An investigation of Proclus' logic of the syllogistic and of negations in the Elements of Theology, On the Parmenides, and Platonic Theology. It is shown that Proclus employs interpretations over a linear semantic structure with operators for scalar negations (hypemegationlalpha-intensivum and privative negation). A natural deduction system for scalar negations and the classical syllogistic (as reconstructed by Corcoran and Smiley) is shown to be sound and complete for the non-Boolean linear structures. It is explained how Proclus' syllogistic presupposes converting the (...) tree of genera and species from Plato's diairesis into the Neoplatonic linear hierarchy of Being by use of scalar hyper and privative negations. (shrink)

In De Mysteriis VIII Iamblichus gives two orderings of first principles, one in purely Neoplatonic terms drawn from his own philosophical system, and the other in the form of several Egyptian gods, glossed with Neoplatonic language again taken from his own system. The first ordering or taxis includes the Simple One and the One Existent, two of the elements of Iamblichus' realm of the One. The second taxis includes the Egyptian (H)eikton, which has now been identified with the god of (...) magic, Heka, glossed as the One Existent. The Egyptian god Kmeph is also a member of this taxis, and is the Egyptian Kematef, a god of creation associated with the solar Amun-Re. Iamblichus refers to this god also as the Hegemon of the celestial gods, which should be equated to Helios, specifically the noeric Helios as described by Julian in his Hymn to Helios. Iamblichus describes Kmeph as an “intellect knowing himself”, and so the noeric Kmeph/Helios should also be seen as the Paternal Demiurgic Zeus, explicitly described also by Proclus as an intellect knowing himself. This notion of a self-thinking intellect may offer a solution to the problematic formulation by Proclus in his Timaeus commentary of Iamblichus' view of the Demiurgy encompassing all the noeric realm. The identification of Kmeph as the noeric Helios now also allows the first direct parallels to de Mysteriis to be found in extant Hermetica. In addition it can be inferred from the specific Neoplatonic terminology employed that the noetic Father of Demiurges, Kronos, appears, as well as the secondary Demiurgic triad of Zeus, Poseidon, and Pluto, in the forms of the Egyptian Amun, Ptah, and Osiris, thus raising the question that much of the theology documented only in Proclus might appear already to have been established by Iamblichus. (shrink)