Supposition Theory Research Articles

The categories in Petrus Hispanus’s Tractatus commentators: John Buridan, John Versor and Peter Tartaret

One of the features of the manuscript transmission of Petrus Hispanus’s Tractatus (or Summulae logicales) is the fact that the treatise on the Categories does not always appear in the same place. In some manuscripts, it appears in third place, after the treatise on Porphyry’s Isagoge, following the traditional order of the logica vetus. But in some others, the treatise on the Categories appears in fifth place, after the treatise on the Topics and right before the treatise on supposition. In both cases, it seems that the place of Aristotle’s Categories in logic is defined by the notion of “term”.
 The purpose of this article is to understand why this variation occurs, since it is not theoretically neutral. Hence, to address the problem of placing the treatise on the Categories within logic, three of the most prominent Tractatus commentators will be presented: John Buridan, John Versor and Peter Tartaret. This exercise will provide some insights on the relation between the categories and the theory of supposition, and also on the vexata quaestio of what categories are about (words, concepts, or things).

Changes in British Logic Teaching During the Sixteenth and Seventeenth Centuries

British logic teaching in the sixteenth and seventeenth centuries was provided in England by Oxford and Cambridge, both medieval foundations, and in Scotland by the universities of St Andrews and Aberdeen, both founded in the fifteenth century, and Edinburgh, founded in 1582. Wales had no university, and high schools in England did not teach logic. This paper explores the effect that the invention of printing, along with organizational, political, and sociological changes, had on the teaching of these institutions as they affected the logic textbooks that were used and the ways in which the material was presented to students. The disappearance of important medieval developments such as supposition theory along with changes in the treatment of Aristotle’s logic are discussed in relation to selected logicians from the period under discussion. In particular, attention is paid to the Cambridge logician John Seton (d. 1567), whose popular Dialectica was published in 1545, the Frenchman Peter Ramus (d. 1572), whose influence in both England and Scotland was less than has been supposed, and the Oxford logician Robert Sanderson (d. 1662/3) whose Logicae artis compendium was reprinted as late as 1841.

Logic and Metaphysics in Vilnius during 16th–18th Centuries: The Most Important Sources of Vilnius Libraries

The aim of the article is to present the results of research conducted as part of the project Polonica Philosophica Orientalia: namely, to give an overview of the most important logical and metaphysical treatises (both manuscripts and printed editions) written in Vilnius between the sixteenth and eighteenth centuries that are currently accessible in some of the Vilnius libraries. Although the research focused primarily on the Vilnius University Library and its resources, some interesting results were also obtained while researching the Wróblewski Library of the Lithuanian Academy of Sciences. Most sources containing information about the state and the nature of metaphysical and logical investigations conducted in Vilnius during the period discussed are the manuscripts of lecture courses delivered for the students of Vilnius University and other schools. The analysis of those manuscripts has revealed a strong and long-lasting influence of scholastic Aristotelianism in both logic and metaphysics. Namely, up to the mid-eighteenth century, the main questions discussed in logic were Aristotelian syllogism, the square of opposition and the medieval topics of semantical antinomies, modalities and supposition theory, while investigations into metaphysical issues were limited to commentaries on Aristotle’s theoretical treatises without seriously questioning their main theses. In the second part of the eighteenth century, a moderate shift towards subjectivism and psychologism was observed in both of these disciplines. This was influenced by modern epistemologists (George Berkeley, John Locke and others). Logicians and metaphysicians of Vilnius University developed an interest in the topics of human understanding and cognition. However, this shift did not take a radical form – while the majority of eighteenth-century authors sought a combination of scholastic and modern ideas, a critical and even hostile stance towards modern philosophy and science is still noticeable in many of the analysed sources. An overview of the research supported by statistical data is followed by some preliminary remarks on how and where investigation of this topic might be continued in the future.

Пустые термины в логике У. Оккама: к чему отсылают химеры

Статья посвящена проблеме суппозиции терминов в предложениях о вымышленных объектах и их условиям истинности в учении Уильяма Оккама. У. Оккам является одной из главных фигур схоластического номинализма. Его онтологическая позиция достаточно радикальна и предполагает признание $\textit{реального}$ существования только двух типов сущностей – единичных субстанций и качеств. Элиминация универсалий из онтологической системы У.~Оккама привела к трансформации существовавших ранее семантических теорий, в частности теории суппозиции. В реконструкции, ставшей классической, суппозиция сближалась с референцией, однако в 2000-е годы К. Дьютил-Новаэш предлагается реконструкция, в рамках которой суппозиция понимается как теория пропозициональных значений. Этот подход предполагает понимание суппозиции как интенсиональной, а не экстенсиональной теории. Одним из ключевых аргументов в пользу данной интерпретации служит суппозиция в предложениях о вымышленных объектах. На наш взгляд, данный аргумент вызывает затруднения. Термин, отсылающий к вымышленным объектам, не может иметь персональную, но лишь простую или материальную суппозицию. Вымышленные объекты У. Оккам называет невозможными. Химера является невозможным объектом, потому что она понимается как то, что составлено из нескольких различных животных. Свойство быть смесью различных животных ведет к тому, что данная вещь должна включать в себя несколько субстанциальных форм, однако это исключено, поскольку то, что имеет больше чем одну субстанциальную форму, не может существовать в мире. Хотя объект является невозможным, термин, который к нему отсылает, может быть как субъектом, так и предикатом предложения. В учении У. Оккама утвердительные предложения о вымышленных объектах всегда будут ложными, так как в мире отсутствуют реально существующие химеры. Это, на наш взгляд, свидетельствует о том, что предложения о невозможных объектах скорее могут быть аргументом для экстенсионального, чем для интенсионального понимания суппозиции.

The formality of Peter of Spain’s theory of supposition

The formality of Peter of Spain’s theory of supposition

John Buridan on the Possibility of Defining Definition

The study of the medieval reception of Aristotle’s Topics has largely been oriented toward debates on dialectical argumentation. And this is surely right. Nonetheless, I wish to approach John Buridan’s commentary on the Topics from another perspective, which highlights some semantic features of the set of predicates around which the work is organized. Thus, in my paper I will first reconstruct Buridan’s account of the identification of the predicates discussed in the Topics. I will argue that, for him, they are different in that they reflect one or more features of the way in which definiens and definiendum relate. By doing this, I will shed light on the role the notion of definition plays in Buridan’s commentary, so that an interpretation of it as a work on definition becomes promising. In the second part of the paper, I will offer an analysis of Buridan’s first move in his commentary toward a theory of definition. It concerns the problem of whether there is a definition of definition. In examining Buridan’s answer, I will argue for the close connection between his treatment of definitions and his theory of supposition, so that distinctions among the different modes of supposition help him to disambiguate statements in their possible meanings, and thus to clarify the difficulty related to the definability of definition.

PETER LOMBARD, STEPHEN LANGTON, AND THE SCHOOL OF PARIS THE MAKING OF THE TWELFTH-CENTURY SCHOLASTIC BIBLICAL TRADITION

This study documents the discovery of Peter Lombard's long-thought-to-be-lost lectures on the Old Testament, which were hidden in plain view in the Old Testament lectures of Stephen Langton, who lectured on the Lombard's lectures. The presence in the Lombard's lectures on Genesis of the logical theory of supposition, the single greatest advance in logical theory during the High Middle Ages, means that those lectures not only postdate the Sentences but also represent the beginning of a radical advance in speculative theology that would continue to develop through the end of the High Middle Ages. This means in turn that lectures on the Bible from the 1150s to 1200, and in particular those of the School of Paris, headed by Peter Lombard, play a central role in one of the greatest speculative developments — logical, philosophical, and theological — of the Middle Ages.

Rameau’s Theory of Supposition and French Baroque Harmonic Practice

Rameau’s Theory of Supposition and French Baroque Harmonic Practice

The Role of ‘Denotatur’ in Ockham’s Theory of Supposition

Abstract In the scholarship on medieval logic and semantics of the last decades, Ockham’s theory of supposition is probably the most extensively studied version of such theories; yet, it seems that we still do not fully understand all its intricacies. In this paper, I focus on a phrase that occurs countless times throughout Ockham’s writings, but in particular in the sections dedicated to supposition in the Summa logicae: the phrase ‘denotatur’. I claim that an adequate understanding of the role of the concept of denotatur within Ockham’s supposition theory shall yield a deeper understanding of the theory as a whole. Here, I first examine a few uses of the term ‘denotatur’ and its variants by other authors. I then turn to Ockham: first I briefly mention some uses of the term in contexts other than his theory of supposition. Following that, I focus on his supposition theory, in particular on how ‘denotatur’ allows him to deal with two crucial puzzles, namely the supposition of empty terms and the supposition of terms in false affirmative propositions. The treatment of these two puzzles suggests that Ockham’s theory of supposition must be understood as a theory chiefly intended for the generation of the meanings of propositions.

Semantic and Ontological Aspects of Wyclif’s Theory of Supposition

Abstract The relationship between thought and reality was a focal point of Wyclif’s reflection. On the one hand, Wyclif believed that thought was linguistically constrained by its own nature; on the other hand, he considered thought to be related to reality in its elements and constitution. Hence he deemed language, thought, and external reality to be of the same logical coherence. Within this context, the theory of supposition was intended to explain the different roles that terms can have in relation to language and the extra-mental world when they appear as extremes in propositions. Characteristically, his theory of supposition provides an account not only of the truth-values of a sentence, but also of its meaning; it is not therefore simply a theory of reference, but a sort of complex analysis of language viewed as a semiotic system whose unique interpretative model was reality itself. It gives clear evidence of Wyclif’s realist stance and of his conviction that any kind of linguistic and semantic features must be grounded on ontological structures.

The Hermeneutical Rehabilitation of Supposition Theory in Seventeenth-Century Protestant Logic

Abstract The paper focuses on some aspects of the early modern aftermath of supposition theory within the framework of the protestant logical tradition. Due to the growing influence of Humanism, supposition theory from the third decade of the sixteenth century was the object of general neglect and contempt. While in the late sixteenth-century a number of standard textbooks of post-Tridentine scholastic logic reintegrated this doctrine, although in a bowdlerized version, it remained for a century out of the scope of Protestant logic. The situation changed when the Strasburg Lutheran theologian J.C. Dannhauer, who in 1630 developed and propagated the program of a new discipline which he called ‘general hermeneutics’ (hermeneutica generalis), accentuating the importance of supposition theory as an indispensable device for the purpose of textual interpretation. Due to Dannhauer’s influence on later developments of hermeneutics, which in the seventeenth and early eighteenth centuries was regarded as a logical discipline, supposition theory is still present in several logical treatises of the eighteenth century. The explication of the underlying views on the notion of supposition and its logico-semantic function may give at least some clues as to how to answer the question of what supposition theory was all about.

Scotus on Supposition

Abstract In his commentaries on Porphyry and Aristotle’s Organon (Categories, Peri hermeneias, Sophistici elenchi, and Topics) and in his other works, John Duns Scotus shows his knowledge of both the modistic theory of language and the theory of supposition. My contribution sheds some light on the relationship between Scotus’ philosophy of language and the theory of supposition, collecting and commenting on all the passages in which he makes use of it or discusses some theoretical points. I take into special account the almost unknown commentary on the Topics, which is preserved in a Vatican manuscript.

Avicenna’s Theory of Supposition

Abstract Although he does not have an explicit theory of supposition as is found in the works of Latin medieval philosophers, Avicenna (Ibn Sīnā) has two doctrines giving something equivalent: the threefold distinction of quiddity (triplex status naturae), corresponding to a division of simple, personal and material supposition, and his analyses of truth conditions for categorical propositions, where sentential context determines in part the reference of their terms. While he does address which individuals are being referred to by the universal terms used there, Avicenna concentrates more on the varied temporal durations of the predications being made. In Western terms, he has incorporated ampliation and restriction into the theory of supposition itself.

Semantics and OntologyAn Assessment of Medieval Terminism

Abstract This paper aims to assess medieval terminism, particularly supposition theory, in the development of Aristotelian thought in the Latin West. The focus is on what the present author considers the gist of Aristotle’s strategy of argument, to wit conceptual focalization and categorization. This argumentative strategy is more interesting as it can be compared to the modern tool known as ‘scope distinction’.

Supposition and the Fallacy of Figure of Speech in the Abstractiones

Abstract I undertake to examine the practice of Richard, Master of Abstractions, with respect to supposition in his dealing with the fallacy of figure of speech. His practice turns out to support the ‘single theory’ account of the theory of personal supposition, as does his treatment of a functional equivalent of simple supposition, but his practice of proposing additional solutions points to changing attitudes with respect to species as separate entities. Questions having to do with material supposition and the like are completely absent, even in discussions where we might expect to find them.

A Quantified Temporal Logic for Ampliation and Restriction

Abstract Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.

Early Supposition Theory II

Abstract In 1981 I published an article called Early Supposition Theory. Then as now, the magisterial work on the subject was L.M. de Rijk’s Logica Modernorum and then as now any discussion of the topic would have to rely to a great extent on the texts published there. This means that many of the problems that existed then still remain, but a couple of important new studies and several new texts have been published in the meantime, so it may be time to try to take stock of the situation. I will first look at the origin of the term suppositio and then at the chronology of our source texts.

Unconfusing Merely Confused Supposition in Albert of Saxony

Abstract In this essay I argue that Albert would reject the need for a separate fourth mode of common personal supposition, and that his view of merely confused supposition has not been fully explicated by modern scholars. I first examine the various examples of conjunct descent given by modern scholars from his Perutilis logica, and show that Albert clearly adopts it in resolving the sophistic examples involved. Second, I explicate the view of merely confused supposition that Albert defends in his Sophismata, and then attempt to answer the question: which view of merely confused supposition was his final view, the view articulated in the Perutilis logica or the view in the Sophismata? I conclude that based upon his Sophismata view of merely confused supposition, Albert came to realize the logical strength his revised theory of personal supposition afforded, and consequently, that he is one of the earliest 14th-century logicians to adopt conjunct terminal descent to resolve various sophisms, a move which gave his theory of personal supposition a logical symmetry having two sorts of propositional descents to singulars, and two sorts of terminal descents to singulars.

Ockham on Supposition Theory, Mental Language, and Angelic Communication

In my previous work on Ockham's theory of supposition, I have argued that it is best understood as a theory of sentential meaning, i.e., as an apparatus for the interpretation of sentences. In this paper, I address the challenge posed to this interpretation of Ockham's theory by the (presumed) existence of different kinds of supposition in mental language through the lenses of Ockham's theory of angelic communication. I identify two potentially problematic implications of Ockham's account of mental language as allowing for different kinds of supposition: the existence of non-significative supposition in mental language; and the possibility of ambiguous mental sentences. I then turn to angelic communication and examine these two issues from that point of view, concluding that there cannot be non-significative supposition in mental language, but also that there may still be room for sentential ambiguity in mental language.

Formalizing Medieval Logic: Suppositio, Consequentiae and Obligationes (review)

Reviewed by: Formalizing Medieval Logic: Suppositio, Consequentiae and Obligationes Mary Sirridge Catarina Dutilh-Novaes . Formalizing Medieval Logic: Suppositio, Consequentiae and Obligationes. Logic, Epistemology and the Unity of Science, 7. Dordrecht: Springer, 2007. Pp. xii + 316. Cloth, $169.00. The overarching aim of this excellent book is to demonstrate the common ground between medieval logic and logical theories of the twentieth century by analyzing some important medieval approaches to three important topics in medieval logic (suppositio, consequentiae, and obligationes) and then showing that in each case, once we determine what is really going on in the medieval theory, it can be formalized in such a way as to show how it resembles one or more developments in twentieth-century logical theory. Analysis in terms of modern logical theory has a lot to offer the study of medieval logical theories, the author claims, and twentieth-century theory can learn some interesting lessons from examining its medieval counterparts. Much of the material in these specific discussions has been presented in earlier versions in the author's published articles. "The Philosophy of Formalization" (part 4), however, is new. English translations are used in the text, though the Latin is supplied in the footnotes. Mature supposition theory (Ockham, Burley, and Buridan) is presented, not as a theory of reference or quantification, but as a unified theory of "algorithmic hermeneutics" (77); it allows us to calculate systematically the possible meanings of a proposition as a whole from the meanings of its component parts, with an eye to "distinguishing" the different contents that can be asserted (denotatur) by speaking, writing, or thinking the expression. Such multiple meanings may be due to allowing terms to be self-referential (material supposition) or to stand for species or the like (simple supposition), but also to the sorts of ambiguities of quantifier scope, modal operators, and the like that regularly turn up in discussions of fallacies and sophisms. Some results agree substantially with earlier analyses of Ockham's logic. Ockham's theory ultimately amounts to "an extensional theory of intensions" (31), and the distinction among personal, simple, and material supposition turns out to be more or less functionally independent of the modes of personal supposition. Still, it is a very interesting metatheoretical point that the two parts of the theory are co-ordinate strategies for achieving a single objective: the calculation of propositional meanings. Moreover, the understanding of the distinctive usage of denotatur is not only new and significant; it sounds right. Part 2, "Buridan's notion of consequentia," energetically pursues a search for twentieth-century near-relatives to Buridan's theory of entailment, an "intriguing combination of semantics and pragmatics" (113). Buridan's "token-based semantics" resembles the "two-dimensional semantics of Kaplan and Stalnaker," on which evaluation of the truth of a proposition involves both its content (abstract meaning) and its particular context of [End Page 469] utterance. Buridan's theory of consequence resembles the "hybrid" view of Shapiro (121); there is a broader notion of consequence (material consequence) similar to Etchemendy's "representational" approach to logical consequence that extends to entailments due to specific intensional content and to the inferability of one proposition from another due to pragmatic factors (inferences involving self-referential propositions or indexicals); a subset of these are valid on the basis of their logical form (formal consequence). One interesting side benefit of comparing Buridan's theory to its twentieth-century relatives is that it becomes clear that his token-based ontology, useful as it is for dramatizing self-reference, needs to be abandoned in favor of linguistic types and schemata if sense is be made of his theory of logical consequence, even if we allow him to avail himself of the notion of "equiform propositions." "Obligationes as Formal Games" (part 3) presents the theories of Burley, Swynshed, and Strode, in which the Respondent must accept or deny propositions put forward by the Opponent based on their relation to an initial supposition (positum), in modern game-theoretical terms as variants of a game of logical consistency, not as exercises for school boys, explorations of counterfactuals, or just a means of dealing with sophismata and Liar-like paradoxes. The game-theoretical analysis of Burley's theory...