Abstract
Both Iamblichus and Proclus are well aware that when they discuss the relation between soul and mathematicals they are treating a traditional problem. Both know that their solution concerning the identification of the soul with all kinds of mathematicals (three in Iamblichus, four in Proclus) is not the only one offered by philosophers. In both the Iamblichus passages we find representatives of three points of view: those who identify the soul with the arithmetical, those who identify it with the geometrical, those who identify it with the harmonical. Proclus enumerates representatives of only two points of view (arithmeticals and geometricals), and there are only two names (Severus and Moderatus) common to both lists. But both obviously feel that they are contributing to the solution of a traditional problem. The question is legitimate: How far back can we trace the problem?
This chapter continues some of the ideas presented previously in: P. Merlan “Beitraege zur Geschichte des antiken Piatonismus”, Philologus 89 (1934) 35-53; 197-214 and idem, “Die Hermetische Pyramide und Sextus”, Museum Helveticum 8 (1951) 100-105.
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References
On the exclusion of astronomy from mathematics in Posidonius see E. Bréhier, “Posidonius d’Apamée, théoricien de la géometrie”, Revue des Etudes grecques 27 (1914) 44–58. On the nonmotive character of geometricals in Posidonius see A. Schmekel, Die positive Philosophie in ihrer geschichtlichen Entwicklung 2 vv. (1938, 1914), v.I 105 f.
Cf. F. M. Cornford, Plato’s Cosmology (1937) 63. See, however, also P. Shorey, “The Timaeus of Plato”, American Journal of Philology 10 (1889) 45–78, esp. 51 f., and idem, “Recent Interpretations of the Timaeus”, Classical Philology 23 (1928) 343-362, esp. 352. But here as in so many cases the question of the correct interpretation of Plato is less important than the question how he was actually interpreted.
Cf. the discussion of this topic in E. R. Goodenough, “A Neo-Pythagorean Source in Philo Judaeus”, Yale Classical Studies 3 (1932) 115–164, esp. 125 f.
Cf. L. Edelstein, “The Philosophical System of Posidonius”, American Journal of Philology, 57 (1936) 286–325, esp. 303; also P. Tannery, La Géometrie grecque (1887) 33 n. 2.
Cf. P. Merlan, “Aristotle’s Unmoved Movers”, Traditio 4 (1946) 1–30, esp. 4 f.
Or two steps, if we accept the theory of F. E. Robbins, “Posidonius and the Sources of Pythagorean Arithmology”, Classical Philology 15 (1920) 309–322 and idem, “The Tradition of Greek Arithmology”, ibid., 16 (1921) 97-123, esp. 123 (cf. K. Staehle, Die Zahlenmystik bei Philon von Alexandreia [1931] 15) according to which there is behind Posidonius some arithmological treatise composed in the 2nd century. Cf. also A. Delatte, Etudes sur la littérature pythagoricienne (1915), esp. 206-208 and idem, “Les doctrines pythagoriciennes des livres de Numa”, Bull, de l’Academie R. de Belgique (Lettres) 22 (1936) 19-40, tracing back the revival of Pythagorism to the beginning of the 2nd century B.C.
The extent to which this problem still is with us can be seen e. g. in V. Kraft, Mathematik, Logik und Erfahrung (1947). Cf. also O. Becker, “Mathematische Existenz”, Jahrbuch fuer Philosophie und phaenomenologische Forschung 8 (1927) 439–809, esp. 764-768; M. Steck, Grundgebiete der Mathematik (1946) 78-95.
Bibliographical Note
A. Boeckh, Ueber die Bildung der Weltseele im Timaeos des Platon (1807) repr. in: Gesammelte kleine Schriften, v. III (1866) 109-180, esp. 131 f; Th. Henri Martin, Études sur le Timée de Platon, 2 vv. (1841), v. I 375-378; A. Schmekel, Die Philosophie der mittleren Stoa (1892) 426 f.; 430-432; R. M. Jones, The Platonism of Plutarch (1916) 68-80, esp. 73 n. 12; 90-94 — his own paraphrase of ή τῶν περάτων ουσία ouata is “the basis of the material world”, with a refutation (93 f.) of G. Altmann, De Posidonio Piatonis commentatore (1906) who interpreted it as geometrice formae; L. Robin, Etudes sur la Signification et la Place de la physique dans la philosophie de Platon (1919), repr. in La Pensée hellénique (1942) 231-366, 52-54; R. M. Jones, “The Ideas as the Thoughts of God”, Classical Philology 21 (1926) 317-326, esp. 319; A. E. Taylor, A Commentary on Plato’s Timaeus (1928) 106-136, equating ή τῶν περάτων ουσία with extension; P. Merlan, “Beitraege zur Geschichte des antiken Piatonismus. II. Poseidonios ueber die Weltseele in Piatons Timaios”, Philologus 89 (1934) 197–214.
Of the more recent literature on Posidonius only W. Jaeger, Nemesios von Emesa (1915) need to be mentioned in the present context. Too speculative for the present topic is
J. R. Mattingly, “Cosmogony and Stereometry in Posidonian Physics”, Osiris 3 (1937) 558–584.
Idées et des Nombres d’après Aristote (1908) 479-498; J. Moreau, La Construction de l’Idéalisme Platonicien (1939), esp. 343-366 (M. identifies ideas and mathematical and takes both to be only products of the mind); idem, L’Ame du Monde de Platon aux Stoiciens (1939), esp. 43-53; F. Solmsen, Die Entwicklung der aristotelischen Logik und Rhetorik (1929) 79-84; 101-103; 237; 250; E. Frank, “The Fundamental Opposition of Plato and Aristotle”, American Journal of Philology 61 (1940) 34–53; 166-185, esp. 48-51.
In many respects my identification of Plato’s world-soul with the mathematicals is a return to F. Ueberweg, “Ueber die Platonische Weltseele”, Rheinisches Museum 9 (1854) 37–84, esp. 56, 74, 77 f.
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Merlan, P. (1953). Posidonius and Neoplatonism. In: From Platonism to Neoplatonism. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-6205-2_3
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