Tuesday, August 9, 2016

Network of Linné's "Philosophia Botanica" editions

Carl von Linné's book Philosophia Botanica (1751) was arranged as a series of botanical aphorisms, expanded over the previous 15 years from when he first developed them. During those years, he settled on binomial nomenclature as his preferred naming system, and he presents this in Philosophia Botanica, so that the book has considerable historical interest for biologists.

Recently, János Podani and András Szilágyi (History and Philosophy of the Life Sciences, in press) have pointed out a basic inconsistency in this book, relating to Linné's calculation of how many possible plant genera there could be, given the morphological features he used to distinguish among them.

Linné did not do a good job with this calculation, as these authors show. Indeed, the correct calculation is far more complex than Linné realized, but even given his simplifications his arithmetic is faulty. There are basic inconsistencies among the aphorisms, where the numbers do not "add up" when some of the aphorisms are compared. In essence, 31 plant parts are defined in one aphorism but this becomes "n=38" in a later aphorism; and then 4n2 is claimed to be "5736" rather than 5776.

This then raises the issue of how this error was treated in subsequent editions of Philosophia Botanica. Podani and Szilágyi trace the error through 14 subsequent editions, showing that the various editors of those editions dealt with the issue in different ways. The history of these editions can be represented as a phylogenetic diagram, which the authors also provide.

This history turns out to be a network, because some of the later editions were compiled from several earlier editions. The network is rooted at the bottom, and each network edge is implicitly directed away from the root. The book editions are named using their place and time of publication.

Note that one particular "solution" to the arithmetical issue arises independently in three separate editions of the book. That is, the three editions on the network's right independently correct the 4n2 problem but do not correct the 31=38 problem

Also, note that no editions since 1787 actually correct both errors (ie. they show both n=31 and 4n2 =3844). Recent editions are reprints of the original erroneous version.

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