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
LeibnizNSA
Stevin
Fermat
Euler
Cauchy
Riemann
Cantor
Skolem
Robinson
Hrbacek
Infinitesimal topics
More on infinitesimals
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