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Abstract

In 1878 the mathematician Joseph Boussinesq pointed out a structural analogy between some features of living beings and singular solutions of differential equations. Sudden transitions between ordinary and singular solutions could represent sudden release of energy in biological process and in the fulfilment of free will. He assumed that a guiding principle rather than a physical action might lead the system beyond the threshold of singular points. Deterministic processes, which corresponded to ordinary solutions, gave way to indeterministic processes, which corresponded to singular solutions. Alongside the mathematical pathway, a different conceptual stream had already emerged in the second half of the nineteenth century. Both physicists and physiologists made use of concepts like triggering actions and guiding principles in order to represent explosions and unstable equilibrium in inanimate matter, and the complex interaction between volitions and motions in human beings. A third conceptual stream was represented by philosophical debates on the problematic link between deterministic physical laws and free will. The new issues stemming from the fields of mathematics, physics, and life sciences found room in philosophical journals, but the interest of philosophers gradually faded away towards the late 1880s. At the same time, the majority of mathematicians and physicists had never shown a systematic interest in this subject matter. We find in Boussinesq an original and almost isolated attempt to merge mathematical, physical, biological issues into a consistent philosophical framework. However questionable his research programme might be, it was actually a daring and systematic one. In the twenty-first century, some philosophers of science rediscovered the problematic link between determinism and singular solutions of differential equations. The memory of late nineteenth-century debates had already disappeared, but recently Marij van Strien has put forward a direct comparison between those debates and recent theses on determinism.