summary of On Logic and the Theory of Science by Jean Cavaillès:

Jean Cavaillès’s On Logic and the Theory of Science is a profound and dense work of philosophy of science that reflects both his training in mathematics and his deep engagement with logic and epistemology. Written in the 1930s and published posthumously after his execution in 1944 as a member of the French Resistance, the book represents his most important philosophical contribution. Cavaillès challenges traditional epistemologies that view science as founded on fixed principles, timeless categories, or the psychology of the knowing subject. Instead, he presents science as a dynamic, evolving system, governed not by immutable laws but by the internal necessity of its own development. Drawing on mathematical logic, the work of Hilbert, and the crisis in the foundations of mathematics (involving paradoxes, Gödel’s incompleteness theorems, and debates around formalism), Cavaillès develops the notion of a “dialectic of concepts,” where scientific progress occurs through transformations of conceptual structures rather than mere accumulation of facts. For him, logic and science are not neutral tools but living, historical processes that embody their own rational necessity. This position sets him against both Kantian transcendentalism, which grounds knowledge in fixed conditions of human cognition, and positivism, which reduces science to empirical verification. By emphasizing the internal logic of scientific development, Cavaillès anticipates later philosophies of science, including structuralism and historical epistemology, influencing figures like Gaston Bachelard, Georges Canguilhem, and Michel Foucault. On Logic and the Theory of Science thus stands as both a rigorous analysis of logic’s relation to science and a manifesto for understanding scientific knowledge as a process of conceptual becoming, reflecting Cavaillès’s unique synthesis of mathematics, philosophy, and historical sensitivity.