Article
ID: CBB383762874

Antieuklidisch oder nichteuklidisch? Tertium datur! Einige methodologische Reflexionen zur Wissenschaftshistorie anlässlich des Anachronismusvorwurfes gegen Imre Tόths Aristotelesdeutung (Anti-Euclidean or non-Euclidean? Tertium datur! Some Methodological Reflections on the History of Science on Occasion of the Accusation of Anachronism against Imre Tóth's Interpretation of Aristotle) (2022)

unapi
Non-euclidean geometry History as a discipline; chronology; study of the past 21st century Ancient Greece Aristotle Toth, Imre

The essay defends the basic claim of Imre Tóth’s book “Fragmente und Spuren nichteuklidischer Geometrie bei Aristoteles” of 2010, namely that the Greeks in the 4th century BC understood the logical consistency of alternatives to Euclidean geometry, against the ill-advised criticism that this ascription is anachronistic. Besides general reflections on the hermeneutics of scientific texts, the essay offers a thorough philological analysis of the most important Aristotelian passage (“De caelo” 281b5-6). It argues furthermore that the famous passage by Proclus on the limiting parallel cannot have originated with him but probably goes back to the discussions in the Academy as well. Against Tóth, it insists that the Greeks’ encounter with spheric geometry was the starting point of their reflections and that the recognition of the alternatives’ consistency did not entail an acceptance of their truth. Their position was therefore neither anti-euclidean like Saccheri’s nor non-euclidean like Gaus’s.

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Authors & Contributors
Ambrosi, Gerhard Michael
Bjerre, Jørn
Erskine, Andrew
Falcon, Andrea
Goulding, Robert
Haehling, Raban von
Journals
Apeiron: Journal for Ancient Philosophy and Science
Archive for History of Exact Sciences
Circumscribere: International Journal for the History of Science
Geographia antiqua
Greek, Roman, and Byzantine Studies
History of the Human Sciences
Publishers
University of Southern California
Einaudi
Parmenides Publishing
Springer
University of Michigan Press
Walter de Gruyter
Concepts
History as a discipline; chronology; study of the past
Geometry
Historiography
Non-euclidean geometry
Mathematics
Science and culture
People
Aristotle
Euclid
Polybios
Apollonius, of Perga
Archimedes
Durkheim, Émile
Time Periods
Ancient
16th century
19th century
20th century, early
Renaissance
4th century, B.C.
Places
Greece
Rome (Italy)
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