On the General Science of Mathematics is the third of four surviving works out of ten by Iamblichus (c. 245 CE–early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers....

Aristotle's Topics is a handbook for dialectic, i.e. the exercise for philosophical debates between a questioner and a respondent. Alexander takes the Topics as a sort of handbook teaching how to defend and how attack any philosophical claim against philosophical adversaries. In book 3, Aristotle develops strategies for arguing about comparative claims, in which properties are said to belong to subjects to a greater, lesser, or equal degree. Aristotle illustrates the different argumentative patterns that can be used to establish or refute a comparative claim through one single example:...

Chapters 5 and 6 of Aristotle's "Categories" describe his first two categories, Substance and Quantity. It is usually taken that Plotinus attacked Aristotle's "Categories", but that Porphyry and Iamblichus restored it to the curriculum once and for all. Nonetheless, the introduction to this text stresses how much of the defence of Aristotle Porphyry was able to draw out of Plotinus' critical discussion. Simplicius' commentary is our most comprehensive account of the debate on the validity of Aristotle's "Categories". One subject discussed by Simplicius in these chapters is where the...

This volume presents a commentary on Aristotle’s Metaphysics Book 12 by pseudo-Alexander in a new translation accompanied by explanatory notes, introduction and indexes. Fred D. Miller, Jr. argues that the author of the commentary is in fact not Alexander of Aphrodisias, Aristotle’s distant successor in early 3rd century CE Athens and his leading defender and interpreter, but Michael of Ephesus from Constantinople as late as the 12th century CE. Robert Browning had earlier made the case that Michael was enlisted by Princess Anna Comnena in a project to restore and complete the ancient...

This commentary records, through notes taken by Hermias, Syrianus' seminar on Plato's Phaedrus, one of the world's most influential celebrations of erotic beauty and love. It is the only Neoplatonic commentary on Plato's Phaedrus to have survived in its entirety. Further interest comes from the recorded interventions by Syrianus' pupils - including those by Proclus, his eventual successor as head of the Athenian school, who went on to teach Hermias' father, Ammonius. The second of two volumes of Hermias' commentary, the chapters translated here begin with a discussion of how the...

Aristotle was a systematic writer who often cross-referred to the definitions of terms given elsewhere in his work. Book 5 of the Metaphysics is important because it consists of definitions of the main uses of key terms in Aristotle's philosophy, and it is extremely valuable to have a commentary on this important text by Alexander of Aphrodisias, the leading commentator of his school.
Alexander provides a detailed commentary on all of the thirty terms analysed in Book 5, weighing alternative interpretations of what Aristotle says one against another, defending Peripatetic views...

In his commentary on a portion of Aristotle's de Anima (On the Soul) known as de Intellectu (On the Intellect), Philoponus drew on both Christian and Neoplatonic traditions as he reinterpreted Aristotle's views on such key questions as the immortality of the soul, the role of images in thought, the character of sense perception and the presence within the soul of universals.
Although it is one of the richest and most interesting of the ancient works on Aristotle, Philoponus' commentary has survived only in William of Moerbeke's thirteenth-century Latin translation from a...