Medieval logic

► JOHN CORCORAN, What syllogisms are: three views, eight centuries.
Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA
E-mail: corcoran@buffalo.edu
  At issue is the nature of “the syllogisms” in Prior Analytics [1]. For centuries from the 1200s, the dominant view was enshrined in the medieval mnemonic “Barbara-Celarent” [2]: syllogisms are certain valid premise-conclusion arguments commonly mislabeled “inferences”.  In the mid-1900s many modern logicians adopted a contrary view credited to Jan Łukasiewicz [3]: syllogisms are certain true universal propositions informally called “implications”. A fruitful two-sided debate ensued producing evidence weakening the Łukasiewicz case.
  Toward the last quarter of the 1900s, a third contender appeared. Independently, John Corcoran [4] and Timothy Smiley [5] took the class of syllogisms to exclude propositions while including not only the valid arguments recognized as syllogisms in medieval times but also deductions establishing validity. A deduction contains, over and above premises and conclusion of an argument, a chain of reasoning showing that the conclusion’s information is contained in that of the premises. The debate became three-sided for twenty years or more.
  The Łukasiewicz view lacks current defenders leaving the debate to the medieval and Corcoran-Smiley views.
  This study details all three views—emphasizing their differences. For example, the medieval syllogisms are valid but ‘true’ does not apply to them, though their premises and conclusions are all true or false. The Łukasiewicz syllogisms are all true but the term ‘valid’ as applied to arguments is inappropriate. The Corcoran-Smiley syllogisms cannot be said to be true in the sense applicable to propositions but they are all valid in the sense that their conclusions follow from their premises. Moreover, many of them containing chains of reasoning are “cogent” [6] in an epistemic sense not applicable either to the Łukasiewicz or to the medieval syllogisms.
  [1] ROBIN SMITH, Aristotle’s Prior Analytics, Hackett, 1989. 
  [2] JOHN CORCORAN, DANIEL NOVOTNÝ, AND KEVIN TRACY,  Deductions and Reductions Decoding Syllogistic Mnemonics, Entelekya Logico-Metaphysical Review,  vol.2 (2018), pp. 5–39.
  [3] JAN ŁUKASIEWICZ, Aristotle’s syllogistic, Oxford UP, 1951.
  [4] JOHN CORCORAN, Aristotle’s Prototype Rule-based Underlying Logic, Logica Universalis, vol. 2 (2018) pp. 9-35.
  [5] TIMOTHY SMILEY, What is a Syllogism?, Journal of Philosophical Logic,
vol. 2 (1973) pp. 136–154.
[6] JOHN CORCORAN, Argumentations and logic, Argumentation, vol. 3 (1989), pp. 17–43.

علم الكلام الأشعري لم يكن نظرا مقتصرا على القضايا المعهودة في أصول الدين، بل كان تشريعا للعقل السني؛ فإذا كان علم أصول الفقه قد اضطلع بالتشريع للميدان العملي، فإن علم الكلام ظل  يروم التشريع للعقل العلمي، ويحدد الأدوات المنهجية والعقلية بما ينسجم مع نصوص الوحي،  علاوة على إصراره على أن يحدث لنفسه تمايزات منهجية عن التقاليد المنهجية الأخرى.

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.

Many scholars believe "On a New List of Categories" is a metaphysical or transcendental deduction. The present essay will argue that Peirce derives the categories by induction and validates their order by prescision. Then the article shall solicit aid from Peirce's early and later writings to explain how the new way to list the categories can serve as a genealogy of signifi cation: how the diff erent types of term, proposition, and argument emerge in the process of reasoning as the diff erent types of signs. Thus, the genealogy of signifi cation would then qualify as a phenomenology of logic as a science of semiotics. Such a science of semiotics will have three types of comparison corresponding to the sign-relation in illation: namely, uniparance, diaparance, and comparance. Then the three types of comparison will occasion three types of relative in diff erent types of propositions: namely, concurrents, disquiparants, and equiparants. Finally, the three types of relative will occasion the diff erent types of sign corresponding to the diff erent types of term: namely, icons, indices, and symbols. With this classifi cation, there is then an explanation of how the process of reasoning is a semiotic process with three forms of valid argument: namely, hypothesis, induction, and deduction.

John Wyclif’s logical works have lain under a kind of fog since they were first published in the 1890s under the collective title Tractatus de logica. My first aim in this paper is to clear up some longstanding confusions by dispelling this fog once and for all. Once the air is clear, a partial identification of Wyclif’s source material will allow me to make a more dramatic claim about persistent misunderstandings of what is generally taken to be his earliest work.

Our investigation has two main points: a contextualization of Abelard’s account of universals and a detailed analysis of his theory as it is formulated in the Logica “ingredientibus.” The interest of the first point is to show that Abelard is just one author among the many who tried to
offer a solution to the debate. In order to do so, we follow and comment upon John of Salisbury’s presentation of contemporary theories on the subject. The interest of the second point, however, is to show how Abelard’s answer is subtle and important in itself. His theory is especially innovative due to the fact that it changes the framework of the debate: it no longer belongs to the domain of metaphysics, but to that of meaning.

Keywords
universal, Abelard, nominalism, realism, John of Salisbury, status theory

St. Thomas Aquinas sometimes uses strictly conceptual and logical insights to draw insights about things in reality. I show that, throughout his career, Aquinas’s metaphysics employs a logical procedure that he calls the “method of predication” (modus praedicandi). This method consists in using what logic teaches about modes of predicating as a tool for deductive reasoning in metaphysics.
The first chapter examines passages in Aquinas’s Commentaries on De Trinitate and on the Metaphysics that describe this method of predication or “logical method” as a “fitting” and “proper” way for metaphysics to proceed. This chapter also provides the context for Aquinas’s method by identifying some important classical and contemporaneous sources (Aristotle, Boethius, Averroes), including a discussion on topical arguments and the distinction between doctrinal and instrumental logic (logica docens, logica utens). 
In chapters two and three, I consider the realist framework behind the method of predication. I discuss cognitive realism in chapter two focusing on the origin and role of essence or nature (absolutely considered) in predication.  I offer an account of how concepts and predications are ultimately caused by (real) things. I discuss metaphysical realism in chapter three focusing on the relationship between the subject of logic, rationate being (ens rationis), and the subject of metaphysics (ens communis), which is real being (ens naturae). This chapter finishes with an examination of essential being (ens secundum se) and different types of predication (e.g., per se, per participationem, denomative).
In chapter four, after examining Aquinas’s rejection of similar types of arguments from previous authors (Parmenides, Plato, Avicebron), I consider the application of the method of predication to various metaphysical issues. Aquinas uses the method of predication in many different contexts. He uses it in order to derive different properties and categories of being, to distinguish esse from essence, to establish the unicity of the substantial form, and to justify the reality of prime matter in a properly metaphysical fashion. These arguments are analyzed for their soundness, and the interpretation of some authors are taken into consideration.

This doctoral dissertation was defended on November 18th, 2016 before Dr. Gregory T. Doolan, Dr. Timothy B. Noone, and Dr. Michael Gorman alongside two external readers at The School of Philosophy, The Catholic University of America in Washington D.C.

Il contributo si propone di produrre un’introduzione sistematica e meditata ad alcune premesse fondamentali della semantica di Giovanni Buridano, il famoso maestro che insegnò all’università di Parigi nel XIV secolo. Inizialmente, l’attenzione è posta sulla cosiddetta dottrina dei “livelli linguistici”, la quale prevede il riconoscimento di tre tipologie divergenti di oratio (scritta, vocale e mentale), e ai parallelismi di tipo semantico, e non sintattico, sussistenti tra di essi. Proseguendo su questa scia, viene trattata la differenza tra termini significativi ad placitum e naturaliter e si riflette – non senza allusioni alla cultura contemporanea – sui divergenti meccanismi impositivo-istitutivi descritti dal maestro piccardo, che condurrebbero all’istituzione e all’elaborazione di nuove tipologie di linguaggio. Successivamente, il focus è posto sulla rielaborazione originale – proposta nei primi paragrafi del De suppositionibus – della nozione di significatio, che viene non soltanto ad assumere una predisposizione cognitivo-intensionale, ma si configura come un processo che, insediandosi nelle normali dinamiche comunicative, può dirsi compiuto soltanto quando c’è un reale intendimento tra le parti. Nelle pagine conclusive, inoltre, viene evidenziata la profonda coerenza di buona parte dei contenuti della semantica buridanea con questa impostazione di base.

This paper, a longer version of a talk given in Kalamazoo, MI in 2018, is an attempt at undertaking a retrieval of the fundamental "situating" of logical science, doing so through a series of vignettes from within the Dominican tradition of philosophical thought.

Certain Byzantine logicians exercised enormous influence in the Orthodox East and were popular enough in the Latin West to merit fifteenth- and sixteenth-century printings. One such polymath was George-Gennadios Scholarios. Trained in the Byzantine scholiast tradition, Scholarios learned Latin and, as an autodidact, subsequently mastered Dominican, Scotist, and modista logical and metaphysical literature. Scholarios’s eclecticism in philosophy was later pressed into the service of religion when he became an Orthodox monk and Patriarch of Constantinople. Scholarios used Bonaventure of Bagnoregio, John Duns Scotus, Hervaeus Natalis and Francis Meyronnes in defense of official Orthodoxy on the question of God’s essence as distinct from his attributes. Hervaeus’s theory of first and second intentions was fundamental for Scholarios to speculate on the distinctiones in divinis.

The main aim of this study is to examine the foundations of Gilbert’s theory of individuality. First, I examine its philosophical and doctrinal background; second, I explain in what sense individuals are wholes; third, I address the most important objections to Gilbert’s reasoning.

La lógica de la Edad Media se presenta a los lógicos contemporáneos, filósofos medievalistas,  historiadores y filósofos de la lógica, como un campo tan fascinante como de difícil acceso. Parece difícil para casi cualquier investigador encontrar la punta del ovillo que conduzca a una presentación ordenada e inteligible de la lógica medieval. Este libro pretende solucionar este problema y presenta de manera ordenada y autocontenida los desarrollos lógicos de la parte técnicamente más evolucionada de la lógica de la Edad Media: el siglo XIV. A diferencia de otras presentaciones no evade los hechos históricos y culturales que conforman el panorama de la época ni las cuestiones filosóficas detrás de los desarrollos lógicos, a fin de entender cabalmente las cuestiones técnicas.
Los primeros tres capítulos se abocan a cuestiones generales, históricas y a la genealogía de los tópicos más importantes. El cuarto capítulo está dedicado a la presentación sintáctica del lenguaje de la lógica medieval. El quinto y el sexto a la metateoría de esta lógica. El séptimo explora y presenta la semántica de esta lógica. Los dos últimos nos brindan una reconstrucción racional en términos del lenguaje simbólico contemporáneo de la lógica de finales del siglo XIV.

Thomistic commentators agree that Thomas Aquinas at least nominally allows for 'to be' (esse) to signify not only an act contrasted with essence in creatures, but also the essence itself of those creatures. Nevertheless, it is almost unheard of for any author to interpret Thomas's use of the word 'esse' as referring to essence. Against this tendency, this paper argues that Thomas's In V Metaphysics argument that every predication signifies esse provides an important instance of Thomas using esse to signify essence. This reading of In V Metaphysics, which this paper defends against an alternative interpretation, entails significant reinterpretations of Thomas's technical terms 'esse substantiale' and 'esse in rerum natura' as well as Thomas's use of 'is,' both as a copula and as a principal predicate.

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.

This article is a study of St. Thomas Aquinas’ De principiis naturae 3. Firstly, matter, form, and matter are not enough to explain the generations: another principle is required, which operates the generation. This is the efficient cause, which does not operate if it is not moved by an end. Acting for an end is proper both to voluntary and to natural agents. He proves this by means of a complex conditional hypothetic syllogism. Then, he distinguishes the senses of cause and principle: a cause is that, from the being of which another thing follows; a principle is simply what is prior to another thing. Lastly, he distinguishes the element’s notion from the one of prime matter. Based on this, we may establish a generic notion of matter, the principal species of which would be the prime matter, the subject and the element.

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 present study focuses on Albert the Great’s reception of Arabic sources – especially of Avicenna – in his commentary on the Isagoge, i.e., the Super Porphyrium de V Universalibus. The paper is articulated into two main sections (I and II) and six appendixes (A-F). The first section (I) offers a preliminary evaluation of Albert’s use of Arabic sources in the SP. The second section (II) aims to assess Avicenna’s impact on Albert from the viewpoint of his doctrinal digressions. Two major doctrines of Avicenna are integrated into Albert’s theory of the predicables: first, the Avicennian distinction between an ontological consideration of the predicables, which pertains to metaphysics, and a logical one, which pertains to logic; second, Avicenna’s redefinition of the epistemological status of logic, which is reassessed as a science in its own right with its own subject-matter, ceasing to be considered as a mere instrument for the other sciences. Both points were crucial to the thirteenth-century debate on the subject-matter of logic and the universal predicables: a comparison between Albert the Great’s and Robert Kilwardby’s treatments of these themes shows that Albert might have engaged in a debate with his colleagues which has gone unnoticed so far. It is argued that the recourse to Avicenna has provided Albert with a set of arguments which, assimilated and rearranged in his theory of the universal predicables, enabled him to elaborate original answers to the problems differently faced by his contemporaries.

How should the phrase 'fides quaerens intellectum' be understood as a characterization of Anselm’s Proslogion specifically and Anselm’s oeuvre more broadly? I argue that 'fides quaerens intellectum' should be understood not in accordance with any of the standard meanings we assign to the words ‘faith’ and ‘understanding’, but in accordance with their meaning in works used to teach grammar and dialectic at Bec in and around Anselm’s lifetime.
I begin by making the structures behind the usual understanding of ‘faith’ and ‘understanding’ explicit. From here, I detail the works used at Bec according to a 12th century library list, and provide justification for thinking these same works were used slightly earlier, in Anselm’s time. Next, I show how the terms 'fides' and 'intellectus' functioned in these works. Finally, I turn to the Proslogion and the exchange with Gaunilo to show how these considerations illuminate Anselm’s method in these works.

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 research focuses on the previously unpublished treatise by Sayyid Sharīf al-Jurjānī, Risāla fī taqsīmal-‘ilm. The research is based on comparative evaluation of available manuscipts and is composed of a critical edition of the treatise and its analysis. The treatise is about the division (taqsīm) of tasawwur (conception) and tasdīq (assent) as divisions of knowledge. Al-Jurjānī presents views from different schools of logic. In the analysis section, I discuss the treatise’s philosophical background and show that the aforementioned division is the first step of a chain of propositions on what the goal and methods of logic are focusing on the possibility of learning. Remaining sections focus on the references in the treatise to various views and summarise them. Finally al-Jurjānī’s position in this scene is made explicit through his critical analysis of competing views advocated by these different schools.
For al-Jurjānī, division of knowledge can be analysed formally and informally. Formally, the division should be restrictive and informally, it should emphasize methods of logic, that are proof (hujja) and definition (ta‘rīf). The article shows that the goal of al-Jurjānī’s discussion on the division of knowledge as conception and assent is basically to take the discussion out the context of traditional discussions on quiddity but rather build it on the division formally and the goals of the division informally.

This MSc thesis addresses three challenges posed by intentionality - the
ability of our mental states and language to be about something - to
a logician: an apparent reference to non-existent objects, intentional
indeterminacy and the failure of substitutivity of coextensive terms
in an intentional context. Since intentionality plays an important role
in our everyday reasoning, a proper formal account of it is highly
desirable, yet it requires a departure from classical logic. One can
modify classical logic and adapt the formal apparatus to account for
the aforementioned problems (Graham Priest’s logic for intentional-
ity serves as an example of such an approach in this work) or one can
make an even more radical shift and seek for inspiration in a different
logical tradition like the terminist logic developed in the Late Middle
Ages by figures like William of Ockham or John Buridan. The sec-
ond path is explored here as a modest attempt to show that once we
abandon the bias against the history of logic as irrelevant, we can ac-
tually get access to firm logical solutions inaccessible from a classical
perspective, while still practicing logic proper.

This is the 1988 collection of my first essays concerning logical semantics published in English. Its age shows in many ways, especially, in its print type. Still, I am presenting it here for a number of reasons. 1. It is somewhat difficult to obtain, although it is available in many libraries all over the world. 2. An unauthorized version of a partially corrected converted file, in which the technical notation is rendered unintelligible, is circulating on the net. 3. There seems to be renewed interest in the kind of approach it presents to a "natural logic", gaining more and more importance in natural language processing by artificial intelligence. 4. Some young European scholars, namely, Guido Alt (who prepared the scan), Giacomo Fornasieri, and  Chris Geudens, have kindly prepared a fully corrected text of the converted file, which I will also publish once I managed to go over their corrections. So, I just wanted to "inaugurate" that version by presenting here the original, along with the original "Corrigenda" sheet that was pasted in most, but not all, copies of the printed original.

In his incarnation as 'Morus' in Utopia, Thomas More asserts his profound disagreement with his fictional character, Raphael Hythlodaeus. Whereas Hythlodaeus extols the merits of commonality and the moral value of pleasure, Morus dismisses the whole project as absurdity, or hopeless wishful thinking. This divergence has been variously interpreted, but mostly played down. This paper argues that the civilized, amicable, and yet genuine discord between Raphael Hythlodaeus and Morus is the key to Utopia. We can appreciate its importance only if we understand who Hythlodaeus is, and what the purpose of the dialogue is. We also have to do justice to Thomas More's politics, which were grounded on the authority of the Christian tradition, in the Old and the New Testament. Over the years, Thomas More maintained a very clear and consistent line of thought on the legitimacy of worldly wealth, the responsibilities inherent in its management, the imperative to curb their enjoyment, the temptation of 'business' and greed, the duty of charity, and the value of penance, remorse, prayer, and other kinds of self-inflicted suffering. In A Dialogue of Comfort against Tribulation, Anthony, the wiser character, conveys Thomas More's relentless praise of pain. Anthony has the last word. So, too, does Morus.

Posing a Halakhic query to a rabbi is often taken for granted, as the backdrop to a legal process that begins with the rabbi composing his responsum. At times, however, the question itself is the product of a calculated decision on the part of a layperson to become involved in the Halakhic process. Focusing on responsa from medieval Provence, this article claims that the tensions that existed within the Jewish community between rabbis and philosophers were sometimes played out by asking Halakhic questions. Sensitivity to rhetorical dimensions in both the question and the answer, and to the cultural and social contexts in which the responsum was created, reveals a hidden polemic about Jewish law and power.

This is an early draft of an article forthcoming in the American Philosophical Quarterly. The paper investigates an aporia in the thought of Bl. John Duns Scotus. The puzzle pertains to Scotus's account of common being and the scope of metaphysical science. First, an argument is made that Scotus's metaphysics should exclude logical being from its subject matter. Next, an argument is made that Scotus's metaphysics should include logical being in its subject matter. Then the paper considers two possible avenues for resolving this aporia and notes problematic aspects of each. Finally, the paper concludes that there is a genuine tension within Scotus's thought regarding the scope of metaphysics and the univocity of being, and that this tension served as a seed for the supertranscendental theorizing in later scholastic thought.

In 1898 C. S. Peirce declares that the medieval doctrine of consequences had been the starting point of his logical investigations in the 1860s. This paper shows that Peirce studied the scholastic theory of consequentiae as early as 1866–67, that he adopted the scholastics’ terminology, and that that theory constituted a source of logical doctrine that sustained Peirce for a lifetime of creative and original work.