Logica Magna Part 1 Fasc 1 Tractatus de Terminis.

This paper analyzes Paul of Venice’s theory of measurement of natural properties and changes. The main sections of the paper correspond to Paul’s analysis of the three types of accidental changes, for which the Augustinian philosopher sought to provide rules of measurement. It appears that Paul achieved an original synthesis borrowing from both Parisian and Oxfordian sources. It is also argued that, on top of this theoretical synthesis, Paul managed to elaborate a quite original theory (...) of intensive properties that marks him out not only from the nominalist framework of his Parisian sources but also from the usual realist treatments of the problem. Finally, it is shown that, to a certain extent, Paul undertook to apply the mathematical and logical tools inherited from the Calculatores tradition to empirical problems of natural philosophy, leading to reevaluate his role in the evolution of scientific thought in early 15th-century Italy. (shrink)

ABSTRACTThis paper examines the theory of artefacts presented by the 15th-century thinker Paul of Venice, paying special attention to the views of authors often referred to as ‘nominalists’ (e.g. O...

Paul of Venice joined the Austin Friars at an early age and was sent by them from Padua to study at Oxford in 1390. When he returned, full of ideas and laden with books, he began his prodigious writing career with several books on logic, including the Logica Magna, which runs to some half a million words. The current volume contains the final treatise, on insolubles - that is, logical paradoxes. After surveying fifteen previous solutions, Paul develops (...) his own, based on the idea that such propositions falsify themselves. Besides a critical edition of the Latin text, the volume also contains an English translation, a detailed commentary, excerpts from two other logical works of Paul, and a substantial introduction. The introduction describes the fourteenth-century background to Paul's treatise; it also gives a detailed rebuttal of a recent claim that the Logica Magna is not by Paul because its content clashes with genuine works of his. All in all, the volume greatly enhances our understanding of the development of logic, in particular of the semantics of propositions, during a crucial century in its history. (shrink)

In this paper, I focus on Paul of Venice’s plurality of forms and souls, i.e., his “two total souls” theory. I argue that this specific theory is a result of Paul’s reception of various positions originating from fourteenth-century Parisian philosophers like John of Jandun, the Anonymous Patar, Nicole Oresme, John Duns Scotus, and Walter Burley. By receiving these positions and by making use of merely parts of their doctrines, Paul creates a theory of the hylomorphic compound (...) that fits well within an Aristotelian framework of an Averroistic flavor. Although his position is not Averroistic in any strict sense, it mirrors quite well the growing interest in an Averroistic interpretation of Aristotle in Padua at his time. By looking at some of his successors, such as Gaetano da Thiene, Nicoletto Vernia, and Agostino Nifo, I show that Paul is on the borderline between a traditional, scholastic philosophical psychology or hylomorphism of Parisian origin and an Averroist reading of philosophical psychology or hylomorphism, which had its promoters in fifteenth-century Padua. (shrink)

In the 1330s Roger Swyneshed formulated a solution to semantic paradoxes based on the distinction between correspondence with reality and self-falsification as truth-making factors. Since Swyneshed states that some valid inferences are not truth-preserving, his view implies the question of the general definition of validity which he does not address explicitly. Logical works attributed to Paul of Venice contain developments of Swyneshed's contextualist semantics substantially modified by the assumption that sentential meanings are objective propositional entities. The main goals (...) of this paper are to show the correlations between the ontological and logical developments of Swyneshed's semantics in the works of Paul of Venice and to outline a context-sensitive formal semantics that could serve as a model of this family of semantic theories. (shrink)

An obligation, in the sense in which it was of interest to medieval logicians from about the early thirteenth century to the end of the scholastic period, is, according to Paul of Venice, a relation limiting one to take some statement affirmatively or negatively. This relation is based on the actions of two individuals: one obligates the other by first putting forward a sentence which the respondent agrees to affirm or deny for a limited time. The sentence the (...) respondent agrees to affirm is called the positum; that which he agrees to deny, the depositum; and his act of agreeing, the admissio. After this relation is established between the opponent and respondent, the opponent proceeds by putting forward a series of sentences to which the respondent replies by granting, denying, or doubting — all in accordance with certain rules the two individuals have previously accepted as governing their exchange. If the respondent at any time grants what is inconsistent with the sentence he agreed to uphold, or responds in a way that violates the accepted rules, the exchange comes to an end. The respondent has failed in his obligation. (shrink)

This paper focuses on Paul of Venice’s realist theory of direct knowledge. In the second half of the 13th century human knowledge was standardly viewed as a process of abstraction enabling the human intellect to grasp the essences of corporeal things, regardless of the matter in which they are embodied. This process was achieved thanks to the mediation of mental entities (species intelligibiles) representing the dematerialised objects in the intellect. By the late 13th and early 14th centuries, however, (...) some authors began to regard this account as unsatisfactory. These authors held that assuming the existence of mediating species (considered themselves as objects of knowledge) amounts to thinking that between ourselves and the world there is a barrier preventing us from acquiring knowledge of reality in itself. Paul of Venice is aware of the sceptical accusations made against the theory of species in the 13th and 14th centuries. Nevertheless, he is a firm advocate of the existence of species. He claims that knowledge, despite coming about through species, is not indirect. Quite the contrary: we have immediate access to reality, and the individual objects that constitute it, precisely because our senses (which are purely passive) receive impressions direct from outside, thanks to species. He points out that species are not object of knowledge. They are not known at all during the cognitive process, as they are a mere means (a mechanical means, so to say), not an image nor a representation of anything, and therefore they are no obstacle between ourselves and the world. Thus, we are able to know reality exactly as it is in itself and, under ordinary conditions, our perceptions are practically infallible and cannot produce false knowledge. (shrink)

In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. Consider this inference concerning some proposition A : A will signify only that everything true will be false, so A will be false. Call this inference B. A and B are the basis of an insoluble-that is, a Liar-like paradox. Like the sequence of statements in Yablo's paradox, B looks ahead to (...) a moment when A will be false, yet that moment may never come. In the Quadratura, Paul follows the solution to insolubles found in the collection of elementary treatises known as the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses a different solution that takes insolubles at face value. We consider how both types of solution apply to A and B : on both, B is valid. But on one, B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected. (shrink)

In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider this inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard doctrine (...) of ampliation, Paul takes A to be equivalent to 'Everything that is or will be true will be false'. But he proceeds to argue that it is possible that B's premise ('A will signify only that everything true will be false') could be true and its conclusion false, so B is not only valid but also invalid. Thus A and B are the basis of an insoluble. In his Logica Parva, a self-confessedly elementary text aimed at students and not necessarily representing his own view, and in the Quadratura, Paul follows the solution found in the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses Swyneshed's solution, which stood out against this ''multiple-meanings'' approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say. On this account, insolubles imply their own falsity, and that is why, in so falsifying themselves, they are false. We consider how both types of solution apply to B and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected. (shrink)

Lo studio si concentra sul modo in cui i commenti alla Metafisica di Paolo di Venezia e Alessandro di Alessandria evidenziano il grado di modificazione della comprensione della dottrina aristotelica sull'essenza, dovuta alla ricezione della dottrina di Tommaso d'Aquino e di Averroè al riguardo. Dopo un'introduzione di inquadramento storico dottrinale dei due commenti, la seconda parte è centrata sulle dottrine dei due maestri relative all'essenza, e l'A. articola la sua ricognizione attorno ai temi del rapporto fra essenza e sostanza, essenza (...) e predicazione, e sulla rispettiva ricezione della dottrina tomista sull'essenza, fondata a sua volta sulla dottrina avicenniana . La terza parte verte su una puntuale ricostruzione della dottrina dell'essenza in Paolo, mentre la quarta evidenzia come Alessandro sia la fonte primaria di Paolo. L'A., infine, esamina il commento di Alessandro in relazione al tema dell'essenza. Nella conclusione ribadisce come Alessandro e Paolo tentino di riconciliare la dottrina averroista con Aristotele, adottando l'interpretazione di Tommaso. Tra i testi dell'Aquinate utilizzati si ricordano il De ente et essentia, il commento alla Metaphysica e quello alle Sentenze, la Summa theologiae. (shrink)

The manuscript Venice, Biblioteca Nazionale Marciana, Class XI n. 12, Zanetti Latini 301 (= 1576), contains on fols. 1r–24v a seemingly unique copy of a series of fifteen logical questions, ten on obligationes and the remaining five on insolubilia.1 The series on obligationes is untitled and unattributed in the manuscript, but the questions on insolubilia begin (fol. 18r11) “Incipiunt quaestiones super insolubilibus,” and are attributed at the end to a certain John of Wesel (fol. 24v41): “Ergo expletae sunt quaestiones (...) insolubilium a Johanne de Vesalia Parixius2 disputatae. Deo gratias. Amen.”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Ovid, Art, and Eros PAUL BAROLSKY OVIDIO, AMORI, miti e altre storie or Ovid: Loves, Myths, and Other Stories is the copiously illustrated catalogue to the monumental exhibition mounted in 2008–2009 at the Scuderie del Quirinale, in Rome, in celebration of the great Roman poet and his world. This handsome tome is many books in one: a beautiful album of color plates illustrating a wide range of fascinating (...) objects, an overview of Ovid’s life, works and influences—a book for amateurs and specialists alike, a book to delight and instruct. The book includes paintings and sculpture but also pottery, coins, and jewelry. There is something for everybody here. Ovidio is divided into relatively brief sections written by numerous scholars who treat such topics as Ovid and myth, Ovid the love poet, Ovid in exile, Ovid and Augustan Rome, Ovid and the figurative arts, and Ovid in the seventeenth century. The book’s attention to illustrated editions of Metamorphoses, and especially the Ovide moralisé, is notable and refreshing. I think it fair to say that the exhibition and its catalogue are, not surprisingly, dominated by Metamorphoses and the ways in which artists illustrated its stories over the centuries. The myths of Venus and Adonis, Narcissus and Echo, Icarus and Daedalus, and Jupiter and Europa are among the numerous Ovidian stories that get extensive treatment here. We need to recall that no ancient author in the Hellenic tradition is so copiously illustrated as is Ovid—a fact that is Ovidio, amori, miti e altre storie, ed Francesca Ghedini et al. Rome 2018, 310 pages; isbn 9788856906486; €33.15. arion 27.2 fall 2019 easily taken for granted. A consummate story teller, Ovid inspired the pictorial tales of Poussin, Rubens, Rembrandt, and Velázquez, among other masters. Often in this book, works of mythological art are seen in the context of Ovid, even when there is no specific association between image and text. Such is the case when, for example, we encounter the well-known Praxitelean Aphrodite pudica in the Uffizi which inspired Botticelli’s similar Aphrodite now in the Musei Reali of Turin. There is nothing that links the statue and the painting to Ovid other than the fact that their makers, like the poet, write about the goddess of love. Ever so many mythological works suggest the arousal of desire. The Praxitelean Aphrodite modestly covers her body with both of her hands. Understandably, since according to an ancient tale, a young man was so aroused by the statue that he left a stain upon her. In short, we are in the realm of erotic art. The Hellenistic statue of Leda and the Swan in the archeology museum of Venice is an excellent example of erotic art featured in this book, even though Leda is mentioned only in passing in Metamorphoses. She seems to swoon in rapture as the bird (Jupiter in avian guise) slithers between her legs, beak seeking lips. Scarcely resisting, Leda reaches ambiguously downward as if in search of something, and we can well imagine what that might be. That her lower hand is invisible contributes to its suggestiveness. Leda’s upper hand is pressed against the swan’s sinuous neck, by no means a gesture of resist170 ovid, art, and eros Figure 1: Leda and the Swan. Venice, Museo Archeologico Nazionale, 2018. Eric Vandeville / akg-images. ance, I believe, even though in the myth she is taken by force. What we see is what the Ovid catalogue calls a “voluptuous amplexus.” The story of Leda and the Swan is forever told by painters in various erotic ways. When, later in the Renaissance, Correggio pictures the momentous event he shows the swan mounting Leda who, in this case, receives the bird in a seated position. As the bird engages the nymph, feathers pressed against her inner thigh, the swan, as in the ancient statue, seeks out her mouth with his beak—a juxtaposition as phallic as it is oral. The Leonardesque smile of Leda betokens not fear or violence but pleasure—a decidedly carnal pleasure. In a different context, Vasari wrote that Correggio painted not colors but flesh. When Leonardo himself pictured Leda, he delicately rendered the... (shrink)

Past, present, and future are reversed in the reader's encounter with the illustrations selected by Gertrude Stein for her Autobiography of Alice B. Toklas.1 After the table of contents there is a table of illustrations that encourages everyone to look at the pictures before they begin reading. During that initial examination, the illustrations forecast what is to be discovered in the text. Expectations are aroused by photographs showing Gertrude Stein in front of the atelier door, rooms hung with paintings, Gertrude (...) and Alice in front of Saint Mark's Cathedral, and both with a car in front of Joffre's birthplace. It is natural—although, as it turns out, not altogether correct—to assume that the accumulation of paintings will be explained, that the life lived within the rooms will be fully depicted, and that conventional narrative explanation will be provided to account for the presence of Gertrude and Alice together in such disparate settings as Venice and the French marshal's home. · 1. For useful comments on several pictures as well as evidence that "even the book's sixteen photographs were carefully placed in the first edition," see Richard Bridgman, Gertrude Stein in Pieces , p. 219. Paul K. Alkon, professor of English at the University of Minnesota, is author of Samuel Johnson and Moral Discipline. Among his recent articles are "Boswellian Time" and "The Historical Development of the Concept of Time." He is writing a book about time in Defoe's fiction. See also: "The Mind, The Body, and Gertrude Stein" by Catharine R. Stimpson in Vol. 3, No. 3; "Gertrude Stein, the Cone Sisters, and the Puzzle of Female Friendship" by Carolyn Burke in Vol. 8, No. 3. (shrink)

Every educated person in the Middle Ages learned logic, which was then always some version of the theory of the syllogism. But until the rise of the universities in the thirteenth century no scholar in Christendom had written a comprehensive commentary on the work of Aristotle's that contains that theory, namely the Prior Analytics. Robert Kilwardby was an English scholar who lectured on logic and grammar at the University of Paris in the 1230s. His lectures earned him widespread fame in (...) Europe. Throughout the thirteenth century and up to the sixteenth,Kilwardby's lectures on Aristotle's Prior Analytics were considered to contain the authoritative exposition of Aristotle's syllogistic logic. They were published at Venice in 1499. (shrink)

Every educated person in the Middle Ages learned logic, which was then always some version of the theory of the syllogism. But until the rise of the universities in the thirteenth century no scholar in Christendom had written a comprehensive commentary on the work of Aristotle's that contains that theory, namely the Prior Analytics. Robert Kilwardby was an English scholar who lectured on logic and grammar at the University of Paris in the 1230s. His lectures earned him widespread fame in (...) Europe. Throughout the thirteenth century and up to the sixteenth,Kilwardby's lectures on Aristotle's Prior Analytics were considered to contain the authoritative exposition of Aristotle's syllogistic logic. They were published at Venice in 1499. (shrink)

This paper explores a specific problem within an important philosophical genre of the fourteenth century: the debates over the perfection of species. It investigates how the problem of defining limits for continuous magnitudes – a problem typical of Aristotelian physics – was integrated into these debates at the levels of genera, species, and individuals as these entities began to be conceptualized in quantitative terms. After explaining the emergence of this problem within fourteenth-century metaphysics, the paper examines the contributions of three (...) philosophers – Hugolinus of Orvieto, John of Ripa, and Paul of Venice – who offered varying solutions to the challenge of defining limits between species. It demonstrates that two primary solutions arose, inspired by continuous and discrete mathematical objects. It is shown that whereas Hugolinus of Orvieto advocates for a continuist model, John of Ripa proposes a discrete one. The last part of the paper examines Paul of Venice's hybrid approach, which combines elements from both models, facilitating a more comprehensive treatment of species particularly difficult to analyse, namely geometric figures. The conclusions of this comparative study underscore how profoundly the metaphysical reflections of the Middle Ages contributed to the analysis of the structure of the continuum and the extension of the notion of quantity to various objects. (shrink)

The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly (...) concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic. (shrink)

The Oxford Calculator Roger Swyneshed put forward three provocative claims in his treatise on insolubles, written in the early 1330s, of which the second states that there is a formally valid inference with true premises and false conclusion. His example deployed the Liar paradox as the conclusion of the inference: ‘The conclusion of this inference is false, so this conclusion is false’. His account of insolubles supported his claim that the conclusion is false, and so the premise, referring to the (...) conclusion, would seem to be true. But what is his account of validity that can allow true premises to lead to a false conclusion? This article considers Roger’s own account, as well as that of Paul of Venice, writing some sixty years later, whose account of the truth and falsehood of insolubles followed Roger’s closely. Paul endorsed Roger’s three claims. But their accounts of validity were different. The question is whether these accounts are coherent and support Paul’s claim in his Logica Magna that he endorsed all the normal rules of inference. (shrink)

Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory (...) pair, in which one statement affirms what the other denies of the same thing, Aristotle himself gave counterexamples to the rule. This gives some credence to Swyneshed’s claim that his solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Insolubles are false, he said, because they falsify themselves; and their contradictories are false because they falsely deny that the insoluble itself is false. Swyneshed’s solution depends crucially on the revision he makes to the acount of truth and falsehood, brought out in his first thesis: that a false proposition can signify as it is, or as Paul of Venice, who took up and developed Swyneshed’s solution some sixty years later, puts it, a false proposition can have a true significate. Swyneshed gave a further counterexample to when he claimed that some insolubles, like future contingents, are neither true nor false. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. Consequently, Swyneshed’s logical heresy is very different from that found in dialetheism. (shrink)

In Formale Logik, published in 1956, J. M. Bocheński presented his first proposal for the solution to the liar paradox, which he related to Paul of Venice's argumentation from Logica Magna. A formalized version of this solution was then presented in Formalisierung einer scholastischen Lösung der Paradoxie des ‘Lügners’ in 1959. The historical references of the resulting formalism turn out to be closer to Albert de Saxon's argument and the later solution by John Buridan. Bocheński did not pose (...) the question of the consistency of his theory. The case was taken up by B. Sobociński in his private letter to Bocheński from 12 August 1954. Sobociński used a smart translation of the language of Bocheński's theory into the classical propositional language with the notions of truth and falsehood inverted. The translation preserves the structure of the formalized solution. We explore Sobociński's idea and reconstruct his original proof. (shrink)

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 ; 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. (shrink)

In his commentary on Aristotle’s Physics, John Buridan (c. 1300–1361) presents his well-known rejection of final causality. The main problem he sees with it is that it requires the cause to exist before the effect. Despite this, he retains the terminology of ends. This has led to some difficulty interpreting Buridan’s view. In this article, I argue that one should not misunderstand Buridan’s terminology and think that he still retains some use or explanatory function for final causality in nature. To (...) make this point, I look first at Buridan’s text, but then also at three thinkers who discuss Buridan’s view in detail: Albert of Saxony (d. 1390), Paul of Venice (d. 1429), and Luis Coronel (d. 1531). They all have a very clear idea of what Buridan’s view was and understand that it entails a rejection of final causality, but they also all preserve his distinctive terminology. Paul of Venice especially discusses and criticizes Buridan’s view in detail. Besides confirming my interpretation of the rejection of final causality, this study also shows that the view was extremely influential well into the sixteenth century and attributed to Buridan throughout two centuries. (shrink)