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The Functional Role of Structures in Bourbaki

In the history of 20th-century mathematical structuralism, the figure of Bourbaki is prominent and sometimes even identified with the philosophical doctrine of structuralism. However, the Bourbaki group consisted of pure mathematicians, among them the greatest of their generation, most of whom seemed little inclined to, and even hesitant about, philosophy. This essay proposes to explore this tension in line with the recent philosophical interest in scientific practice. The working assumption is that the use of the concept of structure in Bourbaki is not mainly conceptual and foundational, but pragmatic and functional. This functional interpretation is governed by the principle of the unity of mathematics. In addition to their deductive “vertical” dimension, taking into account structures can reveal various “horizontal” connections between different theories.