Medieval Logic Research Articles

Historical analysis of formation of logical ideas in the Middle Ages

The article analyzes influence of ancient philosophy on formation of the medieval scholastic logic in writings of the most prominent European philosophers.

Articulating Medieval Logic, by Terence Parsons.

<i>Articulating Medieval Logic</i>, by Terence Parsons.

Articulating Medieval Logic

Medieval logic can often ‘seem to consist of a variety of unsystematic and disparate remarks, and it is not at all obvious whether or how they fit together’ (p. 1). In this ambitious book, Terence Parsons seeks to demonstrate how ‘medieval logic can […] be seen as a group of theories and practices clustered around a core theory which is a paradigm of logic; this theory consists of a number of widely known principles, all of which can be derived from a very simple core of rules and axioms’ (p. 1). Starting from the beginning—that is, Aristotle—Parsons takes the reader from the semantics of the simplest categorical (subject-predicate) statements through a semi-formal notation called ‘Linguish’ (a mix of Latin and English, plus some symbols), to the modes of personal supposition, and eventually to complex statements involving tenses, relatives, anaphora, and other phenomena; along the way, comparisons with contemporary logic and lingusitic theory are regularly made. Because the Organon provided the foundation for developments in the Middle Ages, Parsons begins with Aristotelian logic in ch. 1, presenting not so much Aristotle's views per se but rather what the theory of categorical sentences and syllogisms looked like to medieval logicians (p. 6). This approach focuses on the structure of categorical sentences and arguments, and mostly glosses over questions about what makes these sentences true (though see pp. 9 and 10). In ch. 2, the basic building blocks are extended to categorical sentences which have quantified predicates, predicates which are singular terms, and negative terms, all of which require special analyses, and were explicitly dealt with by medieval authors. The next two chapters are primarily modern in orientation, introducing a new notation, called ‘Linguish’ for representing explicitly the sentence types (‘logical forms’) and proof rules discussed in chs 1 …

Preface: Medieval Logic

Preface: Medieval Logic

Geach's Three Most Inspiring Errors Concerning Medieval Logic

AbstractThis paper analyses the import of three claims extracted from Geach's works concerning (i) theories of predication and the reference of common terms, (ii) the notions of being or existence, and (iii) the force/content distinction and theories of valid inference, respectively. The paper highlights the theoretical and historical errors involved in these claims as well as their enormous influence and inspiration in the field of the philosophical study of medieval logic and metaphysics.

Later medieval metaphysics: ontology, language, and logic

This book begins with standard ontological topics--such as the nature of existence--and of metaphysics generally, such as the status of universals, form, and accidents. What is the proper subject matter of metaphysical speculation? Are essence and existence really distinct in bodies? Does the body lose its unifying form at death? Can an accident of a substance exist in separation from that substance? Are universals real, and, if so, are they anything more than general concepts? Among the figures it examines are Thomas Aquinas, John Duns Scotus, William of Ockham, Walter Chatton, John Buridan, Dietrich of Freiburg, Robert Holcot, Walter Burley, and the 11th-century Islamic philosopher Ibn-Sina (Avicenna). There is also an emphasis on metaphysics broadly conceived. Thus, additional discussions of connected topics in medieval logic, epistemology, and language provide a fuller account of the range of ideas included in the later medieval worldview.

Distributive Terms, Truth, and the Port Royal Logic

The paper shows that in the Art of Thinking (The Port Royal Logic) Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and others, the truth-conditions do not require the introduction of a new concept of ‘indefinite’ term restriction because the notion of conservative quantifier is formulated in terms of the standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in an analysis of truth because it is explained in terms of entailment, and entailment in terms of truth. By abstracting from semantic identities that underlie distribution, the new concept of distributive term is definitionally prior to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic’s truth-conditions for the categorical propositions are stated solely in terms of (1) universal (distributive) term, (2) conservative quantifier, and (3) affirmative and negative proposition. It is explained why the Cartesian notion of extension as a set of ideas is in this context equivalent to medieval and modern notions of extension.

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.

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.

The Expressive Power of Medieval Logic

Abstract This paper is about the development of logic in the Aristotelian tradition, from Aristotle to the mid-fourteenth century. I will compare four systems of logic with regard to their expressive power. 1. Aristotle’s own logic, based mostly on chapters 1-2 and 4-7 of his Prior Analytics 2. An expanded version of Aristotle’s logic that one finds, e.g., in Sherwood’s Introduction to Logic and Peter of Spain’s Tractatus 3-5. Versions of the logic of later supposition theorists such as William Ockham, John Buridan, and Paul of Venice. Version 4 is the logic without relatives (anaphoric pronouns); version 5 adds relatives. I am ignoring modals, conditionals that are not ut nunc, infinitizing negation, exclusives and exceptives, all exponibles, all insolubles, and terms with simple or material supposition, ampliation and restriction, and many other things.

Form and Matter in Later Latin Medieval Logic: The Cases of Suppositio and Consequentia

The paper investigates the influence of Aristotelian metaphysics, especially of the concepts of form and matter, in the development of Latin medieval logical theories, in particular theories of consequence and theories of supposition. More specifically, it presents the main lines in the development of the concepts of formal/material consequence and formal/material supposition in the 13 th and 14 th centuries. It is suggested that the growing influence of Aristotelian metaphysics in the 13 th century is an important element in the development of these logical theories; nevertheless, the early stages of these theories pre-date the rediscovery of Aristotle's metaphysics in the 13 th century. Indeed, other relevant channels of transmission of the metaphysical concepts of form and matter to logical contexts are discussed: the Prior Analytics commentaries of the ancient commentators, Arabic texts, and the neo-Platonic metaphysics of the grammarian tradition stemming from Priscian.

Medieval Logic Diagrams

This article describes the finding, documentation and significance of the set of medieval logic diagrams and associated text, all in highly abbreviated Latin minuscule, sketched on an inside wall of the Romanesque tower of the parish church in Bro, near Visby. The diagrams depict the Square of Opposition, the basic concept to be mastered in introductory logic as taught at medieval schools and universities. A date c.1200-1225 is suggested by their being executed in the earliest plaster when wet (tower built c.1200), while up to 1350 is suggested by palaeography. Dating by textual content is still in progress. Either way the Bro diagrams are among the earliest logic texts written in Scandinavia, and this is the first time for such texts to be found outside a manuscript. They are also the earliest known physical evidence of a teaching session or a discourse in logic. Furthermore they contribute to a growing body of evidence of the high standard of learning that existed in medieval Gotland.

Zum Begriff der einfachen Supposition im 13. Jhdt.

In mediaeval logic a common term is often said to supposit simply, if it supposits for a concept and not for the elements of its extension. Due consideration of the logical texts of the 13th century, however, gives rise to the assumption, that a) the common aspect of the several uses of a term which are referred to as simple suppositions is not so easy to be found and that b) for some authors simple supposition was an extensively used tool for the logical analysis of sentences. In my paper I will enlarge on this second aspect with particular reference to the syncategoremata of William of Sherwood. My study leads to the conclusion that simple supposition in the 13th century is sometimes used to analyse scope ambiguities between the existential quantor and another operator. This is due to the fact that mediaeval logicians did not conceive of anything equalling an existential quantor.

Introduction

This article describes the finding, documentation and significance of the set of medieval logic diagrams and associated text, all in highly abbreviated Latin minuscule, sketched on an inside wall of the Romanesque tower of the parish church in Bro, near Visby. The diagrams depict the Square of Opposition, the basic concept to be mastered in introductory logic as taught at medieval schools and universities. A date c.1200-1225 is suggested by their being executed in the earliest plaster when wet (tower built c.1200), while up to 1350 is suggested by palaeography. Dating by textual content is still in progress. Either way the Bro diagrams are among the earliest logic texts written in Scandinavia, and this is the first time for such texts to be found outside a manuscript. They are also the earliest known physical evidence of a teaching session or a discourse in logic. Furthermore they contribute to a growing body of evidence of the high standard of learning that existed in medieval Gotland.

The Greeks and Their Past: Poetry, Oratory, and History in the Fifth Century BCE (review)

Reviewed by: The Greeks and Their Past: Poetry, Oratory, and History in the Fifth Century BCE Victor Bers Jonas Grethlein . The Greeks and Their Past: Poetry, Oratory, and History in the Fifth Century BCE. Cambridge: Cambridge University Press, 2010. xii + 350 pp. 3 black-and-white figs. Cloth, $95. Coming across the line James Joyce gives Stephen Dedalus, "history is a nightmare from which I am trying to awake," Greeks of the classical period might be puzzled by a wish to escape the past, since for them it was far more a treasure than an affliction, but they would accept a description of the past as immanent and eternal. Evidently aware of the wide gulf between, on the one hand, most British and American classicists, and on the other, scholars versed in hermeneutics and phenomenology, Jonas Grethlein devotes the introductory chapter to a careful statement of his approach. All his principal specimen texts are drawn from fifth-century writers, or to be more precise, writers who were at work for at least part of the fifth century, even if a specific work does not quite make it under the wire, e.g., Lysias' (or at least the Lysianic) Epitaphios. There are out-of-period excursions to supplement a slender corpus, for instance Tyrtaeus and Mimnermus to support the analysis of the "New Simonides" (13). Grethlein's conceptual categories are explicitly modern: as social scientists put it, they are of the "etic," rather than the "emic" variety (5, n. 29). A number of phrases appear with great frequency, but what might look like a leitmotif serving as a rhetorical incantation is there by design, meant to make the discussion of any one of the "commemorative modes" intelligible on its own (12). Grethlein investigates the interplay in the three genres of Greek literature of his title, "commemorative modes of memory" as he calls them, between two persistent, and evidently contradictory, attributes: consistency and contingency. The latter might be understood as equivalent to τύχη "chance," but Grethlein (following Rüdiger Bubner) insists that it is something quite different: the realm defined in medieval logic as quod nec est impossibile nec necessarium, a "frame for actions as well as for chance" (6). I am not competent to evaluate Grethlein's handling of the concepts' doxographic history, but found this no impediment to understanding the text-specific analyses. Grethlein turns first to epinician poetry with a detailed study of Pindar, Olympian 2. Between the praise of Theron that opens and closes the poem fall short mentions of Semele and Io, women compensated for their sufferings, and a more detailed and darker reference to what befell Laius, Oedipus, and Oedipus' sons; there is then a segue to celebration of the athletic victories of Polyneices' sons (Grethlein postpones until 40, n. 60, a reference to Pindar's omission of the brothers' names, i.e., Eteocles and Xenocrates: this could confuse the non-specialist reader, whom the book generally accommodates). The poem as a whole shows how "the traditional and exemplary modes . . . serve as counterweights against the contingency of chance that threatens human identities and actions" (33). The assertion of continuity flows naturally from the connection of an aristocratic family to its (supposed) ancient roots (44). The eschatological section of the poem (57-83a) poses something of a puzzle, but Grethlein is adept at avoiding a potential [End Page 674] trap set by his own favored categories: the eschatology, he suggests, is a foil to human life (no surprise there), but is also linked to our familiar, contingency-filled world (31). These adroit interpretive maneuvers will prompt many readers to think of other challenges to Grethlein's broad interpretation. While reading this chapter I wondered how he could accommodate the on-and-off fortunes noted at Nemean 11.37-44: alternate generations of victory and disappointment are likened to season-to-season variations in crops and trees. The chapter's final page provided Grethlein's answer. Citing the very passage, Grethlein acknowledges that "the tension between continuity and regularity . . . and contingency of chance . . . remains ultimately unresolved"(46). The third chapter moves on to elegy, with particular attention to the "New Simonides," fr. 11 West2, and several other fragments...

Arthur Prior and medieval logic

Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his ground-breaking innovations in the 1950s and 1960s. Because of the important rôle played by Prior’s research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, temporal logic, or hybrid logic should be familiar with the medieval logicians and their work. In this article we give an overview of Prior’s work in ancient and medieval logic.

Logic and Mathematics in the Seventeenth Century

According to the received view (Bocheński, Kneale), from the end of the fourteenth to the second half of nineteenth century, logic enters a period of decadence. If one looks at this period, the richness of the topics and the complexity of the discussions that characterized medieval logic seem to belong to a completely different world: a simplified theory of the syllogism is the only surviving relic of a glorious past. Even though this negative appraisal is grounded on good reasons, it overlooks, however, a remarkable innovation that imposes itself at the beginning of the sixteenth century: the attempt to connect the two previously separated disciplines of logic and mathematics. This happens along two opposite directions: the one aiming to base mathematical proofs on traditional (Aristotelian) logic; the other attempting to reduce logic to a mathematical (algebraical) calculus. This second trend was reinforced by the claim, mainly propagated by Hobbes, that the activity of thinking was the same as that of performing an arithmetical calculus. Thus, in the period of what Bocheński characterizes as ‘classical logic’, one may find the seeds of a process which was completed by Boole and Frege and opened the door to the contemporary, mathematical form of logic.

Postscript: Medieval Logic as Sprachphilosophie

To the question “What is medieval logic after all?”, this postscript suggests the following answer: medieval logic is Sprachphilosophie, that is, philosophy of language as it developed in the early twentieth century in the Austro-German tradition. This claim is based on the fact that: (1) medieval logic textbooks often deal with topics which would not qualify as belonging to logic (e.g., questions pertaining to grammar, semantics, philosophy of mind and metaphysics); and (2) this location at the crossroads of those philosophical domains is precisely a characteristic feature of Sprachphilosophie. In addition, one of the first attempts to grasp the specificity of medieval linguistic theogy (Grabmann’s Sprachlogik, 1920) explicitly derives from the Sprachphilosophie of the Austro-German tradition.

What is Medieval Logic After All? Towards a Scientific Use of Natural Language

The puzzle sketched in this short introduction pinpoints the difficulty experienced by historians of medieval logic to define the very discipline that they are studying. Thus, in spite of all the work done during the last 60 years, the question: “What is medieval logic after all?” remains actual. A general perspective of investigation is suggested, namely the farreaching consequences of the attempt to cope with what one could call the formal and material constraints of medieval logic (i.e., aiming at the elaboration of a scientific language as distinct from dealing with natural language).

Alfonso Maierù / Luisa Valente (edd.), Medieval theories on assertive and non-assertive language. Acts of the 14th European Symposium on Medieval Logic and Semantics, Rome, June 11–15, 2002

Alfonso Maierù / Luisa Valente (edd.), Medieval theories on assertive and non-assertive language. Acts of the 14th European Symposium on Medieval Logic and Semantics, Rome, June 11–15, 2002