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The Neoplatonic triad consists of Existence (hyparxis), Power/Life (dynamis/zoë), and Intellect (nous). This Neoplatonic triad, in turn, reflects a combination of the Chaldean terms for Father/Existence, Power, and Intellect with the Plotinian formula of Being, Life, and Intellect. (See fragment 4 and notes; compare Proclus, Elements of Theology, propositions 101-103.)
Of further interest is the appearance of the term tridynamis (triple-powered) in the writings of Marius Victorinus, used to describe the Christian God (e.g., Against Arius IV.21.26). As such, the Christian Trinity is viewed by Victorinus as consisting of the Father (or Being), the Son (or Intellect), and a median, Holy Spirit (or Life) who is feminine in nature. Victorinus also refers to the "Spirit" as mother (mater) and connection (conexio). A similar unorthodox understanding of the Christian Trinity is found in the Hymns of Synesius who, like Victorinus, views the "Spirit" (or pnoia, not pneuma; see, e.g., Hymn 2(4), 98) as a median, feminine entity, variously termed "birth-pang" (ōdis), "mother" (mātēr), and "daughter" (thygatēr). Although this generative, feminine "Spirit" (for both Synesius and Victorinus) is patterned on the Chaldean Power (dynamis, as mediated through Porphyry),See P. Hadot, Marius Victorinus, Traités Théologiques sur la Trinité, II (Paris, 1960), pp. 868; 874-875; Porphyre et Victorinus, I (Paris, 1968), pp. 455-474. Augustine, however (although influenced by Victorinus), clearly rejected (or misunderstood) this trinitarian scheme at the ontological level. See The City of God, X.23: "He (Porphyry) says that the Father is God and the Son is God, whom he calls in Greek the 'paternal intellect' or 'paternal mind'; but about the Holy Spirit, he says either nothing or nothing clear; however, I do not understand whom he means as the medium between these. For if, like Plotinus, when he discusses the three primary substances, he also wished the nature of the soul to be understood, he would not say the 'medium' of these, that is, the medium of the Father and the Son. Plotinus, indeed, places the nature of the soul after the paternal intellect; but this man, when he says 'medium,' does not place it after, but places it between." However, Augustine’s psychological trinity of mind, love, and knowledge (in the view of Theiler and Hadot) may have been influenced by Chaldean notions (see notes to fragment 44). the occurrence of similar triads in various Gnostic sources (e.g., Father, Mother/Spirit, Son) reflects an important interchange between the school traditions of Platonism and the Platonic "underworld."For further discussion, see J. M. Robinson, "The Three Steles of Seth and the Gnostics of Plotinus," Proceedings of the International Colloquium on Gnosticism (Stockholm, 1977), pp. 132-142; B. Pearson, "The Tractate Marsanes (NHC X) and the Platonic Tradition," in Gnosis, Festschrift für Hans Jonas (Göttingen, 1978), pp. 373-384; ibid., "Gnosticism as Platonism," Harvard Theological Review, 77 (1984), pp. 55-72; J. Turner, "Sethian Gnosticism: A Literary History," in Nag Hammadi, Gnosticism, and Early Christianity, ed. C. W. Hedrick and R. Hodgson, Jr. (Peabody, MA, 1986), pp. 79-86.
In the Chaldean system, a complex "chain" of lesser beings fills the spaces between the Primordial TriadLydus, On the Months, IV, 122, suggests a divine Ennead as well, but the evidence is inconclusive. See Hadot, Porphyre, I, p. 262, n. 1. and the world of matter.