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Analogie und mathematisches Denken
Author(s) -
Knobloch Eberhard
Publication year - 1989
Publication title -
berichte zur wissenschaftsgeschichte
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.109
H-Index - 8
eISSN - 1522-2365
pISSN - 0170-6233
DOI - 10.1002/bewi.19890120105
Subject(s) - analogy , philosophy , meaning (existential) , epistemology , analogical reasoning , kepler , mathematics , calculus (dental) , linguistics , computer science , medicine , dentistry , stars , computer vision
This article deals with six aspects of analogical thinking in mathematics: 1. Platonism and continuity principle or the “geometric voices of analogy” (as Kepler put it), 2. analogies and the surpassing of limits, 3. analogies and rule stretching, 4. analogies and concept stretching, 5. language and the art of inventing, 6. translation, or constructions instead of discovery. It takes especially into account the works of Kepler, Wallis, Leibniz, Euler, and Laplace who all underlined the importance of analogy in finding out new mathematical truth. But the meaning of analogy varies with the different authors. Isomorphic structures are interpreted as an outcome of analogical thinking.