This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.

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)

Resumen En el presente artículo se explora la pertenencia de los libros M y N al programa general de la Metafísica de Aristóteles. Los libros XIII y XIV han quedado en el trasfondo de la Metafísica, como una suerte de agregado editorial, del cual se puede prescindir para la comprensión de la propuesta aristotélica. En el presente artículo, sin embargo, se asume un punto de partida diferente, que consiste en integrar estos libros al núcleo de la propuesta de la Metafísica, (...) enten diendo que ellos son claves para completar el panorama de la teoría general de la sustancia, o ousiología, que guía todos los libros metafísicos. De este modo, la discusión de M y N sobre números y principios viene a concluir la cuestión de la sustancia como causa y principio, anunciada desde el inicio de la Metafísica y desarrollada en sus libros centrales.This article explores the belonging of books M and N to the generalprogram of Aristotle's Metaphysics. Books XIII and XIV have remained in the background of Metaphysics, as a kind of editorial aggregate, which can be dispensed with for the understanding of the Aristotelian proposal. In this article, however, a different startingpoint is assumed, which consists in integrating these books into the core of the proposal of Metaphysics, understanding that they are key to completing the panorama of the general theory of substance, or ousiology, which guides all metaphysical books. Thus, the discussion of numbers and principles within M and N concludes the question of substance as cause and principle, announced from the beginning of Metaphysics and developed in its central books. (shrink)

ABSTRACTThis article examines how Christians who had been deprived of the direct sponsorship of the state articulated their claims for political and religious freedom. I examine four cases from the fifth and sixth century in the Eastern Roman Empire and Sasanian Iran. Here I argue that Scriptural models provided an important reservoir of political ideas that could be used by clerics to undermine state authority, whether to underscore the conditional nature of Roman claims to authority or to deny an equality (...) of religious freedom to non-Christian co-citizens. (shrink)

This paper studies moral education in Proclus and Iamblichus. The first section analyses Proclus’ theory of moral education and its psychological underpinnings. Especially important in this context is the identification of the faculty of choice with the passive or teachable intellect. The second section investigates the implementation of this theory into practice with the help of Iamblichus’ Letter to Sopater: On Bringing up Children. The final section demonstrates how Proclus’ famous tripartite division of poetry should be understood in the context (...) of his program of moral education. (shrink)

In his commentary on Euclid, Proclus says both that the first principle of geometry are self-evident and that they are hypotheses received from the single, highest, unhypothetical science, which is probably dialectic. The implication of this seems to be that a geometer both does and does not know geometrical truths. This dilemma only exists if we assume that Proclus follows Aristotle in his understanding of these terms. This paper shows that this is not the case, and explains what Proclus himself (...) means by definition, hypothesis, axiom, postulate, and the self-evident, and how geometry is a science that receives its principles from dialectic. (shrink)

_ Source: _Volume 63, Issue 4, pp 449 - 476 While we know that the interpretation of the ‘soul’s pilot’ found in Hermias’ _Scholia on Plato’s Phaedrus_ differs considerably from that of Syrianus and Proclus, this difference has not shifted the prevailing opinion that the _Scholia_ are a faithful transcript of Syrianus’ lectures on the _Phaedrus_. I argue, however, that the difference over the soul’s pilot is only the first in a series of elements which are difficult, if not impossible, (...) to ascribe to Syrianus. This, I believe, is compelling evidence that the _Scholia_ contain the ideas of both Syrianus and Hermias. (shrink)

This study aims to examine how becoming like God is handled in Avicenna’s philosophy. Basically the article is based on the need to interpret that Plato and Aristotle and Plotinus are philosophers that complement each other, not diverge, in terms of the topic of becoming like God. First and foremost I present Avicenna’s arguments using the concepts of becoming like god and becoming like the First as a springboard. Moreover, based on the context in which Avicenna uses the concept of (...) manifestation, I examine how the idea of unification with God is transformed into an intellectual ideal. In the last section, I present the connection between the journey of becoming a perfected human and becoming like god which was established in the Metaphysics volume of The Book of Healing as a section of the matter which is related to ethics. (shrink)