In this part of the Posterior Analytics, Aristotle elaborates his assessment of how universal truths of science can be scientifically explained as inevitable in demonstrative proofs. But he introduces complications: some sciences discuss phenomena that can only be explained by higher sciences and again sometimes we reason out a cause from an effect, rather than an effect from a cause. Philoponus takes these issues further. Reasoning from particular to universal is the direction taken by induction, and in mathematics reasoning from a theorem to the higher principles from which it follows is considered particularly valuable. It corresponds to the direction of analysis, as opposed to synthesis. This volume contains an English translation of Philoponus' commentary, a detailed introduction, extensive explanatory notes and a bibliography.

Aristotle's Posterior Analytics elaborates for the first time in the history of Western philosophy the notions of science and the requirements for the distinctive kind of knowledge scientists possess. His model is mathematics and his treatment of science amounts to a philosophical discussion, from the perspective of Aristotelian syllogistic, of mathematical proofs and the principles they are based on. Chapters 1-8 expound the foundations of Aristotle's theory, pointing out the similarities and differences between scientific knowledge and other types of knowledge, establishing the need for basic principles, and identifying the types of principles and the source of necessity associated with scientific facts. Philoponus' massive commentary, the most complete ancient discussion of Posterior Analytics Book 1, offers uniquely valuable testimony to the way this book was read and understood in late antiquity, as well as providing information on earlier interpretations. Of particular interest is Philoponus' account of scientific principles, which is based not only on Aristotle but also on the Greek mathematical tradition, especially Euclid and his commentator Proclus.

The Posterior Analytics contains Aristotle's philosophy of science. In Book 2, Aristotle asks how the scientist discovers what sort of loss of light constitutes lunar eclipse. The scientist has to discover that the moon's darkening is due to the earth's shadow. Once that defining explanation is known the scientist possesses the full scientific concept of lunar eclipse and can use it to explain other necessary features of the phenomenon. The present commentary, arguably ascribed to Philoponus incorrectly, offers some interpretations of Aristotle that are unfamiliar nowadays. For example, the scientific concept of a human is acquired from observing particular humans and repeatedly receiving impressions in the sense image or percept and later in the imagination. The impressions received are not only of particular distinctive characteristics, like paleness, but also of universal human characteristics, like rationality. Perception can thus in a sense apprehend universal qualities in the individual as well as particular ones. This volume contains an English translation of the commentary, accompanied by extensive commentary notes, an introduction and a bibliography.

David Bronstein sheds new light on Aristotle's 'Posterior Analytics' - one of the most important, and difficult, works in the history of Western philosophy. He argues that it is coherently structured around two themes of enduring philosophical interest - knowledge and learning - and goes on to highlight Plato's influence on Aristotle's text.

The commentary of Alexander of Aphrodisias on Aristotle's Prior Analytics 1.8-22 is the main ancient commentary, by the 'greatest' commentator, on the chapters of the Prior Analytics in which Aristotle invented modal logic - the logic of propositions about what is necessary or contingent (possible). In this volume, which covers chapters 1.8-13, Alexander of Aphrodisias reaches the chapter in which Aristotle discusses the notion of contingency. Also included in this volume is Alexander's commentary on that part of Prior Analytics 1.17 which explains the conversion of contingent propositions (the rest of 1.17 is included in the second volume of Mueller's translation). Aristotle also invented the syllogism, a style of argument involving two premises and a conclusion. Modal propositions can be deployed in syllogism, and in the chapters included in this volume Aristotle discusses syllogisms consisting of two necessary propositions as well as the more controversial ones containing one necessary and one non-modal premiss. The discussion of syllogisms containing contingent propositions is reserved for Volume 2. In each volume, Ian Mueller provides a comprehensive explanation of Alexander's commentary on modal logic as a whole.

The philosopher Abu Nasr al-Farabi (c. 870-c. 950 CE) is a key Arabic intermediary figure. He knew Aristotle, and in particular Aristotle's logic, through Greek Neoplatonist interpretations translated into Arabic via Syriac and possibly Persian. For example, he revised a general description of Aristotle's logic by the 6th century Paul the Persian, and further influenced famous later philosophers and theologians writing in Arabic in the 11th to 12th centuries: Avicenna, Al-Ghazali, Avempace and Averroes. Averroes' reports on Farabi were subsequently transmitted to the West in Latin translation. This book is an abridgement of Aristotle's Prior Analytics, rather than a commentary on successive passages. In it Farabi discusses Aristotle's invention, the syllogism, and aims to codify the deductively valid arguments in all disciplines. He describes Aristotle's categorical syllogisms in detail; these are syllogisms with premises such as 'Every A is a B' and 'No A is a B'. He adds a discussion of how categorical syllogisms can codify arguments by induction from known examples or by analogy, and also some kinds of theological argument from perceived facts to conclusions lying beyond perception. He also describes post-Aristotelian hypothetical syllogisms, which draw conclusions from premises such as 'If P then Q' and 'Either P or Q'. His treatment of categorical syllogisms is one of the first to recognise logically productive pairs of premises by using 'conditions of productivity', a device that had appeared in the Greek Philoponus in 6th century Alexandria.

This edition of David the Invincible’s Commentary on the Prior Analytics, surviving only in an old Armenian translation from Greek, includes a revised critical text and the first English translation of the work, textual parallels with other commentaries, trilingual glossaries and other material useful to specialists.

In the Posterior Analytics Aristotle contrasts demonstrations with syllogisms through signs. In the Prior Analytics he defines a sign as a demonstrative premise. One is thus led to ask: is a sign a demonstration? This book reconstructs the history of the notion of “demonstration through signs” from roughly the third through to the thirteenth century. It examines the work of Aristotle’s Greek, Arabic, and Latin commentators, both within and outside the tradition of the Posterior Analytics.

This book offers the first synoptic study of how the primary elements in knowledge structures were analysed in antiquity from Plato to late ancient commentaries. It argues that, in the Platonic-Aristotelian tradition, the question of starting points was treated from two distinct points of view: as a question of how we acquire basic knowledge; and as a question of the premises we may immediately accept in the line of argumentation.

This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.