History of Logic from Aristotle to Gödel (www.historyoflogic.com)

by Raul Corazzon | e-mail: rc@ontology.co

Bibliography on Boethius' logical works and Commentaries (A-Ebb)

Contents of this Section

Studies in English

  1. Ashworth, Earline Jennifer. 1989. "Boethius on Topics, Conditionals and Argument-Forms." History and Philosophy of Logic no. 10:213-225.

    "Eleonore Stump’s splendid translation of Boethius's In Ciceronis Topica (Ithaca and London: Cornell University Press, 1988) is a very welcome companion to her earlier translation of Boethius's De topicis differentiis (Ithaca and London: Cornell University Press, 1978). Together the iwo volumes provide us with a hitherto unequalled opportunity to come to grips with the logical work of an author whose influence on medieval and Renaissance developments in this field was surpassed only by Aristotle himself. Indeed, it was only because of Boethius, his translations and commentaries, that Aristotle was first transmitted to the Latin speaking West. The importance of Boethius's work on the Topics is not purely historical, for it offers us a valuable insight into a type of logic which is aimed not at the production of formal languages or the examination of valid inference forms, but at ways to produce belief in the context of debate and against a background of straightforwardly metaphysical doctrines.

    In this essay review I shall first make some general remarks about the nature of Topics-logic, with particular reference to In Ciceronis Topica. I shall then explore just one Topic, that of incompatibles, which is a particularly interesting Topic for several reasons. First. Boethius's attempt to define incompatibles shows the limitations of any formal approach to the material in hand. Second, Boethius's use of the Topic casts considerable light on his view of conditionals and their basis in metaphysical features of the world. Third, the examination of these issues helps explain Boethius's interpretation of certain key argument forms and their relation to Stoic logic. Finally, I shall make some remarks about Stump’s translation and notes." (p. 213)

  2. Asztalos, Monika. 1993. "Boethius as a Transmitter of Greek Logic to the Latin West: the Categories." Harvard Studies in Classical Philology no. 95:367-407.

    "...my purpose in this paper is to bring out what these commentaries, and especially the ones on the Isagoge and the Categories, reveal about Boethius’ working methods in his earliest works on Greek logic. I intend to deal less with the end product than with the road to it, and to point to the stages of development and improvement exhibited within these early works." (p. 367)

    (...)

    "Boethius devoted his first effort in Greek philosophy to Porphyry’s Isagoge, and later, in the year of his consulate (510), when he was in all likelihood in his late twenties, he spent all his spare time commenting for the first time on a work by Aristotle, the Categories. Ever since Samuel Brandt attempted a chronology of Boethius’ works on the basis of their internal references, it has been commonly held that when Boethius began commenting on the Categories, he had already written both his expositions of Porphyry’s Isagoge (hereafter Isag. 1 and Isag. 2), the first one a dialogue in two books based on Marius Victorinus’ apparently incomplete Latin version, the second a five book commentary on his own, complete translation. (2) This is certainly not the place for a full discussion of the chronology of Boethius’ works, but for the arguments of this paper it is necessary to establish the order between Isag. 2 and the commentary on the Categories (CC)." (p. 368)

    (..)

    "... I am not in a position to judge whether or not Boethius displays real originality in his later, more mature works. But I think that it would be unfair to expect novel interpretations in commentaries like the Isag. 1 and CC, which, if my assumptions in the first sections of this paper are correct, are not only the earliest of Boethius’ works on Greek philosophy but also the context in which he first encountered Aristotle. He seems to have come quite unprepared to both the Isagoge and the Categories, unarmed with proper translations and unfamiliar with the work he was commenting on. Boethius is indeed an epitome of the expression docendo discimus." (p. 407)

    (2) 2 S. Brandt, “Entstehungszeit und zeitliche Folge der Werke von Boethius,” Philologus 62 (1903), 141-154 and 234-275. See also pp. XXVI-XXIX of the Prolegomena to Anicii Manlii Severini Boethii In Isagogen Porphyrii commenta, rec. S. Brandt, Corpus Scriptorum Ecclesiasticorum Latinorum 48, Wien/Leipzig, 1906. In his “ Stylistic Tests and the Chronology of the Works of Boethius,” Harvard Studies in Classical Philology 18 (1907), 123-156, A. P. McKinley’s conclusions concerning the chronology of Isag. 7, Isag. 2, and the commentary on the Categories (hereafter CC) are the same as Brandt’s.

    McKinley studied the frequency of certain particles in these commentaries as well as in Boethius’ translations of the Isagoge and Categories, assuming that Boethius’ language was influenced by his translations of Porphyry and Aristotle. Now, some of McKinley’s data corroborate Brandt’s chronology whereas others support the one I will suggest below. Furthermore, McKinley’s tests were made before the appearance of L. MinioPaluello’s critical editions of Boethius’ translations in the Aristoteles Latinus and would therefore have to be remade. I also believe that a necessary preliminary stage in examining whether Boethius’ translating activities influenced his choice of particles is to compare his Latin commentaries with the extant Greek sources. Since there is no adequate source apparatus in any of the editions of Boethius’ commentaries, this would mean a great deal of work. Concerning the question whether Boethius wrote Isag. 2 before or after CC, L. M. De Rijk follows Brandt’s view on pp. 125-127 of “On the chronology of Boethius’ works on logic,” Vivarium 2 (1964), 1-9 and 125-162, on exactly the same grounds as the ones on which Brandt based his conclusions and without corroborating them further.

  3. ———. 2003. "Boethius on the Categories." In Boèce ou la chaîne des savoirs, edited by Galonnier, Alain, 195-205. Louvain-Paris: Éditions Peeters.

    "Among Boethius’ commentaries on Greek works on logic (that is to say, on Porphyry’s Eisagoge and on Aristotle’s Categories and Peri hermeneias), only the one on the Categories has so far not been critically edited. At present I am editing the text and at the same time preparing an English translation of it to appear in Ancient Commentators on Aristotle. (1) So far only translations of Greek commentaries have appeared in this series, and consequently the fact that Boethius’ work on the Categories will be included is a statement about his heavy dependence on Greek sources. It is of course a well-known fact that all Boethius’ commentaries on Aristotle’s works are heavily dependent on Greek Neoplatonic interpretations. However, the extent to which this is true has so far not been revealed in the form of a source apparatus accompanying the texts edited. In the case of the commentaries on the Peri hermeneias, the two volumes of which appeared in 1877 and 1880 respectively, the editor did not have access to a modern edition of the extensive commentary by Ammonius which has since appeared in Commentaria in Aristotelem Graeca. (2) But for an editor of Boethius’ commentary on the Categories the work is easier: first of all, there are a number of Greek commentaries on this work that have been edited in CAG. In addition, those by Porphyry, Dexippus, and Ammonius have appeared in commented translations in Ancient Commentators on Aristotle.

    So, while in the process of editing Boethius’ work on the Categories, I have provided the text with an apparatus indicating parallels in the Greek commentaries. A great deal of work has already been done in order to map out the nature and extent of Boethius’ dependence on the Greeks in this particular work of his. There is Bidez’ groundbreaking article “Boèce et Porphyre”, where Porphyry’s little commentary on the Categories in the form of questions and answers (3) is described as “la source unique, ou a peu près unique, du commentaire de Boèce” (p. 195); James Shier's provocative papers presenting Boethius as a translator of scholia that he allegedly found in the margins of his copy of Aristotle, some of them originating from the school of Proclus but the majority taken from Q&A; Sten Ebbesen’s article on Boethius as an Aristotelian scholar, in which Q&A is described as Boethius’ main source, a source from which he deviated when he wished to avoid introducing Neoplatonic entities such as the Eternal Mind into his own elementary work; a contribution of my own in which I claim that Boethius used Q&A but also a commentary on the Categories written by a follower and occasional critic of Iamblichus; and the valuable footnotes to Steven Strange’s English translation of Q&A with their references to Boethius’ commentary. (4) What all these different studies have in common is that they consider Porphyry’s Q&A to be Boethius’ main source.

    So, one may justifyibly ask, is there anything really new to be said about Boethius’ use of the Greek sources in his commentary on the Categories? The purpose of this paper is to show that while putting together a source apparatus for Boethius’ text I have come to the conclusion that our view of Boethius’ dependence on Porphyry needs to be modified. (5)" (pp. 195-196)

    (...)

    "To conclude: Boethius naturally used Porphyry’s extant little dialogue on the Categories. But his main source is a later Greek commentary that makes use of Iamblichus’ commentary but whose author takes an uncompromisingly Aristotelian stance. Since Iamblichus made ample use of Porphyry’s no longer extant Ad Gedalium, the influence of Porphyry is quite heavy on Boethius’ commentary. When the two sources (Q&A and the later commentary) expressed different views, for example on the scope of the Categories, Boethius did not bother to try to harmonize between the two. In that respect, he is not a full-fledged scholastic in his commentary on the Categories, which is an early work of his, at least not as full-fledged as he was to become later, when he wrote the Consolation of philosophy." (pp. 204-205)

    (1) General editor: Richard Sorabji.

    (2) Anicii Manlii Severini Boetii commentarii in librum Aristotelis PEPI EPMHNEIAS, rec. Carolus Meiser, I-II, Leipzig, 1877, 1880. Ammonius, In Aristotelis De interpretatione commentarius, ed. A. Busse, Commentaria in Aristotelem Graeca (=CAG) IV:5, Berlin, 1897.

    (3) Porphyrii in Aristotelis Categorias expositio per interrogationem et responsionem, ed. A. Busse, CAG IV: 1, Berlin, 1887. This work is henceforth referred to as Q&A.

    (4) J. Bidez, “Boèce et Porphyre”, Revue belge de philologie et d’histoire, 2, [1923] ρ. 189-201. J. Shiel, “Boethius’ commentaries on Aristotle”, Mediaeval and Renaissance Studies, 4, 1958, p. 217-244; Boethius. Ed. by M. Fuhrmann and J. Gruber. Darmstadt, 1984, p. 155-183; Aristotle transformed. The ancient commentators and their influence. Ed. by R. Sorabji. London, 1990, p. 349-372. S. Ebbesen, “Boethius as an Aristotelian Scholar” in Aristoteles, Werk und Wirkung, Ραμί Moraux gewidmet. Bd II. Ed. J. Wiesner. Berlin-New York, 1987, p. 286-311. M. Asztalos, “Boethius as a Transmitter of Greek Logic to the Latin West: the Categories”, Harvard Studies in Classical Philology, 95, 1993, p. 367-407. Porphyry, On Aristotle Categories. Translated by S. K. Strange. London, 1992.

    (5) I wish to thank Börje Bydén, Göteborg University, for his valuable comments on this paper.

  4. ———. 2014. "Nomen and Vocabulum in Boethius’s Theory of Predication." In Boethius as a Paradigm of Late Ancient Thought, edited by Kirchner, Andreas, Jürgasch, Thomas and Böhm, Thomas, 31-52. Berlin: Walter de Gruyter.

    "Anyone who tries to make sense of Boethius’s commentary on Aristotle’s Categories will be intrigued by his use of the terms nomen and uocabulum. Sometimes it is clear that he cannot be using the terms to refer to names (in our sense of the word) and words, but then how does he use them? They may appear to be interchangeable, (1) but there is a difference in how Boethius uses these terms, and it is important to establish what the difference is, given that they are essential in Boethius’s theory of predication. Then there is a cluster of verbs — uocare, nominare, nuncupare —which are clearly connected with uocabulum and nomen, but how? The purpose of this paper is to present Boethius’s thoughts on predication by exploring the way he uses these key terms.

    I will be quoting extensively from my own forthcoming edition of Boethius’s commentary on the Categories. I have not given references to the text printed in Migne’s Patrologia Latina vol. 64 but have specified which lines in Aristotle’s text the passages quoted comment on. This will make it fairly easy for readers to find the appropriate places in the Migne edition. All translations are my own.

    In Boethius’s commentary on Aristotle’s Categories, nomina and uocabula are couched in a theory involving also res, uox, significare, significatio, and designare.

    These are main protagonists in Boethius’s commentaries on the De interpretatione, a work in which nomina and uocabula take the back seat." (p. 31)

    (...)

    "Does Boethius’s use of uocabulum and nomen make him a paradigm of Late Ancient thought? In the case of nomen as a term for a mental collection of things he could to a certain extent lean on tradition, given that the word is commonly used for a collection like a family or a people in classical Latin. Furthermore, it cannot be ruled out that Aristotle uses ὄνομα in the same way. But what about uocabulum and its connection with uox and uocare? Only a study of earlier Latin texts can confirm that Boethius has introduced a new tool in the theory of predication. And it remains to be investigated whether or not medieval philosophers appreciated the value of the tool and employed it in their own discussions of predication." (p. 50)

    (1) In her recent book Boethius on Mind, Grammar and Logic. A Study of Boethius’ Commentaries on Peri hermeneias, (= Philosophia antiqua; 127), Leiden/Boston 2012, Taki Suto holds: “Even though there may be some difference in Boethius’ usage of these two expressions, the difference is slight, and he may not differentiate between them.” (p. 68, note 109).

  5. Barnes, Jonathan. 1981. "Boethius and the Study of Logic." In Boethius: His Life, Thought and Influence, edited by Gibson, Margaret, 73-89. Oxford: Blackwell.

    Reprinted in J. Barnes, Logical Matters. Essays in Ancient Philosophy II, New York: Oxford University Press, Chapter 26, pp. 666-682.

    "Boethius’ logical oeuvre contains works of three types. First, and at the centre, there are the Latin translations of the Greek texts: Boethius put into Latin the Categories, the de Interpretatione, the Prior and Posterior Analytics, (5) the Topics, the Sophistici Elenchi; and he prefaced his Latin Organon with a version of Porphyry’s Isagoge, the standard Greek introduction to Peripatetic philosophy. (6) Secondly, there are the commentaries: Boethius planned commentaries on the Isagoge and on each book of the Organon, and he added, as a supplement, a commentary on Cicero's Topics. (7) The commentaries on Aristotle's Topics and Analytics have not survived; and some scholars doubt if Boethius lived to complete his commentatorial task. (8) Thirdly, there are the treatises: On Division covered much of the ground tilled in the Categories; On Categorical Syllogisms and the unfinished Introduction to Categorical Syllogisms correspond in part to the de Interpretatione and the Prior Analytics; On Hypothetical Syllogisms has no counterpart in Aristotle’s works, but answers to a fixed feature of later Peripatetic logic; On Topical Differences matches Aristotle’s Topics. (9)

    Thus on three distinct levels Boethius translated Peripatetic logic from Greece to Rome. His achievement is remarkable by any reckoning; and his work in logic stands as a paradigm of sustained and systematic scholarship. The next three sections will discuss separately the translations, the commentaries, and the treatises; but it should not be forgotten that, for Boethius, those three types of scholarly production were complementary parts of a unitary whole." (pp. 74-75)

    (...)

    "What, then, was Boethius’ contribution to the study of logic?

    First, Boethius was not an original logician: he did not pretend to be. He saw himself as a translator, conveying Greek wisdom to a Greekless world; the insights which his works contain are not his own, his knowledge is tralaticious. From time to time we can, I believe, hear Boethius’ own voice; and some at least of the disposition and organisation of his material originated in his own head. But those touches of personality are relatively rare and relatively unimportant: the summa logicae which Boethius determined to present was traditional Peripatetic logic; and it is an error to speak of a Boethian logic.

    Secondly, it must be admitted that today we owe little to Boethius’ immense labours. He strove to transmit Aristotle to the West; but our present knowledge of Aristotle depends hardly at all on his strivings. Aristotle’s texts, and the texts of his Greek commentators, have survived in their original Greek: we can study Peripatetic logic, as Boethius himself did, in the original sources. Had all Boethius’ logical writings been lost, ihr modern student of logic would have little to bewail, apart perhaps from the treatment of hypothetical syllogistic.

    It is rather within the context of his own dark times that Boethius’ service to logic must be sought. Greek learning was increasingly inaccessible, and the Latin world was rude. By his sole efforts Boethius ensured that the study of Aristotle’s Organon, and with it the discipline of logic, was not altogether eclipsed in the West. Boethius’ labours gave logic half a millenium of life: what logician could say as much as that for his work? what logician could desire to say more?" (pp. 84-85)

    (5) The translation of the Posterior Analytics has not survived; but see AL [Aristoteles Latinus], IV. 1-4, pp. XII-XV.

    (6) For the status of the Isagoge see in Isag ed 1. 14-5. Boethius regarded the Organon, prefaced by the Isagoge, as a unitary — but not a fully comprehensive — treatment of logic.

    (7) At first blush, the commentary on Cicero seems anomalous; but in fact Cicero presents his Topics as a version indeed, a translation — of Aristotle’s Topics, and Boethius regarded Cicero’s work as forming an integral part of Peripatetic logic (in Cic Top 271-3).

    (8) (i) Topics: Boethius states categorically that he has written a commentary (Top diff 1191 A, 1209 C, 1216 D). Nothing is known to have survived.

    (ii) Prior Analytics: we possess only preliminary notes (published in AL, III. 1-4) ; at Syll cat 829D Boethius says that he will comment on the Analytics, but he nowhere asserts that he has composed such a commentary.

    (iii) Posterior Analytics: a note to a thirteenth-century commentary on the Sophistici Elenchi quotes from ‘Boethius’ commentary on Book I of the Posterior Analytics': see S. Ebbesen, ‘Manlius Boethius on Aristotle’s Analytica Posteriora, CIMAGL IX (1973), 68-9. If we believe the note, then — contrary to orthodox opinion — Boethius did write such a commentary.

    (9) The dating of Boethius’ logical works is to some extent conjectural: see the long discussion of L. M. de Rijk, 'On the chronology of Boethius’ works on logic’, Vivarium II (1964), 1-49, 125-62. His first opus was in Isag ed 1, composed in 504/5; he was probably working on Intr syll cat and in An Pr in 523; in Cat is dated to 510. There is not much awry with the following ordering: in Isag ed 1; Syll cat; Div; trans Isag; in Isag ed 2; trans Cat; in Cat; trans de Int; in Int ed ι; in Int ed 2; trans Top; trans Soph El, Syll hyp, in Top; in Cic Top; trans An; Top diff; Intr syll cat; in An Pr.

  6. Belli, Margherita. 2014. "Boethius, disciple of Aristotle and master of theological method: The term indemonstrabilis." In Boethius as a Paradigm of Late Ancient Thought, edited by Kirchner, Andreas, Jürgasch, Thomas and Böhm, Thomas, 53-82. Berlin: Walter de Gruyter.

    "Indemonstrabilis. This term belongs to the Late Latin language and is a legacy of Aristotle’s logic, especially of the Analytica posteriora. It can be considered, therefore, a useful tool to focus on three aspects of the deep and wide knowledge of the Aristotelian logic, which contributes to making Boethius a unique figure among the Late Ancient authors of the Latin West and the leading guide of the so-called boethiana aetas. The three aspects entail:

    a) the relationship between Boethius and the Author of the Peri hermeneias, as both committed themselves to transmitting the Aristotelian logic to the Latin West and to developing a suitable terminology;

    b) the methodological meanings that Boethius conveyed to indemonstrabilis, in order to open it to rational theology, through the convergence between maxima propositio and comunis animi conceptio;

    c) the way in which some 12th-century authors transformed the previous convergence into an identity, making it the starting point of a method that distinguishes theological knowledge from the other arts and places it above them all.

    From a research conducted by using the Library of Latin Texts A–B, Aristoteles Latinus Data-base, Patrologia Latina Data-base, and Repertorium edierter Texte des Mittelalters, (1) it results that indemonstrabilis was rarely employed until the first half of the 12th century, when the Analytica Posteriora came back to the Latin West, along with Aristotle’s other treatises. During the Late Antiquity indemonstrabilis was used only by the Author of the Peri hermeneias and by Boethius. It does not matter if the Author of the Peri hermeneias cannot be identified as Apuleius of Madaura, because in the worst hypothesis the Peri hermeneias must be dated no later than the 4th century, having been quoted by Martianus Capella in De nuptiis Philologiae et Mecurii. (2) Among the pages of the Peri hermeneias and Boethius’s De syllogismo categorico (505–506), In librum Aristotelis De interpretatione secunda editio (513–516), and De topicis differentiis (522–523),3 there are 16 occurrences of indemonstrabilis, which signify (for the related passages see the appendix):

    1.1.a. the first four moods in the first figure of categorical syllogism

    1.2. the Stoic hypothetical indemonstrables

    1.3.a. the maximal propositions of dialectic." (pp. 53-54)

    (1) Brepolis Latin, www.brepolis.net (accessed 30/05/2014); Patrologia Latina Database, Alexandria/Cambridge 1995–2008; Repertorium edierter Texte des Mittelalters aus dem Bereich der Philosophie und angrenzender Gebiete, ed. by Rolf Schönberger et alii, Berlin 2011.

    (2) The authorship of the Peri hermeneias is still questioned. Some scholars maintain Apuleius’s paternity of the treatise and others reject it. Among the scholars in favour are Sandy, Sullivan, Londey, Johanson, and Sallmann, whilst Beaujeu, Lumpe, Moreschini, and Harrison are contrary. See Stephen J. Harrison: Apuleius. A Latin Sophist, Oxford/New York 2000, 11; Gerard Sandy: The Greek World of Apuleius. Apuleius and the Second Sophistic, (= Mnemosyne. Supplementum; 174), Leiden/New York/ öln 1997, 38–41; Die Literatur des Umbruchs. Von der römischen zur christlichen Literatur, 117 bis 284 n. Chr., ed. by Klaus Sallmann, (= Handbuch der Altertumswissenschaft; 8,4), Munich 1997, 301; Claudio Moreschini: “Ricerche sulla tradizione manoscritta del De interpretatione pseudoapuleiano”, in: Pan 10 (1990), 61–73; David Londey/Carmen Johanson: The Logic of Apuleius. Including a Complete Latin Text and English Translation of the Peri Hermeneias of Apuleius of Madaura, (= Philosophia antiqua; 47), Leiden/New York 1987, 8–15; Adolf Lumpe: Die Logik des Pseudo-Apuleius: ein Beitrag zur Geschichte der Philosophie, Augsburg 1982, 44–46; Apulée: Opuscules philosophiques et fragments, ed. J. Beaujeu, Paris 1973, vii–viii; Mark W. Sullivan: Apuleian Logic. The Nature, Sources, and Influence of Apuleius’s Peri Hermeneias, (= Studies in logic and the foundations of mathematics; 37), Amsterdam 1967, 235–242.

    (3) Apuleius: Peri hermeneias, in: Apuleius: De Philosophia libri, ed. C. Moreschini, (= Bibliotheca Teubneriana), Stuttgart/Leipzig 1991; Boethius: De syllogismo categorico, ed. C. Thomsen Thörnqvist, (= Studia Graeca et Latina Gothoburgensia; 68), Gothenburg 2008; Boethius: Commentarii in librum Aristotelis Περὶ Ἑρμηνείας, ed. C. Meiser, II, (= Bibliotheca Teubneriana), Leipzig 1880; Boethius: De topicis differentiis und die Byzantinische Rezeption dieses Werkes, ed. D.Z. Nikitas, (= Corpus Philosophorum Medii Aevi. Byzantinoi philosophoi; 5), Athens/Paris/Bruxelles 1990.

  7. Bertagna, Mario. 2017. "Arguments and Proofs in Boethius's De topicis differentiis." In La filosofia medievale tra antichità ed età moderna: saggi in memoria di Francesco Del Punta

    edited by Bertagna, Mario, Bertolacci, Amos and Paravicini Bagliani, Agostino, 101-138. Firenze: Sismel - Edizioni del Galluzzo.

  8. Bird, Otto. 1960. "The Formalizing of the Topics in Mediaeval Logic." Notre Dame Journal of Formal Logic no. 1:138-149.

    "The Topical Difference, or more literally the Difference of the Maximal Proposition, is that by which one Topic differs from another (BDT. 1186A).

    Thus the Topic of Definition, for instance, differs from that of Whole and Part in that the Maxim of the one warrants an inference among terms in which a Definition occurs, while the other warrants an inference among terms in which Whole and Part occur.

    Topical Differences, according to Boethius, "are drawn forth from the terms constituting the question and then discoursed about" (BDT. 1186A).

    Thus in our example, it is the question, whether trees are animals, that makes it possible to appeal to the Topic of Definition, since, knowing the definition of "animal" and that trees do not satisfy it, we are warranted by the Topical Maxim to conclude that trees are not animals.

    The De Differentiis Topicis is little more than a listing of such Topical Differences with representative Maxims for each. Book II gives the compilation of Topics made by Themistius from Aristotle; Book III that of Cicero, followed by a comparison of the two. Book I is a general introduction dealing with the terms used for analysing an argument, and Book IV, the final book, considers the Topics used by rhetoricians.

    This work became the source for mediaeval Topical doctrine. It seems to be the only work Abelard used for his extensive treatise on the Topics.

    Peter of Spain made a precis of it (primarily of the second book) and provided additional Maxims in the fifth tract of his Summulae. Since this became a standard elementary text in logic from the late 13th through the 15th centuries, Boethius thus remained indirectly the auctoritas for the Topics, and this seems to have remained true even after the recovery of the Aristotelian Topic a in the late 12th century." (pp. 140-141)

    References

    BDT = Boethius, De Differentiis Topicis, in Migne, Patrologia Latina, T. 64.

  9. Bobzien, Susanne. 2000. "Wholly hypothetical syllogisms " Phronesis no. 45:87-137.

    Abstract: "In antiquity we encounter a distinction of two types of hypothetical syllogisms.

    One type are the 'mixed hypothetical syllogisms'. The other type is the one to which the present paper is devoted. These arguments went by the name of 'wholly hypothetical syllogisms'. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For instance, we find 'If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C'. The main contentious point about these arguments is what the ancients thought their logical form was.

    Are A, B, C schematic letters for terms or propositions? Is 'is', where it occurs, predicative, existential, or veridical? That is, should 'A ἔστι be translated as 'it is an A', 'A exists', 'As exist' or 'It is true/the case that A'? If A, B, C are term letters, and 'is' is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were.

    In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all taLking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one.

    I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded."

  10. ———. 2002. "A Greek Parallel to Boethius De hypotheticis syllogismis." Mnemosyne no. 55:285-300.

    "In this paper I discuss a longish anonymous scholium to Aristotle's Analytics which is a Greek parallel to Boethius' De Hypotheticis Syllogismis.

    The scholium is available in print only in Theodor Waitz's edition of Aristotle's Organon (Leipzig 1844). It is Codex Laur. 72.5, ff. 210-2, appended at the end of a manuscript of the Prior and Posterior Analytics. Dieter Harlfinger has dated this part of the codex to the second half of the 10th century (7) this gives us a terminus ante quem.

    The scholium has, I believe, so far not been recognized as a parallel to Boethius, nor has it been discussed in the literature on hypothetical syllogisms. (8) I am also not aware of any translation. The scholium is important for the history of hypothetical syllogistic, because it is the only extant Greek text that provides a close parallel to the particular theory Boethius presents in Latin. We can assume that the scholium was composed no later than the 10th century (see above). But it preserves elements of a theory that was most probably developed before the 6th century. There are a number of idiosyncrasies in the terminology, a fact that sets the text apart from all other Greek sources on hypothetical syllogistic, and thus adds to its interest.

    In the following I present the text of the scholium, a translation, and a commentary, including some general remarks about the theory the scholium preserves." (p. 286)

    (...)

    "In the commentary section it should have become increasingly apparent that the anonymous scholium on hypothetical syllogisms in Waitz is Peripatetic, and not Stoic, in its theoretical approach as well as its terminology. There are several elements of early Peripatetic hypothetical syllogistic preserved in it, although section (10) is likely to be witness to a later development of Peripatetic or Platonist hypothetical syllogisms. The most striking feature in the scholium is the large number of close parallels to Boethius' De Hypotheticis Syllogismis. Since it is rather unlikely that the scholium is based on a Latin source, we can assume that there must have been a Greek source from which both the scholium and large parts of Boethius' De Hypotheticis Syllogismis are ultimately derived." (p. 300)

    (7) D. Harlfinger, in: Paul Moraux (ed.), Aristoteles Graecus,vol. 1 (Berlin 1976), Nachtrâge, 475-80, discusses Laur. 72.5.

    (8) Except that Prantl, Geschichte der Logik im Abendlande, vol. I (Leipzig 1855), 656, quotes part of the scholium in footnote 167.

  11. Bosman, Bianca. 2018. "The Roots of the Notion of Containment in Theories of Consequence. Boethius on Topics, Containment, and Consequences." Vivarium no. 56:222-240.

    Abstract: "In medieval theories of consequence, we encounter several criteria of validity. One of these is known as the containment criterion: a consequence is valid when the consequent is contained or understood in the antecedent. The containment criterion was formulated most frequently in the thirteenth and fourteenth centuries, but it can be found in earlier writings as well. In The Tradition of the Topics in the Middle Ages, N.J. Green-Pedersen claimed that this criterion originated with Boethius. In this article, the author shows that a notion of containment is indeed present in Boethius, but is not used to define or describe the relation between antecedent and consequent, i.e., the relation of consequence, as Green-Pedersen asserted. The author then offers two interpretations of the notion of containment that are present in Boethius – a metaphysical and a semantic interpretation – and shows how these relate to the containment criterion."

  12. Cameron, Margaret. 2009. "Boethius on Utterances, Understanding and Reality." In The Cambridge Companion to Boethius, edited by Marenbon, John, 85-104. Cambridge: Cambridge University Press.

    "In this chapter, we will look at the three elements that form the basis of the theory of signification for Boethius, namely expressions, understanding and reality, and their relation to one another. Boethius did not write separate treatises on the philosophy of language, cognition or metaphysics. Instead, he wrote commentaries on Aristotelian logic. By the time he began to work on them around the start of the sixth century, the texts of Aristotelian logic were read in a fixed sequence: the first three were the Isagoge, Categories and On Interpretation, and Boethius treated topics as and when they are discussed in these texts by Porphyry and Aristotle. To grasp Boethius’ theory of signification, we must therefore gather his views on utterances, understanding and reality from a variety of places in his commentaries and put them together. As evidenced by the sheer length of the treatment of Aristotle’s brief comments on signification in his commentaries on On Interpretation, there is no question but that Boethius was aware of the importance of a theory of signification in explaining how the words we use are able to make sense to others and to refer to reality. We might expect, therefore, that Boethius’ views on language broadly cohere with his theory of cognition and metaphysics given elsewhere in the commentaries on the Isagoge and Categories. (1)

    The following sections aim to give a general overview of Boethius’ theory of signification by considering in turn what he says about expressions, understanding and reality in his logical commentaries.

    In the final section, we will consider the ways in which Boethius’ views have been variously interpreted from medieval and contemporary perspectives." (p. 85)

    (1) This is not to suggest that Boethius’ views did not change over the course of writing his several commentaries. With the exception of Aristotle’s Categories, Boethius wrote two commentaries per treatise. Here we are concerned to acquire a general overview of Boethius’ theory of signification, and we will concentrate mainly on two commentaries by Boethius, 2IS [Second Commentary on Isagoge] and 2IN [Second Commentary on On Interpretation], as well as CAT [Commentary on Categories].

  13. Casey, John Patrick. 2012. "Boethius’s Works on Logic in the Middle Ages." In A Companion to Boethius in the Middle Ages, edited by Kaylor Jr., Noel Harold and Phillips, Philip Edward, 193-219. Leiden: Brill.

    "This chapter discusses important Boethian contributions to medieval logic, in particular his definition of the problem of universals and his translation of Aristotelian logical works. It provides a brief introduction to the basic features of ancient logic relevant to Boethius's most noteworthy contributions to medieval logic. The chapter also discusses the three primary avenues of Boethius's influence upon medieval logic: his translations, commentaries, and original logical treatises. In the late ancient world, the Aristotelian and the Stoic systems of logic were considered to be incompatible rivals. The form of Aristotelian logic survived and was translated into the Middle Ages in the work of Boethius. This meant that medieval logicians learned about categorical propositions, syllogisms, and the problem of universals, rather than propositions, disjunctions, and conditionals." (p. 193)

  14. Chadwick, Henry. 1981. Boethius: The Consolations of Music, Logic, Theology, and Philosophy. Oxford: Clarendon Press.

    Chapter III. Logic Part of Philosophy or a Tool of all Philosohy? 108; Logic and Rhetoric 111; Porphyry 120; Neoplatonists after Porphyry: Iamblichus, Syrianus, Proclus, Ammonius 127; Boethius' commentaries on the Isagoge 131; Translator of Aristotle 133; The Ten Categories 141; On Interpretation 152; Future Contingents 157; The Monographs on Logic 163; Propositional Logic and the Hypothetical Syllogism 166.

    "The place of logic in the hierarchy of knowledge was one of the many matters long in dispute between the Aristotelians and the Stoics. To the Stoics 'logic' meant something wide, an independent branch of philosophy, the other two contrasted branches being ethics and 'physics' (the scientific study of nature). The Stoics could point out that this threefold classification had a basis in the Topics (A, 14) of Aristotle himself. The Aristotelians, on the other hand, treated logic almost in our modern sense as a practical instrument for the discovery of fallacies in argument on any subject, an indispensable tool for every department of human inquiry. This Peripatetic attitude, from which the title Organon derives, presupposes a narrow understanding of the discipline as concerned with propositions and syllogisms and terms.

    The Platonic tradition originally preferred to speak of 'dialectic', according to Boethius because it is a power of dividing (In Cic. Top. I, 1045B following Plato, Sophist 253d). Through its distinctions we learn to divide genera into species, and classify different things under their proper genus. But neither the Neoplatonists of Athens and Alexandria nor Boethius mark a significant difference in force between 'logical' and 'dialectical' reasoning. (1) Until the twelfth century, when an attempt was made to classify dialectic with grammar as two branches of Logica, the terms were to be used more or less interchangeably.

    The Peripatetic case for their estimate of logic is most eloquently put by Alexander of Aphrodisias in his commentary on the Prior Analytics (CAG II, 1) in a way that makes minor concessions to the Platonic tradition. We have a number of late Platonist accounts of this dispute, e.g. the commentaries on the Prior Analytics by Ammonius (CAG IV, 6 pp. 811) and Philoponus (CAG XIII, 2 pp. 69). It is incautious to assume with Courcelle that Boethius had Ammonius before him when writing his second commentary on Porphyry in which the dispute is discussed. (2) One major element in Boethius' argument there, that logic is not confined by the limits and aims of other parts of philosophy, and is not restricted to a particular set of questions, stands without parallel in Ammonius. It is difficult to affirm a literary relation when one is dealing with a convention of the schools which every Neoplatonic teacher will think it his duty to expound." (pp. 108-109)

    (1) The contrary is asserted, on a waferthin basis, by G. Pfligersdorffer, ['Zu Boethius, De Interpr. ed sec. I p. 4, 4 sq. Meiser nebst Beobachtungen zur Geschichte der Dialektik bei den Römern'], Wiener Studien 66, 1953, 131-154.] p. 152.

    (2) P. Courcelle, Les Lettres grecques en occident (1948), p. 272 = Late Latin Writers (1969), p. 288.

  15. Clark, Joseph T. 1952. "Boethius and Analytical Techniques." Philosophical Studies of the American Catholic Philosophical Association no. 3:35-37.

  16. ———. 1952. "Boethius and Material Implication." Philosophical Studies of the American Catholic Philosophical Association no. 3:37-38.

  17. Conti, Alessandro D. 2016. "Relations and Relatives in Boethius's Commentary on the Categories: the Invention of Monadic Two-place Predicates." Documenti e studi sulla tradizione filosofica medievale no. 27:107-129.

    Abstract: "That of ad aliquid is the most problematic category among the ten listed by Aristotle in the homonymous treatise. In Late Antiquity and the Middle Ages many authors attempted to develop new formulations of the Aristotelian theory of relatives, since Aristotle’s account of ad aliquid in the Categories is imprecise and incomplete. From a purely theoretic point of view, in Late Antiquity the most successful attempt to improve the Aristotelian doctrine was that of the Greek Neoplatonic commentators. They were able to elaborate a notion of relation (schesis) almost equivalent to a hypostatization of our modern notion of two-place predicates, as they conceived of relations as abstract forms whose distinctive feature was the property of being present-in and joining two different substances at once. Yet, for the history of Medieval philosophy, far and away the most influential attempt to clarify Aristotle’s text was that of Boethius, who, faithful to Aristotelian teaching, maintained that relation was an accident (we could say ‘a property’) which was-in a substance (its substrate of inherence) and simply entailed a reference to another, without inhering in it.

    Thus, unlike Greek Neoplatonic commentators of the Categories (and modern logicians as well), Boethius did not think of a relation as a two-place predicate, but he seems rather to consider it as a sort of monadic two-place predicate, or function. The difference betweenBoethius’s conception and ours is that according to him each relation has only a place empty for individual variables and the other filled by an individual constant. The paper is aimed at clarifying the legacy Boethius left to the Medieval thinkers in relation to the theory of ad aliquid, namely the logical and terminological apparatus drawn up in order to solve the chief problems raised by the seventh chapter of the Categories, with the general interpretative context in which the apparatus itself was set."

  18. Correia, Manuel Antonio. 2001. "Boethius on Syllogisms with Negative Premises." Ancient Philosophy no. 21:161-174.

    "According to Aristotle, no syllogism is conclusive with two negative premisses (Prior Analytics i 4.41 b7-9). The observation is a central rule of his Theory of Syllogism and recognized so by ancient, medieval, and modern logicians. In ancient scholastic discussions, however, there is a case made in support of thepossibility of conclusion from two negative premisses. It takes, as an authoritative proof, a syllogism made by Plato in the Theaetetus and affirms that syllogisms with two negative premisses are more frequent in philosophical literature than one might suppose.

    The problem, recovered especially by Boethius' second commentary on Aristotle's De Interpretatione (Meiser 1877-1880), arises from considerations of the logical properties of indefinite names in categorical or simple propositions." (p. 161)

    (...)

    "The question of whether Plato was conscious of the syllogistic technicality that Boethius indicates is surely controversial. We can instead try to resolve the question of whether this syllogism can be reasonably derived from Plato.

    Meiser's edition gives a valuable notice: the syllogism in question can be found at Theaetetus 186. In fact, the exact passage seems to be Theaet. 186c5-e10." (p. 168)

    (...)

    "I have argued that the case of a syllogism in Plato's Theaetetus, where two apparent negative premisses draw a conclusion, is simply a confirmation of the rule that there are no syllogisms with negative premisses and not, as Boethius suggests, a proof that a universal negation like 'Every man is not just' is equivalent to another one like 'Every man is not-just'. I have discussed this equivalence and similar ones arising from singular, particular, and unquantified propositions.

    but the result is that if the equivalence in question does work, it cannot be a characteristic of every categorical proposition. Indeed, even though formal proofs can be provided for some cases of categoricals, unquantified ones are explicitly stated as consequences by Aristotle (,A man is not just' follows from' A man is not-just', but not vice versa). Moreover, equivalences are indeed inconsistent with the principle that there is only one negation for a single affirmation, which Aristotle emphasizes in De Interpretatione and Prior Analytics. In the end, the question of which was Aristotle's idea of logic arises: whether a formal idea or a dialectical one (i.e., one compatible with the principle that an affirmation can have only one negation)." (p. 174)

  19. ———. 2009. "The Syllogistic Theory of Boethius." Ancient Philosophy no. 29:391-405.

    "Boethius played an important role in transmitting logic to the Latin West. His translations, commentaries, and treatises deal amply with the most important thesis of Aristotelian logic, a theory whose influence is perceptible even in the last century (cf. Corcoran 2009 [‘Aristotle’s Demonstrative Logic’ History and Philosophy of Logic, 30: 1-20]). Two of his surviving logical treatises have traditionally received the title of ‘syllogistic’, the Introductio ad syllogismos categoricos (=ISC) and De syllogismis categoricis (=DSC), but DSC is the only one explaining syllogistic, for ISC does little more than mention, belatedly in the course of the text, its being an introduction to syllogistic." (p. 391)

    (...)

    "Since there has been much discussion concerning the literary unity of DSC’s two books and its relation to ISC—including attempts to take book 2 of DSC as book 2 of ISC (which would be the actual Introductio Boethius wrote), it is my purpose to argue that DSC proposes a unitary view of Aristotelian logic, in which syllogistic comes to be the third of the three branches organizing the main logical inferences of the theory: opposition, conversion, and syllogism. Accordingly, DSC is indivisible from a doctrinal point of view and no book of DSC can be the part of the other treatise. This discussion is long overdue and it should contribute to understanding the scope of the respective treatises and their relation to each other." (p. 393)

  20. ———. 2012. "Boethius on the Square of Opposition." In Around and Beyond the Square of Opposition, edited by Béziau, Jean-Yves and Jacquette, Dale, 41-52. Basel: Birkhäuser.

    Abstract: "This article intends to reconstruct the textual tradition of the square of oppositions from the earliest textual sources just as treated in Boethius’ commentaries on Aristotle’s De Interpretatione and his treatises on syllogistic, De syllogismo categorico and Introductio ad syllogismos categoricos. The research discovers two different tracks. One way comes from Plato’s Sophist and Aristotle’s De Interpretatione, and the aim is to distinguish contrariety from contradiction. The second influence also starts from Aristotle, but now in connection with his Prior Analytics and its commentaries and treatises on categorical syllogistic, where the aim is to show the square as one of the three main chapters of the complete theory of categorical logic. I suggest that this double ingredient has accompanied the development of the square from the very original beginning of logic."

  21. ———. 2017. "Logic in Apuleius and Boethius." Revista portuguesa de filosofia:1035-1052.

    Abstract: "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 (II AD), and De syllogismo categorico, written by Boethius (VI AD).

    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 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 (1953), without clarifying some important dissimilarities and divergences contained in these treatises. Also, our hypothesis does not need to suppose, as Sullivan (1967), that Boethius borrowed from Apuleius."

    References

    Isaac, I. Le Peri hermeneias en Occident de Boèce à Saint Thomas. Histoire littéraire d’un traité d’Aristote. Paris: J. Vrin, 1953.

    Sullivan, M.W. Apuleian Logic. The Nature, Sources and Influence of Apuleius’s Peri Hermeneias. Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland, 1967.

  22. Cranz, Edward F. 2006. "Boethius and Abelard." In Reorientations of Western Thought from Antiquity to the Renaissance, edited by Struever, Nancy, 1-20. Aldershot: Ashgate.

    "Let me conclude with two brief general addenda. First, I have tried to outline the main development of Abelard's logic and the one most dependent upon Boethius. What we have seen may be summarized by saying that, where Boethius closely connects, sometimes even identifies, intellections, universals and propositions with 'res' or beings, Abelard shifts all these relationships to a new context and then denies them all: intellections, universals and propositions are not 'res'' as physical things. To repeat a phrase; he desubstantializes them all.

    But Abelard never stops thinking. Sometimes his conclusions are more new questions than new answers, and his second treatment of a problem is sometimes very different from his first. Some scholars have described the last stage of his thought as a 'return to Platonism': but I think he is more creative and original. He has changed Boethius' res into 'physical things,' and he has denied that intellections or meanings were 'physical things' and turned them into 'nothings.' But there are hints, and there is no time to analyze them here, that at the end he began to move to another new solution in which meanings from having been nothings turn into the ultimate realities. If I had to suggest parallels to his last stage, Petrarch, Lorenzo Valla and Nicholas of Cusa come to mind. So if I have tried to describe Abelard's transformation of Boethius, what was left, and I don't believe it was ever completed, might be called Abelard's transformation of Abelard.

    Second, while Abelard's writings had no wide dispersion and while he was not followed by any school or even by very many pupils, I believe his diffuse influence was greater than one might expect. The reorientations of thought one finds in his logic and elsewhere often spread more widely in his own time than did his specific ideas; they were not destroyed by the reception of Aristotle and in some ways provided a context within which Aristotle was received. So in concluding I cannot resist noting that, while I have characterized what happened as a transformation of Boethius, let us not in this group forget that it was a transformation of Boethius." (p. 20)

  23. Curley III, Thomas. 1987. "The Consolation of Philosophy as a Work of Literature." American Journal of Philology:343-367.

    "Much, in fact most of the scholarship devoted to Boethius' Consolatio has dealt with the work as a philosophical treatise. And this it certainly is. The author is almost ostentatiously conversant with Platonic, Aristotelian, Stoic, Epicurean, and neo-Platonic thought; what is more, he weaves these various strands into an organic whole. But in addition to philosophy the Consolatio is also literature. Formally, it is an example of an ancient literary genre, the Menippean Satire, a medley of alternating verse and prose, which had served the very different purposes of Petronius, the author of the Apocolocyntosis, Martianus Capella, and the mythological allegorist, Fulgentius. But even those critics who do treat the Consolatio as a work of literature too often limit themselves to tracing Boethius' sources and to indicating his influence on subsequent authors, Dante and Chaucer being the most renowned.

    What I should like to do, and the present paper is merely a premier essai in this direction, is to determine Boethius' literary purposes and to suggest what implications the literary aspects of the work may have on its philosophical content. More specifically, I shall try to explain how Menippean Satire functions in the Consolatio and why Boethius chose this medium for a philosophical treatise." (p. 343, notes omitted)

  24. de Rijk, Lambertus Marie. 1964. "On the Chronology of Boethius' Works on Logic. Part I." Vivarium no. 2:1-49.

    "The chronological order of Boethius' works appears to be a rather difficult problem. Hence, it is not surprising that the numerous attempts to establish it led the scholars to results which are neither all conclusive nor uniform. In this article I confine myself to Boethius' works on logic. Before giving my own contribution it would seem to be useful to summarize the results of preceding studies and to make some general remarks of a methodological nature.

    (...)

    My conclusion from this survey is that the best we can do in order to establish approximately the chronological order of Boethius' works on logic is to start a careful and detailed examination of all our data on this matter. In doing so an analysis of their contents seems to be quite indispensable, no less than a thorough examination of doctrinal and terminological differences." (pp. 1 and 4).

  25. ———. 1964. "On the Chronology of Boethius' Works on Logic. Part II." Vivarium no. 2:125-162.

    "We shall now sum up the results of our investigations. First some previous remarks. Our first table gives of nine of the works discussed the chronological interrelation, which can be established with a fair degree of certainty. The figures put after the works give the approximative date of their composition (the second one that of their edition); when printed in heavy types they are based on external data; the other ones are based on calculation.

    Table 1

    Boethius' birth about 480 A.D.

    In Porphyrii Isagogen, editio prima about 504-505

    In Syllogismis categoricis libri duo (= ? Institutio categorica) about 505-506

    In Porphyrii Isagogen, editio secunda about 507-509

    In Aristotelis Categorias (? editio prima) about 509-511

    In Aristotelis Perhemeneias, editio prima not before 513

    In Aristotelis Perhemeneias, editio secundaabout 515-516

    De syllogismis hypotheticis libri tres between 516 and 522

    In Ciceronis Topica Commentaria before 522

    De topicis differentiis libri quattuor before 523

    Boethius' death 524

    The rest of the works discussed cannot be inserted in this table without some qualification. (...)

    We may establish the following table for the works not contained in out first table:

    Table 2

    Liber de divisione between 505 and 509

    possible second edition of the In Categorias after 515-516

    Translations of the Topica (and Sophistici Elenchi) and of the

    Analytica Priora and Analytica Posteriora not after 520

    Commentary on Aristotle's Topica before 523

    the so-called Introductio (? = In Priora Analytica Praedicanda) certainly after 513; probably c. 523

    Scholia on Aristotle's Analytica Priora first months of 523 at the latest"

    pp. 159-161 (notes omitted).

  26. ———. 2003. "The Logic of Indefinite Names in Boethius, Abelard, Duns Scotus, and Radulphus Brito." In Aristotle's Peri hermeneias in the Latin Middle Ages. Essays on the Commentary Tradition, edited by Braakhuis, Henk A.G. and Kneepkens, Corneli Henri, 207-233. Groningen: Ingenium Publishers.

    "Aristotle's doctrine of indefinite names (nouns) was handed down to the Middle Ages together with Boethius' comments and explanations. Boethius' view of the matter has two characteristic features. For one thing, there is a certain ambiguity on his part concerning the precise semantic value of such terms; for another, Boethius deviates considerably from Aristotle in that he explicitly assigns the property of 'holding indifferently of existents and non-existents' not only to the indefinite rhéma (as it is found in Aristotle, De interpr. 3, 16b15) but to the indefinite name (onoma) as well.

    Until the end of the 12th century the logic and grammar (1) of indefinite terms (nouns and verbs) was a much debated issue. Although assiduously echoing the well-known auctoritates Medieval thinkers did not always go the whole way with their predecessors. For example, Abelard and Scotus, starting from their own philosophical tenets, more or less inconspicuously corrected some dubious elements in Boethius' interpretation of Aristotle's doctrine of the indefinite name. Peter Abelard, especially, took great pains to precisely define the meaning of indefinite terms. He focussed his attention on the proper meaning of indefinite terms rather than on the question whether they are 'holding indifferently of existents and non-existens'. In contrast, 13th-century scholars like Duns Scotus and Radulphus Brito based their discussion of the proper meaning of the indefinite name upon the question 'Utrum nomen infinitum aliquid ponat' ("Whether an infinite name posits something"), which calls to mind Boethius' claim that indefinite names 'hold indifferently of existent and non-existents'.

    Abelard's discussion of the proper meaning of the indefinite name is also interesting in that it helps us to gain a good understandiiip of what Boethius had in mind in claiming that the indefinite name 'siginifes an infinite number of things' ('significat infinita'). For, thanks to Äbelard's expositions, it becomes clear that the phrase 'significare infinita', which, on the face of it, may be taken as referring to the extensional of the indefinite name, on closer inspection proves to concern its intension, because the controversy between Abelard and Boethius turns out to be about two different views of the indefinite name's intension rather that about any opposition of intension as against extension." pp. 207-208.

    (1) For the grammatical approaches to the problem of the indefinite term in the 12th century, see C.H. Kneepkens, "Orléans 266 and the Sophismata Collection: Master Joscelin of Soissons and the infinite words in the early twelfth century", in St. Read (ed.) Sophisms in Medieval Logic and Grammar. Acts of the Ninth European Symposium for Medieval Logic and Semantics, held at St Andrews, June 1990 (Nijhoff International Philosophy Series, 48; Dordrectt/Boston/London 1993), 64-85.

  27. Dürr, Karl. 1951. The Propositional Logic of Boethius. Amsterdam: North-Holland.

    Contents: Preface VIII; Abbreviations IX-X; Introduction 1; I. The sources of "De Syllogismo Hypothetico" 4; II. The effects of Boethius' propositional logic in the early scholastic period 16; III. Choice of metascience and metalanguage 19; IV. Analysis of "De Syllogismo Hypothetico" 30; V. Analysis of a section of Boethius' Commentary on Cicero's Topics 66; Appendix by Norman M. Martin 74-79.

    Boe. = Anitii Manlii Severini Boethi . . . opera, quae extant, omnia. Basileae (1570).

    "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 "Aussagenlogik 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. René van den Driessche, "Sur le 'de syllogismo hypothetico' de Boèce", was published in the journal "Methodos" (vol. I, no. 3, [1949]). 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." (From the Preface)

    "§ 1. The Two Books of Boethius on the Theory of the Proposition.

    It is the unique property of propositional logic that the variables which are used are propositional variables, i.e. variables whose values are propositions.

    Among the logical writings of the man whom, for short, is called “Boethius’’ and whose full name is “Anicius Manlius Severinus Boethius”, we find two which can be characterized as presentations of propositional logic.

    The first of these is entitled “de syllogismo hypothetico” (on the hypothetical syllogism).

    Incidentally, it should be noted that this title, as Samuel Brandt has shown, does not originate with Boethius, and it would be more correct to give the book the title “de hypotheticis syllogismis” (on hypothetical syllogisms) (Cf. Samuel Brandt: 'Entstehungszeit und zeitliche Folge der Werke des Boethius'. Philologus, Bd. LXII (1903) p. 238). Nevertheless, one does well to quote the work under its incorrect title “de syllogismo hypothetico” as long as the old editions are in use.

    The second book is a commentary on the Topics of Cicero. Here we do not consider the entire commentary, but only certain sections; we will indicate later which sections come into consideration (Cf. infra § 38)." (p. 1)

    (...)

    "§ 4. More Precise Charactrization of Boethius' Propositional Logic.

    At the beginning of this treatise, we declared that the logic which is represented in the two works of Boethius, may be characterized as propositional logic. We add the remark that all of the sentences that have an independent value (i.e. that do not occur only as auxillary sentences) in this logic were deductive rules, or, which comes to the same thing, inference schemes.

    In this connection we recall the explanation of Clarence Irving Lewis in the book “Symbolic Logic”: “Exact logic can be taken in two ways: (1) as a vehicle and canon of deductive interference, or ( 2 ) as that subject which comprises all principles the statement of which is tautological” (Cf. ClarenceIrving Lewis and Cooper Harald Langford: Symbolic Logic (1932 p. 235). We can now say that the logic of Boethius belongs to the first of these two forms of exact logic. Boethius’ aim is not to set up sentences which are tautological, but rather to present all of the deductive rules." (p. 3)

    (...)

    § 38. The Three Enumerations of the Seven Conditional Syllogisms.

    We now turn to the consideration of the form of propositional logic to be found in Boethius’ commentary on Cicero’s Topics.

    At the beginning of the fifth book of this commentary, Boethius notes that he has treated all the hypothetical syllogisms in another book; he obviously has “de syllogismo hypothetico” in mind (Cf. Boe., p. 823). The exposition which follows this remark covers more than the first half of the fifth book of the commentary; it constitutes that part of the commentary that is of interest to us here (Cf. supra, § 1).

    In order to determine this section more precisely one can best indicate its beginning and its end. It begins with the words “de omnibus quidem hypotheticis syllogismis” (Cf. Boe., p. 823) and continues to the place immediately preceding the following words of Cicero, “proximus est locus” (Cf. Boe., p. 934).

    Boethius notes that Cicero mentioned some modi (inference types). From the exposition that follows, it is to be assumed, that Boethius identifies the modi that Cicero mentioned with the system of the seven conditional syllogisms (Cf. Boe., p. 823). By conditional syllogisms we understand inference schemes.

    At the place which Boethius has in mind, Cicero enumerates seven inference schemes. Boethius quotes this place in the fifth book of his commentary (Cf. Boe., p. 817). We will call the quotation of this place from Cicero’s Topics in Boethius’ commentary “the quotation”.

    In the text of the commentary as given by the editions we find the seven conditional syllogisms enumerated three times. The first and the second enumerations precede the quotation, while the third follows it (Cf. Boe., p. 831-833). It may be mentioned that the second enumeration agrees so closely with the first, that it may be called a duplication of the first.

    Propositional variables are used only in the third enumeration of the seven conditional syllogisms; the system of propositional variables which we called the simple system is used (Cf. supra, § 17). In all three enumerations each of the conditional syllogisms is illustrated by an example. These examples are expressions related to the inference schemes; like the inference schemes, they contain functors and always contain a sign which can be identified with the functor “igitur”; they contain however no propositional variables, instead having simple, i.e. atomic, sentences.

    The examples of conditional syllogisms which Boethius gives with the first and second enumerations, are extremely simple and the two sequences agree almost completely member for member.

    We will quote these examples in English; in this translation the English word “therefore” occurs instead of the functor “igitur” It seems desirable to divide the seven conditional syllogisms into four groups; we will divide them in such a way that the first and second modi constitute the first group, the third modus constituhs the second group, the fourth and fifth modi the third group and finally the sixth and seventh modi form the fourth group." (pp. 66-67)

  28. Ebbesen, Sten. 1973. "Manlius Boethius on Aristotle's Analytica Posteriora." Cahiers de l'Institut du Moyen-Âge Grec et Latin no. 9:68-73.

    "A reference to a Boethian commentary on Posterior Analytics I is found in a thirteen th-century MS (Munich, clm 14246), but this is surely an error. The work referred to was really the translation of Philoponus’ commentary that most schoolmen attributed to Alexander of Aphrodisias. I regret having called attention to the Munich MS in a small article of 1973 (CIMAGL 9: 68–73), and I beg my readers not to waste their time on looking up that article." S. Ebbesen, "The Aristotelian Commentator" in John Marenbon (ed.). The Cambridge Companion to Boethius, Cambridge: Cambridge University Press, 2009, p. 52.

  29. ———. 1987. "Boethius as an Aristotelian Scholar." In Aristoteles. Werk und Wirkung. Paul Moraux zum 65 Geburtstag gewidmet - Band 2: Kommentierung, Uberlieferung, Nachleben, edited by Wiesner, Jürgen, 286-311. Berlin: Walter de Gruyter.

    Reprinted as Boethius as an Aristotelian Commentator in: Richard Sorabji (ed.), Aristotle Transformed. The Ancient Commentators and Their Influence, London: Duckworth, 1990, pp. 373-392.

    Citations are from the reprint in Sorabji 1990.

    "It has been suggested that the only material at Boethius' disposal was a copy of the Organon with marginal scholia, and that this collection of scholia is no longer extant. (14) We may often be able to ascertain the remoter origin of one of the scholia Boethius knew, but we shall never know whether he deviated from his direct source in any way and the standard answer to the question 'Why does Boethius say this?' can only be, 'Because it was in his only source.'

    The 'one source - no thinking' theory has the support of eminent scholars and it cannot be refuted by any means that I can think of. But neither can it be proved by any conceivable means short of finding the supposed manuscript of the Organon with the marginal scholia. To my mind, the circumstantial evidence in favour of this theory, though not negligible, is less than convincing. (15) The observable facts are quite as easily explained on the assumption that Boethius had access to several Greek monographs and commentaries and that he followed the common practice of using for each work one main source while also exploiting secondary sources. It is an old discovery that this hypothesis works well in the case of the extant short commentary on the Categories, the only case in which we still have what may be the main source. Boethius acknowledges a debt to Porphyry (16) and actually keeps so close to the latter's extant minor commentary on the Categories (CAG 4, 1) that it is simpler to assume that he had direct access to a complete copy of it than to assume second-hand acquaintance by way of a book which also contained the post-Porphyrian material detectable in Boethius' commentary.

    Granted that Boethius' main source was Porphyry's extant work, we can begin to examine the way he used it. As it turns out, he follows his predecessor to the extent of reproducing most of the questions he raised and the answers he gave, but not to the extent of reproducing long segments of his text in direct translation. Boethius expanded arguments which he found too compressed while curtailing or suppressing other passages. (17) In fact, he followed the procedure which his own remarks in this and other works indicate (18) -- and that procedure involved making choices. It looks as if it might be worth while to speculate about his possible motives for choosing as he did." (pp. 376-377; note 15, 17 and 18 omitted)

    (14) J. Shiel, 'Boethius' Commentaries on Aristotle': Medieval and Renaissance Studies 4, 1958, 217-44, extensively revised in Chapter 15; id, 'Boethius and Eudemus', Vivarium 12, 1974, 14-17; id, 'A recent discovery: Boethius' notes on the Prior Analytics', Vivarium 20, 1982,128-41.

    (16) Boeth. in Cat. 160A; see n. 20 below.

  30. ———. 2003. "Boethius on the Metaphysics of Words." In Boèce ou la chaîne des savoirs, edited by Galonnier, Alain, 257-275. Louvain-Paris: Éditions Peeters.

    Reprinted in: S. Ebbesen, Greek-Latin Philosophical Interaction. Collected Essays of Sten Ebbesen Volume 1, Aldershot: Ashgate, 2008, pp. 115-128.

    "Boethius distinguished himself from most panegyrical orators by having pursued the study of the words he lived by beyond ordinary grammar and rhetoric school. He may not have delved deeply into the theory of grammar, but his works on topics demonstrate a live interest in the borderland between rhetoric and logic, and he spent much time on Aristotelian logic. He saw logic as fundamentally a language science: logic and grammar study the same matter, he says; but though logic gives a deeper understanding of language than grammar, it cannot replace grammar, for they study the subject from different points of view.

    We might expect Boethius to have thought about the question “What is a word” and the related questions “What is a phrase?” and “What is a sentence?” (pp. 257-258, note omitted)

    (...)

    "Boethius’ discussion of molecular propositions is revealing of his way of thinking. A conjunction of propositions is semantically several propositions, but a conditional is somehow one proposition: ‘If it is day there is light’ does not signify several things, but rather one “following”, one consequently as he says, translating the Greek ακολουθία. In other words: it takes two facts to make two conjoined propositions true, but only one to make a conditional true. A fact that can be described in a conditional is at least as good a fact as one describable in a categorical proposition.

    One might think Boethius should have distinguished between assertion and signification; he could have held that the conditional signifies whatever the antecedent signifies and whatever the consequent signifies, whereas it asserts that one follows from the other. Boethius actually had the necessary tools for so doing. The verb “proponere”, which does occur in the context, would do nicely for “assert”.

    I doubt, though, that he would have embraced the recommendation with alacrity. If I am not mistaken, his intuition was that words signify real things, and things are more real the more they are understood as unit-seeds capable of unfolding in multiplicity. Consequents of true conditionals really are contained in their antecedents in the sense that what the whole conditional signifies is one thing the richness of which may be gauged by seeing it unfold in a conditional. (34) (pp. 272-273, notes omitted)

    (34) For the unity of conditionals and the antecedent-consequent relationship, see Boethius, Top. Cic. IV. 1124-1126.

  31. ———. 2008. "Boethius on Aristotle." In Greek-Latin Philosophical Interaction: Collected Essays of Sten Ebbesen Volume 1, 107-114. Aldershot: Ashgate.

    This chapter was written for the present volume, but to a considerable extent it recapitulates Ebbesen (1987) [‘Boethius as an Aristotelian Scholar’, in Wiesner (ed.) (1987) Aristoteles, Werk und Wirkung, (Berlin–New York: Walter de Gruyter): 2.286–311).]

    "Anicius Manlius Boethius (d. c.525) was the great mediator between ancient Greek and medieval Latin philosophy. He completed a tremendous piece of work by translating all of the Organon (except, it seems, the Posterior Analytics) into Latin and writing commentaries as well as other companion volumes. It is remarkable that there are two commentaries of his on Porphyry and two on Perihermeneias, but only one on the Categories. Actually, there may have existed a second one on that work too, but at least it did not survive for the medievals to use. (2) As for the Ars nova, Boethius himself refers to a commentary on the Topics (3) of which there is no trace in later times. It is uncertain whether he accompanied his translation of the Prior Analytics with a commentary (the question is discussed in Chapter 13 [Analysing Syllogisms or Anonymus Aurelianensis 111 - the (presumably) Earliest Extant Latin Commentary on the Prior Analytics and its Greek Model, pp. 171-186] Boethius’ monographs on categorical and hypothetical syllogistic, on divisions and on topical argumentation were intensely studied from the late eleventh to the early thirteenth century, and they left their mark on Latin logic long after they ceased to be standard reading. A commentary on Cicero's Topics was less influential.

    Finally, it must be mentioned that Boethius composed treatises on the quadrivial arts: arithmetic, music, geometry (uncertain, not extant), and just possibly astronomy •as well. In one famous passage he himself reveals a grandiose plan to translate the whole of Aristotle and Plato. (4)

    Remarkable as the list of Boethius’ accomplishments is, two lacunas stand out. There is no grammar at all and no proper treatise on rhetoric, only the somewhat related commentary on Cicero's Topics and the fourth book of De topicis Differentiis, which was actually used as a textbook of rhetoric in medieval Paris. We can only guess at the reasons, but quite possibly Boethius thought of grammar and rhetoric as sub-philosophic disciplines. After all, as opposed to logic and the quadrivial arts, grammar and rhetoric had traditionally been taught by their own professional teachers, not by philosophers. (5) Moreover, he may have felt that such existing handbooks as Donatus’ Ars were sufficient for the grammatical needs of the Latin world, and there surely was no dearth of rhetorical treatises in the tongue of Cicero." (p. 108)

    (...)

    "So. the way 1 read Porphyry and Boethius, they shared the view that becoming a good Aristotelian is a necessary step on the way to becoming a good Platonist, and what you have learned in the first step of your intellectual career does not become false when you ascend to a higher level -- you are just able to put it into a much wider context.

    The medieval West inherited from late antiquity numerous texts that could help send people off on fanciful Neoplatonic stratospheric flights. The fact that Boethius provided them with a proper set of down-to-earth, but still interesting, logic books ensured that quite a few preferred safer and saner flights closer to the surface of mother earth, or at least tried to secure proper ground support before lifting off." (p. 114)

    (2) See P. Hadot, "Un fragment du commentaire perdu de Boèce sur les Catégories d'Aristote dans le codex Bernensis 363", Archives d'histoire doctrinale et littéraire du Moyen Âge, 26, 1959, pp. 11-27.

    (3) Boethius. Top. Diff. 2.8.8 (PL 64 1191A) and 4.13.2 (PL 64: 1216D).

    (4) Boethius. Comm. Int. ed. 2a. Weiser, pp. 79-80.

    (5) For the quadrivium as the philosophers' domain, see I. Hadot, Arts libéraux et philosophie dans la pensée antique. Contribution à l'histoire de l'éducation et de la culture dans l'antiquité. Seconde édition revue et considérablement augmentée. Paris: Vrin, 2005.

  32. ———. 2009. "The Aristotelian Commentator." In The Cambridge Companion to Boethius, edited by Marenbon, John, 34-55. Cambridge: Cambridge University Press.

    "The point, then, is that we have to start from the lowest level to work our way toward the higher. We have to learn our grammar before we can get a deeper understanding of language-related matters by studying logic.

    We have to achieve a simplified understanding of logic before we can undertake an in-depth study. We have to know our logic properly before we can ascend to higher matters, such as Neoplatonic metaphysics, in the light of which our initial understanding of logic will appear primitive.

    This way of looking upon thingswas not Boethius’ invention. In its essentials it was already Porphyry’s, it was what allowed Porphyry to include the study of Aristotle in a curriculum aimed at producing good Platonists ready to take leave of their bodily frame. As Aristotle’s logic was supposed not to have trespassed on Plato’s metaphysical territory, teachers of Aristotle need not and ought not Platonize him. Boethius’ extant commentaries evince a decision to follow Porphyry, though he was clearly sympathetic to some of the more extravagant Neoplatonists – people of the stripe of Iamblichus, Syrianus and Proclus – and it makes one shudder to imagine what the “Pythagorean” exposition of the Categories that his extant commentary says he was contemplating was or would be like." (p. 51)

  33. ———. 2011. "Boethius as a Translator and Aristotelian Commentator." In Interpreting the Bible and Aristotle in Late Antiquity. The Alexandrian Commentary Tradition between Rome and Baghdad, edited by Lössl, Josef and Watt, John W., 121-133. Farham: Ashgate.

    "Virtually the whole of Boethius’ literary output – including his final Consolation of Philosophy – may be viewed as a Herculean effort to transfer Greek philosophical thought to Latin, but only his Latinizations of the works of the Organon were strictly speaking translations. The commentaries and companion volumes are free adaptations of Greek prototypes. Exactly how free is difficult to gauge because in all cases but one we are sure that we no longer possess any of the Greek texts he used. The exception is Porphyry’s commentary on the Categories.

    There is some scholarly disagreement about whether he used that text directly or only indirectly, but if he did have direct access to it, as I believe, he did not at all follow it slavishly. In any event, even if he made a very free use of his Greek sources, producing the commentaries and companion volumes involved a considerable amount of translation, because he had to find out how to render all the technical terminology of his sources in Latin.

    Boethius did not have to start from scratch. Already in the first century B.C., Cicero and Varro had coined Latin equivalents of many philosophical terms, and more had been added over the centuries. In fact, for most of the technical terms of logic Boethius could depend on his predecessors. He was probably the first to use subalternus and subcontrarius when dealing with the square of opposition, and he was almost certainly the first to translate ἀξίωμα ‘axiom’ as maxima propositio, which is the origin of the English – and pan-European – maxim. But more often than not he would use an existing translation. His problem was rather one of choice, because in several cases Latin usage was not uniform. (pp. 123-124)

    (...)

    "In the short run, Boethius’ translations, commentaries and monographs met with no success, due to the collapse of the political structure and of higher schooling in the western part of the Roman empire shortly after his death. In the long run, he was immensely successful.

    Use of his works began slowly in early Carolingian times, but by 1100 his translations of Porphyry, Categories and Perihermeneias were in common use in several schools, and so were his commentaries on those works and his handbook-like works. By about 1120 people were beginning to also use his translations of the Prior Analytics, the Topics and the Sophistical Refutations.

    This laid the foundation for the Aristotelian scholasticism that was to dominate the study of philosophy in the West for some four centuries. It also meant that it was Boethius’ choices that decided what was to become the technical vocabulary of Latin Aristotelian logic." (p. 124)

  34. ———. 2016. "Boethius as an Aristotelian commentator." In Aristotle Transformed: The Ancient Commentators and Their Influence, edited by Sorabji, Richard, 403-421. New York: Bloomsbury.

    Second revised edition; first edition London: Duckworth 1990, pp. 373-391.

    "In periods when the scholastic attitude to the auctores prevails, the exegesis of the classics of philosophy acquires great importance. By the year 500 a considerable number of commentaries and auxiliary treatises relating to the works of Aristotle and Plato had been written in Greek. Quite a few would be available to anyone with the will and the fi nancial means to obtain them. But in spite of an attempt in the fourth century to produce a Latin scholastic library,(3) philosophy had not come to Latium. It had to wait for Boethius. How little his predecessors had achieved may be gauged from the fact that he has no standard Latin equivalents for several elementary Greek terms. To render organon (instrument) he feels obliged to use a hendiadys, ferramentum et quodammodo supellex.(4) For phantasia he uses visum. The term had been coined by Cicero five hundred years earlier, but Boethius introduces it in a way which shows that he expects his readers to be as unfamiliar with it as were Cicero’s contemporaries.(5) To benefit from Plato’s and Aristotle’s useful writings a mastery of Greek was still required." (pp. 403-404)

    (3) Texts relating to the Organon: Isagoge (free translation) + commentary + monograph on definition, all by Victorinus; paraphrase of Cat. (= ps.-Augustine, Categoriae Decem); paraphrases of An. Pr. and An. Post. by Themistius, translated by Praetextatus; monograph on hypothetical syllogisms by Victorinus. It is very doubtful whether there was a translation or paraphrase of Int. ; possibly Apuleius’ Peri Herm. was used. Instead of Aristotle’s Topics, Cicero’s was read; Victorinus composed a commentary on it. Cf. on these matters, P. Hadot, Marius Victorinus, Paris 1971.

    (4) Boeth. in Isag.1 10; cf. in Isag.2 93.

    (5 Boeth. in Isag.2 25: the Greeks call them phantasiai, we may call them visa. Cicero Acad. 1 40: which they call phantasia we may call it visum.