| 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"
| 24d |
G.W. Leibniz | London Mathematical Society
Newsletter | "A Leibniz/NSA
comparison" | 24b |
G.W. Leibniz | Review of Symbolic Logic |
"Leibniz on bodies and infinities: rerum natura and
mathematical
fictions" | 24c |
|
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
Stevin
Fermat
Euler
Cauchy
Riemann
Cantor
Skolem
Robinson
Hrbacek
Infinitesimal topics
More on infinitesimals
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