Two-Track Depictions of Leibniz’s Fictions

Mikhail Katz (1) , Karl Kuhlemann (2) , David Sherry (3) , Monica Ugaglia , Mark van Atten (4)

1 Bar-Ilan University [Israël]
2 Leibniz Universität Hannover=Leibniz University Hannover
3 Northern Arizona University [Flagstaff]
4 PG,HCP - Pays germaniques , histoire - culture - philosophie (UMR8547)

Leibniz described imaginary roots, negatives, and infinitesimals as useful fictions. But did he view such ‘impossible’ numbers as mathematical entities? Alice and Bob take on the labyrinth of the current Leibniz scholarship.

Mots clés: Bounded infinity; inassignables; incomparables; infinitesimals; part-whole axiom; useful fictions; Johann Bernoulli; Samuel Clarke

Domaines: Histoire, Philosophie et Sociologie des sciences; Philosophie; Histoire et perspectives sur les mathématiques [math.HO]

Mikhail Katz, Karl Kuhlemann, David Sherry, Monica Ugaglia, Mark van Atten. Two-Track Depictions of Leibniz’s Fictions. The Mathematical Intelligencer, 2022, 44 (3), pp.261-266. ⟨10.1007/s00283-021-10140-3⟩. ⟨hal-03738885⟩