25 - SOME PROBLEMS ARISING OUT OF THE DISCUSSION OF CHANCE

Summary

1. There are two classical problems in which attempts have been made to attribute certain astronomical phenomena to a specific cause, rather than to objective chance in some such sense as has been defined in the preceding chapter.

The first of these is concerned with the inclinations to the ecliptic of the orbits of the planets of the solar system. This problem has a long history, but it will be sufficient to take De Morgan's statement of it. If we suppose that each of the orbits might have any inclination, we obtain a vast number of combinations of which only a small number are such that their sum is as small or smaller than the sum of those of the actual system. But the very existence of ourselves and our world can be shown to imply that one of this small number has been selected, and De Morgan derives from this an enormous presumption that ‘there was a necessary cause in the formation of the solar system for the inclinations being what they are’.

The answer to this was pointed out by D'Alembert in criticising Daniel Bernoulli. De Morgan could have reached a similar result whatever the configuration might have happened to be. Any arbitrary disposition over the celestial sphere is vastly improbable à priori, that is to say in the absence of known laws tending to favour particular arrangements. It does not follow from this, as De Morgan argues, that any actual disposition possesses à posteriori a peculiar significance.