Three case studies in current Leibniz scholarship

Two-track depictions of Leibniz's fictions

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.

莱布尼茨有争议的无穷小：进一步的描绘

Leibniz's contested infinitesimals: Further depictions

本文反驳了Arthur和Rabouin关于莱布尼茨视无穷小为矛盾的观点，捍卫莱布尼茨将真正的无穷小视为与负数、虚数同等的虚构数学实体的论点。

Is pluralism in the history of mathematics possible?

Leibniz scholarship is currently an area of lively debate. We respond to some recent criticisms by Archibald et al.

Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks

Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g., Ishiguro, Levey) opt for a default Weierstrassian framework, Arthur compares LC to a non-Archimedean framework SIA (Smooth Infinitesimal Analysis) of Lawvere-Kock-Bell. We analyze Arthur's comparison and find it rife with equivocations and misunderstandings on issues including the non-punctiform nature of the continuum, infinite-sided polygons, and the fictionality of infinitesimals. Rabouin and Arthur cla…

Controversies in the foundations of analysis: Comments on Schubring's Conflicts

Foundations of Science recently published a rebuttal to a portion of our essay it published two years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his 2005 book, Conflicts between generalization, rigor, and intuition. He further argues that our attempt to show that Cauchy is part of a long infinitesimalist tradition confuses text with context and thereby misunderstands the significance of Cauchy's use of infinitesimals. Here we defend our original analysis of variousmisconceptions and misinterpretations concerning the history of infinitesimals and, in particular, t…

Leibniz's well-founded fictions and their interpretations

Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that of Ishiguro and Arthur. Leibniz's own views, expressed in his published articles and correspondence, led Bos to distinguish between two methods in Leibniz's work: (A) one exploiting classical `exhaustion' arguments, and (B) one exploiting inassignable infinitesimals together with a law of continuity. Of particular interest is evidence stemming from Leibniz's work Nouveaux Essais sur l'Entendement Humain …