Article ID: CBB273122416

Bad math in Linnaeus’ Philosophia Botanica (2016)


In Philosophia Botanica (1751), Carolus Linnaeus (1707–1778) presented a calculation of the number of plant genera that may be distinguished based on his taxonomic concepts. In order to derive that number, he relied upon the organs of fructification, which represent the flower and the fruit, by selecting over 30 elements from them, and then assuming that each could vary by four dimensions. However, while Linnaeus was good in counting stamens and pistils, he and many of his followers who edited or translated Philosophia Botanica were less careful, basing their calculations of the number of possible genera on flawed assumptions, or even introducing basic arithmetic errors. Furthermore, although mathematics was quite advanced in the eighteenth century, the gap between combinatorial and botanical thinking was too deep, preventing Linnaeus to seek a reasonable solution to the problem he raised. The authors demonstrate this by a historical analysis of 15 editions of Philosophia Botanica, plus many references to it, and conclude that the desired number almost always appeared in error during the past 265 years. The German botanist J. G. Gleditsch (1714–1786) was the most successful with respect to Linnaeus’ original intention. Elementary mathematics demonstrates that if Linnaeus’ assumptions were taken seriously, then the possible number of genera would be astronomical. The practice he followed in Genera Plantarum (1754) shows, however, that the fructification dimensions served as a universal set for Linnaeus from which he chose only the relevant ones for describing a particular genus empirically. Based on the corrections and modifications implemented in reworked editions, we suggest an evolutionary network for the historical and modern versions or translations of Philosophia Botanica.

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Authors & Contributors
Reeds, Karen
Blunt, Wilfrid
Stearn, William T.
Fara, Patricia
Gribbin, Mary
Gribbin, John R.
Noesis: Travaux du Comité Roumain d'Histoire et de Philosophie des Sciences
Archives of Natural History
Interdisciplinary Science Reviews
Annali dell'Università di Ferrara. Sezione 3, Filosofia. Discussion papers
Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences
Journal of the History of Biology
Princeton University Press
Columbia University Press
Oxford University Press
William Heinemann
Pour la Science
Société Française de Systématique
Classification in biology
Scientific illustration
Terminology and nomenclature
Linnaeus, Carolus
Banks, Joseph
Thunberg, Carl Peter
North, Marianne
Hooker, Joseph Dalton
Masson, Francis
Time Periods
18th century
19th century
Great Britain
Uppsala Universitet
Linnean Society of London
Lund. Universitet

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