on coincidence: 1

In Mill’s Logic, that grand old lumber room, in Chapter 18 of Book three,  a principle is spelled out that, in our day, has been shorthanded into the sometimes tendentious phrase,  correlation does not prove causation:
“Although two or more cases in which the phenomenon a has been met with may have no common antecedent except A, this does not prove that there is any connection between a and A, since a may have many causes, and may have been produced, in these different instances, not by any thing which the instances had in common, but by some of those elements in them which were different.”
Mill, in keeping with his practical bent, distills from this a question: “After how many and what sort of instances may it be concluded that an observed coincidence between two phenomena is not the effect of chance?”
Another way of putting this question is: when is a coincidence really a coincidence?
As Francois Mentre has pointed out, the French mathematician and scientist, Cournot, was also intested in this question, or at least in one of its guises: the reality of probability. Cournot worked in the shadow of Laplace; but where Laplace, finally, came down on the side of a universal determinism, Cournot was sure that this move was not justified by Laplace’s mathematics.  “He could not admit that chance was nothing  but a “vain sound, flatus vocis, which we use, as Laplace said, to disguise our ignorance of true causes.” For him [Cournot], chance had an objective reality independent of our knowledge.” (144) Cournot spelled out his ontological conviction by way of a critique of Laplace. Laplace wrote that Nature obeys “a small number of immutable laws.” Cournot’s disprove of Laplace’s determinism moves from this idea: “it suffices, said Cournot, that there be only two, perfectly independent one from the other, in order that we must make a place for the fortuitous in the government of the world. Whether or not  we do or do not know the literal law for each of the independent two series, as soon as they intersect, there is chance. Chance thus does not derive from our ignorance of the laws of the universe, no more than it diminishes as the measure of our knowledge extends. It subsists in the eyes of the expert as well as those of the ignoramus. It is necessary to accept it as an irreducible, sui generis fact that has a notable part in the government of the world.” (209)
This, though, is hard to accept, either for the expert or the ignoramus or that hybrid of the two, the modern mystic..
One can see that Cournot’s observation blocks two popular explanations of coincidence (or chance – in fact, I am using coincidence here as a proxy for a semantic family that includes the French hasard and the German Zufall). True coincidence can neither be purely the effect of human ignorance of the causes in place, nor can itself be characteristic of some autonomous law – a law of synchronicity or seriality. The same reasoning Cournot applies to other laws would apply in this case, so that any law of synchronicity would inevitably generate coincidences that would fall outside its domain as it intersected with other universal laws, creating, if you will, hypercoincidences.
One way of looking at physics in the 20th century is that the physicists were both moved by the fact that the world given by a structure that was governed by two or more irreducible laws would have to accord a large place to chance – such that probability was no longer a way of mathematically stylizing elements that were, to an all powerful intelligence, always certain – and a movement to unify the laws of physics, to reduce them to some grand single principle, which would drive out coincidence.

However, there was also a tradition, a fringe tradition, that rejected the whole idea that coincidence wasn’t subject to its own proper law. Instead, it sought that law. This was an especially popular theme in Germany in the 20s, coexisting with a faddish interest in psychoanalysis, physiognomics, graphology, paranormal psychology, etc. Psychoanalysis had a tentative relationship with these things, which fascinated Freud, but which, finally, he diagnosed as cultural symptoms of a mass psychopathology.