Leibniz as inventor of conceptual mathematics?

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• David Rabouin (CNRS (Centre national de la recherche scientifique))
• Monday 20 January 2025, 14:30-15:30
• Seminar Room 1, Newton Institute.

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MHMW01 - Modern history of mathematics: emerging themes

On numerous occasions, Leibniz argued that mathematical demonstrations could be resolved into two indemonstrable elements: definitions and axioms, themselves ultimately reducible to “identicals”. Based on the famous demonstration of “2 + 2 = 4” in the Nouveaux Essais sur l’entendement humain, Frege saw in this statement the first evidence of a form of “logicism”. This reading has played a major role in the interpretation of Leibniz right up to the present day, even among those who dispute the “logicist” interpretation and often simply dismiss the role of “reduction to the identicals”. It is then argued that this motto is an ideal that Leibniz never put into practice. In this presentation, based on a recent exploration of the archives, I will show that this classic fracture in commentary is based on two errors of appreciation: on the one hand, “logicist” interpretations have failed to take into account the fact that “identical” axioms are stated in the plural; on the other, interpretations more focused on mathematical practice have failed to see that the strategy of reduction to the identical is indeed at the heart of a certain practice that I propose to call “conceptual”. Following the thread of Leibniz’s drafts, I’ll try to explain how and why this strategy came about, showing in the process how it led to a new way of thinking about mathematics.

This talk is part of the Isaac Newton Institute Seminar Series series.

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