Abstract

In 1874, the French philosopher Émile Boutroux wrote a dissertationon the contingency of the laws of nature that highly influenced academic philosophy during the French Third Republic and led to a more hypothetical view of the natural sciences and mathematics. Boutroux took over the concept of contingency from the neo-Kantian philosopher Eduard Zeller who had insisted against Hegel on the role of contingency in history, and carried it over to nature. From this he tried to show that the sciences are hierarchically structured such that each layer is irreducible to its more basic predecessor. He also distinguished between two kinds of natural laws in a way very similar to Nancy Cartwright in the1980s. It is finally shown that Boutroux’s view on the nature of mathematics as a hypothetical science had a strong impact on Poincaré.