Das griechische Wort syllogismos besteht aus der Vorsilbe syl- und dem Wort logismos. Platon verwendet es gelegentlich im Sinne von ›Überlegung‹. Aristoteles prägt den technischen Begriff des ›Syllogismos‹ im Sinne von ›gültiger deduktiver Schluss‹.

Der Status des sogenannten syllogismos ex hypotheseôs Hypothese") in Aristoteles' Organon mag als kleines rätselhaftes Detail der Logikgeschichte gelten. Interessant ist dieses Detail, weil man leicht in Versuchung gerät, in ihm eine Schnittstelle zwischen antiker Begriffs- und Aussagenlogik zu erblicken. Im folgenden soll dafür plädiert werden, dass man dieser Versuchung lieber nicht nachgeben sollte. Schließlich soll die Vermutung geäußert werden, dass es näherliegend ist, innerhalb der aristotelischen Argumentationslehre eine ganz andere Identifikation vorzunehmen als die übliche.

Alexander W. Hall - Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III-II: De Syllogismo Demonstrativo, and Selections from the Prologue to the Ordinatio - Journal of the History of Philosophy 46:1 Journal of the History of Philosophy 46.1 170-172 Muse Search Journals This Journal Contents Reviewed by Alexander W. Hall Clayton State University John Lee Longeway, translator. Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III–II: De Syllogismo Demonstrativo, and (...) Selections from the Prologue to the Ordinatio. Notre Dame, IN: University of Notre Dame Press, 2007. Pp. xx + 432. Cloth, $58.00. William of Ockham never delivered his promised exposition of Posterior Analytics. In its place, we have Summa Logicae III–II, and the Prologue to his Ordinatio... (shrink)

This book makes available for the first time an English translation of William of Ockham's work on Aristotle's _Posterior Analytics_, which contains his theory of scientific demonstration and philosophy of science. John Lee Longeway also includes an extensive commentary and a detailed history of the intellectual background to Ockham's work. He puts Ockham into context by providing a scholarly account of the reception and study of the _Posterior Analytics_ in the Latin Middle Ages, with a detailed discussion of Robert Grosseteste, (...) Albert the Great, Thomas Aquinas, Duns Scotus, and Giles of Rome. In a series of appendices, Longeway includes shorter translations of some important related work by Giles of Rome and John of Cornwall. In his introductory discussion, Longeway examines the exact character of the highest sort of demonstration, the relations of the empirical sciences to mathematics, natural causation and the manner in which natural laws come to be known, the possibility of natural knowledge, our knowledge of God, and the relation of theology to the other sciences. Longeway discusses the way in which scientific epistemology and theory of demonstration corresponds to the metaphysical position of its interpreter, in particular to the Neoplatonism of Grosseteste, the radical Aristotelianism of Giles of Rome and Albert the Great, the more moderate Aristotelianism of Aquinas, and the nominalistic empiricism of Ockham. Throughout the book, Longeway makes a case for Ockham's importance as the founder of empiricism in the West. _ “The present work is the result of decades of study of Ockham's philosophy of science. The translation and commentary are introduced by a chapter in which Longeway presents an overview of Ockham's thought in this area and highlights its philosophical significance. This introduction is in its own right a significant contribution to the history of philosophy.” — Owen Goldin, Marquette University_ "Like much else in medieval philosophy, medieval theories of demonstrative knowledge are historically important, philosophically interesting, and little understood. There are a few extensive studies into medieval discussions of demonstration and even fewer translations of these important discussions. Longeway's_ Demonstration and Scientific Knowledge in William of Ockham_ is, therefore, an important contribution to the field. This work contains not only an extensive set of translations of Ockham's work on the theory of demonstration, but also a book-length introduction in which Longeway surveys the development of medieval theories of demonstration prior to Ockham and situates Ockham's discussion within that development. The book will be of value to any scholar interested in Ockham's thought as well as to anyone interested more generally in medieval discussions of demonstration, science, and epistemology." —_Susan Brower-Toland, Saint Louis University_. (shrink)

The text of the treatise “The Propositional Logic of Boethius” was finished in 1939. Prof. Jan Lukasiewicz wished at that time to issue it in the second volume of “Collectanea Logica”; as a result of political events, he was not able to carry out his plan. In 1938, I published an article in “Erkenntnis” entitled “AUS- sagenlogik im Mittelalter”; this article included the contents of a paper which I read to the International Congress for the Unity of Science in Cambridge, (...) England, in 1938 (Cf. Erkenntnis, vol. 7, pp. 160-168). The subject matter of this paper touched upon that of the above-mentioned treatise. Recently an article of Mr. Rend van den Driessche, “Sur le ‘de syllogismo hypothetico’ de Boece”, was published in the journal “methodos” (vol. I, no. 3). Mr. van den Driessche referred in this article to the article on propositional logic in the middle ages, which had appeared in “Erkenntnis”. This reminded me of my yet-unpublished treatise on the propositional logic of Boethius. (shrink)

Aristotle determines eristic argument as argument which either operates upon the basis of acceptable premisses (endoxa) and merely give the impression of being deductive, or argument which truly is deductive but operates upon the basis of premisses which seem to be acceptable, but are not (or, again, argument which uses both of these mechanisms). I attempt to understand what Aristotle has in mind when he says that someone is deceived into accepting premisses which seem to be acceptable but which are (...) really not, and how this disqualifies such arguments from being dialectical. In the first section of the paper I interpret Aristotle’s notion of endoxa in terms of a relational concept of acceptability. Real Índoxa are propositions which are accepted by a qualified group or individual. False endoxa may also be accepted by someone or some group, and may even be true, but they are used to serve the purposes of eristical argumentation, which departs from certain standards of dialectical argumentation articulated in the notion of endoxa as a norm for premiss-acceptance. In particular, eristic arguments may even be valid in the sense of a syllogismos while still failing to be proper dialectical arguments. In the second part of the paper I consider how this can be, in examining certain types of fallacies in the Sophistical Refutations and the relationship between fallacious argumentation and false endoxa. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Abaelards Logik by Wolfgang LenzenSten EbbesenWolfgang Lenzen. Abaelards Logik. Paderborn: Brill | mentis, 2021. Pp. 206. Hardback, €59.00.According to its author, this book aims at reconstructing key parts of Abelard's logic while denying him a role as a hero of connexive logic or more generally as one of history's greatest logicians. At the end of the preface, we are told that "Abaelard hat die Logik seiner Zeit nicht (...) revolutioniert; er hat keine Kalküle konstruiert; und er hat auch nicht die Logik seiner Zeit auf ein höheres Niveau gehoben" (xiv).The book is divided into twenty-three chapters with titles such as "'Destruierende' versus 'separierende' Negation," "Vollkommene und unvollkommne Folgerungen," and "'Leere' Begriffe." As the titles show, it ranges over a large field. The results of Lenzen's analyses of Abelard's argumentation are presented in modern logical notation. There are many fine analyses, and despite Lenzen's refusal to see Abelard as a genius, he, too, seems to have been quite impressed by the old logician. However, at the end of the day, I am not sure that I have become any wiser about Abelard's contribution to the history of logic.Lenzen is a newcomer to the study of twelfth-century logic, and the book is marked by this in several ways. Thus, he informs the reader that "Spätestens seit Prantls Publikation der 'Geschichte der Logik im Abendlande' steht fest, dass Abaelards Traktat 'De Sillogismis Ypoteticis' sich stark an das Werk 'De syllogismo hypothetico' von Boethius (470–524) anlehnt" (165). This is quite true, but anything else would have been very remarkable, so the reference to Prantl serves no purpose.Unsurprisingly, the main source texts used are Abelard's Dialectica and his Glosae super Peri hermeneias, a part of the series of commentaries on the Ars vetus that go under the common name of Logica ingredientibus. Lenzen displays a cavalier attitude to philology. He quotes the Dialectica from De Rijk's second edition (1970), but in the bibliography he mentions that there are two editions without stating explicitly which one he quotes. In the case of the Glosae, he uses the obsolete editio princeps by Bernhard Geyer from 1927, and he does not even mention its replacement, Klaus Jacobi and Christian Strub's much superior 2010 edition in the series Corpus Christianorum, Continuatio Mediaevalis. This is inexplicable, for in his preface Lenzen describes his book as the child of a research project he began several years after the publication of the new edition. Now, fortunately, the use of Geyer does not have disastrous consequences for Lenzen's interpretation of Abelard, but had he used Jacobi and Strub's edition, he would not have had to propose a textual emendation in one place (88n17), nor would he have needed to quote, in another place, a Latin text (which he does not translate) with a nonsensical significantem instead of figurative (94n1o).Lenzen sometimes proposes textual emendations, but not always in a perspicuous way, and they are not all felicitous. For example, a quotation of L. M. de Rijk's edition of Introductiones Montane Minores in Logica Modernorum (LM) II.2 (1967) contains the phrase aliquod opposit[or]um (127n2). An unsuspecting reader would think this means De Rijk had conjecturally emended oppositorum into oppositum, for this is what opposit[or]um would mean in LM II.2. In fact, De Rijk just prints oppositum, so Lenzen's opposit[or]um must mean that he wants to correct De Rijk's text by inserting 'or,' but he forgets to tell us that he does not [End Page 520] faithfully reproduce the text quoted and that his square brackets mean something different from what they do in De Rijk's edition. This issue aside, his conjecture is superfluous, as proven by a parallel passage in LM II.2: 118. Similarly, he quotes Abelard as saying "alterum istorum [est]: vel nox vel dies" (152). The "[est]" is Lenzen's own, again superfluous, contribution to the text. By contrast, elsewhere he proposes to insert a non at LM II.2: 64.2. This time, he explains what he is doing, and I think his conjecture... (shrink)

The aim of this paper is to offer an alternative explanation to the notorious similitude detected in two ancient treatises on logic, namely, the Liber Peri Hermeneias, attributed to Apuleius of Madaura, and De syllogismo categorico, written by Boethius. Both were enormously authoritative in posterity. I argue that their similitude is due to the presence of an internal division of categorical propositions that Boethius gives in full in his De syllogismo categoricos, and repeats with extensions in his Introductio ad (...) class='Hi'>syllogismos categorico. The division outlines the three main parts of the theory: opposition, conversion and syllogism. This leads us to argue that similarity and correspondence of these two ancient logical treatises can be sufficiently explained from this resource, and insufficiently explained by a certain common literary source, which was proposed by Isaac, without clarifying some important dissimilarities and divergences contained in these treatises. Also, our hypothesis does not need to suppose, as Sullivan, that Boethius borrowed from Apuleius. (shrink)

La exposición es acerca de la influencia que los tratados lógicos de Boecio ejercieron sobre sus tratados teológicos. La cronología de las obras de Boecio es desde luego propicia, ya que los tratados teológicos fueron escritos después de los tratados lógicos o a lo sumo paralelamente. La idea es reconocer en los tratados teológicos la presencia de elementos y aspectos lógicos que Boecio explicó y comentó en sus monografías sobre lógica categórica el De syllogismo categorico y la Introductio ad (...) class='Hi'>syllogismos categoricos, su tratado sobre lógica hipotética (De hypotheticis syllogismis), y sus comentarios a los escritos lógicos de Aristóteles (básicamente a las Categorías y al De Interpretatione). Desde hace tiempo se sabe que la metodología usada por Boecio en sus tratados teológicos es la lógica aristotélica. La idea de este trabajo es mostrar cuáles son, en concreto, las herramientas lógicas que Boecio usa en el quinto tratado teológico titulado Contra Eutychen. El trabajo quiere hacer un aporte para aclarar y precisar cuál debería ser la actitud de quien hace de la lógica aristotélica un instrumento de la verdad, y cuál sería en particular el método boeciano en teología. (shrink)

Aristotle clearly states that in syllogistic theory local/environmental cognitive factors—external to that peculiar inferential process, for example regarding users/reasoners, are given up. Indeed, to define syllogism Aristotle first of all insists that all syllogisms are valid and contends that the necessity of this kind of reasoning is related to the circumstance that “no further term from outside is needed”, in sum syllogism is the fruit of a kind of eco-cognitive immunization. At the same time Aristotle presents a seminal perspective on (...) abduction, which contrasts with the previous one on syllogismos: the second part of the article considers the famous passage in the chapter B25 of Prior Analytics concerning ἀπαγωγή, also studied by Peirce. I contend that some of the current well-known distinctive characters of abductive cognition are already expressed, which are in tune with what I have called Eco-cognitive Model of abduction. By providing an illustration of the role of the method of analysis and of the middle terms in Plato’s dialectic argumentation, considered as related to the diorismic/poristic process in ancient geometry I maintain that it is just this intellectual heritage which informs Aristotle’ chapter B25 on ἀπαγωγή. Even if, in general, Aristotle seems to sterilize, thanks to the invention of syllogistic theory, every “dialectic” background of reasoning, nevertheless in chapter B25 he is still pointing to the fundamental inferential role in reasoning of those externalities that substantiate the process of “leading away”. Hence, we can gain a new positive perspective about the “constitutive” eco-cognitive character of abduction, just thanks to Aristotle himself. (shrink)

A study of the reception of Aristotle's Prior Analytics in the first half of the twelfth century. It is shown that Peter Abaelard was perhaps acquainted with as much as the first seven chapters of Book I of the Prior Analytics but with no more. The appearance at the beginning of the twelfth century of a short list of dialectical loci which has puzzled earlier commentators is explained by noting that this list formalises the classification of extensional relations between general (...) terms and that this classification had already be put forward by Boethius in his de Syllogismo Categorico and Introductio ad Syllogismos Categoricas . It is pointed out the kind of text referred to as an ` Introductio ' at the beginning of the twelfth-century follows very closely the structure of Boethius own Introductio and adds to it material drawn from his accounts of loci and the conditional propositions. It is argued that the reception of the Prior Analytics has to be understood against the background of this well developed tradition of treating together syllogisms, loci , and conditional propostions. Referring to a challenge to the formal validity of Darapti in the Ars Meliduna the paper concludes by illustrating that the theory of the syllogism presented in Prior Analytics was still controversial in the middle of the twelfth-century. (shrink)

El propósito de este estudio es mostrar que la discusión sobre la autoría del Peri Hermeneias atribuido a Apuleyo, asunto bien difícil de determinar a ciencia cierta, puede recibir elementos de juicio interesantes desde la aclaración de que el De syllogismo categorico de Boecio y el PeriH de Apuleyo son similares entre. Así, este artículo pretende evidenciar que no sólo la exposición sobre lógica aristotélica que hizo el autor de PerH, sino también la de Mario victorino, que no nos ha (...) llegado, la de TuIIíus Marcellus Carthaginensis, que tampoco sobrevivió, y las posteriores de Boecio y Marciano Capella, son todas dependientes de la primera y original exposición de la lógica de aristotélica hecha por Teofrasto en sus analíticos Primeros, o por algún autor de su entorno. (shrink)

En este artículo se describen los contenidos de un tratado sobre lógica aristotélica escrito por Boecio en el VI d. C, llamado por nuestras ediciones modernas De syllogismo categórico. A través de sus contenidos, es posible mostrar: la importancia de este tratado en el proceso de transmisión de la lógica de Aristóteles al medioevo latino; su relación con otro tratado monográfico similar, titulado por la crítica moderna Introductio ad syllogismos categóricos y su relación temática con DSC; las fuentes más (...) probables de ambos tratados; y, finalmente, su influencia en el medioevo latino. La hipótesis que se defiende en este artículo es que los contenidos lógicos de este tratado, en particular la clasificación de las proposiciones categóricas, contenida en el corazón del DSC, entregan no solo el objeto temático al tratado, sino también coherencia argumentativa y unidad. En especial, el estudio de esta clasificación permite demostrar la unidad de DSC y en particular que el segundo libro de DSC es genuino y no espurio como sostuvieron, no hace mucho, los estudiosos Murari y McKinlay; además, esta misma clasificación permite apreciar su diferencia con ISC, por el hecho de que este último tratado posee una clasificación diferente a la de DSC. La base de la hipótesis propuesta se halla en que la clasificación mencionada es un intento por generar, a partir de los elementos preposicionales, las principales operaciones lógicas definidas por Aristóteles en sus escritos lógicos, asunto que en la revisión de De Rijk no quedó totalmente establecido. (shrink)

En este artículo se discuten las más importantes hipótesis modernas que han intentado explicar la interrelation doctrinal que los tratados silogísticos escritos por Boecio tienen entre sí, el De sylhgismo categórico y la Introductio ad syllogismos categóricos. Se revisan las hipótesis que señalan una dependencia fuerte entre ambos tratados y también las que apuntan hacia una dependencia más débil y, luego de criticar estas posiciones, la discusión abre la posibilidad cierta de que los tratados tengan objetos temáticos diferentes y (...) estén relacionados de una manera más extrínseca que lo que se había creído hasta aquí, ya que el segundo de ellos estaría pensado como un complemento al primero. El argumento se basa tanto en la manifiesta falta de utilidad que los términos indefinidos tendrían en las premisas silogísticas como en la casi nula noticia de que, alguna vez en la antigüedad, se desarrolló una silogística con términos indefinidos en las premisas. (shrink)

Of Peter Abelard's logical writings, the fruit of thirty-five years of his activity as a teacher and dialectician, there have been to date only four editions worthy of note: that of Cousin in 1836, of Geyer in 1919 and 1936, of Dal Pra in 1954, and lastly the critical reconstruction of Abelard's literal glosses by L. M. Rijk in 1956. With this handsome second edition of minor but relevant glosses of Abelard, Dal Pra aims to fill the gap still existing (...) in the previous collections. His volume includes Abelard's writings found in the Paris BN manuscripts n. 13.368 and 7493. Chronologically the former belongs to the period when Abelard was given the chair of dialectic at the University of Paris in 1114 and the latter to Abelard's more mature period when he began original speculations on the logical status of propositions in 1121. Dal Pra argues at great length that the glosses in the first manuscript are to be read as the best and only introduction to Abelard's own work on dialectic. Hence he suggests against Rijk the title Introductiones Dialecticae rather than Introductiones Parvulorum. He assembles them according to what he believes was Abelard's intellectual development at the time. They are: the glosses to Porphyrius, to Aristotle's Categories, to the De Interpretatione, and to Boethius' De Devisione. [[sic]] The second section of the volume contains the glosses Super Topica where Abelard discusses among other subjects his first position on the problem of universals. Against Geyer who had consigned these works to the literal glosses of Abelard, Dal Pra offers strong evidence for locating them in the bulk of Abelard's De Ingredientibus precisely between the De Interpretatione and the De Syllogismo Hypothetico. The modernity of Abelard's logical theory is well known among contemporary logicians. Dal Pra's finely planned and handsomely executed edition makes an excellent contribution to the history of medieval logic as well as to contemporary logical theories on names and propositions.--L. M. P. (shrink)

El objetivo de este artículo es mostrar los fundamentos de la investigación en la cual se ha desarrollado Silogismos, un autómata que realiza la inferencia, identifica figura y modo de los silogismos, reconoce y diferencia entimemas y sofismas; éste fue desarrollado en Prolog -una plataforma de Inteligencia Artificial (IA)- como parte de un proyecto de investigación tendiente a representar computacionalmente la mente tal y como la concibió Aristóteles, para el caso de la lógica en el Órganon, para el caso de (...) la persuasión en la Retórica, etcétera. En el §1 se presenta el contexto de esta investigación; en el §2. de manera particular, se caracteriza el aporte de la silogística a la IA y a la filosofía de la mente, en el §3 se establecen las limitaciones de la lógica aristotélica para su automatización; en el §4 se estudia la perspectiva de investigación abierta con los proyectos de automatización. (shrink)