History of Medieval Logic

This paper examines the methodology employed by Thomas Aquinas in his two derivations of the categories, or sufficientiae. In these accounts, he shows the distinctiveness of the ten Aristotelian categories as modes of being (modi essendi) through an analysis of modes of predication (modi praedicandi).  The paper considers why Aquinas sees this logical method of predication (via praedicationis) to be an appropriate tool for the metaphysician.  Similarities between Aquinas’s and Albert’s sufficientiae are shown to clarify Aquinas’s methodology. In particular, the paper examines how both thinkers employ modes of denominative predication and modes of opposition to derive the categories.  The paper not only reveals Aquinas’s full methodology in his sufficientiae, but it also provides further insight into how he uses logical methods in general in his metaphysical investigations.

Sturio of Cremona, a hitherto unknown Italian master of the 13th century, is the author of a logical textbook called 'Tractatus', much in the same vain as the famous work of Peter of Spain.  Utilization of this manual in the teaching of logic is attested in Italy till the 14th century, but surely it was soon superseded in the second half of the 13th century by the one by Peter of Spain. Collecting evidence both from archival sources and from his literary production, it turns out that Sturio was a member of the cathedral chapter of Cremona from at least 1244 to 1266, died not long before 1275 and is the author of the 'De impressionibus aeris', a summary treatise on Aristotle’s Meteora I-III which was known by Miichael Scotus and Albert the Great and was probably written before 1235.

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.

The definition of the relation between expressions (alfāẓ) and meanings (maʿānī) has played a pivotal role in determining the subject-matter of logic all along the so-called “classical period” of Arabic philosophy. This paper focuses on Avicenna’s (d. 427H/1037) view on this fundamental topic taking into account his hitherto neglected correspondence with an anonymous disciple (Mubāḥaṯāt 579-585 in Bīdārfar’s edition). The aim is to frame this correspondence in its original context by analyzing both its direct and indirect tradition. The correspondence, which appears to be quoted in Faḫr al-Dīn al-Rāzī’s (d. 606H/1210) Šarḥ al-Išārāt wa-l-Tanbīhāt, may be one of the earliest – not to say the earliest – signs of an exegetical activity surrounding Avicenna’s Išārāt and Šifāʾ still in its embryonic stage.

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the lo-gicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz,

This article examines the traditional and modern doctrines of categorical
propositions and argues that both doctrines have serious problems.
While the doctrines disagree about existential imports of categorical
propositions, they share a fundamental assumption: matching categorical propositions of the same kind (e.g., universal affirmatives, particular negatives) are logically equivalent (the logical
homogeneity thesis). The article shows that this common thesis is false, and
argues that one cannot deal with the logical diversity of categorical propositions with minor modifications of the traditional or modern
doctrine. It also gives a sketch of an account that pays close attention
to the logical diversity of categorical propositions. In doing so, the article examines differences
among various versions of the traditional doctrine and discusses categorical propositions
involving plural constructions and non-distributive predicates.

Dei 57 manoscritti schedati, conservati presso l'Archivio Capitolare della Basilica di Sant'Ambrogio, il codice M 2 può sicuramente rientrare nel novero di quelli meno studiati: rarissime sono le menzioni bibliografiche e solo tarde le attestazioni negli inventarî capitolari. I due cataloghi che descrivono i libri appartenenti ai canonici all'altezza del sec. XV non ne recano traccia 1 . Né risulta di maggiore aiuto la bibliografia contemporanea. Il Kristeller 2 ne fa menzione en passant proponendo come datazione il sec. XIII. Lo studioso trascrive incipit ed explicit, ma non segnala altre notizie. Poco più diffuse sono le informazioni offerte dalla dottoressa Maria Cesarina Belotti 3 nella sua tesi di laurea: il f. 1r. viene sommariamente trascritto, sebbene con lacune, e vengono * Desidero ringraziare i proff. O. Grassi, M. Petoletti, S. Caroti e la dott.sa M. R.

Il quadro generale di riferimento del volume riguarda l’analisi
delle soluzioni medievali ai cosiddetti insolubilia (definiti come
proposizioni autoreferenziali che discendono direttamente
dalla tradizione del paradosso del mentitore) e la commistione tra queste soluzioni e le teorie note come proprietates terminorum, che analizzano le proprietà dei termini (parole o espressioni) e le differenti funzioni (officia) che questi svolgono all’interno di una proposizione. Questa commistione risulta essere dal punto di vista storico–critico di notevole importanza dato che si approda ad una discussione originale ed indipendente sugli insolubilia esclusivamente all'interno di quella che è stata definita logica modernorum.

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century—before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz,

The Quaestiones Theologiae constitute Langton's chief speculative work. Book III, volume 1, offers a critical edition of 24 disputed questions on Christology and faith. Each question is accompanied by a critical apparatus and source notes. The edition is preceded by an extensive analysis of Langton's views. The volume also contains an important supplement to the study of the whole manuscript tradition of Langton's Quaestiones Theologiae and offers the first general stemma codicum of the Quaestiones.

Developed out of earlier work on Aristotelian topics, syllogistic, and fallacies, by the early fourteenth century the medieval theory of consequence came to provide the first unified framework for the treatment of inference as such. With this development came the task of unifying the various justifications for inferences treated in earlier frameworks.

Prior to the appearance of theories of consequences, the task of providing a real foundation, or grounding, for good inferences is shared between theories of demonstration, such as those provided in commentaries on Aristotle’s Posterior Analytics, and theories of topical inference, passed on to the medievals via Boethius. But by the time of the earliest consequentiae, most consequences were grounded in the theory of supposition, which began its own development in the twelfth
century.

Secondary literature on supposition has generally held that in the most common form of supposition, personal supposition, a term is taken to stand for individuals falling under it. In this paper, I show that for the earliest consequentiae this is false: prior to William of Ockham’s work, personal supposition could also involve descent to concepts or types falling under a term, previously thought to be the exclusive provision of simple supposition. As such, a greater variety of ways of grounding consequence exists in the period than has hitherto been recognized.

A first known Greek translation of Bonaventure is presented in this study, as well as Hervaeus Natalis. Bonaventure's presence is bizarre, for "Disputed Questions on the Trinity" were lost in the 13th century and only rediscovered in the 19th. Scholarius is proven to be wrongly considered an (orthodox) Thomist. This paper uncovers Scholarius' real Latin sources. The Scotistico-Thomist Hervaeus shares multiple affinities with Palamism. The conclusion vindicates some of John Milbank' suspicions about East-West mirror metaphysics in the 14th century.

Blasius Pelacani’s two questions on the paradoxes of implication in his commentary on the 'Tractatus' of Peter of Spain aptly introduce to a substantial discussion of the notion of logical implication in medieval authors such as Abelard, Ockham, Scotus, and Blasius himself. Methodological assumptions on the history of logic in general are also analysed.

The present article studies a fascinating manuscript, a unicum, housed in the British Library, Heb MS Add 27559. This manuscript of works by Ṭodros Ṭodrosi of Arles features a lengthy Hebrew anthology of logical and scientific texts, written by Greek and Arabic philosophers, some of which were translated by him into Hebrew for the first time. In a previous study that appeared in 2021, we examined the section from the book on natural science of this anthology that Ṭodros devoted to the study and explanation of Aristotle’s Physics and which he completed in Trinquetaille in 1333 at the age of twenty. In that paper, we uncovered Ṭodros’s aims and his own unique methodology in this section and sketched a picture of
the ways in which Ṭodros intended to assist his contemporary readers in the study of natural science. In the present paper, we shed new light on this manuscript through an examination of the book on logic that Ṭodros dedicated to the study and explanation of Aristotle’s Organon. We describe Ṭodros’s modus operandi and examine the nature of his discussions in each of the sections of his book on logic, with special attention to the section on the Posterior Analytics, and we show to what extent they correspond to what we uncovered in his treatment of the Physics. The paper analyzes Ṭodros’s use of Averroes’ Long Commentary on the Posterior Analytics in order to explain Averroes’ Middle Commentary on the Posterior Analytics, and it illustrates Ṭodros’s use of al-Fārābī’s Long Commentary on the Topics in order to explain Averroes’ Middle Commentary on that book. The paper, just as our 2021 study that it complements, contributes to our knowledge of the fundamental status of Averroes’ middle commentaries on the Corpus Aristotelicum among medieval Jewish scholars, as well as to our growing awareness and appreciation of the achievements of this fourteenth-century Provençal Jewish scholar, Ṭodros Ṭodrosi.

L’Isagoge de Porphyre a été l’un des textes fondamentaux pour l’enseignement de la logique dans l...’Occident latin. Cet article veut montrer son importance, à partir de l’étude des manuscrits, pour la période 800-980. L’introduction générale est suivie d’un catalogue des manuscrits qui transmettent l’Isagoge, ou bien l’un des commentaires de Boèce à l’Isagoge. Pour chaque manuscrit, sont indiqués la datation, le contenu général, les gloses et les diagrammes liés à l’Isagoge. // Porphyry’s Isagoge was one of the most important fundamental texts for the study of logic throughout the whole Latin Middle Ages. In this article, I document its importance in the period from ca800 to ca 980 by providing an assessment of manuscript evidence. After a general introduction, I list all existing Latin manuscripts transmitting either Porphyry’s Isagoge or one of Boethius’s commentaries on the Isagoge. For each manuscript, I note date, overall content, glosses and diagrams on Isagoge-related material. // L’Isagoge di Porfirio fu una delle opere più importanti fondamentali per lo studio della logica in ambito latino per l’intero medioevo. Questo articolo documenta l’importanza dell’opuscolo porfiriano nel periodo 800-980ca attraverso uno studio dei testimoni manoscritti. Dopo un’introduzione di natura generale, si presenta un catalogo di tutti i manoscritti latini conservati che trasmettono l’Isagoge oppure uno dei due commenti di Boezio allo scritto porfiriano. Per ogni manoscritto si discutono la datazione, il contenuto generale, le glosse e i diagrammi legati all’Isagoge. //

Dopo aver dato una breve introduzione ai recenti sviluppi storiografici riguardanti Guglielmo di Ockham analizzerò il primo paragrafo della Logica dei Termini, evidenziando la definizione di termine, la sua accezione segnica con relative conseguenze.

It has long been uncertain whether Scotus wrote any of the logical works commonly attributed to him. In what follows, I re-examine the question of authorship by an appraisal of the existing evidence, both external and internal, including recent work on the comparatively obscure Questions on the Perihermenias.  I shall argue that the external evidence for authorship is weaker than has been previously thought, but that the internal evidence is consderably stronger. I conclude that there is overwhelming evidence that three works – the Questions on Porphyry, on the Categories, and on the Perihermenias (both versions) are authentic. About the Questions on the Sophistical Refutations there is still doubt.

With William of Ockham and John Buridan, Walter Burley is often listed as one of the most significant logicians of the medieval period. Nevertheless, Burley’s contributions to medieval logic have received notably less attention than those of either Ockham or Buridan. To help rectify this situation, the author here provides a comprehensive examination of Burley’s account of consequences, first recounting Burley’s enumeration, organization, and division of consequences, with particular attention to the shift from natural and accidental to formal and material consequence, and then locating Burley’s contribution to the theory of consequences in the context of fourteenth-century work on the subject, detailing its relation to the earliest treatises on consequences, then to Ockham and Buridan.

In this paper the method of investigation of paths of thinking is applied to analyse St. Thomas Aquinas’s question 23 on predestination from his Summa Theologiae to show how he reached his conclusions, what influenced his thought and what is the status of his statements. It reveals before all that, despite following the lines of St. Augustine (what can be said about the main conclusions), he designed original paths of thinking, often based on logically correct deductive reasonings, starting from carefully chosen statements (sometimes axioms) and creating together a logically combined network.

Tanto el Chartiludium institute summarie como el Chartiludium logice de Thomas Murner son los primeros usos didácticos de un juego de naipes en toda la historia.  Aprender deleitándose, aprender con distracción y usando recursos lúdicos es una gran ocurrencia de Murner. Y es que no sólo tiene la fortuna de ser el primero en haber puesto los naipes al servicio del saber, sino el primer lógico en hacer un ejercicio de didáctica de la lógica y el primer jurista en hacer una didáctica lúdica del derecho. Con naipes ayudaba a memorizar las Instituciones de Justiniano o el Tractatus de Pedro Hispano resumiendo a Aristóteles en la abstracta y árida lógica. Además de las cartas, Murner supo hacer uso del tablero de ajedrez o del backgammon para explicar las reglas de la prosodia y la cuantificación de los versos en su Ludus studentum Friburgensium. Tal vez, pues, desde sus estudios tempranos en artes liberales supo encontrar, como estudiante, un modo de aprender que luego supo transmitir como profesor. Algunos de los puntos que más de 100 años después escribirá Comenio en su Didáctica Magna, Murner los llevó a cabo con maestría, versatilidad y creatividad. Thomas Murner merece un lugar tanto en la historia de la pedagogía, como en la de la didáctica.

Résumé. – La notion de « par soi » (καθ’ αὑτό) fait partie des éléments clés de l’ontologie et de l’épistémologie aristotéliciennes. Nulle part, toutefois, Aristote n’en fournit une étude systématique, au point que l’on voit mal l’articulation de ses différentes acceptions et le sens m.me du projet général dans lequel cette notion est inscrite. La présente étude se propose d’étudier l’interprétation qu’Averroès fournit de cette notion dans son Grand Commentaire des Analytiques Postérieurs. En traduisant pour la première fois dans une langue moderne de longs extraits de ce commentaire, on montrera la place centrale que cette notion occupe dans la théorie scientifique du Cordouan et notamment dans sa théorie de la démonstration du signe.

Abstract. – The notion of “per se” (καθ’ αὑτό) is one of the key elements of Aristotle’s ontology and epistemology. Nowhere, however, does Aristotle provide a systematic study of it, so as the articulation of its different meanings and the significance of the general project in which this notion is inscribed remain unclear. This paper aims at studying the interpretation that Averroes provides of this notion in his Long Commentary to the Posterior Analytics. In translating for the first time in a modern language some long quotations of this commentary, we will show the central role that this notion plays in Averroes’ scientific theory and in particular in his theory of demonstration of sign.

Questions, dilfinicions, lausors, entencions, son los tbnaments d'aquest Libre (Uibre de sanla Maria. OKI. X. 3) 0. Premessa II concello di delinizione intcressa lutli i canipi dei sapere niedievale. dalla relorica alla dialettica, dalla logica alla nascentc lessicografia. Nei dizionari, quando non e usato comc sinonimo di «glossa» o. nci rcpertori bilingui. di «tradu/ione». il termine definitio e uno dei sinonimi correnti. insieme a declaratio e descriptio, del piii diffuso expositio. 1 Uexpositio (e percio il sinonimo definitio) inelude. nella sua acce/ione ampia. anche V etimologitt. con la qualc si indicano tanto l'origine quanto il profondo signilicato dellc parole oltenuto attraverso liinalisi dei tcrmini. secondo il metodo proprio della scienza. Nellc grandi compilazioni (come le Derivationes di Uguccione da Pisa o 17:lementarium di Papias) si trovano diversi tipi di definizione: quella per sinoni-1 Sul valore della parola definitio si vedano: Olga Weijers. Dirtionnaires et repertoires att Moyen Age. Une fitttlf tltt vorabulaire (Tumhout: Brepols, 19911: Olga Weijers (a cura di). Tenninologie de la vie iiiifllffittfllf aii Moyen Age. Actes du Collocjue. Leyden-La Haye. 20-21 seplembre 1985 (Turnhout: Brepols. 1998); Brian Mcrrilees. «Translation and Defmition in llie Medieval Bilingual Dictionary». in: Translation Theory and Prarlire in tlir Middle Ages, cdilcd by Jcanette Bccr t Kalania/.oo. Michigan: Wcsiern Michigan Univcrsity. 1997). pp. 199-214: e Mariken Teeuwen. The Vorabulary of Intelterlnal l.ifr in llir MiJtllr Ages iTurnhoul: Brcpols 2003). Hl.hNA PISTOl.HSI mo. quella data altraverso resempio e quclla per interpretumenta, che sconllna da LI 11 lato neirenciclopcdia. dalTallro nclla filosolia. Solo a parlire dal xin secolo si diffonde 1'LISO di definitio come sinonimo di sententia nella locu/.ione «sententia magistralis», con cui si isolano le citazioni tratte dalle auctoritates o di uso comune.' La distinzione tra la definizione dei relori e la deilnizione dci filosoli. volta a spccillcarc il valorc del termine in rapporto alLambito di applicazione, c svolta nel piu antico testo a noi giunto interamentc dedicalo aH'argomento. il Liber de definitionibus di Mario Vittorino (iv sccolo d.C".). 1 II primo tipo si colloca nel campo delTopinione c corrisponde alla tcsi da sostenere nelPargomentazione: Lina volta cnunciata. essa deve esserc dimostrata. sviluppata negli esempi (cioe applicata a casi particolari) e servire a confutare le posizioni deH'avversario." La definizione dei filosofi, al contrario, c necessaria e rigorosa, la sola lcgittima secondo Vittorino: «Hoc ut apertius tlat, hic docebimus nullam esse dcfinilionem certam integram approbandam nisi eam quam dicunt philosophi substantia-

The transmission of the Arabic Logic in Medieval Europe is a reality that marks an important period in the cultural history. The main purpose of this article is reflected in three main ideas. The first one reveals a classification of Arabic logicians and a comparison of their role both in the Arab way of thinking and in the European medieval thinking. The second idea touches the problem of the typologies of transmitted subjects and focalizes on the way in which European medieval thinkers either assimilated or criticized Arabic Logic ideas in their corpus. Finally, a description of actual exegesis of this subject will be proposed, by pointing out the specificity of the actual thinking concerning the transmitted ideas and a reconsideration of the importance of these themes. In this way, a presentation of the evolution of the transmission phenomenon will be made, in addition to a presentation of the actual perception concerning this subject by means of emphasizing the role of Arabic Logic ideas both in the history of logic and in the history of universal ideas.

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz, a scholar equally at home in philosophy, classics, mathematics, and logic. Perhaps surprisingly, the then-prominent syllogistic mnemonic played no role in the Łukasiewicz work. His 1950 masterpiece does not even mention the mnemonic or its two earliest champions William and Peter. The syllogistic mnemonic is equally ...