Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks
Jacques Bair, Piotr Blaszczyk, Robert Ely, Mikhail G. Katz, Karl, Kuhlemann

TL;DR
This paper critically examines various modern frameworks for Leibnizian calculus, highlighting misunderstandings in recent scholarship and proposing Robinson's infinitesimal analysis as the most faithful formalization.
Contribution
It clarifies foundational issues in Leibnizian calculus and formalizes it within Robinson's SPOT framework, emphasizing key distinctions like boundedness and the law of continuity.
Findings
Robinson's framework best captures Leibnizian procedures
Identifies errors in Arthur's comparison of frameworks
Formalizes Leibnizian concepts using SPOT
Abstract
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 claim that Leibniz considers infinities as contradictory, and that Leibniz' definition of incomparables should be understood as nominal rather than as semantic. However, such claims hinge upon a conflation of Leibnizian notions of bounded infinity and unbounded infinity, a distinction emphasized by…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
