Examines the role played by the Aristotelian logic in Neoplatonic philosophers. To start with, it is remarked that Aristotelian Organon was regarded not only as a corpus of logical texts but also as an introduction to philosophy. Focuses on several Neoplatonic Aristotelian commentators, from Alexander of Aphrodisias to Byzantine thinkers, presenting both the characteristics of their works and their lack of interest in discussing their own philosophical view. Finally, it is observed that, although not original, these commentaries provide a rather (...) reliable and correct investigation of Aristotle. (shrink)

In contrast with the different views of some recent scholars, Ch. 7 constitutes an important attempt to point out the importance played by non‐discursive thought in Plotinus and Proclus in several ways. Firstly, the differences between the doctrines of Plotinus and Proclus are investigated. Secondly, it is considered the role of the ‘Loving Intellect’ in both Plotinus’ and Proclus’ philosophy. Thirdly, it is indicated how the One plays a crucial role in the mystical experience and how this kind of experience (...) may be an evidence of the activity of the One. Finally, it is shown how some problems and difficulties of Plotinus’ philosophy may be explained through reference to the mystical experience. (shrink)

Devoted to the key Neoplatonic concepts of procession and emanation. The two terms are taken to express the same idea, although procession is preferred as more neutral. Points out how procession can be explained in Aristotelian terms. More specifically, it is demonstrated how Plotinus’ notion of procession uses the Aristotelian theory of the actualization of an activity by a potency in order to explain how a higher activity can actualize a lower one. Finally, considers the doctrine of Proclus who expresses (...) the procession, involving the theory of causal relation, in a way opposite to Plotinus. (shrink)

Focuses on Porphyry's semantic and more specifically on his theory of ‘imposition of names’, i.e. how names are related to things. Examines Porphyry's treatment of genus and species and also of individual, singular, and general terms to emphasize his peculiarity in Neoplatonic philosophy. Infers that Porphyry's attitude is not to develop a metaphysical and a logical semantics, but only a metaphysical one. Finally, considers how Porphyry's metaphysical approach towards semantics was maintained by eleventh and twelfth century Byzantine Neoplatonists.

The core of the third chapter is the study of the P‐series. This theory is presented after a detailed discussion of the relationship of individuals to species and genus. A P‐series is a sequence of terms classified according to priority and posteriority starting from the most universal one. This theory is the result of the evolution of the Aristotelian doctrine of pros en done in order to fit with the not strictly Aristotelian notion of ‘genus’ of some Neoplatonic philosophers.

The purpose of Ch. 6 is to outline the role played by the P‐series theory in Neoplatonic epistemology. To start with, it is explained that knowledge of a P‐series consists in an order of priority and posteriority of the terms: intellect, scientific knowledge, belief, presentation, and perception. In second place, some peculiar Neoplatonic epistemological issues, e.g. how can the divine possibly know temporal truths, are carefully examined. To conclude, some particular Neoplatonic rules, which allow higher entities to have knowledge of (...) lower ones, are investigated. (shrink)

Investigates how, given their ontological status between the One and animals, men can either ascend to the intellectual life or fall into the inferior kinds of life. Different issues involved in the doctrine of the rise to the intellectual life are considered. Firstly, the restriction to men of the possibility of an intellectual life is explained through the reference to Neoplatonists’ own personal experiences. Secondly, the experience of the ascent is defined by the term ‘inclination’ rather than the too broad (...) ‘reversion’ used by most of the scholars. The former term, indeed, seems to fit better in the case of men. Finally, the experience of inclination is explained in terms of logical necessity. (shrink)

The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge – especially mathematical knowledge – is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected its historically dominant Euclidean form. By contrast, this book offers a detailed examination of Euclidean foundationalism, which, following Lakatos, the authors call the Euclidean Programme. The book rationally reconstructs the programme's key principles, showing it to be an epistemological interpretation of the axiomatic method. It (...) then compares the reconstructed programme with select historical sources: Euclid's Elements, Aristotle's Posterior Analytics, Descartes's Discourse on Method, Pascal's On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme, exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme. (shrink)

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof?The answer is an emphatic yes, as I explain in this chapter. I argue that non-deductive justification is in fact pervasive in mathematics, and that it is in (...) good epistemic standing. (shrink)