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realm of nature. Immediately after the absolute one, Iamblichus introduced a second superexistent unity to stand between it and the many as the producer of intellect, and made the three succeeding moments of the development (intellect, soul and nature) undergo various modifications. He speaks of them as intellectual (θεοὶ νοεροί), supramundane (ὑπερκόσμιοι), and mundane gods (ἐγκόσμιοι). The first of these—which Plotinus represented under the three stages of (objective) being (ὄν), (subjective) life (ζωή), and (realized) intellect (νοῦς)—is distinguished by him into spheres of intelligible gods (θεοὶ νοητοί) and of intellectual gods (θεοὶ νοεροί), each subdivided into triads, the latter sphere being the place of ideas, the former of the archetypes of these ideas. Between these two worlds, at once separating and uniting them, some scholars think there was inserted by Iamblichus, as afterwards by Proclus, a third sphere partaking of the nature of both (θεοὶ νοητοὶ καὶ νοεροί). But this supposition depends on a merely conjectural emendation of the text. We read, however, that “in the intellectual hebdomad he assigned the third rank among the fathers to the Demiurge.” The Demiurge, Zeus, or world-creating potency, is thus identified with the perfected νοῦς, the intellectual triad being increased to a hebdomad, probably (as Zeller supposes) through the subdivision of its first two members. As in Plotinus νοῦς produced nature by mediation of ψυχή, so here the intelligible gods are followed by a triad of psychic gods. The first of these is incommunicable and supramundane, while the other two seem to be mundane though rational. In the third class, or mundane gods (θεοὶ ἐγκόσμιοι), there is a still greater wealth of divinities, of various local position, function, and rank. We read of gods, angels, demons and heroes, of twelve heavenly gods whose number is increased to thirty-six or three hundred and sixty, and of seventy-two other gods proceeding from them, of twenty-one chiefs (ἡγεμόνες) and forty-two nature-gods (θεοὶ γενεσιουργοί), besides guardian divinities, of particular individuals and nations. The world is thus peopled by a crowd of superhuman beings influencing natural events, possessing and communicating knowledge of the future, and not inaccessible to prayers and offerings.

The whole of this complex theory is ruled by a mathematical formulism of triad, hebdomad, &c., while the first principle is identified with the monad, νοῦς with the dyad, and ψυχή with the triad, symbolic meanings being also assigned to the other numbers. “The theorems of mathematics,” he says, “apply absolutely to all things,” from things divine to original matter (ὕλη). But though he thus subjects all things to number, he holds elsewhere that numbers are independent existences, and occupy a middle place between the limited and unlimited.

Another difficulty of the system is the account given of nature. It is said to be “bound by the indissoluble chains of necessity which men call fate,” as distinguished from divine things which are not subject to fate. Yet, being itself the result of higher powers becoming corporeal, a continual stream of elevating influence flows from them to it, interfering with its necessary laws and turning to good ends the imperfect and evil. Of evil no satisfactory account is given; it is said to have been generated accidentally.

In his doctrine of man Iamblichus retains for the soul the middle place between intellect and nature which it occupies in the universal order. He rejects the passionless and purely intellectual character ascribed to the human soul by Plotinus, distinguishing it sharply both from those above and those below it. He maintains that it moves between the higher and lower spheres, that it descends by a necessary law (not solely for trial or punishment) into the body, and, passing perhaps from one human body to another, returns again to the supersensible. This return is effected by the virtuous activities which the soul performs through its own power of free will, and by the assistance of the gods. These virtues were classified by Porphyry as political, purifying (καθαρτικαί), theoretical, and paradigmatic; and to these Iamblichus adds a fifth class of priestly virtues (ἱερατικαὶ ἀρεταί), in which the divinest part of the soul raises itself above intellect to absolute being.

Iamblichus does not seem ever to have attained to that ecstatic communion with and absorption in deity which was the aim of earlier Neoplatonism, and which Plotinus enjoyed four times in his life, Porphyry once. Indeed his tendency was not so much to raise man to God as to bring the gods down to men—a tendency shown still more plainly in the “Answer of Abamon the master to Porphyry’s letter to Anebo and solutions of the doubts therein expressed,” afterwards entitled the Liber de mysteriis, and ascribed to Iamblichus.

In answer to questions raised and doubts expressed by Porphyry, the writer of this treatise appeals to the innate idea all men have of the gods as testifying to the existence of divinities countless in number and various in rank (to the correct arrangement of which he, like Iamblichus, attaches the greatest importance). He holds with the latter that above all principles of being and intelligence stands the absolute one, from whom the first god and king spontaneously proceeds; while after these follow the ethereal, empyrean, and heavenly gods, and the various orders of archangels, angels, demons, and heroes distinguished in nature, power, and activity, and in greater profusion than even the imagination of Iamblichus had conceived. He says that all the gods are good (though he in another place admits the existence of evil demons who must be propitiated), and traces the source of evil to matter; rebuts the objection that their answering prayer implies passivity on the part of gods or demons; defends divination, soothsaying, and theurgic practices as manifestations of the divine activity; describes the appearances of the different sorts of divinities; discusses the various kinds of sacrifice, which he says must be suitable to the different natures of the gods, material and immaterial, and to the double condition of the sacrificer as bound to the body or free from it (differing thus in his psychology from Iamblichus); and, in conclusion, states that the only way to happiness is through knowledge of and union with the gods, and that theurgic practices alone prepare the mind for this union—again going beyond his master, who held assiduous contemplation of divine things to be sufficient. It is the passionless nature of the soul which permits it to be thus united to divine beings,—knowledge of this mystic union and of the worship associated with it having been derived from the Egyptian priests, who learnt it from Hermes.

On one point only does the author of the De mysteriis seem not to go so far as Iamblichus in thus making philosophy subservient to priestcraft. He condemns as folly and impiety the worship of images of the gods, though his master held that these simulacra were filled with divine power, whether made by the hand of man or (as he believed) fallen from heaven. But images could easily be dispensed with from the point of view of the writer, who not only held that all things were full of gods (πάντα πλήρη θεῶν, as Thales said), but thought that each man had a special divinity of his own—an ἴδιος δαίμων—as his guard and companion.

The following are the extant works of Iamblichus: (1) On the

Pythagorean (Life (Περὶ τοῦ Πυθαγορικοῦ βίου), ed. T. Kiessling (1815), A. Nauck (St Petersburg, 1884); for a discussion of the authorities used see E. Rohde in Rheinisches Museum, xxvi., xxvii. (1871, 1872); Eng. trans. by Thomas Taylor (1818), (2) The Exhortation to Philosophy (Λόγος προτρεπτικὸς εἰς φιλοσοφίαν), ed. T. Kiessling (1813); H. Piselli (1888). (3) The treatise On the General Science of Mathematics (Περὶ τῆς κοινῆς μαθηματικῆς ἐπιστήμης), ed. J. G. Friis (Copenhagen, 1790), N. Festa (Leipzig, 1891). (4) The book On the Arithmetic of Nicomachus (Περὶ τῆς Νικομάχου ἀριθμητικῆς εἰσαγωγῆς), along with fragments on fate (Περὶ εἱμαρμένης) and prayer (Περὶ εὐχῆς), ed. S. Tennulius (1688), the Arithmetic by H. Pistelli (1894). (5) The Theological Principles of Arithmetic (Θεολογούμενα τῆς ἀριθμητικῆς)—the seventh book of the series—by F. Ast (Leipzig, 1817). Two lost books, treating of the physical and ethical signification of numbers, stood fifth and sixth, while books on music, geometry and astronomy followed. The emperor Julian had a great admiration for Iamblichus, whom he considered “intellectually not inferior to Plato”; but the Letters to Iamblicus the Philosopher which bear

his name are now generally considered spurious.
The so-called Liber de mysteriis was first edited, with Latin

translation and notes, by T. Gale (Oxford, 1678), and more recently by C. Parthey (Berlin, 1857); Eng. trans. by Thomas Taylor (1821).