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 LUH - Leibniz Universität Hannover [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.

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

Domains: Humanities and Social Sciences; History, Philosophy and Sociology of Sciences; Humanities and Social Sciences; Philosophy; Mathematics [math]; History and Overview [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⟩