is that Hempel actually also supports sub-thesis (ii), although after some discussion he admits that it is an “open question” (p. 376). However, it is crystal-clear that sub-thesis (ii) is false, as several philosophers have shown. Let me take the refutation by Wesley C. Salmon of (ii) (pp. 101-2) for making clear why.

We can predict a lunar eclipse if we know the positions of sun, earth and moon and the relevant laws of motion. This eclipse can be retrodicted using posterior conditions and the same laws. However, so Salmon, “if explanations are arguments, then only the predictive arguments can qualify as an explanation, and not the retrodictive one. The reason is obvious. We explain events on the basis of antecedent causes, not on the basis of subsequent effects (or other subsequent conditions)”. This becomes even clearer from Sylvan Bromberger’s flagpole example. If we know the elevation of the sun in the sky and the height of a flagpole, we can compute the length of the shadow of the flagpole; or if we know the length of the shadow, we can compute the height of the flagpole. However, only the presence and height of the flagpole explains the occurrence and length of the shadow but not the other way round. It is because “a causal process is involved, and that the light from the sun must either pass or be blocked by the flagpole before it reaches the ground where the shadow is cast” (italics Salmon). This refutation of sub-thesis (ii) is considered by some so fundamental that they call it the “killer” (Peter Godfrey-Smith) of Hempel’s covering law theory. Nonetheless, Hempel never revised his theory in light of the flagpole counterexample, which was put forward already one year after the publication of his Aspects... .

References: - Carl G. Hempel, Aspects of Scientific Explanation and other Essays in the Philosophy of Science. New York: The Free Press, 1965.

- Wesley C. Salmon, Causality and Explanation. New York/Oxford: Oxford University Press, 1998.