Drawing on recent scholarship and delving systematically into Iamblichean texts, these ten papers establish Iamblichus as the great innovator of Neoplatonic philosophy who broadened its appeal for future generations of philosophers.

This paper critically examines the use of the name 'Pseudo-Archytas' to refer to two aspects of the reception of Archytas of Tarentum in antiquity: the 'author-inflection' and the 'authority-inflection'. In order to make progress on our understanding of authority and authorship within the Pythagorean tradition, it attempts to reconstruct Porphyry's views on the importance of Archytas as guarantor of Pythagorean authenticity in the former's lost work On the History of the Philosophers by considering a fragment preserved in Arabic by Ibn (...) Abī Uṣaybi‘a. The article finally argues that a range of problems attend our use of the term 'pseudo-Archytas', which is not fit for purpose when considering the evidence regarding authorship and authority in the Pythagorean tradition. It recommends a more critical approach to the notion of authenticity within the Pythagorean tradition and suggests a new term, 'Archytism', as a more useful point of reference. (shrink)

Eugene Afonasin highlights the wealth of information on Pythagoras and his tradition preserved in Clement of Alexandria’s Stromateis and presents them against the background of Later Platonic philosophy. He  rst outlines what Clement knew about the Pythagoreans, and then what he made of the Pythagorean ideal and how he reinterpreted it for his own purposes. Clement clearly occupies an intermediate position between the Neopythagorean biographical tradition, rmly based on Nicomachus, and that more or less vague and difuse literary situation (...) which preceded the later developments, and in this respect is a very good source, worth studying for its own sake and as supplementary material which can help to understand the great Pythagorean synthesis attempted by Iamblichus. Developing their variants of the “exhortation to philosophy” (protreptikoi logoi), these men were much concerned with the educational value of the Pythagorean way of life rather than biographical circumstances, designed to place the ancient sage in the proper cultural context. (shrink)

_ Source: _Volume 10, Issue 1, pp 40 - 64 This paper focuses on the four preserved commentaries to a Pythagorean poem known as the _Golden Verses_. It deals with two Greek texts—Iamblichus’ _Protrepticus_ and Hierocles’ _Commentary to the Golden Verses_—as well as two commentaries preserved in Arabic, attributed to Iamblichus and Proclus. The article analyses how each of these commentators understood the relationship between man and god in the context of the eschatological vision presented in the poem. It also (...) demonstrates how differences in the interpretation of particular verses and ideas within the poem were dependent on an author’s philosophical views and cultural background. (shrink)

I aim to clarify the argument for space that Newton presents in De Gravitatione (composed prior to 1687) by putting Newton's remarks into conversation with the account of geometrical knowledge found in Proclus's Commentary on the First Book of Euclid's Elements (ca. 450). What I highlight is that both Newton and Proclus adopt an epistemic progression (or “order of knowing”) according to which geometrical knowledge necessarily precedes our knowledge of metaphysical truths concerning the ontological state of affairs. As I argue, (...) Newton's commitment to this order of knowing clarifies the interplay of the imagination and understanding in geometrical inquiry and illuminates how geometrical knowledge of space can lead to knowledge that space depends on and is related to God. In general, appreciating the Proclean elements of Newton's argument brings added light to the significance of geometrical inquiry for his general natural philosophical program and grants us insight into the philosophical grounding for the notion of absolute space that is presented in the Principia mathematica (1687). (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)

In this paper I show that Proclus is an adherent of the Classical Model of Science as set out elsewhere in this issue (de Jong and Betti 2008), and that he adjusts certain conditions of the Model to his Neoplatonic epistemology and metaphysics. In order to show this, I develop a case study concerning philosophy of nature, which, despite its unstable subject matter, Proclus considers to be a science. To give this science a firm foundation Proclus distills from Plato’s Timaeus (...) the basic concepts Being and Becoming and a number of basic propositions, among others the quasi-definitions of the basic concepts. He subsequently explains the use of these quasi-definitions, that are actually epistemic guides, in such a way that he obtains a connection between a rational and an empirical approach to the natural world. A crucial task in establishing the connection is performed by the faculty of doxa and by geometrical conversion. The result is that Proclus secures a universal, necessary and known foundation for all of philosophy of nature. (shrink)

From the first century BCE onwards, philosophers started to write commentaries on those Aristotle’s treatises that were meant for the internal use of his school. Plato’s works had been commented on already earlier, the first reported commentary originates in the 300s BCE. Commentaries are treatises that follow an object text in a more or less linear fashion. The format was not unknown before the first century BCE but new in extensive philosophical use. This review essay focuses on authors who commented (...) on Aristotle’s works. The commentaries emerged when Platonists and Aristotelians observed the need to teach the philosophy of these ancient masters to their students and to systematise their philosophy to respond to rival schools. In the late ancient schools, Plato and Aristotle were considered great thinkers, whose views needed to be studied carefully when considering any matter at hand. Many also argued that, despite the initial appearance to the contrary, there is no deep disagreement between Plato and Aristotle but, rather, a division of labour; Aristotle is dominant in natural philosophy and Plato in theology. However, this harmony thesis was not universally accepted. Despite their respect for Plato and Aristotle, the commentators were not mere followers of these authors. They developed, criticised and transformed the doctrines in significant ways, not only by suggesting different answers to the same questions but also by transforming the questions themselves. (shrink)

Descartes’ Rules for the direction of the mind presents us with a theory of knowledge in which imagination, considered as an “aid” for the intellect, plays a key role. This function of schematization, which strongly resembles key features of Proclus’ philosophy of mathematics, is in full accordance with Descartes’ mathematical practice in later works such as La Géométrie from 1637. Although due to its reliance on a form of geometric intuition, it may sound obsolete, I would like to show that (...) this has strong echoes in contemporary philosophy of mathematics, in particular in the trend of the so called “philosophy of mathematical practice”. Indeed Ken Manders’ study on the Euclidean practice, along with Reviel Netz’s historical studies on ancient Greek Geometry, indicate that mathematical imagination can play a central role in mathematical knowledge as bearing specific forms of inference. Moreover, this role can be formalized into sound logical systems. One question of general epistemology is thus to understand this mysterious role of the imagination in reasoning and to assess its relevance for other mathematical practices. Drawing from Edwin Hutchins’ study of “material anchors” in human reasoning, I would like to show that Descartes’ epistemology of mathematics may prove to be a helpful resource in the analysis of mathematical knowledge. (shrink)

Sometime between 1589 and 1591, a momentous discovery was announced in Florence; or, at least, a discovery thought to be momentous by its promoter: "The true form of the octave is the octuple [ratio 8:1] and not the duple [2:1]".1 Thus taken out of context, we might be forgiven if we failed either to share the author's enthusiasm or to recognize the importance of his finding. But the fact remains that, sadly, nobody else did either: not only did his contemporaries (...) decline to adopt this dramatic solution to the problem of the musical consonances,2 but even those who may take an almost perverse interest at times in the forgotten or the misbegotten—among others, historians of... (shrink)

In The First Principle, Jonathan Greig examines the philosophical theology of the two Neoplatonists, Proclus and Damascius (5th–6th centuries A.D.), on the One as the first cause. Both philosophers address a tension in the Neoplatonic tradition: namely that the One was seen as absolutely transcendent, yet it was also seen as intimately related to other things as the source of their unity and being. Proclus’ solution is to posit intermediate causes after the One, while Damascius posits a distinct principle, the (...) ‘Ineffable’, above the One. This book provides a new, thorough study of the theories of causation that lead each to their respective position and reveals crucial insights involved in a rigorous negative theology employed in metaphysics. (shrink)

The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.

This paper analyzes and explains certain parts of Syrianus’s Commentary on book M of Aristotle’s Metaphysics, which details Syrianus’s response to Aristotle’s attack against the Platonic position of the separate existence of numbers. Syrianus defends the separate existence not only of eidetic but also of mathematical numbers, following a line of argumentation which involves a hylomorphic approach to the latter. He proceeds with an analysis of the mathematical number into matter and form, but his interpretation entails that form is the (...) constituent of number, which has the status and role of a Platonic Form. This solution allows him not only to explain and justify the unity of number, but also to apply the Platonic thesis of the separate existence of numbers, to the mathematical or monadic numbers themselves. It also betrays its tendency to combine theses of the Platonic Ontology with fundamental Aristotelian doctrines. (shrink)

One of the aims of the Neoplatonists is to demonstrate that ancient Presocratic thought is, in fact, a Preplatonic thought. According to the Neoplatonists, Presocratics, who were not far from the truth, employed an inaccurate and ambiguous language, whereas Plato spoke about the truth in a more appropriate and clear way. That is why the Presocratics are not necessarily erroneous and their theoretical originality and their terminology can be incorporated into the Neoplatonic philosophy. I would like to show how some (...) Presocratic theories are embedded in the Neoplatonic metaphysical system of the three Hypostases. Regarding the One and the Intellect, Plotinus, Proclus and the Anonymous Author of the Prolegomena to Platonic Philosophy read and employ some Presocratic texts in order to harmonize the Platonic and the Presocratic accounts. Although the Neoplatonists see themselves as continuing the Greek philosophical tradition started by the Presocratics, their interpretation of Presocratic thought illustrates the birth of exegetic philosophy which is able to apply ancient concepts and predicates to its own metaphysical theory. (shrink)