In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

I am grateful to the editors of the Canadian Journal of Philosophy for inviting me to write a comment on Kathleen Gill’s ‘On the Metaphysical Distinction Between Processes and Events’. I readily concede that she is right in the central criticism she makes of my 1978 paper: that a properly metaphysical or ontological distinction between processes and events, if it is to be made at all, cannot be sustained on the basis of the informal linguistic criteria I offered in ‘Events, (...) Processes, and States.’ My main concern in that paper was to show that discussions of the Kenny-Vendler typology of activities, performances, and states had focused too narrowly on verb types, on adverbial phrases, on the domain of human action, and on English-language intuitions. Mine was one of several voices urging in the late 1970s that issues of tense logic and of the logic of verb types had to be placed in the broader context of verb aspect — a salient and pervasive structure in natural languages generally, and one that had been studied by philologists and linguists since the nineteenth century. Captivated, as I and others had become at the time, by evidence that the distinction between count nouns and mass nouns appears to be mirrored in verb predications, I went on to make some rather venturesome ‘ontological’ claims. It is satisfying, of course, that Gill accepts not only that there is ‘substantial evidence in favor of recognizing a grammatical distinction between the language of processes and [the language of] events’ but also that ‘similarities with count and mass expressions will allow us to apply techniques for han dling nominal expressions to verbal expressions’. It is more than satisfying that the phenomenon of verb aspect is now noticed and investigated by philosophers as well as by linguists. (shrink)

"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 against actual and possible criticisms, and attempting to integrate what is said in Book 5 into the context of the Metaphysics as a whole."--Bloomsbury Publishing. (shrink)

This user-friendly text covers key issues in the philosophy of science in an accessible and philosophically serious way. It will prove valuable to students studying philosophy of science as well as science students. Prize-winning author Alex Rosenberg explores the philosophical problems that science raises by its very nature and method. He skilfully demonstrates that scientific explanation, laws, causation, theory, models, evidence, reductionism, probability, teleology, realism and instrumentalism actually pose the same questions that Plato, Aristotle, Descartes, Hume, Kant and their (...) successors have grappled with for centuries. (shrink)

Translation of Alexander of Aphrodisias Commentary on Metaphysics Book I by William Dooley.

The last 14 chapters of book 1 of Aristotle's "Prior Analytics" are concerned with the representation in the formal language of syllogistic of propositions and arguments expressed in more or less everyday Greek. In his commentary on those chapters, Alexander of Aphrodisias explains some of Aristotle's more opaque assertions and discusses post-Aristotelian ideas in semantics and the philosophy of language. In doing so he provides an unusual insight into the way in which these disciplines developed in the (...) Hellenistic era. He also shows a more sophisticated understanding of these fields than Aristotle himself, while remaining a staunch defender of Aristotle's emphasis on meaning as opposed to Stoics concern with verbal formulation. In his commentary on the final chapter of book 1 Alexander offers a thorough discussion of Aristotle's distinction between denying that something is, e.g., white and asserting that it is non-white. (shrink)

What is honor? Has its meaning changed since ancient times? Is it an outmoded notion? Does it still have the power to direct our behavior? In this provocative book Alexander Welsh considers the history and meaning of honor and dismisses the idea that we live in a post-honor culture. He notes that we have words other than _honor_, such as _respect_, _self-respect_, and personal _identity_, that show we do indeed care deeply about honor. Honor, he argues, is a continuing (...) process of respect that motivates or constrains members of a peer group. Honor’s dictates function as moral imperatives. Surprisingly, little systematic study of the history of honor in Western culture has been attempted. Offering a welcome remedy, Welsh provides a genealogy of approaches to the subject, mining some of the most influential texts of the Western tradition. He rereads with fascinating results the works of Aristotle, Cicero, Shakespeare, Mandeville, Montesquieu, Rousseau, Kant, Adam Smith, and others. With a sharp focus on the intersection of honor and ethics in both literature and philosophy, Welsh invites new and constructive debate on a topic of vital interest. (shrink)

This paper discusses two passages from Alexander of Aphrodisias’s commentary on Aristotle’s _ Topics _ that are transmitted in Ps-Jābir’s _ Kitāb al-Nukhab _. It argues that the Arabic translation of Alexander’s commentary may have been made from a fuller version than what came down to us in Greek. Especially since the author(s) of the Jābir-corpus form a tradition different from the school of Ḥunayn b. Isḥāq (d. 873) and authors associated to the ‘Baghdad school’, whose earliest (...) figure is Abū Bishr Mattā b. Yūnus (d. 940), the Arabic fragments of Alexander’s commentary preserved in the _ Kitāb al-Nukhab _ promise to shed more light on the early reception of the _ Topics _ and the different contexts in which Aristotelian dialectic was studied in the Islamic world. (shrink)

Essentialism as applied to individuals is the claim that for at least some individuals there are properties that those individuals possess essentially. What it is to possess a property essentially is a matter of debate. To possess a property essentially is often taken to be akin to possessing a property necessarily, but stronger, although this is not a feature of Aristotle’s essentialism, according to which essential properties are those thing could not lose without ceasing to exist. Kit Fine (1994) (...) takes essential properties to be those that an object has in virtue of its identity, while other essentialists refer (as Fine also does) to the nature of an object as the source of its essential properties. It is sometimes important to distinguish the essential properties of a thing and the ‘full’ essence of a thing. The latter is the set of the essential properties of a thing, when that set necessarily suffices to determine the thing’s identity. One might hold that something has essential properties without agreeing that it has an identity-determining essence. Essentialism was largely in abeyance during the first two thirds of the twentieth century thanks to the domination of analytic philosophy by anti-metaphysical logical empiricism and the linguistic turn. The rehabilitation of essentialism owes much to the development of a formal apparatus for the understanding of modality more generally, thanks to C. I. Lewis, Ruth Barcan Marcus, and Saul Kripke. Kripke’s discussion of essentialism both about individuals and also about about natural kinds brought essentialism to wider philosophical prominence. Natural kind essentialism, which finds its modern genesis also in the work of Hilary Putnam, claims that natural kinds have essential properties: to say that possession of property P is is part of the essence of the kind K implies that, necessarily, every member or sample of the kind K possesses P. Essentialism about individuals has been linked to thinking about natural kinds by the contentious claim that one of the essential properties of any entity is that it belongs to the natural kind (or kinds) it actually belongs to. In this chapter I shall first outline certain claims and arguments concerning essentialism concerning individuals (Section 2).. (shrink)

Aristotle, great Greek philosopher, researcher, reasoner, and writer, born at Stagirus in 384 BCE, was the son of Nicomachus, a physician, and Phaestis. He studied under Plato at Athens and taught there ; subsequently he spent three years at the court of a former pupil, Hermeias, in Asia Minor and at this time married Pythias, one of Hermeias's relations. After some time at Mitylene, in 343?2 he was appointed by King Philip of Macedon to be tutor of his teen-aged (...) son Alexander. After Philip's death in 336, Aristotle became head of his own school, the Lyceum at Athens. Because of anti-Macedonian feeling there after Alexander's death in 323, he withdrew to Chalcis in Euboea, where he died in 322. Nearly all the works Aristotle prepared for publication are lost; the priceless ones extant are lecture-materials, notes, and memoranda. They can be categorized as follows: I Practical: Nicomachean Ethics; Great Ethics ; Eudemian Ethics; Politics; Economics ; On Virtues and Vices. II Logical: Categories; Analytics ; Interpretation; Refutations used by Sophists; Topica. III Physical: Twenty-six works including astronomy, generation and destruction, the senses, memory, sleep, dreams, life, facts about animals, etc. IV Metaphysics: on being as being. V Art: Rhetoric and Poetics. VI Other works including the Constitution of Athens; more works also of doubtful authorship. VII Fragments of various works such as dialogues on philosophy and literature; and of treatises on rhetoric, politics and metaphysics. The Loeb Classical Library edition of Aristotle is in twenty-three volumes. (shrink)

A new translation and edition of Aristotle's Protrepticus (with critical comments on the fragments) -/- Welcome -/- The Protrepticus was an early work of Aristotle, written while he was still a member of Plato's Academy, but it soon became one of the most famous works in the whole history of philosophy. Unfortunately it was not directly copied in the middle ages and so did not survive in its own manuscript tradition. But substantial fragments of it have been preserved (...) in several works by Iamblichus of Chalcis, a third century A.D. neo-Pythagorean philosopher and educator. On the basis of a close study of Iamblichus' extensive use and excerption of Aristotle's Protrepticus, it is possible to reconstruct the backbone of the lost work, and then to flesh it out with the other surviving reports about the work from antiquity (for example in Alexander of Aphrodisias and other ancient commentators on Aristotle). It is also possible to identify several papyrus fragments of the work, and many references and literary allusions in later authors, especially Cicero, whose own lost dialogue Hortensius was a defense of philosophy modeleld on Aristotle's. (shrink)

This paper attempts to situate Thomas Aquinas with respect to philosophical discussions of the nature of metaphorical language. I consider Aquinas’s comments in the Summa Theologiae on Scriptural metaphor and allegory in the light of two theses in current discussions of metaphor: the substitution thesis and the dual-meaning thesis. I compare Aquinas’s view to those of Aristotle and Donald Davidson. The substitution thesis asserts that figurative expressions can be replaced by semantically equivalent literal expressions. The dual-meaning thesis asserts that, (...) in addition to a literal meaning (or sense), metaphorical language possesses another meaning, viz. a figurative one. I claim that Aquinas’s view is complex. He affirms the dual-meaning thesis with regard to Scriptural allegory. Yet he rejects the dual-meaning thesis and affirms the substitution thesis with regard to predicates ascribed metaphorically to God. (shrink)

Attributed to Alexander of Aphrodisias -the leading ancient commentator on Aristotle -the Quaestiones exemplify the process through which Aristotle's thought was organized and came to be interpreted as "Aristotelianism." This volume of R.W. Sharples's translation, together with his earlier translation of Quaestiones 1.1-2.15, makes the Quaestiones available in its entirety for the first time in a modern language. The Quaestiones are concerned with problems of physics and metaphysics, psychology and divine providence. Readers interested in Aristotle's psychological (...) views will find the second half of the Quaestiones particularly valuable. Ten of the problems discussed involve issues raised in Aristotle's On the Soul, including the unity of apperception and the transition from first to second actuality in the act of contemplation. An additional twelve problems relate to aspects of physical theory such as infinity, necessity, and potentiality. Quaestio 2.21 concerns divine providence and helps supplement our knowledge of Alexander's position. A study of the Quaestiones also suggests how interpretations of Aristotle were influenced by doctrines of Hellenistic philosophy. Translated first into Arabic and then into Latin, excerpts from the Quaestiones played a significant role in the transmission of ancient Greek philosophy to the medieval world. (shrink)

Alexander von Aphrodisias (ca. 200 n. Chr.) schrieb nicht nur uber das Buch De anima, sondern auch uber viele naturwissenschaftliche und uber samtliche logische Schriften des Aristoteles. Gegen Ende des 15. Jahrhunderts wiesen die Humanisten auf die Bedeutung der griechischen Ausleger fur das Verstandnis der aristotelischen Logik hin. In diesem Zusammenhang wurden um die Mitte des 16. Jahrhunderts samtliche Kommentare Alexanders zur aristotelischen Logik ins Lateinische ubersetzt. Die vorliegenden Kommentare zur Topik und Sophistik wurden von dem bekannten Ubersetzer Dorotheus (...) ins Lateinische ubertragen. (shrink)

In this article, I present and explain ten different possible meanings of a chance event – some ontological, some epistemic – and provide examples whenever possible. I describe and illustrate more carefully the view of chance (tychē) expressed by Aristotle in his Physics, a demanding and complex notion, and contrast it to the other senses examined. The etymology of chance also reveals a cross-reference between chance and indeterminism. I draw attention to the fact that most of the definitions of (...) chance on offer need not conflict with causal determinism. (shrink)

Adam Smith's ethics have long been thought to be much closer to the Stoic school than to any other school of the ancient world. Recent scholarship however has focused on the fact that Smith also appears to be quite close to Aristotle. I shall attend to Smith's deployment of a version of the doctrine of the mean, shall show that it is quite close to Aristotle's, shall demonstrate that in its detailed application it is seriously at odds with (...) Stoic teaching on the passions, and particularly with their teachings on anger, and shall conclude that on a central issue of ethics Smith is a good deal closer to Aristotelian than to Stoic thinking. (shrink)

trans. R. W. Sharples. Alexander addresses a number of questions drawn from a range of topics in Aristotle's works.

Italian translation with facing Greek text of Alexander's commentary on Aristotle's Metaphysics I-V, and of pseudo-Alexander's commentary on the remaining books of the Metaphysics.

Thomas Reid saw the three subjects of logic, rhetoric, and the fine arts as closely cohering aspects of one endeavor that he called the culture of the mind. This was a topic on which Reid lectured for many years in Glasgow, and this volume presents as near a reconstruction of these lectures as is now possible. Though virtually unknown today, this material in fact relates closely to Reid’s published works and in particular to the late _Essays on the Intellectual Powers (...) of Man_ and _Essays on the Active Powers of Man_. When composing these works, Reid drew primarily on his lectures on “pneumatology,” which presented a theory of the mental powers, broadly conceived. These lectures were basic to the course on the culture of the mind that explained the cultivation of the mental powers. Although the _Essays_ also included some elements from the material on the culture of the mind, the bulk of the latter was left in manuscript form, and Alexander Broadie’s edition restores this important extension of Reid’s overall work. In addition, this volume continues the attractive combination of manuscript material and published work, in this case Reid’s important and well-known essay on Aristotle’s logic. This text was corrupted in earlier editions of Reid’s works and is now restored to the state in which Reid left it. This volume underscores Reid’s great and growing significance, viewed both as a historical figure and as a philosopher. At the same time, it is of great interdisciplinary importance. While the material emerges directly from the core of Reid’s philosophy, as now understood, it will appeal widely to people in literary, cultural, historical, and communications studies. In this regard, the present volume is a true fruit of the Scottish Enlightenment. (shrink)

Introduction -- Epistemology, metaphysics, and rhetoric : contexts of imagination -- Aristotle, Phantasia, and the problem of epistemology -- Plato, the neoplatonists, and the vagaries of the sublunar world -- Phantasia and ecstatic knowledge -- A more skillful artist than imitation -- Dreams, doubts, and evil demons : Descartes and imagination -- Mediatio prima : certainty, the cogito, and imagination -- Imagination in the rules -- Meditatio secunda : the world of the cogito -- Descartes, Montaigne, and Pascal -- (...) Analogies and enthusiasm -- Excogitations : fabulating the cogito -- The reasonable imagination : Immanuel Kant's critical philosophy -- Imagination in the limits of pure reason -- Dreamers and madmen : imagination in the anthropology -- Natural art and sublime madness : imagination in the critique of judgment -- The highest point of philosophy : Fichte's reimagining of the kantian system -- The logics of positing intellectual intuition and the absolute subject -- Ecstasy, inspired communication, and philosophical genius -- Light, dusk, and darkness : the reconciliation of opposites -- The metaphysics of oscillation and the truth of imagination -- Reason fixations : arresting imagination -- A system without foundations : poetic subjectivity in Friedrich von Hardenberg's Ordo inversus -- A system without foundations -- Fantasy and the body -- Divine law and abject subjectivity : Coleridge and the double knowledge of imagination -- Divine imagination -- The abyss of the empirical self -- Coda: Imagining ideology. (shrink)

In Predication and Ontology A. Kalbarczyk provides the first monograph-length study of the Arabic reception of Aristotle’s Categories. At the center of attention is the critical reappraisal of that treatise by Ibn Sīnā, better known in the Latin West as Avicenna. Ibn Sīnā’s reading of the Categories is examined in the context of his wider project of rearranging the transmitted body of philosophical knowledge. Against the background of the late ancient commentary tradition and subsequent exegetical efforts, Ibn Sīnā’s Kitāb (...) al-Maqūlāt of the Šifāʾ is interpreted as a milestone in the gradual reshuffle of the relationship between logic proper and ontology. In order to assess the philosophical impact of this realignment, some of the subsequent developments in Ibn Sīnā’s writings and in the emerging post-Avicennian tradition are also taken into account. The thematic focus lies on the two fundamental classification schemes which Aristotle introduces in the treatise: the fourfold division of Cat. 2 and the tenfold scheme of Cat. 4. They both pose the question of whether and how the manner in which an expression is predicated relates to extra-linguistic reality. As the study intends to show, this question is one of the driving forces of Ibn Sīnā’s momentous reform of the Aristotelian curriculum. (shrink)

This essay narrates what I have learned from Søren Kierkegaard & John Dewey about teaching philosophy. It consists of three sections: 1) a Deweyan pragmatist’s translation of Kierkegaard’s religious insights on Christianity, as a way of life, into ethical insights on philosophy, as a way of life; 2) a brief description of the introductory course that I teach most frequently: Ethics, Happiness, & The Good Life; and 3) an exploration of three spiritual exercises from the course: a) self-cultivation by means (...) of writing in an Ethics Notebook, b) an “existential experiment” in which we practice one of Aristotle’s virtues for a week, and c) a 15-hour service-learning component. (shrink)

A trait that is often associated with a good person is caring about the truth. Thomas Aquinas, following Aristotle, describes a virtue that concerns truths (truthfulness). However, he limits the virtue to being truthful about who one is and what one's achievements are. This restriction seems almost arbitrary and exceedingly narrow. In this paper, I explore the motivation for Aquinas's restricted account and argue that his view is motivated by broader virtue theoretical commitments and that his approach to the (...) role of truth for being a good person is distinct and worthwhile. (shrink)

This paper examines a commentary of Aristotle's Peri hermeneias, preserved in a single manuscript in the Biblioteca Nacional de España, that is commonly attributed to the fourteenth-century theolog...