Proclus argues that place (topos) is a body of light, identified as the luminous vehicle of the soul, which mediates between soul and body and facilitates motion. Simplicius (in Phys. 611,10–13) suggests that this theory is original to Proclus, and unique in describing light as a body. This paper focuses on the function of this theory as a bridge between Proclus’ physics and metaphysics, allowing the Aristotelian physical notion of “natural place” to serve as a mechanism for (...) the descent and ascent of the soul. (shrink)

I examine one aspect of the central role which mathematics plays in Proclus's ontology and epistemology, with particular reference to his Elements of Theology. I focus on his peculiar views about the ontological status of mathematical objects and the special faculties of the soul that are involved in understanding them. If they are merely abstract objects that are "stripped away" from sensible things, then they are unlikely to reorient the mind towards the intelligible realm, as envisioned by Plato in (...) the Republic. Thus, in order to defend the function of mathematics as a prodaideutic to dialectic, Proclus rejects Aristotelian abstractionism in favor of an elaborate account in terms of Nous projecting images of its Forms through the medium of the imagination. In metaphorical terms, he replaces the Aristotelian image of the soul as a blank tablet with that of a tablet that has always been inscribed and is always writing itself, while also being written on by Nous. The mediating function of mathematics for understanding the higher realities is grounded in the fact that its central principles of Limit and Unlimited have a universal provenance in Proclus's whole system of reality. (shrink)

Aquinas contradicts Isaiah VI. 6 because of his following of the ps. Dionysius, who is in turn reproducing the logical structures of Iamblichus and Proclus. These came to prevail despite doubts raised by earlier medieval theologians with the exception of Eriugena. Here are considered Thomas’ principles of biblical interpretation and the character of his Aristotelianism. His thought is shown to be a form of neoplatonic systematizing as developed by Iamblichus and Proclus.

These two texts are fundamental for the understanding not only of Neoplatonism but also of the conventions of biography in late antiquity. Neither has received such extensive annotation before in English, and this new commentary makes full use of recent scholarship. The long introduction is intended both as a beginner’s guide to Neoplatonism and as a survey of ancient biographical writing.

Sara Rappe has given us a stimulating book full of interesting suggestions concerning philosophers hardly known, in some cases, in the English-speaking world. She raises a question concerning these philosophers that has not previously been discussed on this scale. The question arises from the comparison of two features of Neoplatonism. For the Neoplatonist philosopher, discursive thinking does not yield knowledge. By discursive thought is meant the kind of thinking we normally practice. It has to do with objects external to thought, (...) objects mediated by images derived from sense perception or also from a higher form of thought. From these images discursive thought elaborates further ideas derived by methods of reasoning such as those codified in Aristotelian logic. This kind of thinking is open, however, to the attacks of Skepticism, against which the Neoplatonist argues by appealing to another form of thinking and to the knowledge it constitutes, a form of thinking free of all mediation separating subject and object of thought, where subject and object of thought are identical. This is not discursive thought; dis- cursive thought does not yield knowledge that is immune to skeptical attack and that is obtained by a form of thought beyond discursive thinking. To the extent that language is the expression of discursive thought, this knowledge is not expressed in language. Yet the Neoplatonists of Late Antiquity were plunged in discursivity. In particular, they did philosophy by interpreting texts, the authoritative texts of their tradition, not only Plato’s dialogues, but also the Aristotelian corpus and what they supposed were the more ancient sources of their philosophy, Pythagorean and Orphic texts and the Chaldaean Oracles. How are and to be reconciled? The thesis explored by Rappe in this book is that the Neoplatonists had recourse to nondiscursive textual strategies, images, symbols, myths, ritual formulae, so as to convey nondiscursive thought and knowledge through their reading of discursive texts. (shrink)

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

Traditional monotheism has long faced logical puzzles. We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed logic but an appendix is offered as a brief review.

Until recently, more scholarly careers were being devoted to the study of the teaching of St Thomas Aquinas than to any other philosophical or theological doctrine, with the possible exception of Marxism. Roman Catholic scholars have tended, however, to isolate his philosophical theology from its neo-Platonism, while others have treated the various parts of his Summa Theologiae without regard to their historical context. Dr Hankey's main contention is that Aquinas was less of an Aristotelian than is commonly supposed, and that (...) a proper appreciation of his work requires us to take fuller notice of his reliance on neo-Platonism. In setting out his case, Dr Hankey pays special attention to the influence of Proclus, whose work receives a critical exposition. The author supports his position by making a careful analysis of the first 45 questions of the Summa Theologiae. (shrink)

It was Plato who informed the Greek philosophical tradition of how the King of Egypt declared that writing will inevitably “implant forgetfulness in men’s souls; they will cease to exercise memory because they rely on that which is written, calling things to remembrance no longer from within themselves, but by means of external marks”. Plotinus likewise knew how these “wise men of Egypt” therefore chose to inscribe only one image in their temples and thus “manifested the non-discursiveness of the intelligible (...) world”. Sara Rappe reminds us that such passages are not infrequent throughout the history of Neoplatonism, suggesting how Plato and his followers struggled to understand the proper use of the written word, the role of images and symbol, as well as the very possibility of the transmission of truth itself. Focusing on the question: “How is intuitive wisdom communicated, especially within the context of a philosophy that repudiates language but continues to practice speculative metaphysics?”, Rappe has produced a helpful work aimed at examining the Neoplatonic hermeneutic. (shrink)

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Once more these annals offer the reader a substantial collection of varied articles and studies, mostly pertaining to issues of medieval philosophy and metaphysics. The contributors are from Austria, West Germany, and South Korea. Especially interesting are: the study on Kant's early writing, "The Only Possible Proof of God," by J. Bauer; a very strict analysis of the thirteenth chapter of Cusanus' book, De Visione Dei, by the Proclus specialist W. Beierwaltes; and an attempt at the "reconciliation" of metaphysics (...) and positivism by R. Wohlgenannt. There are a number of shorter book reviews and a lengthy instructive review article on R. Berlinger's recent book on Augustine's dialectical metaphysics. This review article is at least as interesting and inspiring as the major articles making up the bulk of the book.--M. J. V. (shrink)

Deterministic models in population dynamics often are really approximations to stochastic models, justified by an appeal to the law of large numbers. It is proposed to call such models pseudodeterministic. Four questions are discussed in this article: (1) What errors may be made by equating deterministically predicted values to expectations? (2) When, and in what sense, may numbers be assumed to be large? (3) How large are the variances, coefficients of variations, etc., as assigned to the variables in the stochastic (...) versions of the models? (4) What role may pseudodeterministic models play in empirical research, where problems of statistical reliability arise?As an example, a modified Nicholson-Bailey model of the interaction between insect parasitoids and their hosts is discussed; the modification consists of assigning a random (density-independent) mortality to the parasitoid population. A stochastic version of this model is discussed. The expectation of the final host density is compared with the value computed from the deterministic model. The latter value is systematically lower than the former. The magnitude of the difference depends on parameter values. The variability to be expected with the stochastic model is characterized by the coefficient of variation of the final host density; its dependence on parameter values and initial conditions is discussed. It is concluded that it is worthwhile in practical applications to estimate parasitoid mortality, and that the coefficient of variation in real situations may be far from negligible. (shrink)

In this paper the author discusses the complex question of whether Proclus regards theology as a demonstrative science along the lines of Euclidean geometry, or as a different kind of science that follows the dialectical model of Plato's Parmenides. This question is focused by considering the applicability to the Elements of Theology of the Euclidean model of science, while examining the limitations of this hermeneutical approach.

This volume represents some of the activities of the Boston Area Colloquium in Ancient Philosophy from the academic year 1997-98. It contains nine colloquia that were hosted by eight different colleges and universities in the greater Boston area. Discussions of the works of Plato dominate this volume, with six of the nine colloquia based on Platonic texts. Appropriately, the colloquia begin with an analysis of division in the ancient atomists. Later, a study of truth in Aristotle gives a counterpoint to (...) the Platonic interplay of drama and pedagogy or logic and rhetoric examined in papers about the "Theaetetus" and "Symposium". A presentation of Proclus’s account of evil revisits some of the issues of sophistry and morality discussed in relation to Plato’s "Republic" and "Euthydemus". Finally, the remaining Platonic papers are in a way not about Plato at all, but about Socrates and Xanthippe, supplementing Platonic dialogues with Xenophon and others. Underneath these discussions of ancient texts current modes of philosophy run along, providing a score of alternative interpretative schemes._ This publication has also been published in paperback, please click here_ for details. (shrink)

The word τερθρεία, which L. and S.8 derived from τερατεία and translated ‘the use of claptraps’, is perhaps best known from its occurrence in Isocrates , but the new edition has spread the net more widely, citing Philo, Philodemus, Proclus, Galen, Dion. Hal., and giving its meaning as ‘the use of extreme subtlety, hair-splitting, formal pedantry’. This agrees better with the gloss / κενοσπονδία attributed to Orus of Miletus in Et. Mag. 753. 4. Aristotle, Demosthenes, and Plutarch each use (...) τερθρεύομαι once. In the Helen Isocrates, condemning the futile ingenuity of the Sophists in writing encomia on such unworthy objects as salt and humble-bees, holds that such tours de force are immoral, as tending to deceive, representing a literary form of the vice περιεργία. Τερθρεία, then, should take its place, as a recognized term for the idle over-elaboration of a banausic theme, in the vocabulary of Greek literary criticism. It does not, however, appear in Rhys Roberts's ‘Glossary of Greek Rhetoric’ appended to his edition of D.H.'s On Literary Composition. No doubt this is because τερθρεία does not occur in this or any other of D.H.'s Scripta Rhetorica. But D.H. himself uses the word in Antiq. Rom. . Similarly J. F. Lockwood does not discuss the term in his lists in C.Q. xxxi and xxxii, where he collects words which are used metaphorically by D.H. in literary criticism. The metaphor in τερθρεία is certainly not obvious; but the literary sense must have involved some transference of meaning, for it is not to be expected that the word τερθρεία sprang, in full panoply of critical significance, from the brain of the Muse of Rhetoric; and it is part of the purpose of this paper to point the way to an explanation, or at least to set forth some known facts about the word and its possible congeners. (shrink)