BMCR 2015.09.46

Zenon von Elea: Studien zu den ‘Argumenten gegen die Vielheit’ und zum sogenannten ‘Argument des Orts’. Beiträge zur Altertumskunde, Bd 330

, Zenon von Elea: Studien zu den 'Argumenten gegen die Vielheit' und zum sogenannten 'Argument des Orts'. Beiträge zur Altertumskunde, Bd 330. Berlin; München; Boston: De Gruyter, 2014. viii, 440. ISBN 9783110362923. €109.95.

Table of Contents

« In this capricious world, nothing is more capricious than posthumous fame. One of the most notable victims of posterity’s lack of judgment is the Eleatic Zeno ».1 The authoritative warning of Bertrand Russell to take Zeno of Elea into serious consideration represents both concrete proof of the vitality of this pre-Socratic philosopher within contemporary thought, and an indication of the risk frequently run by his renowned paradoxes of being misunderstood or considered as sheer sophisms.2 The new book by Gerhard Köhler on the figure of Zeno undoubtedly represents an important contribution to the understanding of the most controversial topics of his thought. The monograph consists of nine chapters, of which ch. 7 is a summary of the conclusions reached; while the last two chapters contain a complete and detailed bibliography with reference editions and secondary literature (ch. 8), and a series of indices with the sources, the corresponding concordance to the Diels-Kranz collection, and the relevant names of persons and things (ch. 9). Because of the high complexity of the issue, Köhler devotes the entire introductory chapter to methodological questions (pp. 1-7). As is always the case with the pre-Socratic philosophers, the crucial problem with studying Zeno in depth is represented by the tradition of his fragments. The extant sources have to be handled with a great deal of care, taking into account the lack of the general context and the reasons for their later selection. These preliminary operations are performed by Köhler on DK 29 B 1-3, handing down the ‘arguments against plurality’, and DK 29 B 5, devoted to the so-called ‘paradox against place’.

In ch. 2 (pp. 8-13), Köhler classifies the sources on Zeno into three groups: a) the sources that are very likely based on a direct (total or partial) knowledge of Zeno, handing down first-hand information (Plato, Aristotle, Simplicius); b) the authors for whom it is impossible to ascertain whether they had a direct knowledge of Zeno or drew on secondary texts (on the one hand, Themistius, Proclus, and John Philoponus; on the other, Eudemus of Rhodes, Alexander of Aphrodisias, and Porphyry, with the last three sources polemically referred by Simplicius within his account of frs. B 1-3); c) finally, the authors who do not give any further information on Zeno and, in the majority of instances, just paraphrase sources quoted before (Syrianus, Asclepius, Alexander of Aphrodisias, and Elias).

Ch. 3 (pp. 14-42) represents a useful and complete introduction to Zeno’s life3 and philosophy. After a cursory discussion of his main points of thought according to Diogenes Laërtius (IX 29, 50-55 Dorandi = DK 29 A 1),4 Köhler tackles the question of the real number of his writings (cf. Procl., in Parm. 694, 17-695, 1 Steel; Elias, in Cat. 109, 15-20 Busse = DK 29 A 15) and systematically lists the Zenonian arguments transmitted to us: both those against motion and those against plurality. Köhler highlights the common methodological strategy of all these paradoxes ( reductio ad absurdum) and tries to detect their aims and addressees. As to this last point, Köhler does not believe – as some scholars did – that Zeno polemicized directly against the Pythagoreans. On the contrary – and convincingly, in my view – he accepts the thesis that Zeno’s polemical target is not to be identified with a specific philosophical ‘party’, but more generally with “common human opinions” ( gesunder Menschenverstand), as seems to be suggested by Plato’s Parmenides (127e8-10: παρὰ πάντα τὰ λεγόμενα).

In ch. 4 (pp. 43-84), Köhler deals with the tricky question of Zeno’s argument against the place. Following the conclusions of Guido Calogero,5 in the Nachträge to the 6th edition of the Vorsokratiker (1951 6, I, p. 498), Walther Kranz maintained that Simplicius’ testimonium on this argument ( in Phys. 562, 4-6 Diels) was a textual quotation from Zeno’s writing. Since then, in the Diels-Kranz collection B 5 has been steadily added to the corpus of Zenonian fragments in Diels-Kranz. But the thesis of the great Italian scholar, which was already criticized by Kurt von Fritz6 and others, now seems to have been definitively demolished by Köhler through doxographical and stylistic arguments that, I believe, will lead future editors of Zeno to leave out B 5 from the list of his fragments.

The pages of the chapter devoted to the interpretation of Zeno’s so-called ‘paradox of place’ are even more interesting. Against the traditional view, which reduces it to a mere denial of τόπος, Köhler tries in an original way to go beyond the ‘barricades’ of the Peripatetic doxography (Aristot., Phys. Δ 3, 210b22; 1, 209 a 23; Eudem., Phys., fr. 78 Wehrli = DK 29 A 24). In particular, he suggests substituting the Greek expression ἐν τόπῳ ( in one place) with ἐν ἄλλῳ ( in something else). In fact, in his opinion it is « insgesamt also nicht unplausibel, dass der Begriff ‚Ort‘ bei Zenon selbst noch gefehlt hat und erst von Aristoteles hinzugefügt worden ist » (p. 65). On the basis of this assumption, Köhler shows, first, that the real target of the paradox was not the place, but the idea that each thing has to be also in something else (ἐν ἄλλῳ); and, secondly, that Zeno’s real philosophical aim was to prove that certain things can exist only in themselves (ἐν αὑτοῖς μόνον). Consequently, Köhler concludes by taking the opportunity to rename this paradox as «‚Zenons Argument über die Inklusion (von Dingen)‘» (p. 83), and by considering it as an argument in defence of Parmenides’ ontology only in this sense (DK 28 B 8, 29; 36-37).

Ch. 5 (pp. 85-301) is yet more complex and articulated. Here Köhler undertakes to examine the difficult frs. B 1-3, which hand down the so-called Zenonian ‘arguments against the plurality’. These three texts are standardly considered to share two separate arguments, to one of which should be ascribed B 1-2, to the other B 3. Against this thesis, Köhler tries instead to demonstrate that B 1-3 are strictly connected on a logical level because they pursue a unique line of reasoning, characterized by Köhler as Argumentation A. For this purpose, Köhler begins by contextualizing the tradition of the arguments against plurality. In particular, he examines the famous testimonium of Plato’s Parmenides (127e8-128d6 = DK 29 A 12), drawing attention to the fact that Zeno seems there to consider both the pluralistic (πολλά ἐστι τὰ ὄντα) and the monistic (ἕν ἐστι τὸ ὄν) thesis exclusively from a mereological perspective, i.e. reducing them to a question about the plurality or absence of parts. But we have no certain proof that Zeno stated the matter in this way. On the other hand, it cannot be ruled out that Plato restated the argument incorrectly. One possibility, Köhler observes, is to translate the two theses of Plato’s dialogue according to mereological criteria (‚Jedes einzelne Ding stellt eine Vielheit von Teilen dar‘/‚Das Seiende ist eine teillose Einheit‘), while others are to understand them according to numerical criteria (‚Es gibt eine Vielzahl von Dingen‘/‚Das Seiende stellt nur eine einzige Entität dar‘) or qualitative ones (‚Jedes einzelne Ding weist eine Vielzahl von Eigenschaften auf‘/‚Das Seiende besitzt nur eine einzige Eigenschaft‘).

All this represents the premise for the most demanding section of the monograph, where Köhler accurately contextualizes the tradition of frs. B 1-3 within the commentary of Simplicius to p. 187a1-3 of Aristotle’s Physics (138, 3-141, 20 Diels). For this purpose, Köhler studies in depth the position of Simplicius towards the four authors that he mentions with regard to the Aristotelian passage: Alexander of Aphrodisias (Simpl., in Phys. 138, 3-28 Diels), Eudemus (Simpl., in Phys. 138, 29-139, 19 Diels), Themistius (Simpl., in Phys. 139, 19-23 Diels), and Porphyry (Simpl., in Phys. 139, 24-141, 20 Diels). After this careful examination, Köhler is finally in a position to show, against the communis opinio, that frs. B 1-3 belong to a sole Zenonian argument grounded on the following assumption: everything that has an extension is always divisible and therefore constituted by a plurality of parts. If this is true, Zeno’s argument is not directed against the many, but against the numerical and mereological plurality of things (Köhler reconstructs the conclusions of the paradox in the following way at p. 260: that « weder [a] jedes einzelne der vielen (wahrnehmbaren) Dinge eine Einheit sei, noch [b´] jedes einzelne dieser vielen Dinge eine Vielheit von Teilen sei, die ihrerseits je für sich eine mereologische Einheit darstellten, noch (b´´) jedes einzelne dieser vielen Dinge eine Vielheit von Teilen sei, die ihrerseits wiederum mereologische Vielheiten seien »).

The book concludes with an interesting excursus (ch. 6: pp. 302-336) on the Fortwirkung of Zeno’s thought in the history of ancient philosophy. Here, Köhler reviews the use of Zeno’s paradoxes made by Plato’s Parmenides, and their fortune in the philosophy of Anaxagoras and above all in the first atomists (Leucippus and Democritus). This last topic, among other things, was already considered by John Burnet as « the most important point in the history of early Greek philosophy ».7 Each paragraph of this chapter provides useful starting points for further research on the individual philosophers discussed. The brief appendix on the alleged reminiscence of Zeno within Epicurus’ Letter to Herodotus (41, 6-9; 56, 4-57, 10) gives a proper end to a work that is stimulating, well-documented, and certainly fated to revive debate on Zeno of Elea for years to come.


1. B. Russell, The Principles of Mathematics, Cambridge: Cambridge University Press, 1903; London: Allen and Unwin, 1937 2, § 327, p. 347.

2. A survey of Zeno’s fortune from the 19th Century until today has been recently made by Livio Rossetti in J. Barnes et al., Eleatica 2008: Zenone e l’infinito, eds. L. Rossetti-M. Pulpito (“Eleatica”, 2), Sankt Augustin: Academia Verlag, 2011, pp. 13-18.

3. As for the βίος, paragraph 3.1 weighs accurately all the sources concerning the life of the pre-Socratic philosopher. With regard to Zeno’s death and his anti-tyrannical attitude, Köhler could have added two papyrological texts to those listed at p. 16, n. 45: Did., Comm. in Ps. 34, 15, P.Tura V 217, 33-218, 2 Gronewald (= CPF I.1***, 109, 1T), although this is considered an uncertain testimonium; and Philod., Mort. IV, P.Herc. 1050, col. 35, 25-34 Henry, which represents the only evidence for Zeno in the Herculaneum papyri. In this last passage Zeno is mentioned, together with Socrates and Anaxarchus, as an example of someone who underwent a heroic death. The testimonium is missing in the Stellenregister as well (pp. 383-394), although Köhler quotes T. Dorandi, De Zénon d’Élée à Anaxarque. Fortune d’un topos littéraire, in: L. Jerphagnon-J. Lagrée-D. Delattre (eds.), Ainsi parlaient les anciens. In honorem J.-P. Dumont, Lille: Presses Universitaires de Lille, 1994, pp. 27-37, where the Herculanean passage is briefly taken into account (p. 31).

4. For Diogenes Laërtius’ text, Köhler uses the edition of M. Marcovich. It would have been desiderable, in my opinion, to quote (or, at least, to mention in the list of the editions) the new text of T. Dorandi, Diogenes Laertius. Lives of Eminent Philosophers (“Cambridge Classical Texts and Commentaries”, 50), Cambridge: Cambridge University Press, 2013.

5. G. Calogero, Studi sull’Eleatismo (“Pubblicazioni della Scuola di filosofia della R. Università di Roma”, 3), Rome: Tipografia del Senato, 1932 (Florence: La Nuova Italia, 1977 2), p. 93, n. 1.

6. Cf. Kurt von Fritz, in: Gnomon 14 (1938), pp. 91-109, esp. 104-105.

7. J. Burnet, Early Greek Philosophy, London: Adam and Charles Black, 1892; 1908 2, p. 385.