Aristotle's Logic and Metaphysics

The paper presents Hegel's view on the link between logic and metaphysics. Hegel criticizes, not unlike Kant, the pre-Kantian dogmatic meaning of “metaphysics”, but explicitly defends an ancient and specifically Aristotelian view. In particular, I show that Hegel aims at both tracing metaphysics back to its logical roots and logic back to its metaphysical roots, thus developing the idea of an interplay between the two disciplines. My claim is that this idea is the main reason of Hegel’s importance for contemporary debates in philosophical logic and metaphysics.

Jan Łukasiewicz’ work on Aristotle and the principle of non-contradiction, originally published in 1910, presents one of the first and truly pioneering investigation into the logical and metaphysical foundations of this principle.

Łukasiewicz applies the newly developed analytic tools of mathematical logic to Aristotle’s seminal defense of the principle in Book IV of the Metaphysics and aims to show that the principle is not nearly as secure as the generally accepted, mostly uncritical, and often dogmatic belief in its universal truth would have it.

This introduction to examines the historical and philosophical background of Łukasiewicz’ work, its relation to Hegel 's metaphysical logic which gave rise to the debate about Die logische Frage (the question of logic), and Łukasiewicz’ attempt to develop a first Non-Aristotelian logic, a logic that does not require or endorse Aristotle's principle of non-contradiction.

This book offers a new edition, with English translation and commentary, of the Kitāb al-Madḫal, which opens Avicenna’s (d. 1037) most comprehensive summa of Peripatetic philosophy, namely the Kitāb al-Šifāʾ. For the first time, the text is established together with a stemma codicum showing the genealogical relations among 34 manuscripts, the twelfth-century Latin translation, and the literal quotations by Avicenna’s first and second-generation students. In this book, Avicenna’s reappraisal of Porphyry’s Isagoge is examined from both a historical and a philosophical point of view. The key-features of Avicenna’s theory of predicables are analyzed in the General Introduction and in the Commentary both in their own right and against the background of the Greek and Arabic exegetical tradition. Readers shall find in this book the first systematic study of the Madḫal which, in addition to being the only logical work of the Šifāʾ ever transmitted in its entirety both in Arabic and in Latin, is crucial for understanding Avicenna’s conception of universal predicables at the crossroads between logic and metaphysics.

This essay examines Giannantoni’s historiographical production regarding ancient logic. In particular, two works are considered: the first one, on Aristotle’s modal logic, published in 1964; the second one, appeared in 1981, concerning the κυρεύων λόγος of Diodorus Cronus. While the study of modal logic is valuable for its philological rigor and its hermeneutic sobriety, the latter is a true example of a historiographical method applied to ancient texts.

The relation between APORIAI and DIALECTICAL PROBLEMS. Thesis: Aporiai are rarely mentioned in the Aristotle's Topics; however, his notion of a dialectical problem is crucial for what his philosophical and scientific works regard as aporia.



Published in: George Karamanolis/Vasilis Politis (eds.), Aporia in Ancient Philosophy, Cambridge: Cambridge University Press.

Aristotle, though not really an admirer of Heraclitus’ philosophy, did on the one hand acknowledge Heraclitus as a philosopher of nature in the Ionian tradition. On the other hand, he was highly suspicious of certain consequences derivable from Heraclitus’ thinking. His main target is not Heraclitus himself, but the use of these consequences within a sophistical/eristic context; however, he seems to blame Heraclitus for fostering these tendencies by overstating his views to the point that they seem paradoxical.

“His Dearest Enemy. Heraclitus in the Aristotelian Oeuvre“, in: Enrica Fantino/Ulrike Muss/Kurt Sier/Charlotte Schubert (Hgg.): Heraklit im Kontext, Berlin/Boston: De Gruyter, 415-438.

The doctrine that symbolic logic contains the syllogistic logic inaugurated by Aristotle as a whole contains one of its parts represents the prevailing conviction among logicians of our age and constitutes an assumption of modern philosophical education.  Upon inspection, the received opinion proves to have been laid down without sufficient justification, and may indeed be incapable of it. Through an investigation of Frege’s Begriffsschrift and Aristotle’s Analytics, I aim in this essay to show that the expression traditionally regarded as capturing in logical symbolism the universal affirmative proposition of formal syllogistic logic does not, in fact, succeed in doing so. With the discovery that a satisfactory symbolic equivalent of the primary and most characteristic type of syllogistic proposition has not yet been invented, the traditional assumption about the relationship between the two sorts of logic loses its hold, and the path lies open for philosophical reflection upon the natures, scopes, and mutual relations of symbolic and syllogistic logic to become, at long last, a priority for contemporary philosophers of logic.

Face aux tentatives des logiciens de démontrer la validité ou l'invalidité du Maître-argument de Diodore Kronos en s'empressant de déclarer un gagnant à l'argumentaire opposant le philosophe de Mégare à Aristote, nous esquissons par ce présent article une analyse globale du dogme diodoréen qui considère l'ensemble des témoignages antiques répertoriés sur sa pensée, permettant de dresser un portait cohérent d'une pensée positive qui le plus souvent n'est considérée que de façon éristique. Cette approche permet de mettre en lumière les assises dogmatiques du Maître-argument, notamment en relation avec les arguments sur les corps sans parties (άμερῆ); si le monde physique est composé d'ultimes corps indivisibles et sans parties, ces unités ne peuvent être dans le même lieu et dans un autre lieu au même instant, alors « rien ne se meut » (Sextus Empiricus, Adv. Math., X, 86). Si Diodore reprend la thèse éléatique de l'impossibilité d'appréhender logiquement le mouvement, il renouvèle toutefois la tradition mégarique en affirmant l'existence du mouvement achevé, car l'on constate bien qu'un corps est passé d'un lieu à l'autre, et donc qu'il s'est mû! Or nous démontrons que l'affirmation singulière d'un mouvement exclusivement conjugué au passé, et donc jamais soumis au devenir, a vraisemblablement des origines aristotéliciennes. En effet, Diodore semble soumettre certains développements de La Physique à une analyse strictement logique en fondant sa conception du temps dans son unité (l'instant), là où Aristote privilégiait l'analyse empirique dans une conception continue du temps et du mouvement. C'est donc à partir de cette divergence fondamentale d'approche épistémologique qu'il faut comprendre le débat sur le possible. En définissant le mouvement comme « l'acte de l'étant en puissance » (201a10), Aristote pense le possible (δυνατόν) à partir des possibilités ontiques de la substance (δύναμις), tandis que Diodore, en identifiant le possible à l'acte, évite le danger de spéculer sur des possibles qui ne se réalisent pas et ainsi de confondre être et non-être; or en distinguant le possible et le nécessaire, il dément la tradition qui lui attribuait un simple nécessitarisme et renouvèle véritablement l'ontologie éléate. À partir de développements préliminaires de Robert Muller, ce présent article démontre ainsi la pertinence d'interpréter la pensée diodoréenne comme une ontologie du dévoilement rendue possible par une critique et une appropriation mégarique de la pensée aristotélicienne.

Cet ouvrage contient la première édition des fragments conservés, en grec et en arabe, du philosophe péripatéticien Boéthos de Sidon (Ier siècle av. J.-C.), ainsi que leur traduction française et un commentaire exhaustif. Il intéressera les historiens de l'aristotélisme et, plus généralement, de la philosophie grecque dans son ensemble

L’article a pour but la présentation d’un nouveau stemma codicum de la Métaphysique. Au cours de son introduction, la série des stemma codicum précédents est reconstruite : Gercke (1892), Bernardinello (1970), Harlfinger (1979), Harlfinger révisé par Fazzo (2010), Golitsis (2015). Toute reconstruction précédente traite la Métaphysique de tradition se disant ‘ouverte’,  dans le sillage sans doute des études de Werner Jaeger, qui comptait pourvoir trouver la trace des Additamenta Aristotelis – donc des variantes d’auteur – dans les différences parmi les deux recensiones principales. En fait, sur la base des données disponibles à ce jour,  il est possible de postuler un seul archétype, qui peut se reconstruire avec une certaine précision par biais des deux témoins qui l’ont utilisé directement, à savoir, le deux mains (J, J2) qui travaillent sur le manuscrit le plus ancien (Vind. Phil. gr. 100, l’ ‘Aristote de Vienne’) et du manuscrit de Paris (E, le Paris. gr. 1853). Celui-ci sera le fond de toute édition critique par le future, comme déjà le souhaitaient Michael  Frede et Günther Patzig en 1988. Par contre, la branche dite β de la tradition relève d’une activité d’édition, de collation, de révision, qui fait des savants byzantins qui se sont occupé de ce texte dès le 10ème siècle les vrai prédécesseurs des philologues qui ont pratiqué la critique textuelle à l’âge moderne. L’Appendice I répond à une intervention récente et pose la question de savoir  dans quelle mesure certaines des corrections proposées par Giorgio Pasquali à la théorie textuelle de Paul Maas s’appliquent à notre cas d’étude. L’Appendice II résume la chronologie des différent témoins pris en considérations ici.



This is the preliminary version of the paper published in 2017. Please quote the published version only. Comments welcome!

U više verzija " Uvoda u Aristetolove kategorije " (" Isagog ") pronalazimo slikoviti prikaz dijagrama "Porfirijevog Drveta". Ovaj dijagram je povezivan sa kvadratom suprotnosti, figurom prirodnog drveta sa vegetativnim ornamentima, te sa antropomorfnom figurom. Porfirij je preuzeo Aristotelovu podjelu na pet predikabilija, te je od njih kreirao scala praedicamentalis (Arbor Porphyriana). Porfirijev neoplatonistički-aristotelizam doveo je u srednjem vijeku do povratka interesa za Aristotelovu logiku kroz prijevode Boethiusa i Al-Farabija. Njihova djela logike bila su temelj za proučavanje mnogih tema, pogotovo onih koje su se bavile teologijom. Kasnije prikaze dijagrama predstavljene simbolikom drveta sa vegetativnim ornamentima i ljudske figure (syndesmos) pronalazimo u 13 st. u " Traktatu " (" Summulae logicales ") Petra Španskog pod različitim imenima poput: Drvo Ljubavi, Drvo Plemenitosti, Drvo Nauke, Drvo Života, Drvo Znanja, Drvo Mudrosti itd. Kršćanski misticizam (mistična teologija), islamski misticizam (sufizam) i jevrejski misticizam (kabala) pod utjecajem neoplatonističke filozofije također sadrže različite varijante dijagrama "Drveta" unutar mnogih mističnih zajednica srednjovjekovnog svijeta. Pod utjecajem neoplatonističke procesije i reverzije, mistik treba biti istovremeno uključen u obje katafatičnu i apofatičnu teologiju kako bi uistinu razumio Boga. Drugim riječima, spiritualna osoba mora oscilirati između iznošenja tvrdnji o Drvetu Života (bitak) i negacije tih istih tvrdnji kako bi uistinu uhvatio srž spoznaje šta je to Bog.

The Kitāb al-Šifāʾ is by far the philosophical summa in which Avicenna’s allegiance to previous exegetical tradition is most evident, thus representing a unique standpoint to the inquiry into Avicenna’s sources. The present paper aims at showing how the Kitāb al-Madḫal of the Šifāʾ is able to provide new insights into Avicenna’s reception of Porphyry’s Isagoge and to allow a more precise study of Avicenna’s acquaintance with previous and contemporary literature on the subject. As a result of the survey, new evidence is found that allows reconstructing a debate between Avicenna and leading Baġdād Aristotelians like Yaḥyā Ibn ʿAdī concerning the notion of ‘individual’ in logic.

Aristoteles mantığında bilimsel bilgi elde etmek için kıyas oluşturabilmek ve kıyas oluşturabilmek için öncülleri uygun formlarda birbirine bağlamak gereklidir. Bu aşamalarda bağlayıcı, belirleyici ve gerçekleştirici unsur olarak orta terimi görmekteyiz. Bu çalışmada orta terimin ne olduğunu tartışarak, bilimsel bilginin elde edilmesi sürecinde hangi rolleri oynadığını tespit edilmeye çalışılmıştır. Aristoteles’in mantığının her aşamasında etkin olan orta terimin, etkilerini belirleyerek, mantık ve bilgi ilişkisinde orta terimi nasıl kullandığı araştırılmıştır.

This essay examines how Aristotle creates propositions. It evaluates his use of quality and quantity in his theory of syllogism. In De Interpretatione, Aristotle used the term, 'apophansis', but he preferred 'protasis' in Analytica Priora. While Aristotle classified these as affirmative and negative due to their qualities, he embraced a different point of view about classifications based on quantity. Differences in apophansis are evaluated on the basis of their singular and universal structures, and their predications are also taken into consideration. As he studied protasis, however, he rearranged the classifications of apophansis and reshaped them according to their predicative properties. The structural difference between De Interpretatione and Analytica Priora are revealed through a careful examination of Aristotle's use of these two concepts.

By resolving the account of phenomenological method presented in Husserl's Logical Investigations to its account of the logical character of science as such, and by contrasting the latter with the logical doctrines of Aristotle and St. Thomas, this essay argues that the two philosophical approaches are, in a crucial respect, opposed.

This paper investigates whether Aristotle was aware of the fourth figure, and if he was aware of the fourth figure, why he excluded it from his system. Various commentators have explained why this figure does not exist in the system, so this paper compiles ane examines these arguments through a certain logical frame. By inquiring into why the fourth figure was not included in his logical system, the paper considers whether logical factors may explain this exclusion.

A discussion of Burnyeat's groundbreaking book on Aristotle's Metaphysics Z, with a focus on his two main theses, non-linearity (Aristotle starts afresh four times and argues that substantial being is form) and the two levels hypothesis (Aristotle moves between two levels of discourse, logical and metaphysical). This discussion focuses mainly on the second thesis.

The possibility of formal representation of Aristotle’s discussion about singular predication in Categories 10, 13b27-35 is investigated through three symbolic idioms: the first-order language with identity, with and without definitive description, and through the languages of free logics. I show that such representations are not fully adequate. According to the first option, we are committing Aristotle with some (meta)logical implications he is not willing to accept. According to the second option, we are burdening Aristotle with Russell’s theory of names. Finally, the third option leaves us with the assumption that ‘exist(s)’ could be represented with a predicate. This assumption, however, Aristotle emphatically rejects.

Основная задача статьи – конкретизация вклада Аристотеля в «создание логики». Решение этой задачи связано с рядом проблем. Первая из рассмотренных проблем – проблема институционального формирования логики (в античности). Один из сделанных выводов – формирование логики как отдельной дисциплины происходит к концу античности, то есть уже после жизни Аристотеля. Второй вопрос – о содержательном вкладе Аристотеля в создание логики. Мнение автора – основной вклад Аристотеля в создание логики состоит в применении новой методологии анализа, конституирующим моментом которой было использование особого вида буквенных обозначений. После обзора упоминаний античных и современных авторов о буквенных обозначениях Аристотеля автор переходит к обсуждению двух взаимосвязанных проблем: интерпретации типа буквенных обозначений Аристотеля и их происхождения у Аристотеля. Среди современных буквенных обозначений автор различает несколько видов, в том числе: «переменные», «параметры» и «условные имена». По мнению автора, буквенные обозначения, использующиеся Аристотелем в «Первой Аналитике», ближе всего к современным «параметрам». В этом автор полемизирует с Лукасевичем, утверждавшим, что буквенные обозначения Аристотеля являются переменными. В вопросе о происхождении буквенных обозначений автор оспаривает гипотезу Николя Бурбаки о возможности их заимствования Аристотелем из современной ему «математики». Единственный вид буквенных обозначений, использовавшийся в античной математике аристотелевского и ближайшего постаристотелевского времени, – это «условные имена». Буквенные обозначения Аристотеля (даже, если принять их интерпретацию Лукасевичем) не являются «условными именами», а значит, не могло быть их заимствования (возможность влияния – отдельный вопрос) из «математики».
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The main goal of the article is to give a specification of Aristotle’s contribution to the creation of logic. The achievement of the goal depends of a number of problems solution. The first of the considered problems is the problem of the institutional forming of logic (in antique time). One of the conclusions is that the forming of logic as a discipline took place at the end of antiquity, that is, at the time long after Aristotle’s life. The second question is about Aristotle’s contribution to the creation of logic in the plane of content. The author’s opinion is that a major Aristotle’s contribution to the creation of logic was to apply a new methodology for the analysis, the constitutive moment of which was the use of a special type of lettering. After a review of ancient and modern authors, who had mentioned about Aristotle’s lettering, the author discusses upon two issues: the interpretation of the type of Aristotle’s lettering and its source. Among contemporary lettering author distinguishes several types, including: “variables”, “parameters” and “conditional names”. According to the author, letter symbols, used by Aristotle in the “Analytica Priora”, the closest to the modern “parameters”. The author argues in this aspect with Lukasiewicz asserted that Aristotle’s letter symbols are variables. On the question about the source of Aristotle’s lettering the author challenges the hypothesis by Nicolas Bourbaki that Aristotle possibly took his of lettering from “mathematics” of his time. The only type of lettering used (as we know) in ancient mathematics of Aristotle’s nearest time is a “conditional names”. Aristotle’s letter symbols (even if we accept its interpretation by Lukasiewicz) are not “conditional names” and therefore could not be taken from “mathematics”.

In this highly significant paper, I outline the implications of the critical methodology used in Demonstrations of Degree Absolutism: Zero-and-Four-Quarters Ontologies and objectively-coherent category theory in general (predominately in the work of Nathan Coppedge).

Aquinas divides knowledge into two types: certain and probable. Broadly construed, certain knowledge (scientia) is of what is either necessary or true for the most part. Necessity pertains to axiomatic systems, indemonstrable principles of demonstration and perhaps certain natural phenomena such as eclipses. Statistical natural phenomena are the subject of knowledge that is true for the most part. Probabilistic knowledge, on the other hand, comprises a variety of epistemic attitudes that correlate with degrees of assent that fall short of certainty, ranging from low (mere fancy) to high (belief). Scientia is the product of a syllogism that either (1) demonstrates the inherence of a property in a subject by a middle term that immediately designates the essence of the subject, or (2) demonstrates a necessary connection between an essence and a state of affairs by a middle term that indirectly designates the essence.