On the borderline between Science and Philosophy: A debate on determinism in France around 1880

• Interest in instabilities and bifurcations emerged in the late nineteenth century.
• New concepts appeared: principe directeur, Auslösung, trigger-work, …
• These developments revived philosophical debates on determinism.
• Mathematicians, physicists, physiologists and philosophers were involved.
• The French mathematician Joseph Boussinesq played an important role in that debate.

In the second half of the nineteenth century, a new interest in explosive chemical reactions, sudden release of energy in living beings, physical instabilities, and bifurcations in the solutions of differential equations drew the attention of some scholars. New concepts like triggering actions and guiding principles also emerged. Mathematicians, physicists, physiologists, and philosophers were attracted by this kind of phenomena since they raised a question about the actual existence of a strict determinism in science. In 1878 the mathematical physicist Joseph Boussinesq pointed out a structural analogy among physical instabilities, some essential features of living beings, and singular solutions of differential equations. These developments revived long-lasting philosophical debates on the problematic link between deterministic physical laws and free will. We find in Boussinesq an original and almost isolated attempt to merge mathematical, physical, biological, and philosophical issues into a complex intellectual framework. In the last decades, some philosophers of science rediscovered the connection between physical instabilities and determinism, both in the context of chaos theory, and in the debates on the Norton dome. I put forward a consistent historical reconstruction of the main issues and characters involved.