Selected Bibliography on Abelard's Logic and Ontology. Second Part Ham - Mar

Hamelin, Guy, and Maia, Danilo Luiz Silva. 2015. "Nominalism and Semantics in Abelard and Ockham." Logica Universalis no. 9:155–190.

Abstract: "Peter Abelard and William of Ockham represent the two main figures of the nominalism of the Middle Ages. Both share the fundamental thesis of that doctrine, according to which only individual entities exist.

The repercussions of nominalism are quite evident in relation to the question of universals, which constitutes a subject that, until now, won the attention of the majority of contemporary studies on the two most important logicians of their time. Nevertheless the nominalism of each of these two protagonists apparently diverges in a significant manner, especially in respect to the role exercised by the mind in the semantic process. Ockham seems to distance himself definitely from his predecessors, including Abelard, when he transfers grammar and semantic functions of conventional language to the level of mental language. In the present article, the chief intention is to expound the theory of sign and signification of each of the authors under consideration. The ultimate objective is to compare their respective semantic positions and indicate the principal points of agreement and disagreement, keeping in mind the hypothesis according to which these two medieval nominalists should have more theoretical elements in common than not."

Hansen, Heine. 2024. "Abelard’s Ontology of Forms: Some New Evidence from the Nominales and the Albricani." Open Philosophy no. 7:1–13.

Abstract: "This article concerns existents as a contentious issue in contemporary Abelardian scholarship.

More precisely, it concerns the ontological standing of forms in Abelard’s metaphysics. Take, for example, the apple on my desk. What ontological standing does its redness have? Is it an actual entity over and above the apple or is it in some sense “reducible” to it? Abelard, famously, was a nominalist, so the question is not about some purported universal redness. Rather, it is about the particular redness of the particular apple on my desk. The issue is contentious in that the best current accounts of Abelard’s metaphysics disagree strongly about how to answer this question. Here, rather than focusing on Abelard’s own writings – which so far have yielded no definitive answer – I will consider some anonymously transmitted and mainly unedited logical texts from the twelfth century and show how his contemporaries understood Abelard’s view and how the followers of his philosophical nemesis, Alberic of Paris, reacted to it."

Hellemans, Babette. 2010. "The 'Whole Abelard' and the Availability of Language." In How the West Was Won. Essays on Literary Imagination, the Canon and the Christian Middle Ages for Burcht Pranger, edited by Otten, Willemien, Vanderjagt, Arjo and de Vries, Hent, 349–376. Leiden: Brill.

"In what follows I want to point out the ‘philosophical’ implications that a distinctively Abelardian ‘questioning’ of the status of language and its provision might involve. This singular type of inquiry in order to understand the human condition is what I mean by Abelard’s ‘epistemological project.’ My hopes are modest, since the topic is extremely complex. So when I speak of ‘Abelard’, the topic is selected with the intent of demonstrating his skeptical method of understanding language within a specific historical context.(8) Such an investigation cannot be based upon some consenting or dissenting reference to Abelard in some of his works, or on the status of his work as it was shaped by the nature of his ‘profession’ (master, logician, philosopher, theologian, lover and so forth). Thus, to get a grip on Abelard’s epistemological project, I will refrain, as far as possible, from applying external categories to his work. Instead, the hermeneutical problem which underlies the (in)accessibility of ‘Abelard’, in his works as well as in the factual information concerning his historical persona, is my approach of understanding his epistemological project." (pp. 351-362)

(8) I use the term ‘skeptic’ and ‘skepticism’ with the caveat that we do not mean quite the same thing when we speak of skepticism as conceived by a thinker conditioned by a Christian Weltanschauung as when we speak of skepticism as a philosophical enterprise.

In the case of Abelard, his skeptical method of questioning can be illustrated by his famous aphorism in the prologue of Sic et Non: “By doubting we come to examine, and by examining we reach the truth.”

Hennig, Boris. 2015. "Instance Is the Converse of Aspect." Australasian Journal of Philosophy no. 93:3–20.

Abstract: "According to the aspect theory of instantiation, a particular A instantiates a universal B if and only if an aspect of A is cross-count identical with an aspect of B. This involves the assumption that both particulars and universals have aspects, and that aspects can mediate between different ways of counting things. I will ask what is new about this account of instantiation and, more importantly, whether it is an improvement on its older relatives. It will turn out that the part of it that is new is the notion of cross-count identity among aspects. As I will show, this notion is both dubious and unnecessary. I will end by presenting a simplified aspect theory of instantiation that does not involve cross-count identity."

Henry, Desmond Paul. 1985. "Abelard's mereological terminology." In Mediaeval Semantics and Metaphysics: Studies Dedicated to L. M. de Rijk, Ph. D. on the Occasion of His 60th Birthday, edited by Bos, Egbert P., 65–92. Nijmegen: Ingenium Publishers.

———. 1990. "Master Peter's Mereology." In De Ortu Grammaticae: Studies in Medieval Grammar and Linguistic Theory in Memory of Jan Pinborg, edited by Bursill-Hall, Geoffrey L., Ebbesen, Sten and Koerner, Konrad, 99–115. Amsterdam: John Benjamin.

"The paradox of the Sententie, at least in relation to the question of Abelardian authorship, is that the objections to which the piece is mainly engaged in replying evince a higher degree of generality than do the replies.

Again, the objections are for the most part coherent with well-known, if not notorious, Abelardian theses. At the same time those misdirected replies are not lacking in their own sort of mereological acumen. The fact that the objections are attributed to the partisans of voces (utterances) could suggest that the piece is an early one, dating from near to the time when Abelard was hearing the 'insane' arguments of his master Roscelin. It can be suggested that such arguments are intended to call attention to quite valid points in the mereological area (cf. HMT). The later, and more general Abelard could then have taken over the marrow of those points, thus explicating the known Abelardian nature of some of the objections themselves.

Thus in the end it may well be possible, given a progressive sharpening of our appreciation of the significance of the discussions contained in the Sententie, to hypothesise more definitively as to whether Abelard was indeed the author of the piece. One might even emit conjectures as to the point in the chronology of his works at which it could feasibly be situated.

For this, however, a more comprehensive perspective of the mereological aspects of his work is required, and this, for the moment, is lacking." (p. 114)

References

HMT = Henry, D.P. "Abelard's Mereological Terminology." Medieval Semantics and Metaphysics: Studies dedicated to L.M. de Rijky Ph.D. on the occasion of his 60th birthday, 65-92. Nijmegen: Ingenium Publishers.

———. 1991. Medieval Mereology. Philadelphia: Grüner.

Chapter 2: Abelard and His Contemporaries, pp. 64-217.

"0.1 Mereology, Ancient and Contemporary

0.11 Mereology is, strictly speaking, the theory of the part in its concrete (as opposed to abstract) sense; it may hence, by implication, deal with wholes also, although this need not necessarily be so. Systematic work on these topics was produced in 1916 by the Polish philosopher S. Lesniewski; his paper on the general theory of sets was in that year published in Moscow (cf. SLM, LF). My own acquaintance with his mereology is due to the teaching of Czeslaw Lejewski, who studied under Lesniewski."

(,,,)

"0.2 Medieval Mereology and Metaphysics

0.21 Nevertheless, the mereology covered by the present work remains within the confines of the medieval Latin West, but without in any way claiming that it was an exclusive property of that West. The temporal scope will range forward from the time of that precursor Boethius whom we may sometimes call 'the Roman' (470 - 525 A.D.) in order to distinguish him from another Boethius, namely Boethius of Dacia (flourished 1270 - 80), a Danish philosopher to whom we are to be indebted hereunder for his excellently clear elucidations. The main final figure will be Paul of Venice (c. 1369 - 1429) whose monumental embodiment of what for him was all possible logic, the Logica Magna, contains sections expressly devoted to mereology (section 8 below). The later John of St. Thomas has also been incidentally included, given his prologations of certain of Aquinas' theses (section 3.75)." (pp. 2-3)

(...)

"0.7 Summary

In brief, it has been contended above that the medieval section of the history of mereology may be recounted, understood, and appreciated in the light of an introductory exploitation

of the present-day form of the discipline, as axiomatised by S. Lesniewski and his successors. The medieval philosopher, Boethius of Dacia, has been shown to explain the theoretical location of mereology in relation to metaphysics in a way which is compatible with and corresponds to contemporary axiomatised bodies of knowledge, of the sort outlined in the Presuppositional Explicitation (section 10 below). Further, a likewise elementary version of a contemporary form of logical grammar, ultimately overlapping in its aims with the speculative grammar established by Boethius of Dacia (i.e. the resolution of grammatical ambiguity by recourse to quasi-universal grammar) has already inaugurated the task of keeping under control the logical-grammatical situation of material with which a history of medieval mereology is going to have to deal. Although by this present point applications of such grammar have been excessively elementary, it and the categorial language constituted by Lesniewski's ontology on which it is based are quite essential for any thorough understanding and appreciation of texts in which quidditative-level terms mingle with collective-class discourse (e.g. in the work of the ps-Joscelin of Soissons, or in the commentaries of Gilbert of Poitiers: cf. 2.7). It should be clear, of course, that the importation of Boethius of Dacia has not been for the purpose of using him as some sort of authority, but chiefly in order to bear witness to the continuity of the medieval and present-day disciplines, as well as to illustrate the sympathy between the two. In some respects such was also the intention of Lesniewski himself, as LSE reminds us." (pp. 30-31)

References

LF= Lesniewski, Stanislaw, Sur les Fondements de la Mathématique (fragments: traduit du polonais par G. Kalinowski) Hermes, Paris, 1989

LSE= Lejewski, C. , 'Aristotle's Syllogistic and its Extensions', Synthese, XV, 1963

SLM = Sobocinski, B., 'Studies in Lesniewski's Mereology', Yearbook of the Polish Society of Arts and Sciences Abroad, 1954-5

———. 1991. "Abelard and Medieval Mereology." In Peter Geach: Philosophical Encounters, edited by Lewis, Harry A., 49–64. Dordrecht: Kluwer.

"It is a pity that the stock story of early medieval thought tends to concentrate on something called the 'universals controversy' and does so in a way which inappropriately subsumes the twists and turns of a highly complex situation under somewhat ill-fitting headings. Although a start has now been made on a saner account of the matter both in general (1) and insofar as it affects Abelard, (2) nevertheless the usual connotations of a term such as 'realism' when applied to the topic of universals render somewhat startling the realisation that one such theory attacked by Abelard was the polar opposite of any otherworldly Platonic-style theory, namely the 'collectio' theory. It is yet a greater pity that in his attack on this theory (3) Abelard by no means does justice either to it or to his own wide-ranging account of part/ whole relations. At the time of his attack his maturer thoughts (in the Dialectica) were still to come, yet some of the essentials of that later work are already to be found in his gloss on Boethius' De Divisione, a gloss dated as belonging to the end of his first teaching phase. (4)

In II below is presented a brief and inadequate characterisation of some of Abelard's theories and themes; in III these are applied to contemporary discussions which have a bearing on his own sad fate and on that of a certain cat to whom we have been genially introduced by Professor Geach."

(1) E.g. De Rijk, Logica Modernorum (3 volumes), Van Gorcum, Assen, 1962-7; Kretzmann Article on "Semantics, History of", in Paul Edwards (ed.), The Encyclopedia of Philosophy, New York, Macmillan, 1967, vol. 7, pp. 358-406, the Cambridge History of Later Medieval Philosophy and various of the Cahiers de l'Institut du Moyen-age Grec et Latin of the University of Copenhagen.

(2) Tweedale Abailard on Universals, Amsterdam, North-Holland, 1976.

(3) Geyer, Abelard's Logica 'Ingredientibus' Munster, 1919.

(4) Dal Pra, Pietro Abelardo: Scritti di Logica, Firenze, La Nuova Italia, 1969, p XXVII: 'fin dal primo periodo del suo insegnamento' [from the first period of his teaching].

———. 1999. "Signification, Superfluity, and Indeterminacy in Abelard and other Medievals." In Signs and Signification. Vol. I, edited by Gill, Harjeet Singh and Manetti, Giovanni, 69–83. New Delhi: Bahri Publications.

"1.1. For Boethius and the medievals, signification is primarily linked with definition and understanding (intellectus). Abelard maintains these links as also does Aquinas, for example.

1.2. Definition canonically so-called is of nominal terms and is effectuated by means of genus, species, and differentia, at least where substance-names are concerned. Paronyms, or denominative names, involve incompletenesses which both Anselm of Canterbury and Abelard characterise most competently according to frameworks other than the strictly canonical. Non-canonical characterisations in general were said to be descriptions. The process of definition stricto sensu would accordingly comprise or entail sentences such as 'Man is a species', 'Animal is a genus', and so on. It was in his commentary on Aristotle's Categoriae that Boethius noted how such sentences embodied the threat of fallacious arguments such as the following: 'Man is a species; but Socrates is a man; therefore Socrates is a species'. One solution, he suggested, would be to reconstrue the 'species' of 'Man is a species' as one of the names of names (nominum nomina), the named name being in his case 'man'. Thus the middle teen of the inference becomes ambiguous, and the illation fails. At the same time, we witness the foundation of the description 'nominalism' upon this intra-linguistic analysis of propositions such as the one now in question, which superficially concern the 'universal' man, and so forth. (Ockham and Hobbes are two thinkers often characterised as nominalists, and who quite consciously and overtly preserve this nominum nomina terminology, in the same sort of context).

1.3. But although definition in the strict medieval sense thus appears to be of isolated terms, taken out of context, in practice contextual presuppositions did intervene, and this in various ways. It became common to work on the significatio of whole propositions, thus directing attention to the sense or significatio of the whole within which the defined terms were embedded. The propositions, in their turn, were taken to occur within at least three generally specifiable non-exclusive anticipated contexts, namely either that of the theoretical (or 'quidditative'), wherein definitional propositions are basic, or within that of the syllogistic (largely, the four canonical A, E, I, and O forms) or within that of usus loquendi, the context of usage, whence the classical grammarians took their starting point, and which was recognised by medieval investigators of significatio as an area distinguishable (because of its contingent irregularities) from that of special technical usages. This latter distinction is already highly marked in the work of St. Anselm (1033 - 1109). These possible varieties of presupposed context will be taken account of in my own remarks, and attention called to them when the occasion arises." pp. 69-70 (notes omitted).

Iwakuma, Yukio. 1992. "Vocales, or Early Nominalists." Traditio no. 47:37–111.

"In Section I of the present essay I present evidence that in the early twelfth-century nominalists were called vocales, a name that only later was replaced by nominales. In Section 2 I argue that ‘vocalism’ arose about 1080, one generation of scholars before Roscelin. Since Garlandus’ vocalistic Dialectica could be thought to provide evidence of an even earlier origin of the theory, Section 3 will deal with the date of this work, which has wrongly been assigned to the mid-eleventh century or earlier. Sections 4-6 will present a number of unpublished texts by vocalist authors, and the Appendix will supply editions of vocalist texts commenting on or otherwise discussing Porphyry’s Isagoge." (p. 37(

Appendix (pp. 65-133): Edition of Vocalist texts commenting or discussing Porphyry's Isagoge: I. (Petri Abaelardi (?) Positio Vocum Sententia (pp. 66-73); II. Roscelini Compendiensis (?) Disputata Porphyrii pp. 74-102); III.1 Excerpta Pommersfeldensia I pp. 103-107; III.2 Excerpta Pommersfeldensia II pp. 108-110; III.3 Excerpta Pommersfeldensia III pp. 110-111.

———. 1992. "Twelfth-Century Nominales. The Posthumous School of Peter Abelard." Vivarium no. 30:97–109.

"Otto [of Freising] says that Abelard held the 'sententia vocum seu nominum' in natural philosophy and introduced it into theology, and Walter Map says that he was 'princeps' among the Nominales. We know that Abelard was a charismatic and popular teacher, and we have no evidence at all of his followers (who must have been many) being called by any other name. We must conclude, then, that either he did not found a distinctive school or that the Nominales are that school. On the other hand I know of no text which both identifies itself as from the Nominales and calls Abelard 'our master' and no text which attributes views identified in the text as Abelard' s to the Nominales. The identification of the Nominales as Abelard's followers would, then, have to rest squarely on finding them characterized by distinctive theses which we have independent reasons to think of as in some way peculiar to Abelard.(9)" (p. 82)

(9) The need to find distinctive theses and not merely theses which Abelard and the Nominales both held is emphasized in Courtenay [1992a.

References

Courtenay, W.J., 1992a, ' Nominales ' and Rules of Inference , in: theorie = Argumentationstheorie. Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgens (Eighth European Symposium for Medieval Logic and Semantics, Freiburg i.B., May 24-27, 1988), ed. K. Jacobi, Leiden: Brill 1993.

———. 1995. "Nominalia." Didascalia no. 1:47–88.

"I have elsewhere asserted that the logic of twelfth century nominales is characterized by nine theses not shared by other rival schools, and their origins can be found in the teachings of Peter Abelard.[1] The aim of this paper is to show evidence for my assertion. For each thesis peculiar to the nominales I shall show (1) evidence to prove that it was in fact held by nominales, (2) its Abelardian origin, and (3) what the rival schools asserted on the issue concerned against the nominalists’ theory. I shall also attach as Appendix an edition of three nominalist texts which all contain discussions relevant to the universal problems."

[1] Iwakuma Y., “Twelfth-Century Nominales: The Posthumous School of Peter Abelard”, Vivarium XXX (1992), pp. 97-109, at p. 104.

———. 2004. "Are Argumentations Propositions?" In Medieval Theories on Assertive and Non-Assertive Language, edited by Maierù, Alfonso and Valente, Luisa, 81–110. Firenze: Olschki.

———. 2004. "Influence." In The Cambridge Companion to Abelard, edited by Brower, Jeffrey E. and Guilfoy, Kevin, 305–340. Cambridge: Cambridge University Press.

"In this chapter, I attempt to provide some indication of Abelard’s overall historical influence. I shall focus, however, on the influence he had on his contemporaries, taking up three areas of twelfth century logic to which contributed – areas that we would nowadays think of falling within the domain of metaphysics, philosophy of language, and logic, respectively – and then examining his contemporaries’ reactions to them. Along the way, however, I will also have something to say about the school of the Nominales and some of their distinctive theories." (p. 305)

———. 2009. "Vocales Revisited." In The Word in Medieval Logic, Theology and Psychology: Acts of the XIIIth International Colloquium of the Société Internationale pour l'Étude de la Philosophie Médiévale, Kyoto, 27 September - 1 October 2005, edited by Shimizu, Tetsuro and Burnett, Charles, 81–172. Turnhout: Brepols.

"The aim of this study is to show the struggles between the master [William of Champeaux] and his student [Peter Abelard] concerning Aristotle’s Categories before their conflict over universals. The young Abelard first brought into Paris a new wave of logic, which I shall call “proto-vocalism”, to challenge William to examine it seriously. William tried to harmonize the new logic with his basically Boethian logic. Abelard pitted himself against William, sharpening his “proto-vocalism”; but the struggles with his master finally transformed Abelard into an original logician, into becoming a “vocalist”, so to speak.

I shall divide this study into three parts. In Part I, I shall discuss some preliminary issues—my general answer to John Marenbon’s comments to my loose understanding of “vocalism”—and introduce two texts so far little known, which I focus on in this essay. In Part II, I shall show William’s attempts to harmonize the new logic, which Abelard had brought into Paris, with his basically Boethian logic. In Part III, I shall discuss an issue in which the struggles between the master and the student came to its culmination, which resulted in the renewal of Abelard’s logic." (pp. 81-82)

References

J. Marenbon, “Life, Milieu, and Intellectual Contexts”, in The Cambridge Companion to Abelard, ed. J.E. Browerr and K. Guilfoy, Cambridge 2004, 13-44. The term ‘vocalism’ was first introduced into scholarly discussion in Y. Iwakuma, “Vocales, or Early Nominalists”, Traditio 47 (1992), 37-111.

———. 2011. "Alberic of Paris on Mont Ste Geneviève against Peter Abelard." In Logic and Language in the Middle Ages: A Volume in Honour of Sten Ebbesen, edited by Fink, Jakob Leth, Hansen, Heine and Mora-Márquez, Ana María 27–47. Leiden: Brill.

"Sten Ebbesen and I have composed a list of sources which refer to the logico-theological schools of the twelfth century.(1) As a supplement to it, I have composed another list, this time covering references by name to masters in logical texts written ca. 1130–1200. In the present paper, I shall give some introductory remarks on this second list, which mainly concern the controversies between Alberic of Paris and Peter Abelard on Mont Ste Geneviève." (p. 27)

(...)

"Conclusion and Further Perspectives

I have so far discussed, in a preparatory way, major disputed issues between Abelard and Alberic, mainly from sources by the Albricani. Some opinions ascribed to Abelard are actually found in his writings, some are not. There are many other texts in my list not touched upon in the present paper. More detailed study of the list should shed new light on Abelard’s teachings on Mont Ste Geneviève in his last years—a period from which we have none of his own writings.

But I have yet another purpose in composing this new list. Our texts are always full of anonymous references to other philosophers’ theories, such as quidam dicunt, etc. My list, together with the list in ‘Logico-theological Schools’, makes it easier for us to identify those quidam, and perhaps also the provenance of anonymous texts, along the lines of what I have just shown above: B13 (not in the list of sources) is a work of an Albricanus, B14 of a Meludinensis, and B15 (not in the list of sources) of a Porretanus.

Such future studies would provide a better understanding of twelfth-century logic." (p. 43)

(1) Y. Iwakuma and S. Ebbesen, ‘Logico-theological schools from the second half of the 12th century: A list of sources’, Vivarium 30 (1992), 173–210.

Iwakuma, Yukio, and Ebbesen, Sten. 1992. "Logico-Theological Schools from the Second-Half of the 12th Century: A List of Sources." Vivarium no. 30:173–210.

"Several logico-theological schools are known to have been active in the second half of the 12th century. This is an exhaustive collection of the sources we know in which any of those schools are referred to by name. We have only omitted the Helistae , who appear solely in Glossa Promisimus (see texts in Hunt 1940/43, pp. 52-54). For the two early 12th-century schools known, Waldicelli/Waldilli and vocales, see sources in De Rijk 1966, p. 4 and Iwakuma 1992b, § 1, respectively. Our collection does not include passages in which the adjective for a school-name is attached to the name of the school-founder (e.g. Parvipontanus attached to Adam." (p. 173)

References

De Rijk, L.M., 1966, Some New Evidence on Twelfth-Century Logic. Alberic and the School of Mont Ste Geneviève (Montani), in: Vivarium, 4, 1-57

Hunt, R.W., 1941-43, Studies on Priscian in the Eleventh and Twelfth Centuries , I: Petrus Helias and His Predecessors, in: MARS, 1, 194-231; repr. in his The History of Grammar in the Middle Ages. Collected Papers (Amsterdam Studies in the History of Linguistic Science, ser. III, vol. 5), ed. G.L. Bursill-Hall. Amsterdam, 1980, 1-38.

Iwakuma, Y. [1992b], 'Vocales', or early nominalists, in: Traditio, forthcoming [1992]

Jacobi, Klaus. 1983. "Abelard and Frege: the Semantics of Words and Propositions." In Atti del convegno internazionale di storia della logica, edited by Abrusci, Michele, Casari, Ettore and Mugnai, Massimo, 81–96. Bologna: CLUEB.

"Frege was not familiar with Abelard or any of the other scholastics. There is no historical connection between the two philosophers, be it direct or indirect. When I speak on Abelard and Frege here, the theme is selected with different intentions from those for a paper on say Freqe and Leibniz. I intend to conduct a comparison in systematic perspective. This comparison cannot be based on the demonstration of an influence of Abelard on Frege undiscovered until now or upon some agreeing or dissenting reference to Abelard in Freqe's works. Thus I would like to provide you with a brief explanation of what motivated me to the comparison.

First, I wish to make clear that in selecting this theme I do not intend to open a debate on progress or regression in philosophy or the field of logic. I am not going to have the two philosophers compete with each other. I am not going to measure the one against the other. Thus no attempt will be made here to demonstrate that Abelard "anticipated" later insights of Frege or that Frege "rediscovered" earlier insights which Abelard had reached." (pp. 81-82)

———. 1985. "Peter Abelard's Investigations into the Meaning and Functions of the Speech Sign Est." In The Logic of Being, edited by Knuuttila , Simo and Hintikka, Jaakko, 1–15. Dordrecht: Reidel.

"Although Peter Abelard was the most distinguished teacher of logic of his time, a logic understood to be the science of argumentative discourse, he was not destined to found a new philosophical tradition. The historical situation offers at Least a partial explanation -- the pace of philosophical and theological research was so brisk in the twelfth century that many of the established schools enjoyed life spans of at most two or three generations of teachers. The restlessness of the times is embodied to a special degree in Abelard.(1) His writings include commentaries, in many cases several to a work, on the logical works of Aristotle and Porphyry then available, handed down in the form of Boethius' translations, and on Boethius' own logical works. Abelard has to take a number of positions into consideration here: several commentaries on Aristotle by ancient scholars, by Boethius, and by Abelard's own predecessors and teachers, and furthermore the grammatical theories of Priscian and those deriving from Abelard's contemporaries. He discovers with distinctive acumen that the tradition he is examining is disunited and full of tensions on basic questions. It is in the analysis and discussion of these tensions that he finds the field of his own philosophical research. He expects to reach solutions by intensifying the controversies, not by seeking harmony. Thus he traces argument and counter-argument in great thoroughness of detail and from a dizzying succession of points of view, abandoning theses and offering countertheses. What his students could learn from him was not so much a particular theory as his method of formulating and discussing problems.

The situation is much the same for us. If we turn to Abelard in our inquiry into the logic and semantics of the speech sign 'est', we must discover anew the questions which concerned him. In the first Part of this Paper, I will sketch some of the discussions conducted by Abelard in order to make clear in what contexts he found himself confronting questions on the variations of meaning, function, or use of the expression 'est'. In the second part, I will group various theses which Abelard deals with appropriately. It is my intention to plot out the full range of the theories discussed and to mark points of conflict. In the third and final part, I will make some cautious comments on the deeper current of unity to be observed in Abelard's reflections, a current perhaps more easily discernible to the modern eye then it was to Abelard himself." (pp. 145-146)

(1) Cf. Jolivet (1969), Chapter IV; de Rijk (1980). Also compare Häring (1975), who explains the meager transmission of Abelard's works as at least partially attributable to Abelard's style of thinking and writing. His philosophical "works" were not written as books intended to be recopied and handed down but as records of his own thinking to be used in teaching. A thesis which he adheres to with conviction at one point in his writings may reappear later or even in a reworking of the first source as being subject lo doubt or in need of revision.

———. 2004. "Philosophy of Language." In The Cambridge Companion to Abelard, edited by Brower, Jeffrey E. and Guilfoy, Kevin, 126–157. Cambridge: Cambridge University Press.

"My discussion in what follows is divided into two main parts. In the first part (§ i), I provide some general orientation to those texts and issues that are most important for understanding Abelard’s views

in philosophy of language. As we shall see, these particular texts and issues lead Abelard to place questions of semantics at the very center of his logical studies.(8) In this respect Abelard’s approach to

logic differs from that of contemporary logicians, for whom questions of possible semantic interpretations are typically secondary to the syntactic construction of a calculus. In the second, and longer part of the chapter (§§ ii–v), I turn to those aspects of Abelard’s philosophy of language that constitute his most enduring legacy, namely, his views about the semantics of terms and propositions. In the course of examining these views, we shall see that Abelard’s distinctive approach in logic is determined in large part by “metaphysical issues such as the status of universals as well as psychological topics such as the role of images in thought.”(9)" (p, 128)

(8) Cf. de Rijk 1981b, 19: “Whoever . . . speaks of semantics cannot ignore the questions of ontology and metaphysics.” Tweedale 1998, 8: “The objective grounds for logical relationships lie in what these xpressions signify.”

(9) Tweedale 1998, 8.

References

de Rijk, L. M. 1981b. Die Wirkung der neuplatonischen Semantik auf das mittelalterliche Denken über das Sein. In Sprache und Erkenntnis im Mittelalter, ed. W. Klunxen, 19–35. Berlin: W. de Gruyter.

Tweedale, M. M. 1998. Abelard, Peter (1079–1142). In Routledge Encyclopedia of Philosophy, ed. E. Craig, 196–226. London and New York: Routledge.

Jacobi, Klaus, Strub, Christian, and King, Peter. 1996. "From intellectus verus/falsus to the dictum propositionis: The semantics of Peter Abelard and his circle." Vivarium no. 34:15–40.

"In his Commentary on Aristotle's "Peri hermeneias, " (1) Abelard distinguishes the form of an expression(2) {oratio) from what it says, that is, its content. The content of an expression is its understanding {intellectus). This distinction is surely the most well-known and central idea in Abelard's commentary. It provides him with the opportunity to distinguish statements {enuntiationes) from other kinds of expressions without implying a difference in their content, since the ability of a statement to signify something true or false {verum vel falsum) cannot be found in its content. More precisely, Abelard distinguishes statements both from complete expressions (orationes perfectae) that are not statements but rather questions, requests, commands, etc. and from incomplete expressions, that is, mere word strings {orationes imperfectae), such as homo albus. These kinds of expressions, according to Abelard, do not differ in the understanding they present but in the way they present it."

(1) The text of Abelard's Commentary on Aristotle's " Perì hermeneias " was published from the Milan manuscript in Geyer [1927]. Minio-Paluello [1958] 125-8 published some additions and corrections to Geyer's edition based on the Berlin manuscript. We are preparing a new and complete edition of the full text for the Corpus chrislianorum series, to appear shortly; we give references to the page and line number of Geyer [1927], but we supply our own version of Abelard's text, which differs in some cases from Geyer.(...)

(2) We use "expression" to pick out strings of more than one word which are in grammatical agreement. A single word is not an oratio but a dictio - in our terminology, not an expression but merely a word.

(3) That a statement is an expression signifying something true or false is implied by Aristotle, who said that "not every expression is a statement, but only those in which there is truth or falsity" (Peri hermeneias 1 7a2-3), and stated explicidy in Boethius, De topicis diffrrentiis 1174B (oratio significare verum falsumve). See also 375.29-32.

References

Geyer [1927] Abelard, Logica "ingredientibus" III (Glosses on the "De interpretatione"), edited by Bernhard Geyer, Münster.

Minio-Paluello, L. [1958], Abaelardiana inedita, Roma.

Jussila, Paivi H. 1995. Peter Abelard on Imagery: Theory and practice, with special reference to his Hymns. Helsinki: Suomalainen Tiedeakatemia.

Kahn, Charles H. 1972. "On the Terminology for Copula and Existence." In Islamic Philosophy and the Classical Tradition. Essays Presented by his Friends and Pupils to Richard Walzer on His Seventieth Birthday, edited by Stern, S.M., Hourani, Albert and Brown, Vivian, 141–158. London: Bruno Cassirer.

Reprinted in C. H. Kahn, Essays on Being, New York: Oxford University Press, 2009, pp. 41-61.

"I am concerned here not with the pairing of the terms copula and existentia in the eighteenth or nineteenth century but with their separate history in the earlier period. Both Latin terms are fixed in their standard uses in medieval philosophy. The term copula occurs in Abelard and almost every later writer on logic. The technical sense of existentia (specifying the use of esse which contrasts with essentia, together with a connotation of actuality as opposed to potency) is perhaps not clearly attested before the esse existentiae of Duns Scotus. In both cases there are obvious roots for the medieval usage in classical Greek philosophy.

Yet in both cases the connection between the ancient and medieval terminology is more problematic than one might suppose." (p 42 of the reprint)

"Prantl tells us that Abelard is the first extant Latin author to use copula as a technical term for est in the categorical proposition homo est mortalis.(3) The Kneales give this as the usual view, but suggest that the term may have appeared in earlier medieval discussions of the role of est in such propositions.(4) I do not venture any guesses about the terminology of unrecorded or unpublished discussions but, as we shall see, Abelard’s early usage of the word suggests that copula was not yet a fixed term. If that is so, Abelard must be personally responsible for the classical terminology. It is clear that (as Prantl noted) the noun does not occur in the corresponding sense either in Boethius, who is Abelard’s chief authority, or in the latter’s translation of Aristotle. Boethius does use the verb copulare and its abstract noun copulatio to describe the function of est, following Aristotle’s use of the terms and It is easy enough to see how Abelard’s use of the term copula develops in a natural way out of Boethius’ language. But the impression remains that both the term copula and, in part, the theory it is designed to convey are Abelard’s own." (pp. 42-43)

(3) C. Prantl, Geschichte der Logik im Abendlande, 2nd edn. (Graz: Druck, 1885, repr. 1955), ii. 197 with n. 370. Prantl cites from the Dialectica (p. 161 in the edition of De Rijk, 1956). He did not know Abelard’s earlier work on logic, the so-called Logica ‘Ingredientibus’ (quoted below as ‘LI’ ), first published by Geyer in 1919–27, where the term copula appears in the relevant sense in at least two passages. See below.

(4) W. Kneale and M. Kneale The Development of Logic (Oxford: Clarendon, 1962), 208.

Kaldramova, Elitza. 2019. "Peter Abelard’s Conceptualism and Its Influence." Archive for Medieval Philosophy and Culture no. 25:71–81.

Abstract: "The problem of the universals is associated with the universals’ existence and reasons for classifying objects as one species or genus. It inquires what notions and their features are. The problem’s importance is related to the detailed study of dialectics and the notion. The latter is the link between sensible objects and the mind and is essential for building sentences and propositions. Abelard’s conceptualism is moderate position considering universals as notions and focusing on the linguistic and logical aspects of the problem. The ontological aspect is not excluded which is evident due to the notion of status. The influence of Abelard’s conceptualism in modern times is associated with the theory of direct reference for nouns, the account of formal validity and the theory of propositional content. Common features between Abelard’s conceptualism and Rand’s objectivism are also discussed such as the abstraction, the important role of reason, the individual and the subjective element."

King, Peter. 1982. Peter Abailard and the Problem of Universals in the Twelfth Century, Princeton University.

Available at ProQuest Dissertation Express. Order number: 8220415.

———. 2004. "Metaphysics." In The Cambridge Companion to Abelard, edited by Brower, Jeffrey E. and Guilfoy, Kevin, 65–125. Cambridge: Cambridge University Press.

"Abelard's philosophy is the first example in the Western tradition of the cast of mind that is now called nominalism. Although his view that universals are mere words (nomina) is typically thought to justify the label, Abelard's nominalism - or better, his irrealism - is in fact the hallmark of his metaphysics. He is an irrealist not only about universals, but also about propositions, events, times other than the present, natural kinds, relations, wholes, absolute space, hylomorphic composites, and the like. Instead, Abelard holds that the concrete individual, in all its richness and variety, is more than enough to populate the world."

(...)

"I’ll begin with Abelard’s antirealism about universals (§ i), since it is the key to his irrealism. It provides the foundation for his conviction that only individuals exist, a thesis that calls for further analysis of the nature of individuals (§ ii). Most individuals are a kind of integral whole, namely, a hylomorphic compound of form and matter, belonging to natural kinds. Abelard clarifies how the elements of such complex individuals are related to one another with his theory of identity (§ iii), and he develops a theory of how individuals interact to make up the world, using far less by way of ontological resources than other philosophers (§ iv). The result is a subtle and sophisticated irrealist metaphysics, one of the most interesting and original in the history of philosophy." (pp. 65-66, a note omitted)

———. 2007. "Abelard on Mental Language." American Catholic Philosophical Quarterly no. 81:169–187.

Abstract: "I argue that Abelard was the author of the first theory of mental language in the Middle Ages, devising a "language of thought" to provide the semantics for ordinary languages, based on the idea that thoughts have linguistic character. I examine Abelard's semantic framework with special attention to his principle of compositionality (the meaning of a whole is a function of the meanings of the parts); the results are then applied to Abelard's distinction between complete and incomplete expressions, as well as the distinction between sentences and the statements which the sentences are used to make. Abelard's theory of mental language is shown to be subtle and sophisticated, the forerunner of the great theories of the fourteenth century."

———. 2007. "Abelard's Answers to Porphyry." Documenti e Studi sulla Tradizione Filosofica Medievale no. 18:249–270.

"Abelard inherited a tradition that began philosophical investigation with the initial questions of Porphyry’s Isagoge, a tradition putting metaphysics, and in particular the problem of universals, at the centre of philosophy. In Abelard’s version of Boethius’s Latin translation, Porphyry’s questions are as follows: (1)

[Latin text omiited]

As regards genera and species, for the present I shall refuse to say whether they subsist or are postulated in understandings that are alone and bare and pure; or whether, if they subsist, they are corporeal or

incorporeal; and whether they are separated from sensibles or are postulated in sensibles and things going along with them." (p. 249)

"The focus here is on what Abelard understands to be involved in Porphyry’s questions and what they entail, not on the details of his critique of realist theories of universals, or even the details of his own positive account of universal words; these aren’t needed to understand Abelard’s claims about Porphyry. Section 1 focuses on Abelard’s claim that Porphyry’s questions do not have a special status. Section 2 considers Abelard’s twofold way of construing of Porphyry’s final phrase “and things going along with them.” Section 3 takes up Abelard’s strategy for dealing with the traditional reading of Porphyry’s questions. Section 4 describes Abelard’s many answers to Porphyry. I conclude by reflecting on whether Abelard’s strategy is successful." (p. 250)

(1) Porphyry, isag. 1.9–13 (...)

———. 2023. "Abelard on Existential Inference." In Metaphysics Through Semantics: The Philosophical Recovery of the Medieval Mind. Essays in Honor of Gyula Klima, edited by Hochschild, Joshua P., Nevitt, Turner C., Adam Wood, Adam and Borbély, Gábor, 21–38. Cham (Switzerland): Springer.

"On closer inspection it turns out that Abelard’s views surrounding existential import are complex. For while Abelard does talk about empty terms, and about subalternation and quantification and related matters, his discussion addresses many subtle nuances of the “problem” of existential import—or, as I shall call it to highlight its perhaps unproblematic nature and Abelard’s more general interest in it, existential inference.

The best way to begin, I think, is to take a step back from the texts and the contemporary discussion to see what is involved in existential inference of the sort at issue (§1), and then to see what Abelard has to say about it from the ground up: the distinction of the logical and grammatical parts of the simple categorical sentence (§2), his views about the nature of existential commitment (§3), and the role of quantifiers (§4). In the end, things are rather messy, and a good deal the more interesting for it." (pp. 22-23)

Knuuttila, Simo. 1993. Modalities in Medieval Philosophy. New York: Routledge.

See Chapter 2: Philosophical and Theological Modalities in Early Medieval Thought: Boethius' Modal Conceptions 45, New Theological Modalities: from Augustine to Anselm of Canterbury 62; Gilbert of Poitiers, Peter Abelard and Thierry of Chartres 75-98.

"The basic conceptions of Abelard's modal theory are to be found in a survey serving as an introduction to Chapters XII-XIII of his long commentary on De interpretatione (Super Periermenias, edited by L. Minio-Paluello, 3-47). A rather different and possibly earlier account occurs in the section on modality in the Dialectica (191.1-210.19).

According to Abelard, modal terms in the most proper sense of the word are adverbs expressing the way in which the determinant predicated of a subject inheres in it. Terms like 'necessarily', 'well' or 'rapidly' are used in this manner; some other adverbs like 'possibly' and 'falsely' are also called modals, but this is due to their position in sentences rather than to their meaning; their task does not consist in modifying actual inherences. When nominal modes (casuales), for example, 'it is necessary that' or 'it is possible that', are understood in an adverbial manner, they are in the same way divided into proper and improper modes. Abelard thinks that the reason why Aristotle treated mainly nominal modes in De interpretatione 12-13 was that they involve more problems than simple adverbial modes." (p. 83)

———. 2008. "Medieval Modal Theories and Modal Logic." In Handbook of the History of Logic, Vol. 2: Mediaeval and Renaissance Logic, edited by Gabbay, Dov and Woods, John, 505–578. Amsterdam: Elsevier.

"According to Abelard, the possibilities and necessities belonging to the individuals of a species are determined by their shared nature. What nature demands or allows and what is repugnant to it is the same for all members of a species, and what is possible is seen in what has taken place in the representatives of the species.(47) One could regard these essentialist possibilities as abstract Philonian possibilities, many of which never become or even can become actual in an individual.(48) This is one aspect of Abelard’s modal views, but there are others. He assumes that what is actual is temporally necessary at a certain point of time as no longer avoidable, but he also argues that unrealized alternatives are possible at the same time in the sense that they could have happened at that time. Some of the alternatives of a singular being are real counterfactual alternatives. These are unrealizable because of some previous changes in the conditions of the subject.

There are also merely imaginable alternatives, such as Socrates’ being a bishop, which never had a real basis in things.(49)" (p. 521)

(47) Dialectica 193.36-194.3; 385.1-8.

(48) Philo’s definitions of modal concepts are described in Boethius’s commentary on De interpretatione (II, 234.10-21). One of his examples was that it is possible for a piece of wood at the bottom of the sea to be burnt, in virtue of the fitness of the subject. See also Alexander of Aphrodisias, In Aristotelis Analyticorum priorum librum I commentarium, ed. M. Wallies, Commentaria in Aristotelem Graeca 2.1 (Berlin: Reimer, 1883), 184.6-12; John Philoponus, In Aristotelis Analytica Priora commentaria, ed. M. Wallies, Commentaria in Aristotelem Graeca 13.2 (Berlin: Reimer, 1905), 169.19-20.

(49) See the discussion of Logica ‘Ingredientibus’, 272.39-273.19, and some other texts in C.J. Martin, ‘An Amputee is Biped. The Role of the Categories in the Development of Abelard’s

Theory of Possibility’ in J. Biard and I. Catach-Rosier (eds.), La Tradition médiévale des Categories (XIIe-XIVe siècles), Philosophes médiévaux 45 (Louvain-la-Neuve: ´Editions de l’Institut Supérieur de Philosophie, Louvain and Paris: Peeters, 2003), 225-42.

———. 2010. "Medieval Commentators on Future Contingents in De Interpretatione 9." Vivarium no. 48:79–95.

Abstract: "This article considers three medieval approaches to the problem of future contingent propositions in chapter 9 of Aristotle's De Interpretatione. While Boethius assumed that God's atemporal knowledge infallibly pertains to historical events, he was inclined to believe that Aristotle correctly taught that future contingent propositions are not antecedently true or false, even though they may be characterized as true-or-false. Aquinas also tried to combine the allegedly Aristotelian view of the disjunctive truth-value of future contingent propositions with the conception of all things being timelessly present to God's knowledge. The second approach was formulated by Peter Abelard who argued that in Aristotle's view future contingent propositions are true or false, not merely true-or-false, and that the antecedent truth of future propositions does not necessitate things in the world. After Duns Scotus, many late medieval thinkers thought like Abelard, particularly because of their new interpretation of contingency, but they did not believe, with the exception of John Buridan, that this was an Aristotelian view."

———. 2012. "A history of modal traditions." In Handbook of the History of Logic, Vol. 11: Logic: A History of His Central Concepts, edited by Gabbay, Dov, Pelletier, Francis Jeffry and Woods, John, 309–339. Amsterdam: Elsevier.

"My aim is to shed light on long-lived assumptions in Western modal conceptions as well as some clashes between them. In the first section, I shall deal with those trends in ancient and medieval modal thought which were inclined to codify the meaning of modal notions in frequency terms. The second section concentrates on the emergence of a different paradigm in which the analysis of necessity and possibility is separated from a one world model, and which considerably modified late medieval modal logic. The third section is about the interplay of these traditions in the early modern period and their influence up to the nineteenth century." (p. 309)

"Abelard thought that what was actual was temporally necessary as being no longer avoidable, but he argued that mutually exclusive alternatives are possible at the same time in the sense that one or another of them could have happened at that time.(25) As distinct from Boethius’s diachronic modalities, Abelard also operates with simultaneous alternatives of the present."

(...)

"Abelard argued that future contingent statements are either true or false although they are not determinately true or determinately false, by which he means that their truth or falsity does not imply that the things which make them true or false are determinate.(28)" (p. 318)

(25) Logica ‘Ingredientibus’, 273.39–274.19; see [Martin, 2003, pp. 238–9].

(28) See [Lewis, 1987]. Later medieval authors usually regarded future contingent statements as either true or false. While Abelard ascribed this view to Aristotle as well, the majority of later writers believed that Aristotle gave up bivalence with respect to these statements; see [Knuuttila, 2010a].

References

[Knuuttila, 2010a] S. Knuuttila. Medieval commentators on future contingents in de interpretatione 9. Vivarium, 48:75–95, 2010.

[Lewis, 1987] N. Lewis. Determinate truth in Abelard. Vivarium, 25:81–109, 1987.

[Martin, 2003] C. Martin. An amputee is bipedal: The role of the categories in the development of Abelard’s theory of possibility. In J. Biard and I. Rosier-Catach, editors, La Tradition médiévale des Catégories (XIIe-XIVe siècles), pages 225–242. Peeters, Louvain and Paris, 2003.

———. 2012. "Modality." In The Oxford Handbook of Medieval Philosophy, edited by Marenbon, John, 312–341. New York Oxford University Press.

"Before the intensional modal semantics of John Duns Scotus, various new modal ideas were developed in the twelfth century. According to Abelard, what nature demands or allows and what is repugnant to it is the same for all members of a species, and what is possible in this sense for one member of a species can be derived from what is actualised in other members of the same species (Abelard 1956, Dialectica , 193:36–194:3; 385:1–8). Th is is in agreement with the traditional ideaof partial potencies, but Abelard also developed some aspects of the model of simultaneous alternatives." (p. 322)

Kretzmann, Norman. 1982. "The Culmination of the Old Logic in Peter Abelard." In Renaissance and Renewal in the Twelfth Century, edited by Benson, Robert L. and Constable, Giles, 488–511. Oxford: Clarendon Press.

"Concentrating on Abelard, whom Haskins rightly calls "one of the first philosophical minds of the whole Middle Ages" ( 351), needs no justification; if Anselm is assigned to the eleventh century, Abelard is the philosopher of the twelfth century. But why focus on the Old Logic, which had been the main secular source of intellectual sustenance since the earliest Middle Ages and which therefore scarcely qualifies as the stuff of a renaissance? Because the Old Logic is all that Abelard had,(10) and because in many respects Abelard's philosophical accomplishments are a worthy culmination of the half-millennium of the Old Logic. Abelard's contribution to the twelfth-century renaissance, the single most important philosophical contribution, is not that of a sower nor that of a reviver, but the contribution of a harvester. Some of the glory of the twelfth century is not vernal but autumnal." (pp. 490-491)

(10) Abelard was evidently at least acquainted with some treatises of the New Logic (de Rijk ed., Dialectica, Introduction, xvi- xviii), but his surviving work is in no important way influenced by the recovery of Aristotle, still far from complete when Abelard died in 1142.

Kunitz-Dick, Alisa. 2014. "Peter Abelard's Various Conceptions of Place (locus): from Attributes of Substances to Collections." Medioevo. Rivista di Storia della Filosofia Medievale no. 39:31–36.

Abstract: "This article traces the development of Peter Abelard's innovative conceptions of place, from the Dialectica to his theological writings. It proposes that there were a number of shifts in his models, the most important of which was the reduction of place, both substantial and quantitative, which had been classified as accidental or semi-accidental, to his ultimate view in which place is a collection of things which are contained in some way. Other variations, such as the relationships between God and place or incorporeals and place, differed less regularly between his works, and there are even occasional internal discrepancies within them. In the conclusion, I summarise this article's findings and discuss possible reasons for Abelard's shifting models."

Lenz, Martin. 2005. "Peculiar Perfection: Peter Abelard on Propositional Attitudes." Journal of the History of Philosophy no. 43:377–386.

"Peter Abelard is one of the first and few authors in the tradition of mediaeval logic who drew a distinction not only between propositional content and assertive force but also between propositional content and propositional attitude. The latter kind of distinction does not only involve the consideration of statements but of sentences in general, including expressions of wishes, orders, questions and such like. He thereby departs from the Aristotelian way of analysing sentences in terms of predication, and propounds a structural model that allows for a more coherent account both of the units of language and of how they relate to the mind.

(...)

So the modest aim of my paper is to raise the question whether this distinction might have been underestimated in the history of the mediaeval philosophy of language. A thorough study of this distinction might eventually provide an answer to the more general question of how we came to think of the sentence as a complete or peculiarly perfect unit of language."

———. 2007. "Are Thoughts and Sentences Compositional? A Controversy between Abelard and a Pupil of Alberic on the Reconciliation of Ancient Theses on Mind and Language." Vivarium no. 45:169–188.

Abstract: "This paper reconstructs a controversy between a pupil of Alberic of Paris and Peter Abelard which illustrates two competing ways of reconciling different ancient traditions. I shall argue that their accounts of the relation between sentences and thoughts are incompatible with one another, although they rely on the same set of sources. The key to understanding their different views on assertive and non-assertive sentences lies in their disparate views about the structure of thoughts: whereas Abelard takes thoughts to be compositional, the opponent's arguments seem to rely on the premise that the mental states which correspond to sentences cannot be compositional in the way that Abelard suggested. Although, at a first glance, Abelard's position appears to be more coherent, it turns out that his opponent convincingly argues against weaknesses in Abelard's semantic theory by proposing a pragmatic approach."

Lenzen, Wolfgang. 2022. "Rewriting the History of Connexive Logic." Journal of Philosophical Logic no. 51:525–553.

Abstract: "The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into nonclassical calculi which partly concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties (like the condition that no proposition implies its own negation) only apply to “normal” (e.g., self-consistent) antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions.

It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning (“humbly”) connexive implication don’t give rise, however, to anything like a non-classical logic."

References

McCall, S. (2012). A history of Connexivity. In D. M. Gabbay, F. J. Pelletier, & J. Woods (Eds.), Handbook of the history of logic, Vol. 11, Logic: A history of its central concepts (pp. 415–449). Elsevier

———. 2023. "Abelard and the Development of Connexive Logic." In The Logica Yearbook 2022, edited by Sedlár, Igor, 55–78. London: College Publications.

Lewis, Neil T. 1987. "Determinate Truth in Abelard." Vivarium no. 25:81–109.

"I wish to show in this paper that when read in this broader context we can see (i) that Abelard does not adopt different views in LI [Logca Ingredientibus] [*] and D [Dialectica] , in that the same solution is offered in each to this line of argument; (ii) that Abelard in these passages does not rely on the claim that valid inference preserves determinancy.

(...)

"Before we consider these issues in detail it will prove useful to set out some more general points pertaining to the concept of deter- minancy, an important but little studied notion in Abelard. I shall not try here to iron out all of the considerable difficulties Abelard's texts pose, but rather I shall outline some general themes useful for the more detailed discussion in section III on." (pp. 81-82)

[*] LI, p. 424.36-40. The longer discussion of concern to us occupies pp. 421.16- 422.40. The text of this passage in Geyer's edition contains a number of incorrect readings and the apparatus contains some errors and omissions. The reedited text may be found in the appendix to this paper (pp. 106-108).

MacFarlane, John. 2016. "Abelard’s Argument for Formality." In Formal Approaches and Natural Language in Medieval Logic: Proceedings of the Xixth European Symposium of Medieval Logic and Semantics, Geneva, 12-16 June 2012, edited by Cesalli, Laurent, Goubier, Frédéric and Libera, Alain de, 41–57. Turnhout: Brepols.

"Generalizing, we might say that formally valid inferences are inferences whose validity is not grounded in any fact about the world. Of course, the claim that there are such inferences is a substantive one. Let us call it the Formality Thesis:

There are inferences whose validity is entirely grounded in their forms, and does not depend on any fact about the world(5)" (p 42)

"Abelard interests me because, unlike later medieval logicians, he offers an argument for the Formality Thesis –a thesis his predecessors seem to have rejected. This argument motivates his distinction between formal and material consequence –or, in his terminology, perfect and imperfect entailment (inferentia(6). He does not slide from «good in all matter» to «good in virtue of form»; indeed, he recognizes inferences that are good in all matter but depend for their validity on facts about the world. He gives a much subtler argument –and it is a good argument, in its philosophical context. But it is not an argument that can give us a good reason to accept the Formality Thesis."(pp. 43-44)

(5) As stated, the Formality Thesis is ambiguous between a metaphysical thesis (there are inferences that are valid solely in virtue of their forms, and not at all in virtue of any facts about the world) and an epistemological thesis (there are inferences that we can know to be valid solely on the basis of knowledge of their forms, and independently of any knowledge of facts about the world).

(6) translating inferentia as «entailment», I follow C. Martin «Logic», in J. E. Brower, K. Guilfoy (eds.), The Cambridge Companion to Abelard, Cambridge University Press, Cambridge 2004, pp. 158-199.

Malcolm, John. 1979. "A Reconsideration of the Identity and Inherence Theories of the Copula." Journal of the History of Philosophy no. 17:383–400.

"Scholars concerned with medieval logic have recently made much of a distinction between two alleged theories as to the logical function of the copula: the identity theory and the inherence theory."

(...)

"My thesis will be that the identity-inherence dichotomy has been applied much too broadly and uncritically, for it does not hold for cases of accidental predication. I shall first try to get an adequate formulation of the two theories and shall then contrast them with what I shall call the normal theory of accidental predication. I then turn to Abelard and maintain that he does not go from an inherence theory in the Logica lngredientibus (5) to an identity theory in the Dialectica but, rather, holds to the normal theory in both works. After this I shall examine Ockham and his followers and shall conclude that they are not, as is usually supposed, identity theorists.

The question remains whether there are any bona fide inherence theorists. I shall suggest that the attempts to consider Aquinas and Ferrer to be such are inconclusive, but I shall not, in contrast with the alleged identity theorists, give a conclusive rebuttal of this possibility. Finally, I shall indicate that the true scope of the controversy between identity and inherence should be limited to essential predication." (pp. 383-384 a note omitted)

Maloney, Christopher J. 1982. "Abailard's Theory of Universals." Notre Dame Journal of Formal Logic no. 23:27–38.

"Abailard like Porphyry asks, but unlike Porphyry answers, three questions of the semantics and ontology of universals:

(1) What is the common cause by which the universal word, a predicate, is correctly imposed or predicated?

(2) What kind of concept of commonality is understood in an intelligent act of predication?

(3) Is a predicate called common because of the common cause of imposition, the concept understood in predication or both?

Abailard's responses to these questions are notorious and raise as many issues as they resolve. It is my primary purpose to reconstruct Abailard's answers in such a way that his nominalism and conceptualism are intelligible.

This requires an analysis of what he calls the common cause of the imposition of a predicate as well as his view of abstract concepts. To assess his theory, it is first necessary to survey briefly his objections to William and Joscelin. We shall find that Abailard's own theory is subject to much the same criticism he levies against his rivals. Indeed, far from the nominalism he hopes to defend, Abailard's theory runs off toward Platonic realism." (pp. 27.28, a note omitted)

Marenbon, John. 1991. "Abelard's Concept of Possibility." In Historia Philosophiae Medii Aevi. Studien zur Geschichte der Philosophie des Mittelalters. Festschrift für Kurt Flasch zu seinem 60. Geburtstag. (vol. II), edited by Mojsisch, Burkhard and Pluta, Olaf, 595–609. Amsterdam: B. R. Grüner.

Reprinted as Essay X in: John Marenbon, Aristotelian Logic, Platonism, and the Context of Early Medieval Philosophy in the West.

"In the following pages, I will argue that Abelard’s view of possibility is more unusual and more complex than these scholars [*] have allowed. Strange though it may seem, Abelard accepted the notion of genuine

counterfactuality and set out to analyze it, and yet he rejected the idea of alternative possible worlds on which modern logicians found their analysis of counterfactuality. The reasons why he did so go to the very heart of his philosophy and theology.

The main works of Abelard’s which will be used in this discussion are his Dialectica — a textbook of logic; the glosses to Aristotle’s Categories and De interpretatione from his Logica ingredientibus; his Theologia christiana and his Theologia scholarium. Both the Dialectica and the glosses probably date from between 1117 and 1121: neither work as a whole seems to be earlier than the other, although in individual sections one or the other appears to be more developed.(7) Both of the theological works, however, are later: the Theologia christiana, in its various recensions, dates from c. 1121-6, and the Theologia scholarium from 1133-40.(8)" (p. 596, a note omitted)

[*] Simo Knuutila and Hermann WEideman.

(7) 7 See C. Mews, «On dating the works of Peter Abelard», Archives d'histoire doctrinale et littéraire du moyen âge 52 (1985), pp. 73-134, esp. p. 88, as corrected by L.M. De Rijk, «Peter Abelard’s semantics and his doctrine of being», Vivarium 24 (1986), pp. 85-127, at pp. 103-8.

(8) Cf. Mews, op. cit., pp. 131-2.

———. 1992. "Vocalism, Nominalism and the Commentaries on the Categories from the Earlier Twelfth Century." Vivarium no. 30:51–61.

Reprinted as Essay XIII in: John Marenbon, Aristotelian Logic, Platonism, and the Context of Early Medieval Philosophy in the West.

"Commentaries on Aristotle's Categories are a rich, and hardly explored, source of information about twelfth-century logic.(1) The evidence they offer about nominalism supports the traditional view of its origins against those historians who have argued that the nominales were so called, not because they were said to describe genera and species as nomina, but because they adhered to a theory of the 'unity of the noun.'This paper will explore three main aspects of this evidence: the use of the word nomen in logic; the controversy between Abelard and Alberic over universals; and the origins of the thesis quod semel est uerum, semper est uerum." (p. 51, a note omitted)

(1) See Marenbon, Medieval latin commentaries for a catalogue and general discussion of the material. References to this catalogue are made in brackets in bold print - eg. (C 8).

References

Marenbon, J., Medieval latin commentaries and glosses on aristotelian logical texts before ca. 1150 A.D., in: Glosses and Commentaries on Aristotelian Logical Texts: The Syriac, Arabic and Medieval Latin Traditions; , ed. C. Burnett. London, 1993.

———. 1992. "Abelard, Ens and Unity." Topoi no. 11:149–158.

Abstract: "Although Abelard arrived at a view of "ens" nearer to Aristotle's than his sources would suggest, unlike Thirteenth-century thinkers he did not work out a view of transcendentals in terms of "ens", its attributes and their convertibility. He did, however, regard unity (though not goodness or truth) as an attribute of everything. At first, Abelard suggested that unity, being inseparable, could not be an accident according to Porphyry's definition (' that which can come and leave a subject without the subject being corrupted') either it is some type of form not classified by Porphyry, or not a form at all. In his later logical work, Abelard argued differently. Unity, he said, is an accidental form, but Porphyry's definition of an accident must be understood negatively, not as asserting something about what could happen in reality (since the form of unity could never leave its subject) but rather something about an absence of connection: were it, per impossible, to occur, the loss by a subject of its form of unity would not lead to the loss of its specific or generic status."

———. 1997. "The Platonisms of Peter Abelard." In Néoplatonisme et philosophie médiévale, edited by Benakis, Linos G., 109–129. Turnhout: Brepols.

Reprinted as Essay XII in: John Marenbon, Aristotelian Logic, Platonism, and the Context of Early Medieval Philosophy in the West.

"When, in 1966, Father Chenu published Les platonismes au XII siècle, twelfth-century Platonism had already been a topic of scholarly interest for nearly a century. (1) Chenu's novelty lay in his plural: not «Platonism» but «Platonisms». He distinguished a strand going back to Augustine, another deriving from the Timaeus and Boethius, one linked to pseudo-Dionysius and another to Arab writers. Chenu's is a useful analytical method which allows the scholar to avoid broad, oversimplifying labels whilst continuing to see the history of medieval philosophy in the neat terms of interrelated and interacting traditions. No doubt it could be fruitfully applied to Abelard -- but that is not my intention here. The Platonisms I shall be discussing are not those of the historian, but Abelard' s own: some of the diverse ways in which he used a notion of Plato and Platonic teaching to formulate, structure and convey his own thought (2). At the end of this paper, I shall return to the question of method, and ask what my procedure has to offer by contrast with other ways of discussing Platon- or any other -ism."

(1) In M.-D. Chenu, La théologie au douzième siècle (Études de philosophie médiévale, 45). Paris, 1966, pp. 108-141. For a sketch of the historiography of twelfth-century Platonism, see J. Marenbon, "Platonismus im zwólften Jahrhundert: alte und neue Zugangsweisen" (translation by A. Snell & O. Summerell), in T. Kobusch and B. Moisisch (eds.), Platon in der abendländischen Geistesgeschichte, neue Forschungen zum Plaumismus, Darmstadt, forthcoming. [Darmstadt, Wissenschaftliche Buchgesellschaft, 1997 pp. 101-119]

(2) In my general presentation of Abelard's use of Plato and attitude to him, I summarize arguments put forward in various places and different contexts in my The Philosophy of Peter Abelard. Cambridge, 1997. But in my longer and more detailed discussions here -- of Plato universals, the Timaeus and optimism, and «the Platonism of the Republic» -- I develop and extend what I have written in the book.

———. 1997. The Philosophy of Peter Abelard. Cambridge: Cambridge University Press.

Paperback edition, with corrections and bibliographical note, 1999.

"Outside quite technical matters of logic, it is implied, Abelard must be seen as important only in matters of detail and method - an attitude strengthened by an idea which has been taken up by more recent historians but goes back at least to the fifteenth-century historian Trithemius: that Abelard's theology is characterized by its application of the methods of logic to discussing Christian doctrine.(3)

The aim of this book is to show that this view of Abelard as a mainly critical thinker is inaccurate and unjust. His was more than a fleeting, superficial brilliance. He was a constructive and, at times, systematic philosopher; and, although it is certainly true that he (like many of his contemporaries) used the methods of logic in treating Christian doctrine, his theology is remarkable for much more than its method. Abelard's writings do not, however, form a single, coherent system. Abelard's interests and achievements fall into two roughly chronological phases. As a logician, he worked within the structure provided by the ancient texts which made up the logical curriculum. He provided cogent and often original answer to the philosophical questions which this study raised, but he did not pursue them systematically. He developed a sophisticated account of the semantics of universal words, but he did not resolve an underlying tension which runs through his ontology. As a writer on Christian doctrine, by contrast, Abelard strove to create his own theological system. Although he used methods and concepts he had developed within his logic, they were incidental to his main suppositions and aims. The bearing of Abelard's theological system was predominantly ethical: in the course of developing it, he elaborated a coherent, systematic and wide-ranging moral theory.

(...)

"The plan is simple. Part I gives a general account of Abelard as a whole: his life, his writings and teaching and the overall shape and growth of his thought. Part II looks at the mainly coherent, but unsystematic philosophy which he developed in close connection with his study of logic. Part III examines the ethical system which binds together his theology. (pp. 2-3)

(3) See appendix (below, pp. 344-5).

———. 1998. "The Twelfth Century." In Routledge History of Philosophy. Volume III: Medieval Philosophy, edited by Marenbon, John, 150–187. New York: Routledge.

On Abelard see pp. 155-166.

"The following pages can give only an impression of some of the most philosophically interesting aspects of a thinker whose originality and breadth of vision would entitle him to much more space in a History of Philosophy had it not been his misfortune to live in the Middle Ages. First, his ideas on two areas connected with the more formal side of logic will be sketched: his treatment of conditionals, and his analysis of modal statements. (Many other of his more formal developments are also of great interest: for instance, his treatment of ‘impersonal statements’, such as ‘It is good that you are here’, and his discussion of the copula.(9) Second, after a glance at his basic metaphysics, Abelard’s approach to the problem of universals will be examined. Third, his account of a central area in ethics, the ethical act, will be discussed and set in context." (pp. 156-157)

(9) On impersonal statements, see Jacobi [7.53]; on the copula, see de Rijk [7.76] (acute discussion and full bibliography on the question).

References

7.53 = Jacobi, K. ‘Diskussionen über unpersönlichen Aussagen in Peter Abaelards Kommentar zu Peri Hermeneias’, in E.P.Bos (ed.) Mediaeval Semantics and Metaphysics (Artistarium supplements 2), Nijmegen, 1985, pp. 1–63.

7.76 = Rijk, L.M. de, 'Peter Abelard’s semantics and his doctrine of being’, Vivarium 24 (1986): 85–128.

———. 2004. ""Dicta", Assertion and Speech Acts: Abelard and Some Modern Interpreters." In Medieval Theories on Assertive and Non-Assertive Language, edited by Maierù, Alfonso and Valente, Luisa, 59–80. Firenze: Olschki.

"The dictum is one of Abelard's most striking philosophical inventions, and one of the most controversial for his modern interpreters.(1) A dictum - as the Latin word indicates - is what is said by a propositio {a propositional sentence (2)." (p. 59)

(...)

"Too much remains hypothetical to speak of conclusions_ in the proper sense but this train of argument, stimulated by the speculations of Jacobi, Strub and King has led me to assert what twelfth-century logicians might have called a series of positiones (perhaps, the critic might say, no less paradoxical than some of theirs!). First, although Abelard is absolutely clear in seeing propositional sentences as assertive language, he does not use his concept of dicta to elaborate a theory of speech acts, which would distinguish between utterances with same content but different sorts of force - assertive, interrogative, exhortatory, desiderative. Second, there is no reason to suppose that Abelard introduced his theory of dicta in the first place so as to clarify the distinction between assertive and non-assertive language.

Rather Abelard needed the notion of dicta as an integral part of the metaphysics which he worked out in the course of his logical teaching. Third, it is extremely improbable that Abelard added the excursuses discussing dicta to his Logica commentary on De interpretatione only after he had written the literal commentary and some of the other excursuses. Indeed, i! is altogether unlikely that Abelard added excursuses at a later stage to literal commentaries he had already written. Fourth Abelard may well have given up his theory of dicta in his last years of teaching, unable perhaps to resolve the problems It posed and wanting to concentrate on his ethical and theological project.

It is !he last, and most tentative, of these conclusions which is the most far-reachmg, and not Just for how it bears out a view of Abelard's career I have urged elsewhere, in which he moves away from elaborating a metaphysical theory that ultimately failed to cohere to concentrating on providing a rational account of Christian belief, organized around ethical doctrine.(35) It also contains the implication that Abelard himself found his views about dicta unsatisfactory, and, although, such an argument from silence can never be conclusive, his and his followers' failure to use the notion of dicta to discuss the object of faith is remarkable.

(1) Irene Rosier-Catach gives an up-to-date list of the main modern discussions in n. 1 of Les discussions sur le signifié des propositions chez Abelard et ses contemporains in this volume. I am very grateful to her for allowing me to use the text of her article and for discussing my views with me, and to her and Martin Lenz for reading through and commenting on this paper.

(2) The usual translation of propositio by 'proposition' is particularly confusing in this context.

By a propositio, Abelard means a token affirming or denying sentence: I shall therefore use the rather clumsy 'propositional sentence' as an English equivalent of the Latin propositio.

(35) See Marenbon, The Philosophy of Peter Abelard, esp. p. 208-215.

References

Klaus Jacobi, Christian Strub and Peter King. From intellectus verus/falsus to the dictum propositionis: the Semantics of Peter Abelard and his Circle, « Vivarium», 34, 1996, p, 15-40.

———. 2006. "The Rediscovery of Peter Abelard's Philosophy." Journal of the History of Philosophy no. 44:331–351.

Abstract: "My article surveys philosophical discussions of Abelard over the last twenty years. Although Abelard has been a well-known figure for centuries, his most important logical works were published only in the twentieth century and, so I argue, the rediscovery of him as an important philosopher is recent and continuing. I concentrate especially on work that shows Abelard as the re-discoverer of propositional logic (Chris Martin); as a subtle explorer of problems about modality (Simo Knuuttila, Herbert Weidemann) and semantics (Klaus Jacobi); as a metaphysician before the reception of Aristotle's Metaphysics (Peter King); and as an ethical thinker who echoes the Stoics (Calvin Normore) and anticipates Kant (Peter King)."

———. 2007. "Abelard's Changing Thoughts on Sameness and Difference in Logic and Theology." American Catholic Philosophical Quarterly no. 81:229–250.

Abstract: "The discussion of sameness and difference in the three versions of the Theologia has been analyzed by a number of recent writers (for example, Ian Wilks, Jeff Brower, and Peter King). Despite some disagreements, they concur that Abelard's views are best expressed in the Theologia christiana and that he is putting forward a theory that-perhaps adapted-can help philosophers now in considering the material constitution of objects. By contrast, I argue that his views, which should be seen as developing and reaching their final form in the Theologia "scholarium," are much more closely linked than these scholars have thought to the particular theological problems involved in discussing the Trinity."

———. 2007. "Peter Abelard and Peter the Lombard." In Pietro Lombardo. Atti del XLIII Convegno Storico Internazionale, 225–239. Spoleto: Fondazione Centro italiano di studi sull'alto Medioevo.

———. 2007. Medieval Philosophy: An historical and philosophical introduction. New York: Routledge.

Peter Abelard, pp. 135-148.

"The system of logic Abelard devised was – so it has recently been shown (Martin, 1987, 1991, 2004) – a propositional logic. As logicians since Alcuin had done, he accepted Aristotelian syllogistic, though he saw the problems in, and adjusted, the modal syllogistic. As well as Aristotelian predicate logic,there had been in the ancient world a propositional logic – that of the Stoics.

But by late antiquity it was no longer understood, and so Boethius’s usefulness as an intermediary was limited (Chapter 3, section 1). None the less, Abelard seems, partly through a perspicacious reading through Boethius’s work on hypothetical syllogisms, partly through his own imagination, to have reinvented a fully propositional system. A precondition for this discovery, to which his tendency to analyse and disambiguate sentences may have disposed him, was his grasp of propositionality. Abelard, by striking contrast with Boethius, understood the idea of propositional content and propositional operations (such as negation and consequence) on it; so, for example, he was fully aware of how negating ‘If p, then q’ is not a matter of negating the antecedent or the consequent (let alone any of the terms which constitute them), but of denying that q is entailed by p." (p. 137)

References

Brower, J.E. and Guilfoy, K. (2004) The Cambridge Companion to Abelard, Cambridge: Cambridge University Press.

Jolivet, J. and De Libera, A. (1987) Gilbert de Poitiers et ses contemporains, Naples: Bibliopolis (History of Knowledge).

Martin, C.J. (1987) ‘Embarrassing arguments and surprising conclusions in the Development of theories of the conditional in the twelfth century’ in Jolivet and De Libera (1987), 377–400.

Martin, C.J. (1991) ‘The logic of negation in Boethius’, Phronesis 36 (1991) 277–304.

Martin, C.J. (2004) ‘Logic’ in Brower and Guilfoy (2004), 158–99.