This paper seeks to articulate the relationship between medieval logic and theology. Reviewing modern scholarship, we find that the purpose of medieval logic, when it is even inquired about, has proven difficult to articulate without reference to theology. This prompts reflection on the metaphors of logic as a “tool” and a “game”: a tool is not merely instrumental, insofar as it can have its own intrinsic goods and can shape and be shaped by that which (...) it serves; likewise a game, with its own intrinsic goods, may yet contribute to extrinsic goods as well. After reviewing some distinctive ways in which theology shaped developments of medieval logic, this paper summarizes key examples from the work of Thomas Aquinas where medieval logic shaped the articulation of, and is therefore crucial to a proper understanding of, theological arguments and claims. The conclusion suggests implications for future philosophical and theological work. (shrink)

The present volume brings together work that will be of interest both to specialists in medieval philosophy and to those working in contemporary or more recent historical periods of metaphysics. Th...

In 1989, Cambridge University Press announced the publication of a new, three-volume book series: The Cambridge Translations of Medieval Philosophical Texts. The first volume – edited by Norman Kretzmann and Eleonore Stump, and dedicated to logic and the philosophy of language – contained 15 medieval texts, of which 15 were composed by Christian authors. The second volume in the series, this time focusing on ethics and political philosophy, appeared in 2000. Seventeen of the 17 texts included in (...) this collection – edited by Arthur S McGrade, John Kilcullen and Matthew Kempshall – were authored by Christian writers. Late-medieval Jewish or Islamic texts on ethics or politics? Not in our school. (shrink)

With regard to the new directions in the Humanities, here I am going to consider and examine the approach of al-Farabi as a medieval thinker in introducing a new outlook to “language” in difference with the other views. Thereby, I will explore his challenges in the frame of “philosophical humanism” as a term given by Arkoun (1970) and Kraemer (1984) to the humanism of the Islamic philosophers and their circles, mainly in the tenth and eleventh centuries. Al-Farabi’s conception of (...) philosophical humanism, in which philosophy is thick and religion is thin, makes its agony with the other versions of humanism and also orthodox Islam. It means that his introduction of a humanistic understanding of language should be placed in such a multi-level contested environment. According to al-Farabi, language as a universal category has relation with reason that logic should function as its proper instrument. As a result, there is no specific privileged predetermined language, but the position of any language is shaped by its relation with human reason and formal logic that is something human-made. And such a conception means language in human terms. Key Terms: Al-Farabi; Language; Philosophical Humanism; Arabic: Greek . (shrink)

The 13th-15th centuries were witness to lively and broad-ranging debates about the nature of persons. In this paper, I look at how the uses of ‘person’ in logical/grammatical, legal/political, and theological contexts overlap in the works of 13th-15th century contemplatives in the Latin West, such as Hadewijch, Meister Eckhart, and Catherine of Siena. After explicating the key concepts of individuality, dignity, and rationality, I show how these ideas combine with the contemplative use of first- and second-person perspectives, personification, and introspection (...) to yield a concept of 'person' that both prefigures Locke's classic 17th century definition and deeply influences the development of personalism. (shrink)

The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. -/- Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. I (...) argue that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. -/- I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.”. (shrink)

This paper considers the nature of the changes that took place in logic teaching at the University of Oxford from the beginning of the sixteenth century, when students attended university lectures on Aristotle’s texts as well as studying short works dealing with specifically medieval developments, to the beginning of the eighteenth century when teaching was centred in the colleges, the medieval developments had largely disappeared, and manuals summarizing Aristotelian logic were used. The paper also considers the (...) reasons for these changes, including changes in English society, and the effect of humanism and the more scholarly Aristotelianism that it produced. (shrink)

A lean hylomorphism stands as a metaphysical holy grail. An embarrassing feature of traditional hylomorphic ontologies is prime matter. Prime matter is both so basic that it cannot be examined (in principle) and its engagement with the other hylomorphic elements is far from clear. One particular problem posed by prime matter is how it is to be understood both as a principle of individuation for material substances and as pure potency. I present Thomas Aquinas’s way of squeezing some intelligibility out (...) of prime matter by modeling it on the idea of logical genus. Such a modeling provides insight into understanding prime matter as substratum, as maximally indeterminate, and as ontologically vague. One of the unusual but exciting things that fall out from this analysis of prime matter is the Entirety Thesis: “For any substance x, if x has prime matter then the prime matter of x is the same* as x,” where ‘same*’ is understood as “indeterminately identical.”. (shrink)

Because we tend to study fight books in isolation, we often forget how difficult it is to understand the precise place they occupy in the sociocultural and historical fabric of their time, and spill the many clues they inevitably contain on their owner, their local society, their precise purpose. In order to unlock that information, we need to study them in their broader sociocultural and historical context. This requires a background and research skills that are not always easily accessible to (...) everyone. To illustrate the point, in this paper I show in some detail what is required to make sense of the claim that Aristotelian philosophy and science influenced the medieval fight books in relevant ways, and that understanding this influence helps us to better understand the fight books per se. I give an outline of the general historical framework, and apply it to a testcase: Talhoffer’s Thott 290 2° Ms., with some interesting results. My hope is that this framework may be of some use to other researchers in HEMA Studies who want to dig deeper in sources of interest to them. (shrink)

This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers an unusual (...) solution to the paradox, but in a traditional spirit that contrasts a number of trends prevailing in the XiVth century. It also counts as a remarkable piece of evidence for the reconstruction of the reception of English logic in italy, as it is inspired by the views of John Wyclif. Three approaches addressing the Liar paradox (Albert of Saxony, William Heytesbury and a version of strong restrictionism) are first criticised by Peter of Mantua, before he presents his own alternative solution. The latter seems to have a prima facie intuitive justification, but is in fact acceptable only on a very restricted understanding, since its generalisation is subject to the so-called revenge problem. (shrink)

One of the singularities of Latin exegesis of Aristotle’s Sophistici elenchi, is that it arbitrarily brought together two families of fallacies, the «figure of speech» and the «accident», despite the fact that they are on either side of the divide between sophisms related to expression and sophisms independent of expression, a divide that lays at the heart of Aristotle’s taxonomy of sophistic arguments. What is behind this surprising identification? The talk is meant to show that it actually originates from a (...) curious mistake in Boethius’ translation of Aristotle’s Sophistici elenchi, 22, 178b 36-37 which radically transformed the nature of the argument at stake. While it was originally an example of the fallacies related to the «figure of speech», Boethius’ translation wrongly brings about two arguments instead of one, both related to the «accident». This explains why authors from the Latin tradition came to think that fallacies of «figure of speech» were linked to fallacies of «accident» closely enough to ask whether they actually fell outside expression, even though it does not at first glance appear that such a possibility was allowed or even suggested by Aristotle’s text. This odd question illustrates some of the remarkable features of the medieval archive and how some of its most peculiar problems came to be. It specifically allows us to reconstruct the mechanisms through which a minor disturbance in the letter of the text leads to a whole new way of organising its exegetical material. (shrink)

Abu Nasr Muhammad Al-Farabi (870–950 AD), the second outstanding representative of the Muslim peripatetic after al Kindi (801–873 AD), was born in Turkestan about 870 AD. Al-Farabi’s studies commenced in Farab, then he travelled to Baghdad, where he studied logic with a Christian scholar named Yuhanna b. Hailan. Al-Farabi wrote numerous works dealing with almost every branch of science in the medieval world. In addition to a large number of books on logic and other sciences, he came (...) to be known as the “Second Teacher” (al-Mou’allim al-Thani), Aristotle being the first. One of Al-Farabi’s most important contributions was clarifying the func- tions of logic as follows: 1. He defined logic and compared it with grammar, and discussed the clas- sification and fundamental principles of science in a unique and useful manner. 2. He made the study of logic easier by dividing it into two categories: Takhayyul (idea) and Thubut (proof). 3. He believed that the objective of logic is to correct faults we may find in ourselves and in others, and faults that others find in us. 4. He said that if we do not comprehend logic, we must either have faith in all people, or mistrust all people, or differentiate between them. Such actions would be undertaken without a basis of evidence or experimen- tation. In this paper, I will analyse the functions of logic in Al-Farabi’s works, Enumeration of the Sciences, Book on the Syllogism, Book on Dialectic, Book on Demonstration and Ring Stones of Wisdom, in order to present his contributions in the field of logic. (shrink)

The present volume is a sequel to Deontic Logic: Introductory and Systematic Readings : its purpose is to offer a view of some of the main directions of research in contemporary deontic logic. Most of the articles included in Introductory and Systematic Readings represent what may be called the standard modal approach to deontic logic, in which de on tic logic is treated as a branch of modal logic, and the normative concepts of obligation, permission (...) and prohibition are regarded as analogous to the "alethic" modalities necessity, possibility and impossibility. As Simo Knuuttila shows in his contribution to the present volume, this approach goes back to late medieval philosophy. Several 14th century philosophers observed the analogies between deontic and alethic modalities and discussed the deontic interpretations of various laws of modal logic. In contemporary deontic logic the modal approach was revived by G. H. von Wright's classic paper 'Deontic Logic'. Certain analogies between deontic and alethic modalities are obvious and uncontroversial, but the standard approach has often been criticized on the ground that it exaggerates the analogies and tends to ignore those features of normative concepts which distinguish them from other modalities. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the (...) many fallacious ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

This paper argues that three characteristic modern positions concerning intentionality – namely, (1) that intentionality is ‘the mark of the mental’; (2) that intentionality concerns a specific type of objects having intentional inexistence; and (3) that intentionality somehow defies logic – are just three ‘modern myths’ that medieval philosophers, from whom the modern notion supposedly originated, would definitely reject.

Multiple generality has long been known to cause confusion. For example, “Everyone has a donkey that is running” has two readings: either (i) there is a donkey, owned by everyone, and it is running; or (ii) everyone owns some donkey or other, and all such donkeys run. Medieval logicians were acutely aware of such ambiguities, and the logical problems they pose, and sought to sort them out. One of the most ambitious undertakings in this regard is a pair of (...) massive diagrams (magnae figurae) which map out the logical interrelations of two sets of doubly-general forms. These appear in a fourteenth-century MS of John Buridan’s Summulae de Propositionibus. In this paper, I present these diagrams, and determine the truth conditions of their different forms. To that end, I have developed a bespoke system of diagrams to display their truth conditions. As we will see, such forms present significant difficulties for an all-encompassing account of the role form plays in logic. Accordingly, they can tell us important things about the role logical form plays in Buridan’s account of logical foundations. (shrink)

Today, philosophers interested in self-knowledge usually look to the scholastic tradition, where the topic is addressed in a systematic and familiar way. Contemporary conceptions of what medieval figures thought about self-knowledge thus skew toward the epistemological. In so doing, however, they often fail to capture the crucial ethical and theological importance that self-knowledge possesses throughout the Middle Ages. -/- Human beings are not transparent to themselves: in particular, knowing oneself in the way needed for moral progress requires hard and (...) rigorous work. Yet, medieval contemplatives insist, without this work we will never attain our final end. In this paper, I trace the connection drawn in this tradition between self-knowledge, humility, and self-fulfillment, arguing in section 1 that the humility that results from introspection needs to be understood in the context of contemplative expectations for eventual perfection. Self-knowledge is key for developing the relationship with God that leads to mystical union, but (as I show in section 2) in the affective tradition of the 13th-14th centuries, which emphasizes the role of emotion and the body, such union with God tends to restore rather than annihilate us. In fact, I argue in section 3, the outcome of such union even in this life is often knowledge that benefits not only the individual who experiences it but also their broader community. (shrink)

It has been argued recently that classical theism and Lewisian modal realism are incompatible theses. The most substantial argument to this effect takes the form of a trilemma. It argues that no sense can be made of God’s being a necessary being in the modal realistic picture, on pain of, among other things, modal collapse. The question of this essay is: Is that so? My goal here is to detail the reasons that have been offered in support of this contention (...) and then defend the coherence of theistic modal realism from the trilemma. I call my reply to the argument an “Anselmian-Thomistic” defense, since it appeals to resources from classical medieval philosophy, especially from Anselm and Aquinas. (shrink)

Marsilius of Inghen’s account of imaginable impossibilities became paradigmatic in logic, semantics, and metaphysics throughout the later Middle Ages and well into the early modern period. The present study focuses on imaginable impossibilities in 14th-century logic, underlining the relevance of Marsilius of Inghen’s innovative approach through a comparison with the semantic accounts proposed by other mid-14th-century Parisian nominalists, namely John Buridan and Albert of Saxony. In particular, this paper tracks the specific issue of the admissibility of absolute impossibilities (...) – such as the chimera – within Marsilius of Inghen’s semantic analysis, proving that there is a sense in which the chimera is indeed treatable. The present study does so by analysing the issues involved in impossibilities on the levels of signification, supposition, and extended reference. In doing so it provides a clearer picture of the problems involved, where they emerge and why, as well as of the significance and range of Marsilius of Inghen’s approach. (shrink)

What makes a valid argument valid? Generally speaking, in a valid argument, if the premisses are true, then the conclusion must necessarily also be true. But on its own, this doesn’t tell us all that much. What is truth? And what is necessity? In what follows, I consider answers to these questions proposed by the fourteenth century logician John Buridan († ca. 1358). My central claim is that Buridan’s logic is downstream from his metaphysics. Accordingly, I treat his metaphysical (...) discussions as the key to his logic. As has been often noted, Buridan’s metaphysics are radically anti-realist about universals, though I think the depth and scope of his anti-realism has at times been papered over. Buridan constructs his logic on an amazingly spartan ontology, and this accomplishment is overdue for reconsideration. To the foregoing questions: truth is a feature of propositions, and of propositions only—not of proposition-like states of affairs, or anything like that. It is a function of the reference or supposition (suppositio) of their terms, which depends on predication in a propositional context. And necessary truth is grounded in causation: a predication is necessary if it cannot be falsified by any power, natural or supernatural, without ii annihilating what its terms stand for. “Socrates is a human”, for instance, can only be falsified by annihilating Socrates, and so it is a necessary truth. -/- These considerations provide an ample theoretical basis for a thorough examination of Buridan’s modal logic. This is what the thesis culminates with. In the final chapter, I set forth some novel and surprising findings, chief of which is this: Buridan’s modal syntax and semantics are nothing like Kripke’s—and indeed are incompatible with them. This has significant implications not only for modal logic and metaphysics, but for how we think about medieval logic and philosophy more generally. -/- Throughout the thesis, I advocate a methodology of emphasising the differences, rather than the similarities, between past and present thought. Buridan is wildly unlike what we’re used to, and we should let him speak for himself. (shrink)

This paper traces a rather peculiar debate between William Ockham, Walter Chatton, and Robert Holcot over whether it is possible for God to know more than he knows. Although the debate specifically addresses a theological question about divine knowledge, the central issue at stake in it is a purely philosophical question about the nature and ontological status of propositions. The theories of propositions that emerge from the discussion appear deeply puzzling, however. My aim in this paper is to show that (...) there is a way of making sense of these views (and, by implication, of much of what is puzzling about medieval theories of propositions). The key, I argue, lies in getting clear about the precise theoretical roles these thinkers assign to propositions in their accounts of propositional attitudes. (shrink)

The suggestion of Logical Quanta (LQ) is a bidirectional synthesis of the theory of logos of Maximus the Confessor and the philosophical interpretation of quantum mechanics. The result of such a synthesis is enrichment to the ontology of classical mechanics that enable us to have a unified view and an explanatory frame of the whole cosmos. It also enables us to overcome the Cartesian duality both on biology and the interaction of body and mind. Finally, one can reconstruct a new (...) understanding of religion. (shrink)

In this article, we discuss the notion of merely confused supposition as it arose in the medieval theory of suppositio personalis. The context of our analysis is our formalization of William of Ockham's theory of supposition sketched in Mind 86 (1977), 109-13. The present paper is, however, self-contained, although we assume a basic acquaintance with supposition theory. The detailed aims of the paper are: to look at the tasks that supposition theory took on itself and to use our formalization (...) to relate them to more modern ideas; to explain the notion of merely confused supposition and to defend it against certain criticisms; and to discuss two issues closely related to the idea of merely confused supposition which we could not broach in a shorter article: the mode of supposition of terms in intensional contexts, and the possible existence of a fourth mode, often called suppositio copulatim. (shrink)

A sound historiographical account of the role of logic in the development of medieval philosophical and theological reflection requires a thorough examination of its historical roots and its theoretical implications. An apparent historiographical bias, due to the idea that only the development of contemporary formal logic enables a proper reconstruction of the whole history of logic, can be exposed by taking into account the case of the medieval discussions on the topics, starting from their late-antiquity (...) legacy. An attentive inspection of the successive stages of the gradual formalisation process of medieval topical logic brings to the fore significant theoretical aspects in the philosophy of logic, all too often left aside in common contemporary discussions. In particular, the distinction between topical maxims and topical differences, or principles according to and principles from which an inference is drawn, highlights the specific nature of a major part of medieval logic, that deals with meta-logical issues by means of higher-order logical resources. It is precisely this special character of medieval logic that proves to be of the highest significance in the discussion of the most subtle theological—and just as well philosophical—questions that engaged medieval authors, thus testifying to the essential role of logic in the overall development of medieval thought. (shrink)

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 demasiado intrincado para casi cualquier investigador de estas áreas encontrar la punta del ovillo que lo conduzca a transitar una presentación ordenada e inteligible de la lógica medieval. Este libro pretende solucionar este problema. Para ello, 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 y no desnaturalizar la propuesta medieval. Los primeros tres capítulos se abocan a cuestiones introductorias, 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. Los dos últimos nos brindan una reconstrucción racional, en términos del lenguaje simbólico contemporáneo, de la lógica de finales del siglo XIV. (shrink)

The discussion on the 900 Conclusiones projected and sponsored by Giovanni Pico della Mirandola in Rome was cut short by the condemnation of 13 of them by the papal commission in 1487. Princeps Concordiae’s counter-arguments presented in his Apologia, published in the same year, can not be certainly considered a disputatio as Pico had called for; the papal intervention removed in this way the possibility to have a better acquaintance with a work which is still a very difficult one, just (...) for its “unfinished” form. Pedro Garsia’s Determinationes magistrales against Pico’s Apologia are a very poor reply to Pico. In this paper Pico’s arguments against some of the condemned Conclusiones are considered as well as Pedro Garsia’s counter-arguments. Giovanni Pico della Mirandola displays a deep familiarity with medieval logical and semantical doctrines, while Pedro Garsia’s arguments betray a solid ignorance. (shrink)

This paper makes two main arguments. First, that to understand analogy in St. Thomas Aquinas, one must distinguish two logically distinct concepts he inherited from Aristotle: one a kind of likeness between things, the other a kind of relation between linguistic functions. Second, that analogy (in both of these senses) plays a relatively small role in Aquinas's treatment of divine naming, compared to the realist semantic framework in which questions about divine naming are formulated and resolved, and on which the (...) coherence of the doctrine of divine simplicity—which is what gives rise to the questions of divine naming in the first place—depends. (shrink)

A short reconstruction of the analytic-synthetic method, a key idea in Medieval and Early Modern Logic.

In hindsight, it is not surprising that the exegesis of Aristotle’s Sophistici elenchi developed into one of the most substantial parts of the Latin commentary tradition. To make a long story short, in its customary capacity as the art of arts and the science of sciences, medieval logic was primarily concerned with discerning the true from the false in arguments as they occur in natural, ordinary speech as opposed to the more formalised parlance later logicians will resort to. (...) It makes perfect sense, then, that medieval logicians paid special attention to everything that threatens sound reasoning and that prevents us from speaking the truth. Indeed, they were second to none and better than most at exposing and elucidating arguments’ flaws and shortcomings. After all, as John Buridan – faithful to a long and illustrious tradition – aptly put it, «rooting out errors» is logic’s first order of business. As early as the 1140s, Aristotle’s Sophistici elenchi provided the most fertile ground for such keen interest in fallacies; which, in turn, explains etc. This much is uncontroversial or, at any rate, can withstand any amount of scrutiny we care to throw at it. Courtesy – first and foremost – of Sten Ebbesen, whose long-standing interest in medieval writings on bad arguments has turned the Byzantine and Latin aftermath of Aristotle’s Sophistici elenchi into well-charted territory, by all standards. The Anonymus Cantabrigiensis has played no small part in shaping this picture. As a matter of fact, time and again over the last forty years or so, quotes and insights from the anonymous work have kept showing up in Ebbesen’s editions and studies: since he first discovered the commentary in the late 1970s and brought it to the general attention, Ebbesen has routinely drawn on the Anonymus as an early witness of the circulation of Aristotelian logical works and related texts, as a convenient illustration of major trends and distinctive features of the Latin literature on fallacies, and as a sensible interpreter in his own right. (shrink)

Analytical philosophy is ruled by the alliance of logic, linguistics and mathematics since its beginnings in the syllogistic calculus of terms and premises in Aristotle's Analytica protera, in the theories of medieval logic that dealt with what are Proprietatis Terminorum (significatio, suppositio, appellatio), in the theological apologetics of argumentation with the combinatorics of symbols by Raymundus Llullus in the work Ars Magna, Generalis et Ultima (1305-08), in what is presented as Theologia Combinata (cf. Tomus II.p.251) in Ars (...) Magna Sciendi sive Combinatoria by Athanasius Kircher (1669), in analytical combinatorics based in Leibniz's dissertation Ars Combinatoria (1666), where language is understood as a lingua characteristica and as a calculus ratiocinator, in the combinatorics of classes that have the meanings 1 or 0 given in the idea of Boolean functions (1854), in Frege's work Begriffschrift, eine der arithmeticeschen nachgebildete Fomelsprache des reinen Denkens (Concept letter, the language of formulas of pure thought made according to the model in arithmetical language), in Cantor's study of set theory / Grundlagen einer allgemeinen Mannigfaltigkeitstheorie (1883) and up to algorithms of fuzzy logic as a "means of approximate thinking that is in the human prior" (Zadeh, 1990) and fuzzy linguistics in computer semantics (Burghard B. Rieger, 1993). These are all the philosophical ideas of mathematicians and logicians that founded what we call logical pragmatism here as a demand that logic be absolutely used in every way in which it will dominate the grammar of language until logic itself becomes the philosophical grammar of the mind!!! (shrink)

This paper tries to understand how three medieval philosophers (Roger Bacon, Albert the Great and John Buridan) developed the idea of a special logic for ethics, taking into account Aristotle's thesis according to which ethics does not need theoretical syllogisms and uses a special kind of scientific reasoning. If rhetoric is a good candidate, we find three different readings of this approach and then three different theories of ethical reasoning.

Scholarly dissatisfaction with Aristotle’s fallacy of accident has traditionally focused on his examples, whose compatibility with the fallacy’s definition has been doubted time and again. Besides a unified account of the fallacy of accident itself, the paper provides a formalized analysis of its several examples in Aristotle’s Sophistici elenchi. The most problematic instances are dealt with by means of an internal reconstruction of their features as conveyed by Aristotle’s text and an extensive survey of their interpretation in the Byzantine and (...) Latin exegetical tradition. Carefully handled a doxographical approach, as opposed to rapid results oriented practices, proves to be most effective in that it supplies both useful albeit ordinarily overlooked insights and a comprehensive framework of reference for further investigations. (shrink)

Petrus Nigri (Schwarz) se narodil západočeské Kadani (něm. Kaaden) kolem roku 1435 a spolu se svými třemi bratry vstoupil v Německu do dominikánského řádu. Během svého studia prošel velkou část Evropy (Německo, Itálii, Španělsko, Čechy a Maďarsko) a nakonec se stal rektorem generálního studia v Budíně (1481). Obecně je znám spíše jako význačný středověký hebraista. Do dějin filosofie se zapsal zvláště jako autor Clipeus thomsitarum (před r. 1474), což je filosofický komentář na Porfýriův Úvod (Isagoge) a na aristotelovské Kategorie, formou (...) otázek. Třebaže Nigriho práce není originální, představuje v zaalpských zemích významnou recepci pojetí pomyslného jsoucna (Clipeus, část I, ot. 3-4) tak, jak ho koncipoval Hervaeus Natalis († 1323) ve svém traktátu De secundis intentionisbus. -/- Petrus Nigri (Peter Schwarz, born in Kadaň/Kaaden before 1435, died in Buda 1483), is author of Clipeus thomistarum (printed 1481), a philosophical commentary on Porphyry's Introduction (Isagoge), and on Aristotle's Categories in the form of questions. While Nigri's discussion of the concept of being of reason (Clipeus thomistarum, part I, qq. 3-4) is not original, his work is important for contributing to this concept’s reception, and with it the teaching of Hervaeus Natalis (died 1323) in his treatise De secundis intentionibus, in the transalpine countries. Being of reason (ens rationis) is conceived as not a categorial being, nor is it an intellectual operation, nor is it caused, but is only identifiable by the human intellect. Nigri's being of reason has no subjective existence, but only an objective character, which differs both from categorial being and from mere nothingness. (shrink)

Les commentateurs latins ont rencontré pour la première fois le « Troisième homme » d’Aristote dans le chapitre vingt-deux des Sophistici elenchi. Cette rencontre illustre bien à la fois leur respect de la lettre et la radicalité de certaines de leurs innovations. Influencée par la traduction de Boèce, leur exégèse de l’argument a tenu compte de l’ensemble des indications du texte tout en lui conférant une tournure inédite.

Latin commentators came across the « Third Man » in Aristotle’s Sophistici elenchi. The way they dealt with the argument is a fair illustration of how they were both faithful to the text and innovative in their understanding of its most challenging issues. Besides providing a detailed survey of all manuscript sources, the introductory essay shows that Latin interpretation originates from a mistake in Boethius’ translation which radically transformed the argument. The edition makes available for the first time a considerable (...) amount of new documentary evidence which made it possible to solve the riddle of the Latin « Third Man ». (shrink)

In the first of the Insolubles in Chapter 8 of his Sophismata, Buridan contends that the inference Omnis propositio est affirmativa; ergo, nulla propositio est negativa (PS) is valid, even though it appeals to the self-reference in the conclusion to show that what we (following Read 2001) call the classical conception of validity (CCV) fails. This requires that we accept that there are good inferences in which a false conclusion follows from true premises. Partially following Hughes’ proposal (1982), we argue (...) that the First Sophism (PS) involves three different notions of validity. Two of them correspond to the ones described by Hughes (1982, 80–86), who calls them Theory A and Theory B. The third one—that will we call Theory C—is not mentioned by Hughes; instead, it is suggested by Buridan himself in the first three arguments in favor of the validity of PS. We show that: a) from what Buridan says in his Theory C it follows that PS is a formal and material consequence, and hence, a valid one. Then we show that: b) the rejection of CCV and the acceptance of Nulla propositio est negativa (NPN) as a (formal) consequence of Omnis propositio est affirmativa (OPA) leads to a paradox that bears similarities with the one put forward by Pseudo Scotus—which has been studied by Read (2001) and is related to Curry’s paradox. However, there are enough differences to merit considering this paradox separately, especially in relation to the so-called validity paradoxes. Interestingly, our work suggests that Buridan was aware of these problems, which explains why he introduced a new criterion for validity, one that is not based on truth-preservation but on what Spade (1988) calls firmness, and Klima (2016) correspondence. (shrink)

The phrase _secundum quid et simpliciter_ is the Latin expression translating and labelling the sophism described by Aristotle as connected with the use of some particular expression “absolutely or in a certain respect and not in its proper sense.” This paper presents an overview of the analysis of this fallacy in the history of dialectics, reconstructing the different explanations provided in the Aristotelian texts, the Latin and medieval dialectical tradition, and the modern logical approaches. The _secundum quid_ emerges as (...) a strategy that is based on the pragmatic dimension of arguments, and in particular the complex passage from an utterance (what is said) to its logical form (a proposition in an argument). The medieval and modern logical theories attempted to explain from different philosophical perspectives how the pragmatically enriched semantic representation can be achieved, justified, and most importantly manipulated. The different analyses of this fallacy bring to light various dimensions of the pragmatics of arguments, and the complex interdependence between context, meaning, and inferences. (shrink)

Universals appear to be as central in today's computational-based ontology as they were in medieval ontological investigations. As the author of a recent work on the history of universals (Pinzani, 2018), I was asked for a commentary on Augusto’s article “Bridging Mainstream and Formal Ontology” (Augusto, 2021), which aims at showing that medieval ontological investigations can be relevant for contemporary ontology engineering. In this commentary, I begin by saying something about my way of reading 12th-century logical literature and (...) then offer some modest considerations on the general theme addressed in Augusto's article. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

The aim of this paper is to offer a critical assessment of Buridan's proposed solution to the bridge-keeper paradox. First, I will outline his proposed solution to the paradox, and, second, carefully analyse each issue mentioned in the proposed solution. Finally, I will attempt to conclude that Burden has implicitly accepted a three-valued logic that does not allow him to conclude that Plato ought not do anything.

In this essay, I consider some logical treatises and commentaries from the first decades of the 12th century (many of which are still unedited) which contain a discussion on modalities and modal logic. After presenting a short catalogue of these sources and a description of their common features, I shall focus on some definitions of the modal term “necessarium” which are provided in them. As we will see, Abelard and logicians of his time advanced three different characterizations of this (...) term: necessity was either defined in terms of unavoidability (ineuitabilitas), or in terms of immutability and omnitemporality (impermutabilitas, sempiternitas), or again in terms of absolute necessity as opposed to conditioned one (necessitas absoluta vs. determinata). I argue that the temporal understanding of necessity in terms of omnitemporality, inherited from ancient sources and extensively used by Abelard and others in the first years of the twelfth-century, started to disappear in texts datable from around the 1120, perhaps due to several difficulties that were related to this definition when applied in logical contexts. I also discuss how the notion of necessitas determinata was used by Abelard’s contemporaries to qualify the modal status of present and past events, which were generally believed to be necessary only in a “weak” and harmless sense that did not prevent them from being contingent. -/- . (shrink)

Plato’s partition argument infers that the soul has parts from the fact that the soul experiences mental conflict. We consider an ambiguity in the concept of mental conflict. According to the first sense of conflict, a soul is in conflict when it has desires whose satisfaction is logically incompatible. According to the second sense of conflict, a soul is in conflict when it has desires which are logically incompatible even when they are unsatisfied. This raises a dilemma: if the mental (...) conflict is supposed to be the latter kind of conflict, then the partition argument is valid but is likely unsound; if it’s supposed to be the former kind, then the partition argument has true premises but is invalid. We explain this dilemma in detail and defend a dispositionalist solution to it. (shrink)

Rondo Keele makes a foray into what he calls 'applied logic', investigating a complex argument strategy employed against Ockham by his greatest contemporary opponent, Walter Chatton. Chatton conceives a two-part strategy which attempts to force a kind of iteration of conceptual analysis, together with an infinite explanatory regress, in order to establish that one particular philosophical analysis is ultimately dependent on another. Chatton uses this strategy against Ockham in order to show that the latter's reductionist metaphysics depends ultimately upon (...) a deeper level of realist assumptions that he can neither evade nor explain away. Keele then shows how, earlier in his career, Chatton found himself on the receiving end of this same strategy, defending his own highly original solution to the problem of future contingents from the very iteration-regress attack he would subsequently use on Ockham. Keele concludes with an examination of Chatton's attempts to avoid the consequences of his own strategy, and draws some connections between this argument strategy and modal collapse in modern logics. (shrink)

Many things can be other than they are. Many other things cannot. But what are statements like these about? One answer to this question is that we are speaking of possible worlds: if something can be other than it is, then it actually is that way in some possible world. If something cannot be otherwise, it is not otherwise in any world. This answer is presently dominant in analytical philosophy of language and logic. What are these worlds? David Lewis (...) famously claimed that every world exists, just like ours does: there is no difference between the other worlds and ours. In contrast, the medieval thinker John Buridan understands modal logic in terms of objects and causal powers in this world: if something can be other than it is, then there is a causal power that can make it that way. If it cannot, then no causal power—not even God—can alter it, at least without destroying its nature. As we’ll see, the Lewisian plurality is not possible on Buridan’s account; accordingly, a basic tenet of classical theism is untenable on Lewis’s metaphysics. In short, either the Lewisian plurality is incoherent, or a core monotheistic tenet is impossible. (shrink)

Settler colonialism is structured in part according to the principle of civilizational progress yet the roots of this doctrine are not well understood. Disparate ideas of progress and practices related to colonial dispossession and domination can be traced back to the Enlightenment, and as far back as ancient Greece, but there remain unexplored logics and continuities. I argue that civilizational progress and settler colonialism are structured according to the opposition between politics governed by reason or faith and the figure of (...) the child as sinful or bestial. Thus, it is not contingent, but rather necessary that justificatory frameworks of European empire and colonialism depict Indigenous peoples as children. To illustrate how the theoretical link between Indigenous peoples and children emerges not as a simple analogy, but rather, as the source of the premodern/modern and savage/civilized binaries, I trace the various historical iterations of the political/childhood opposition through the classical, medieval, enlightenment, and modern eras. I show how the model of civilizational progress from a premodern and savage state of childhood continues to serve as the model for settler colonial exclusion and domination of Indigenous peoples. (shrink)

This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's conclusion does (...) not follow from its premises? This result does nothing to vitiate the theories of distribution developed over the period beginning in medieval times. What it does vitiate is many if not all attempts to use distribution in tests of invalidity outside of the standard two-premise categorical arguments—where they were verified on a case-by-case basis without further theoretical grounding. In addition it shows that there was no theoretical basis for many if not all claims of fundamental status of rules of distribution. These results are further support for approaching historical texts using mathematical archeology. (shrink)

Abstract: By the second half of the eleventh century, in the Christian West, the theological doctrine of St. Anslem sought to re‐establish the place of reason within the domain of faith. Anselm arrived at a possible re‐enactment of this relation under the condition regulated by the principle fides quaerens intellectum – faith seeking reason. This paper is an attempt to explore not only the possible implications of this principle but to understand the internal logic which constitutes it and holds (...) it together. It is the contention of this paper that this regulative principle (fides quaerens intellectum) could complete such a process of logically constituting itself through a violent forcing of thought which gathered and maintained within itself an anomy. This internal paradox produced a logical excess which at one hand threatened constantly to expose a crisis, inhabiting the very centre of the theological system it sought to build, but on the other hand it also became the very ground on which such a system constituted itself. To that extent this paper would try to understand the metaphysical forcing of this moment of crisis back into the theological system it sought to express and normalize at the same time. (shrink)