One of the manuscripts of Buridan’s Summulae contains three figures, each in the form of an octagon. At each node of each octagon there are nine propositions. Buridan uses the figures to illustrate his doctrine of the syllogism, revising Aristotle's theory of the modal syllogism and adding theories of syllogisms with propositions containing oblique terms (such as ‘man’s donkey’) and with ‘propositions of non-normal construction’ (where the predicate precedes the copula). O-propositions of non-normal construction (i.e., ‘Some S (some) P is (...) not’) allow Buridan to extend and systematize the theory of the assertoric (i.e., non-modal) syllogism. Buridan points to a revealing analogy between the three octagons. To understand their importance we need to rehearse the medieval theories of signification, supposition, truth and consequence. (shrink)

In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I will (...) conclude with some consideration on scope interactions between quantifiers. (shrink)

RésuméLa théorie avicenienne du mouvement des orbes célestes représente un aspect important de sa cosmologie qui n'a cependant pas encore été l'objet d'une étude approfondie. Cet article compte combler ce manque en fournissant une analyse des différents principes à l'origine du mouvement céleste, ainsi qu'une réflexion sur le rôle des disciplines astronomique, physique, et métaphysique dans les explications que fournit Ibn Sīnā à ce sujet. L'accent est mis sur le rapport des intelligences aux orbes et sur la problématique du passage (...) de l'intellectif au physique, un moment charnière dans la cinématique avicenienne. En outre, l'étude remet en question l'adhésion d'Ibn Sīnā à la théorie farabienne des dix intelligences et entreprend une reconstitution de son modèle cosmologique. (shrink)

Simplicius’ project of harmonizing previous philosophers deserves to be taken seriously as both a philosophical and an interpretive project. Simplicius follows Aristotle himself in developing charitable interpretations of his predecessors: his distinctive project, in the Neoplatonic context, is the rehabilitation of the Presocratics (especially Parmenides, Anaxagoras and Empedocles) from a Platonic-Aristotelian perspective. Simplicius’ harmonizations involve hermeneutic techniques which are recognisably those of the serious historian of philosophy; and harmonization itself has a distinguished history as a constructive philosophical method.

Scholarship on Aristotle’s NICOMACHEAN ETHICS (hereafter “the Ethics”) flourishes in an almost unprecedented fashion. In the last ten years, universities in North America have produced on average over ten doctoral dissertations a year that discuss the practical philosophy that Aristotle espouses in his Nicomachean Ethics, Eudemian Ethics, and Politics. Since the beginning of the millennium there have been three new translations of the entire Ethics into English alone, several more that translate parts of the work into English and other modern (...) languages, and half a dozen collections of new articles discussing Aristotle’s Ethics. Such an outpouring of scholarship has produced an almost unmanageable wave of books, articles, and reviews. Through my topical bibliography, I seek to organize this wealth of scholarly writing so as to make it manageable both to scholars working across the disciplines of philosophy, classics, history, and politics, and to scholars pursuing theses on specific topics within the Ethics. The bibliography takes as its model and is much indebted to that compiled by Barnes, Schofield, and Sorabji in their Articles on Aristotle, Volume 2: Ethics and Politics (1977), which was further updated and incorporated into the complete bibliography to all of Aristotle’s writings in Barnes’s Cambridge Companion to Aristotle (1995). Although I have taken guidance from their model, my bibliography differs in one main respect. Whereas Barnes et al. were more selective and annotated their bibliography, I have been more comprehensive in my inclusion of items. I have sought to include all books and journal articles concerned with the Ethics written in English over the last 120 years; additionally, I have sought to include representative and central works of scholarship written on the Ethics in French, German, and Italian during the same period of time. (shrink)

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books, from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. (...) He ascribes a special status to the categories Quantity and Quality, whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics. (shrink)

This paper (in Finnish) concerns the ontological status of categories of entities. I argue that categories are not be considered as further entities. Rather, it is suffcient for entities belonging to the same category that they are in exactly the same formal ontological relations and have the same general category features.

The article examines the state of research on Michael of Ephesus as a probable author of the Commentaries on Metaphysics E–N, mainly the works of Leonardo Tarán and Concetta Luna. In spite of their opposed views, they both agree on the mediocrity of the Byzantine author. The article questions the criteria for this negative appraisal and offers some material for reconsidering Michael of Ephesus’ idea of philo­sophical culture.

Aristotle’s Naïve Somatism is a re-interpretation of Aristotle’s cognitive psychology in light of certain presuppositions he holds about the living animal body. The living animal body is presumed to be sensitive, and Aristotle grounds his account of cognition in a rudimentary proprioceptive awareness one has of her body. With that presupposed metaphysics under our belts, we are in a position to see that Aristotle in de Anima (cognition chapters at least) has a di erent explanatory aim in view than that (...) which the literature generally imputes to him. He is not explicating what we would call the “mental”—the private, inner realm which some take to be of a di erent kind than the physical—as most take him to be. His explanandum is content acquisition; the explanans is showing how the body becomes like various aspects of objects. Although he famously describes the mind (nous) as unmixed with the body, he is guided by functional constrains—nous cannot be limited or qualified if it is to potentially think all things. Thus, his inquiry into cognition is philosophically limited from a contemporary perspective. Aristotle is not doing philosophy of mind, for he doesn’t seem to find the “mental” philosophically perplexing. (shrink)

I try to explain the difference between three kinds of negation: external negation, negation of the predicate and privation. Further I use polygons of opposition as heuristic devices to show that a logic which contains all three mentioned kinds of negation must be a fragment of a Łukasiewicz-four-valued predicate logic. I show, further, that, this analysis can be elaborated so as to comprise additional kinds of privation. This would increase the truth-values in question and bring fragments of (more generally speaking) (...) Łukasiewicz-n-valued predicate logics into the scene. (shrink)

The square of opposition (as part of a lattice) is used as a natural way to represent different and opposite ways of who makes decisions, and in what way, in/for a group or a society. Majority logic is characterized by multiple logical squares (one for each possible majority), with the “discursive dilemma” as a consequence. Three-valued logics of majority decisions with discursive dilemma undecided, of veto, consensus, and sequential voting are analyzed from the semantic point of view. For instance, the (...) paraconsistent and paracomplete logics M3, M3veto and C3 are described. The distinction of designated and non-designated values is not used, and instead, the consequence relation is defined as a preservation of the minimum truth-value of the implying set of sentences. The consequence and opposition relations of the logics described are compared, and an ordering of the logics with respect to their opposition relations is established. (shrink)

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

This paper lists and examines the explicit references to Aristotle’s Topics in the Greek Neoplatonic commentaries on the Categories. The references to the Topics by Porphyry, Dexippus, Ammonius, Simplicius, Olympiodorus, Philoponus and David are listed according the usual prolegomena to Aristotle’s works. In particular, the paper reconstructs David ’s original thesis about the proponents of the title Pre-Topics for the Categories and compares Ammonius’, Simplicius’ and Olympiodorus’ doxographies about the postpraedicamenta. Moreover, the study identifies two general trends. The first one (...) is that all the commentators after Proclus share the same general view about: the authenticity of the Topics, Aristotle’s writing style in them, the part of philosophy to which they belong, their purpose, their usefulness and their place in the reading order. The second one is that whereas Porphyry, Dexippus and Simplicius use the Topics as an aid to understanding the Categories, Ammonius, Olympiodorus and David do not. (shrink)

Platonism and Christian Thought in Late Antiquity examines the various ways in which Christian intellectuals engaged with Platonism both as a pagan competitor and as a source of philosophical material useful to the Christian faith. The chapters are united in their goal to explore transformations that took place in the reception and interaction process between Platonism and Christianity in this period. -/- The contributions in this volume explore the reception of Platonic material in Christian thought, showing that the transmission of (...) cultural content is always mediated, and ought to be studied as a transformative process by way of selection and interpretation. Some chapters also deal with various aspects of the wider discussion on how Platonic, and Hellenic, philosophy and early Christian thought related to each other, examining the differences and common ground between these traditions. -/- Platonism and Christian Thought in Late Antiquity offers an insightful and broad ranging study on the subject, which will be of interest to students of both philosophy and theology in the Late Antique period, as well as anyone working on the reception and history of Platonic thought, and the development of Christian thought. (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)

The present chapter aims at offering insights into Dionysius the Areopagite’s notion of theurgy, both with respect to the metaphysical principles that connect with “θεουργία” and the particular sacramental reality that emerges from it. Pavlos argues that despite the linguistic affinities and terminological appropriations - whether Iamblichean or Proclean - Dionysius’ premises on the matter remain radically different from that of Neoplatonism, both in terms of the sacramental tradition he recapitulates and the wider Christian metaphysical contours he adheres to. Of (...) central importance in the argument is the striking fact that, throughout the Corpus Dionysiacum, “theurgy” is a term exclusively used by the author to refer to the works of Christ in His earthly historical presence, and to the whole divine providential, creative, sustaining, and divinising activity and work of God. Consequently, if for Dionysius a “theurgist” (θεουργός) could not be any human being, but only Christ Himself, the God-Man, Dionysian theurgy aims at the deification of man, which is nothing other than Christ-likeness. (shrink)