Procedures of Leibnizian infinitesimal calculus: an account in three modern frameworks
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Publication:5030479
DOI10.1080/26375451.2020.1851120OpenAlexW3121573947WikidataQ128213450 ScholiaQ128213450MaRDI QIDQ5030479
Karl Kuhlemann, Piotr Błaszczyk, R. Ely, Mikhail G. Katz, Jacques Bair
Publication date: 17 February 2022
Published in: British Journal for the History of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2011.12628
Related Items
Infinitesimal analysis without the axiom of choice ⋮ LEIBNIZ ON BODIES AND INFINITIES: RERUM NATURA AND MATHEMATICAL FICTIONS ⋮ Three case studies in current Leibniz scholarship ⋮ Two-track depictions of Leibniz's fictions ⋮ Effective infinitesimals in \(\mathbb{R}\) ⋮ Infinitesimals via Cauchy sequences: refining the classical equivalence
Cites Work
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- Leibniz's syncategorematic infinitesimals
- Leibniz's infinitesimals: their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond
- One of Berkeley's arguments on compensating errors in the calculus
- Set theory. An introduction to independence proofs
- Differentials, higher-order differentials and the derivative in the Leibnizian calculus
- Non-nonstandard analysis: Real infinitesimals
- Galileo and Leibniz: Different approaches to infinity
- Toward a history of mathematics focused on procedures
- Book review of: G. W. Leibniz, De quadratura arithmetica circuli ellipseos et hyperbolae cujus corollarium est trigonometria sine tabulis
- Reverse mathematics and parameter-free transfer
- Approaches to analysis with infinitesimals following Robinson, Nelson, and others
- Infinity in early modern philosophy
- The metaphysics of the calculus: A foundational debate in the Paris Academy of Sciences, 1700-1706
- Leibniz's rigorous foundation of infinitesimal geometry by means of Riemannian sums
- Euler and the structure of mathematics
- Leibniz's syncategorematic infinitesimals. II: Their existence, their use and their role in the justification of the differential calculus
- On mathematical realism and applicability of hyperreals
- L'Hôpital's \textit{Analyse des infiniments petits}. An annotated translation from the French with source material by Johann Bernoulli
- Letter to the editors of the journal \textit{Historia Mathematica}
- Cauchy, infinitesimals and ghosts of departed quantifiers
- The continuous, the discrete and the infinitesimal in philosophy and mathematics
- Fermat's method of maxima and minima and of tangents. A reconstruction
- Infinitesimal analysis without the axiom of choice
- The Real and the Complex: A History of Analysis in the 19th Century
- Leibniz’s Rigorous Foundations of the Method of Indivisibles
- Formalizing non-standard arguments in second-order arithmetic
- Leibniz in Cantor’s Paradise: A Dialogue on the Actual Infinite
- A short life of Euler
- The wake of Berkeley's analyst: Rigor mathematicae?
- Radically Elementary Probability Theory. (AM-117)
- Axiomatic foundations for Nonstandard Analysis
- Internal set theory: A new approach to nonstandard analysis
- A topological interpretation of three Leibnizian principles within the functional extensions
- Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen
- Internality, transfer, and infinitesimal modeling of infinite processes†
- The unreasonable effectiveness of Nonstandard Analysis
- Continuity between Cauchy and Bolzano: issues of antecedents and priority
- The Indivisibles of the Continuum
- The Continuum, the Infinitely Small, and the Law of Continuity in Leibniz
- Intuitionistic/Constructive Accounts of the Continuum Today
- Contemporary Infinitesimalist Theories of Continua and Their Late Nineteenth- and Early Twentieth-Century Forerunners
- Leibniz’s Actual Infinite in Relation to His Analysis of Matter
- Leibniz on The Elimination of Infinitesimals
- Leibniz’s Laws of Continuity and Homogeneity
- Rings of Real-Valued Continuous Functions. I
- Non-standard analysis
- Mathematical Conquerors, Unguru Polarity, and the Task of History
- 19th-century real analysis, forward and backward
