G. W. Leibniz

Pioneer Journal where reappraisal appeared Title Link to article containing reappraisal
G.W. Leibniz Notices AMS "Leibniz's laws of continuity and homogeneity" 12e
G.W. Leibniz Erkenntnis "Leibniz's infinitesimals: Their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond" 13f
G.W. Leibniz Studia Leibnitiana "Infinitesimals, imaginaries, ideals, and fictions" 14c
G.W. Leibniz HOPOS "Leibniz versus Ishiguro: Closing a Quarter Century of Syncategoremania" 16a
G.W. Leibniz Mat. Stud. "Leibniz's well-founded fictions and their interpretations" 18a
G.W. Leibniz British Journal for the History of Mathematics "Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks" 21a
G.W. Leibniz Antiquitates Mathematicae "Three studies in current Leibniz scholarship" 21g
G.W. Leibniz The Mathematical Intelligencer "Two-track depictions of Leibniz's fictions" 22b
G.W. Leibniz Antiquitates Mathematicae "Historical infinitesimalists and modern historiography of infinitesimals" 22a
G.W. Leibniz The Mathematical Intelligencer "Is pluralism in the history of mathematics possible?" 23a
G.W. Leibniz Revista Latinoamericana de Filosofía "When does a hyperbola meet its asymptote? Bounded infinities, fictions, and contradictions in Leibniz" 23h
G.W. Leibniz Handbook of the History and Philosophy of Mathematical Practice "Evolution of Leibniz's thought in the matter of fictions and infinitesimals" 23i
G.W. Leibniz Review of Symbolic Logic "Leibniz on bodies and infinities: rerum natura and mathematical fictions" 24a

G. W. Leibniz (1646-1716) wrote in a 14/24 june 1695 letter to l'Hospital:
"I use the term incomparable magnitudes to refer to [magnitudes] of which one multiplied by any finite number whatsoever, will be unable to exceed the other, in the same way [adopted by] Euclid in the fifth definition of the fifth book [of The Elements]."
In modern editions of The Elements, the definition of comparability appears in Book V, Definition 4.

Leibniz's comment in the original French can be viewed here, page 288

See also Depictions.

Leibniz NSA
relation of infinite proximity standard part
law of continuity transfer principle
infinitum terminatum line segment of unlimited length
assignable vs inassignable number standard vs nonstandard number
infinitesimal violates Euclid V.4 infinitesimal violates Archimedean property
constant differentials uniform partition into infinitesimal subsegments

See also Salvaging Leibniz
Infinitesimal topics
More on infinitesimals
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