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The Number Ten Reconsidered: Did the Pythagoreans Have an Account of the Dekad?

Irina Deretić and Višnja Knežević
From the journal Rhizomata

Abstract

We critically reconsider an old hypothesis of the role of the dekad in Pythagorean philosophy. Unlike Zhmud, we claim that: 1) the dekad did play a role in Philolaus’ astronomical system, and 2) Aristotle did not project Plato’s theory of the ten eidetic numbers onto the Pythagoreans. We claim that the dekad, as the τέλειος ἀριθμός, should be understood in Philolaus’ philosophy as completeness and the basis of counting in Greek – as in most other languages – in a decimal system. Additionally, we argue that the number ten is not even a candidate for the τέλειος ἀριθμός in Plato’s philosophy. As a final result of our discussion, we compare and contrast Philolaus’, Plato’s, and Speusippus’ accounts of completeness in relation to numbers.

Acknowledgments

We are grateful to our anonymous referee and the editor for their helpful comments, which improve the quality of our paper. We gratefully acknowledge the insightful comments and suggestions given to us on this paper by Nicholas D. Smith. We have also benefited from the remarks given by Zoran Markovic, Darko Todorovic, Constantinos Macris, Caterina Pello and Orsat Ligorio. The first draft of this paper was presented at the 2018 Conference of the International Association for Presocratic Studies. Many thanks to the conference participants for their feedback, and we are responsible for any remaining flaws.

Abbreviations

DK

Diels, Hermann & Kranz, Walther (1951), Die Fragmente der Vorsokratiker. 3 Vols. 6th Ed. Berlin: Weidman.

DL

Diogenes Laertius, Lives of Eminent Philosophers

Dox. Gr.

Diels, Hermannus (1965), Doxographi Graeci. Editio Quarta. Berolini: Apud Walter de Gruyter et Socios.

Huffman

Huffman, Carl (1993), Philolaus of Croton: Pythagorean and Presocratic. Cambridge: Cambridge University Press.

Iambl. Theol. Arithm.

[Iamblichus] Theologoumena Arithmeticae edidit V. de Falco Stuttgart: Teubner, 1975

Iamb. VP.

Iamblichus, On the Pythagorean Way of Life

Isnardi Parente

Isnardi Parente, Margherita, ed. (1980): Speusippo Frammenti. Naples: Bibliopolis.

Rose

Rose, Valentinus (1886), Aristotelis fragmenta. Leipzig: Teubner.

Ross

Ross, David (1955), Aristotelis fragmenta selecta. Oxford: Clarendon Press.

SE Adv. Math.

Sextus Empiricus, Against the Mathematicians

Stob. Eclog.

Stobaeus, Eclogues

Tarán

Tarán, Leonardo (1981), Speusippus of Athens. Leiden: Brill

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Published Online: 2020-11-25
Published in Print: 2020-11-25

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