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Plato and Pythagoreanism. (English) Zbl 1295.01002

Oxford: Oxford University Press (ISBN 978-0-19-989822-0/hbk). xxi, 305 p. (2013).
This book investigates the reception of Pythagoreanism, its early heritage and its impact on the philosophies of Plato (and Aristotle). The book does not aim at providing “a comprehensive account of all the ways Pythagoreanism, broadly conceived, might have influenced Plato’s philosophy. Its project is to open up new ways of understanding Plato’s intervention in a series of philosophical ideas that we can associate, with some plausibility, with a particular strand of early Pythagorean thought” (p. xiv). In the first three chapters the author focuses on the historiography of Pythagoreanism, picturing the split among the Pythagoreans in both philosophical and political respects. The second half of the book with four chapters is devoted to using this historical picture “in order to use it as a means to reconfigure our understanding of Plato’s response to mathematical Pythagorean philosophy” (p. 126).
The distinction between “so-called” or mathematical Pythagoreans and the “acousmatic” Pythagoreans can be traced back to Aristotle and is discussed in Chapter 1. Contrary to acousmatic Pythagoreans, who are devoted to the facts, mathematical Pythagoreans attempt to make use of demonstrations, but, according to the author’s suggestion, Aristotle criticizes both: “while the demonstrations offered by the mathematical Pythagoreans represent a significant philosophical innovation over the uncritical reflection on the so-called ‘facts’ by the acousmatic Pythagoreans, the mathematical Pythagoreans’ activity of hasty assimilation across categories leads to confusions in logic and metaphysics” (pp. 3–4).
Chapter 2 is devoted to the mathematical Pythagorean Hippasus of Metapontum (ca. 520–440 BCE?), later regarded as the progenitor of mathematical Pythagoreanism. The author argues that Aristoteles saw in Hippasus a natural philosopher putting forward theories of making the world, but he may have also seen in him “the first Pythagorean to perform demonstrations of the sort that produce a ‘reason why’ (\(\delta\)\(\iota\)ó\(\tau\)\(\iota\)), especially involving mathematics” (p. 83). The third chapter, entitled “Exoterism and the history of Pythagorean politics”, deals with the political history, i.e., the Pythagorean place in Greek history. In Chapter 4, the work of early mathematical Pythagoreans, as represented in genuine fragments and testimonies, is analyzed with respect to metaphysical positions, among them approaches to personal identity, number, priority and preexistence, and epistemology, which were reactions to Parmenidean monism and Heraclitean fluxism. Plato’s discussion of these ideas in the dialogue Cratylus, among them the “growing argument”, “in which the identity of names is challenged when there is addition, subtraction, or transposition of letters” (p. 165). Chapter 5 concentrates on Plato’s challenging of Pythagorean theories, especially in his Phaedo, seeking in his metaphysics “to supersede mathematical Pythagorean ideas concerning the nature of number” (p. 168). The final chapter “The method of Gods” has the purpose “to try to understand how Plato strategically employs the ‘first-discoverer’ myths of Prometheus, Palademes, and Theuth in order to explore what the methods of inquiry practiced by the mathematical Pythagoreans might offer to his philosophy in the later dialogues” (p. 201).
This is an inspiring book, widening the view on the Pythagoreans and their concept of number. The material is perfectly organized. Each chapter is provided with an introduction and a summary of conclusions. An index of places and a general index are added.

MSC:

01-02 Research exposition (monographs, survey articles) pertaining to history and biography
01A20 History of Greek and Roman mathematics
00A30 Philosophy of mathematics
03A05 Philosophical and critical aspects of logic and foundations
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