"Medieval Supposition Theory." 1997. Topoi. An International Review of Philosophy no. 16.

Guest Editors: Gareth Matthews, Calvin Normore and Terence Parsons.

Contents: Gareth Matthews, Calvin Normore and Terence Parsons: Introduction 1; Paul Vincent Spade: Walter Burley on the Simple Supposition of Singular Terms 7; Mikko Yrjönsuuri: Supposition and Truth in Ockham’s Mental Language 15; Calvin G. Normore: Material Supposition and the Mental Language of Ockham’s Summa Logicae 27; Gareth B. Matthews: Two Theories of Supposition? 35; Terence Parsons: Supposition as Quantification versus Supposition as Global Quantificational Effect 41; Elizabeth Karger: Some 15th and Early 16th Century Logicians on the Quantification of Categorical Sentences 65; Stephen Barney, Wendy Lewis, Calvin Normore and Terence Parsons: On the Properties of Discourse. A Translation of Tractatus de Proprietatibus Sermonum (Author Anonymous) 77; Paul Vincent Spade: Walter Burley, From the Beginning of his Treatise on the Kinds of Supposition (De suppositionibus) 95-102.

"This issue of Topoi centers on medieval supposition theory, with two new translations of original sources and six papers on issues regarding the interpretation of the theory.(1)

Supposition theory came into full formulation sometime in the latter half of the 12th century, and flourished until sometime after the end of the 15th century. It was mostly discounted during Renaissance times, and mostly unknown from then until the second half of the 20th century.

Current scholars have become interested in supposition theory partly because some portions of it closely resemble twentieth century developments in semantics, including a recognition of quantificational phenomena that goes well beyond almost all other developments before Frege. In this introduction we explain briefly what supposition theory was, and we relate the translations and papers to issues in the development of the theory." (p. 1)

(1) The papers in this volume mostly developed out of a conference on “Signifier and Supposita” that was held at the University of California at Irvine in Spring 1996. We are grateful to the UCI Council for Collaborative Research in the Humanities for support for that conference.
Adams, Marilyn McCord. 1976. "What Does Ockham Means by 'Supposition'?" Notre Dame Journal of Formal Logic no. 17:5-37.

"Supposition theory is one of the most unique and important aspects of thirteenth and fourteenth century logic. The role played by the notion of supposition in medieval logic can be compared with the role of the notions of satisfaction and reference in modern logic. As the notion of satisfaction is introduced into modern discussions of truth, so supposition and truth are related in William Ockham's discussion, and their relation was debated by late fourteenth and early fifteenth century logicians.(1) And what little there is of a medieval attempt at developing a theory of quantification is imbedded in medieval discussions of the divisions of personal supposition.(2)

Despite the demonstrated importance of the notion of supposition, medieval logicians did not bother to make it very clear just what it was for a term to supposit for something in a proposition. William Ockham's

general account of this at the outset of his discussion of supposition in the Summa Logicae I, c. 63, is among the fullest and, on the face of it, looks fairly explicit." (p. 375)

(1) Boehner, Philotheus, Medieval Logic, The University Press, Manchester (1952).

(2) Boehner, Philotheus, "Ockham's theory of supposition and the notion of truth," Collected Articles on Ockham, #16, The Franciscan Institute, St. Bonaventure, New York (1958), pp. 232-267.
Amerini, Fabrizio. 2013. "Thomas Aquinas and Some Italian Dominicans (Francis of Prato, Georgius Rovegnatinus and Girolamo Savonarola) on Signification and Supposition." Vivarium no. 51:327-351.

Abstract: "Supposition is a controversial logical theory. Scholars have investigated many points of this doctrine such as its historical origin, its use in theology, the logical function of the theory, or the relationship between supposition and signification. In the article I focus on this latter aspect by discussing how some Italian, and in particular Florentine, Dominican followers of Aquinas—Francis of Prato (d. 1348), Girolamo Savonarola (d. 1498), and Georgius Rovegnatinus (d. after 1500)—explained the relation betviieen the linguistic terms' properties of signifying and suppositing, and hence the division of supposition. After sketching out Thomas Aquinas, Hervaeus Natalis, and William of Ockham's positions on the relationship between signification and supposition, I closely examine Francis's criticism of Ockham. Francis follows Walter Burle/s account of supposition and considers the statement that a term has simple supposition when (i) it Is taken not significatively and (ii) stands for an intention of mind as the weak point of Ockham's explanation of supposition. According to Francis, If this were the case, there would be no semantic basis for differentiating simple from material supposition. Francis is however hesitant about the full subordination of supposition to signification, especially witb regards to material supposition, when a term, suppositing for itself, is taken to signify itself besides its meaning. More than one hundred years later, Girolamo Savonarola and Georgius Rovegnatinus have no doubt about the fact that terms may supposit only for what they signify."
Ashworth, Earline Jennifer. 1969. "The Doctrine of Supposition in the Sixteenth and Seventeenth Centuries." Archiv fur Geschichte der Philosophie no. 51:260-285.

"It is often assumed that the logic of terms, including supposition theory, was despised and ignored by the logicians of the sixteenth and seventeenth centuries, in spite of the sophistication with which it had been developed during the later middle ages.

(...)

It is perhaps not surprising that when I looked at some eighty textbooks written during the period in question, I discovered that as many as twenty authors not only referred to the doctrine of supposition sympathetically, but usually went on to offer a detailed analysis which is neither a slavish nor an inept echo of what the mediaeval logicians had said." (pp. 260-271)

(...)

"The claim that with the end of the fifteenth Century all interest in the more sophisticated doctrines of the mediaeval logicians also came to an end, is clearly without foundation; and the practice of those writers I have examined clearly belies the humanist claim that past learning, other than classical, was no longer to be taken seriously." (p. 285)
———. 1973. "Priority of Analysis and Merely Confused Supposition." Franciscan Studies no. 33:38-41.

"In a recent article John J. Swiniarski discusses William of Ockham's use of merely confused supposition. 1 He claims that, in the case of universal affirmative propositions, Ockham's method of attributing merely confused supposition to the predicate accom- plishes much the same result as Peter Thomas Geach's method of attributing determinate supposition to the predicate and using a priority of analysis rule, whereby the subject is always analysed first. However, he notes, Ockham's analytical procedures when ap- plied to particular negative propositions can lead to erroneous re- sults, which are only avoided by the adoption of a priority of analysis rule. Since such a rule renders merely confused supposition unnec- essary, he concludes that Geach was right and that Ockham ought to have employed only distributive and determinate supposition together with a priority of analysis rule in his treatment of standard categorical propositions. I do not wish to criticize what Swiniarski has to say about the interpretation of Ockham. Instead, I wish to make a few remarks about the use of merely confused supposition by sixteenth century logicians in order to show that it is not in ge- neral so easily dispensed with.(2)" (p. 38)

(1) Swiniarski, John J., "A New Presentation of Ockham's Theory of Sup- position with an Evaluation of Some Contemporary Criticisms, " Franciscan Studies, 30 (1970), 209-217. Those readers who are not familiar with supposition theory should be reminded that merely confused supposition involves an analysis into a disjunctive subject or predicate, whereas distributive supposition involves an analysis into a conjunction of propositions and determinate supposition involves an analysis into a disjunction of propositions.

(2) For further details about supposition theory in the sixteenth century, see my paper: " The Doctrine of Supposition in the Sixteenth and Seventeenth Centuries, " Archiv für Geschichte der Philosophie, 51 (1969), 260-285.
———. 1978. "Multiple Quantification and the Use of Special Quantifiers in Early Sixteenth Century Logic." Notre Dame Journal of Formal Logic no. 19:599-613.

"I have three reasons for writing this paper. In the first place, I want to explain the early sixteenth century practice of using the letters 'a', 'b', 'c', and 'd' as special signs governing the interpretation of terms within sentences. In the second place, I want to investigate the analysis which logicians in the medieval tradition gave of such sentences as "There is somebody all of whose donkeys are running", "Everybody has at least one donkey which is running", and "At least one of the donkeys which everybody owns is running".(2) In the third place, I want to show that, despite what Geach has suggested,(3 logicians in the medieval tradition were capable of offering good reasons for rejecting such inferences as "Every boy loves some girl, therefore there is some girl that every boy loves". My discussion will be based mainly on the work of a group of logicians who were at the University of Paris in the first two decades of the sixteenth century, in particular Fernando de Enzinas, Antonio Coronel, and Domingo de Soto." (p. 599 a note omitted)

(2) Cf. P. T. Geach, Reference and Generality, Ithaca, New York (1962), p. 15 ff.

(3) P. T. Geach, "History of a fallacy" in Logic Matters, Oxford (1972), pp. 1-13.
———. 2010. "Terminist Logic." In The Cambridge History of Medieval Philosophy. Vol I, edited by Pasnau, Robert and Dyke, Christina van, 146-158. Cambridge: Cambridge University Press.

Supposition theory pp. 152-158.

"The vocabulary of supposition theory seems to be first found in the grammarians.

Peter Helias, the twelfth-century commentator on Priscian, used the term suppositum semantically, to indicate the bearer of a form or property,(12) but, shortly afterwards, from the 1260s onward, grammarians also used the notion purely syntactically. The verb supponere meant “to put as a subject term,” and it was contrasted with apponere, “to put as a predicate term.”(13) The terminology made its way into logical treatises, and both uses are needed to make sense of thirteenth-century discussions, particularly of the questions whether supposition is only a property of substantival nouns, and whether supposition is only a property of grammatical subjects." (pp. 152-153)

(12) e.g., Peter Helias, Summa super Priscianum, ed. Reilly, p. 891. For discussion, see Sten Ebbesen, “Early Supposition Theory (12th–13th Century),” Histoire Epistémologie Langage 3 (1981) 35–48.

Cf. Aquinas, Summa theol. 3a 2.3c on why “this man” is called a suppositum.

(13) H. Kneepkens, “‘Suppositio’ and ‘supponere’ in 12th-Century Grammar,” in J. Jolivet and A. de Libera (eds.) Gilbert de Poitiers et ses contemporains: aux origines de la Logica modernorum (Naples: Bibliopolis, 1987) 325–51. The passage about supponere and apponere frequently attributed to Peter Helias is a later interpolation (ed. Reilly, p. 448, apparatus).
———. 2013. "Descent and Ascent from Ockham to Domingo de Soto: An Answer to Paul Spade." In Medieval Supposition Theory Revisited: Studies in Memory of L. M. de Rijk, edited by Bos, Egbert Peter, 385-410. Leiden: Brill.

Also published as Volume 51, 1-4 (2013) of Vivarium.

Acts of the XVIIth European Symposium for Medieval Logic and Semantics, held the University of Leiden, 2nd, 7th June. 2008.

Abstract: "Paul Spade has attacked the theory of the modes of personal supposition as found in Ockham and Buridan, partly on the grounds that the details of the theory are incompatible with the equivalence between propositions and their descended forms which is implied by the appeal to suppositional descent and ascent. I trace the development of the doctrines of ascent and descent from the mid-fourteenth century to the early sixteenth century, and I investigate Domingo de Soto's elaborate account of how descent and ascent actually worked. I show that although Soto himself shared some of Spade's doubts, including those about the use of merely confused supposition, he had a way of reducing at least some propositions containing terms with such supposition to equivalent disjunctions and conjunctions of singular propositions. Moreover, he gave explicit instructions on how to avoid the supposed problem of O-propositions."
Bäck, Allan. 2013. "Avicenna's Theory of Supposition." Vivarium no. 51:81-115.

Abstract: "Although he does not have an explicit theory of supposition as is found in the works of Latin medieval philosophers, Avicenna (Ibn Sînâ) has two doctrines giving something equivalent: the threefold distinction of quiddity {triplex status naturae), corresponding to a division of simple, personal and material supposition, and his analyses of truth conditions for categorical propositions, where sentential context determines in part the reference of their terms. While he does address which individuals are being referred to by the universal terms used there, Avicenna concentrates more on the varied temporal durations of the predications being made. In Western terms, he has incorporated ampliation and restriction into the theory of supposition itself."
Barth, Else M. 1974. The Logic of the Articles in Traditional Philosophy: A Contribution to the Study of Conceptual Structures. Dordrecht: Reidel.

Part Two. Historical Survey.

Chapter IV. From the history of the logic of indefinite propositions 75-140; Chapter XII. Summary and conclusion 457-481.

"In the entirely unoriginal albeit influential Summulae logicales by Peter of Spain (ca. 1205-1277; cp. de Rijk 1970), probably written around 1232, we find a division into four kinds of categorical proposition:

“Propositionum categoricarum alia est universalis, alia particularis, alia indefinita, alia singularis” (Section 1.08). The author then gives an example of an indefinite proposition: “Indefinita est ilia in quia subicitur

terminus communis sine signo, ut “homo currit”; vel aliter: propositio indefinita est quae significat inesse vel non inesse” (Section 1.09).

This sentence, “homo currit”, we find in the theory of suppositio of William of Sherwood (1200/1210-1266/1271) as well in the theory of suppositio of Peter of Spain himself. This gives us sufficient reason to enquire into that theory. This famous scholastic theory of suppositio is a theory of the senses of terms in different kinds of propositions. Since this theory starts out from and studies combinations of terms with other terms, Moody considers the doctrine of the suppositio of terms as a syntactic theory (1953/22). Geach, however, often translates “suppositio" by “mode of reference” (1968/56). We might speak of a syntactic theory of meaning. De Rijk holds that “the Mediaeval logicians based the suppositio on the capacity of a term, when used in a proposition, to be interpreted for one or more individuals” (1967/571). This capacity is the significatio of the term, not its suppositio. But in the opinion of de Rijk, there is, in the theories of authors like William of Sherwood and Peter of Spain, in fact no sharp difference between the significatio (being the first proprietas termini) and the suppositio of a given term." (pp. 79-80)

References

Geach, P. T., 1968 [1962], Reference and Generality. An Examination of Some Medieval and Modern Theories. Revised edition. Ithaca, N.Y.

Moody, E. A., 1953, Truth and Consequence in Mediaeval Logic, Amsterdam.

Rijk, L. M. de, 1962, 67, Logica Modernorum. A Contribution to the History of Early Terministic Logic I: On the Twelfth Century Theories of Fallacy (1962). II, I The Origin and Early Development of the Theory of Supposition. (1967). Assen.
Berger, Harald. 1991. "Simple Supposition in William of Ockham, John Buridan and Albert of Saxony." In Itinéraires d'Albert de Saxe, Paris-Vienne au XIV Siécle, edited by Biard, Joël, 31-43. Paris: Vrin.

"My paper is based on the following two observations: (1) William of Ockham lays down a definition of simple supposition which reflects his anti-realistic stance; John Buridan, however, dispenses with this traditional kind of supposition altogether, whereas Albert of Saxony reintroduces it. In particular with respect to Albert, who is familiar with the doctrines of both Ockham and Buridan, the question, what Albert’s reasons are for his returning back behind Buridan, suggests itself. (2) In modem interpretations concerning the theory of Ockham some immanent problems have been pointed out; some features of Buridan’s theory, in turn, have been drawn to attention which are apt to avoid Ockham’s problems. On this background I shall try to give an interpretation of Albert’s peculiar position. Thus my paper consists of three sections, one for each philosopher; in each of these sections I shall, firstly, present the supposition theory of each author briefly, and, then, I shall discuss some relevant issues. The title of my paper originates in the fact that the analysis of the traditional paradigm of simple supposition, viz. “homo est species”, exhibits the relevant differences of the authors in question, in particular on the level of mental language." (p- 31)
———. 2016. ""Sortes differt ab omni homine". A Tension in Albert of Saxony's Concept of Merely Confused Supposition." In Formal Approaches and Natural Language in Medieval Logic, edited by Cesalli, Laurent, Goubier, Frédéric and Libera, Alain de, 283-302. Barcelona - Roma: Fédération Internationale des Instituts d’Études Médiévales.

"In his Logica, Albert of Saxony defi nes merely confused supposition thus, that a descent under the general term to the singular terms can be done by way of a sentence with a disjunct extreme, but not by way of a disjunctive sentence or a conjunctive sentence, that is in scholastic terms, a descent can be done disiunctim, but not disiunctive nor copulative:(1)

(...)

He then adds a longer passage in which he criticizes the view of «some» who add to this defi nition «vel copulatim», that is, that the relevant descent can be done by way of a sentence with a disjunct extreme or with a conjunct extreme. This addition, however, is superfl uous according to Albert(2).

This view criticized here by Albert is clearly that of Thomas Maulfelt who defi nes merely confused supposition thus, that a descent can be done by way of a sentence with a disjunct (and conditionalized) extreme or with a conjunct extreme. (The clause «condicionatim = de condicionato extremo» need not concern us here.) Thomas for his part states that the definition which only comprises a descent by way of a sentence with a disjunct extreme is insuffi cient, indeed false(3)." (pp. 283-284)

(1) Albert von Sachsen, Logik, Lateinisch – Deutsch, übersetzt, mit einer Einleitung und Anmerkungen hg. v. H. Berger, Meiner, Hamburg 2010, ch. II.3, pp. 262-264 (Philosophische Bibliothek, 611). Cf. also rule 11 in ch. II.6, ibid., pp. 310-312. On this regula antiqua ‘Quidquid mobilitat immobilitatum, hoc immobilitat mobilitatum’ see, e.g., F. Schupp, Logical Problems of the Medieval Theory of Consequences. With the Edition of the Liber consequentiarum, Bibliopolis, Napoli 1988, pp. 161-162 (History of Logic, 6).

(2) Albert von Sachsen, Logik, op. cit., pp. 264, 266 and 268. The rejection is on pp. 266 and 268, «Breviter dico, quod non oportet addere […] propter hoc tamen non sequitur, quod supponat confuse tantum».

(3) Thomas Maulfelt, Suppositiones, Ms Erfurt, Universitätsbibliothek, Dep. Erf., Cod. Amplon. Q. 271, f. 45r-v. Cf., e.g., S. Read, «Thomas of Cleves and Collective Supposition», Vivarium, 29 (1991) 50-84, at p. 71 and n. 66.
Biard, Joël. 2021. "John Buridan and Natural Supposition: From the Semantics of Names to Atemporal Propositions." Medioevo no. 44:123-140.

"John Buridan’s adoption of natural supposition is surprising, and it has been seen as such. The concept of natural supposition was originally tied to the positing of a common nature as that which is signified by a common term, a theory which Buridan rejects in its various versions in his Questions on the Metaphysics. It would obviously not be sufficient to say that his Summulae logicae take as its guide a reworked version of Peter of Spain’s Tractatus, which divide supposition in general into natural supposition and accidental supposition,(1) for it is clear that on many points Buridan does not hesitate to depart from the text that he uses both as manual and as material for his commentary. Moreover, he adopts and uses the concept of natural supposition in several other works. It is therefore necessary to understand the reasons internal to Buridan’s system that not only make this adoption possible, but even require it.

This task will be made easier if we recall that in the 13th-century natural supposition was not connected only, or even primarily, with the question of universals, but also with the question of the temporal determinations entailed by the way a general term is used in a proposition. Of course, the two issues are related, since singulars cease to be while the universal remains; however, even if common natures are rejected, there remains the question of the indexing of a proposition to a certain temporal determination.

The question arises when one has to specify the conditions of utterance of a necessary truth, at least if necessity is tied to omnitemporality.

Such truths pertain to propositions such as ‘Every human being is an animal’, but also – especially – those used in the sciences, in particular the natural sciences, in which there is an unavoidable tension between the contingency of things on the one hand and the necessity of its propositions on the other. This is why natural supposition will be called “demonstrative supposition”. (pp. 123-124)

(1) Peter of Spain (Petrus Hispanus Portugalensis), Tractatus called afterwards Summule logicales, VI, 4, ed. L.M. De Rijk, Van Gorcum, Assen 1972, 81.
Boehner, Philotheus. 1946. "Ockham's Theory of Supposition and the Notion of Truth." Franciscan Studies no. 6:261-292.

Reprinted in: P. Boehner, Collected Articles on Ockham, Louvain: E. Nauwelaerts, 1958, pp. 232-267.

"Our discussion of Ockham’s theory of signification,^(b) though limited to essentials, has prepared the way for an understanding of his theory of supposition and, consequently, of the notion of truth. This ingenious medieval theory of supposition, which unfortunately is much neglected by modern schoolmen and even misunderstood by historians of Medieval Philosophy, will finally answer the question: What is truth or falsity as applied to a proposition? For truth is given when and only when the subject and predicate of the same proposition stand or supposite for the same thing. To be sure, suppo¬ sition is not truth, but supposition enters the definition of truth, at least if we are interested in a semantic definition of truth (sometimes called logical truth) and if we are not to indulge in vague circum¬ locutions about the relation of correspondence between a proposition and a state of affairs, which relation of correspondence in a general way characterizes every scholastic theory of truth. As we have shown in our first study o.n the notion of truth, a semantic elucidation of the notion of truth seems to have been attempted by almost all the scholastics. That Ockham did the same can hardly be called an innovation; that he made a more careful analysis than others before him, is his distinct contribution to scholastic philosophy. In order to show that, we must first acquaint ourselves with Ockham’s theory of supposition, and then show its bearing on the notion of truth." (pp. 232-233 of the reprint)

(b) Cfr. the preceding art. in the present volume. [Okham's theory of signification (1946), pp. 201-232]
———. 1958. "A Medieval Theory of Supposition." Franciscan Studies no. 18:240-289.

"Supposition, on the other hand, is, in a strict sense, the property of a term that belongs to it as subject; thus tracts on supposition, in this narrower sense, analyze the significative function of the subject as it is determined by the context of the proposition. In a broader sense, however, the name 'supposition' is applied to both supposition in this narrower sense, and to appellation. Ockham, in his Summa logicae takes supposition in this broader sense and deals in one tract, De Suppositione, (p. I, c. 63 - 77) with all the problems which are connected with appellation as well.(2)

In the following we are going to take supposition in this broader sense and bring in discussions of the other properties at their proper places. However, our discussions will not follow a strictly historical order. Two reasons discourage this order. First, the material is so vast even in spite of the fact that most of the logical writings are still in manuscript form, that it is impossible to give a faithful historical account in a limited space. Secondly, there is a general agreement on the main teachings of this theory among all the scholastics, certainly of the 14th and 15th centuries, which warrants the presentation of one theory and by calling attention occasionally to differences in opinion on minor details." (pp. 249-250 of the reprint, anoter omitted)

(2) It is interesting to note that Burleigh in his De puritate artis logicae, written after and against Ockham' s Summa, has fundamentally the same position: Suppositio communiter accepta est proprietas termini ad alium terminům in propositione comparati. Et isto modo convenit suppositio tam subiecto quam praedicato quam etiam verbo seu consignificatis ipsius verbi. Et isto modo . . . accepta est in plus quam appellatio, quia suppositio competit tam subiecto quam praedicato, et appellatio competit praedicato tantum. Suppositio proprie dieta est proprietas termini subiecti ad praedicatum comparati ... Op. cit., [Tractatus Longior] Tr. I, p. i, c. 1; p. i s.
Boh, Ivan. 1965. "Paul of Pergola on Supposition and Consequences." Franciscan Studies no. 25:30-89.

"Although Paul of Pergula’s Logica is primarily a summary of various logical topics designed to help students to learn the subject quickly and painlessly, its six tracts and their arrangement reflect rather accurately the state of logic in the early fifteenth century.(1) In fact, this is one of the basic reasons for studying it; the other is the intrinsic interest of the content.

The tracts comprising the work are the following: (i) the summulae, i. e. subjects of the On Interpretation, Categories and Porphyry, Prior Analytics, and Boethius, together with an introductory enumeration of the transcendentals (23 pages in the modem edition); (2) on suppositions (21 pages); (3) on examination of terms, i. e. those terms which enter propositions as form-determining elements either because they are syncategorematics or because they are used syncategorematically (41 pages); (4) on consequences (14 pages); (5) on obligations, i. e. rales for consistent disputations (32 pages); and (6) on insolubles (14 pages). In an introductory remark Paul promises the seventh tract,dealing with objections against the first, second, and fourth tract, but this part has not yet been found either in manuscripts or in early printed editions. There is, however, in several editions an additional short work, “On the Composite and the Divisive Sense” in which nine rules are given to deal with difficulties arising from the presence of certain syncategoremata and intentional functors in propositions. (2)

Comparing the subjects and the amount of space given to their discussion with those of most textbooks on traditional logic current today, we find striking differences. Most of the materials found in our textbooks belong to Paul's first tract; they are accompanied, however, with many epistemological, ontological, and even psychological problems, irrelevant to logic considered as a science of form or structure or syntax. The distinctions between various kinds of terms other than those of structure, between various kinds of definition, between realism and nominalism, and especially between major and minor logic, are for the most part non-logical in character; some of them would be such even if one granted that logic is to be understood in a broader sense, i. e. that it is not to deal merely with the syntactical, but also with the semantic and the pragmatic dimensions of language." (pp. 30-31)

(1) Cf. statement made by the editor of the Logica Sister Mary Anthony Brown, O.S.F. in the introduction to the work: "The Logica should be regarded, not as an innovation, but rather as a mosaic of the treasury of logic known at that time." Logica and Tractatus de Sensu Composito et Diviso, St. Bonaventure, 1961, p. viii. It is on the basis of this work that the translations given below were made, and all the references made in the commentary to the text are, unless otherwise noted, to this edition. P. Boehner, speaking of the rules of consequences, views Paul’s work in much the same way: "Wir müssen . . . hervorheben, daß all diese Regeln nur die Frucht einer fast 200 jährigen Arbeit der mittelalterlichen Logiker sind.” Cf. "Bemerkungen zur Geschichte der DeMorganschen Gesetze in der Scholastik” in Archiv für Philosophie 4 (1951), p. 199.

(2) Sister Mary Anthony points out that this tract is usually appended to the printed editions of Paul’s Logica and adds that "the manuscript tradition testifies that this is certainly an authentic work of Paul of Pergula” (cf. her edition of Paul’s Logica, p. ix). There is, moreover, at least one explicit claim even in a printed work that a tract by this name was written by Paul and was later commented upon by others, namely by Antonius Francantianus, Quaestiones de sensu composito et diviso Pauli Pergulensi et in consequentiis Strodi (Venice, 1494).
———. 1966. "Propositional Connectives, Supposition and Consequence in Paul of Pergola." Notre Dame Journal of Formal Logic no. 7:109-128.

"Studying the rules of those consequentiae the validity of which depends on the internal structure of propositions, one quite often comes across Paul's remarks on various suppositions of terms; an understanding of his supposition theory is therefore essential for understanding such rules.

However, reading of the tract on supposition itself presupposes a grasp*

(a) of propositional connectives 'or', 'and', and 'if;

(b) of modal determinations;

and (c) of the validity-conditions of consequence in general;

and (d) of some specific rules of consequence.

The propositional connectives mentioned under (a) have been discussed by Paul in his Summulae,(1) a tract which treats of the topics of the logica υetus and the logica nova; and the modal functors were at least enumerated in the same tract.(2) His discussion of consequence and of the rules of consequences, however, follow the tract on supposition and should not have been used at this stage. But Paul can be excused from the charge of assuming a knowledge of what he will discuss later on the ground that even the logica nova should give the reader an idea of 'logically following from' and of the validity conditions for an inference." (p. 109)

* Paul of Pergola was born in the end of the 14th or the beginning of the 15th century, probably in Italy, and died in 1451. He studied under Paul of Venice (d. 1429) who lectured at the Universities of Padua and Siena. Paul of Pergola was a successful teacher of philosophy; although a member of the order of Augustinian Hermites, he was a publicly paid lecturer in Venice. His numerous works include Logica, found in at least 10 mss. and 8 printed editions; De sensu composito et diviso; Dubia super consequentiis Strodi; and his commentaries on the insolubles and the sophismata of Heytesbury. Cf. the introduction to his Logica by the editor Sister Mary Anthony Brown, ofm, pp. v-xiii, published by The Franciscan Institute, St. Bonaventure, N.Y., 1961.

(1) This tract forms the first part of Paul's manual Logica, edited by S. M. Anthony Brown, OSF, St. Bonaventure, New York, 1961. All the references to Paul of Pergola are to this work in its modern edition.

By the subjects of the logica υetus are meant such topics as are discussed in On Interpretation, Categories, Isagoge, and in Boethius' logical works; the subjects of logica nova contain, in addition to the above, the remaining portions of the Organon, and Gilbert de la Porre's Liber de sex principiis. The collective name for both, the logica υetus and the logica nova was logica antiqua, which was opposed to logica moderna; the latter includes the typically medieval logical topics, in particular the syncategoremata, properties of terms, consequences, obligations, and sophismata and insolubilia.

(2) "Modi sunt sex: Possibile, Impossibile, Necessarium, Contigens, Verum, Falsum". Logica, 11.
Boler, John. 1985. "Connotative Terms in Ockham." History of Philosophy Quarterly no. 2:21-37.

"The problem with Ockham's treatment of connotative terms is that he seems to do just what such a system should avoid. For example, his exposition of sentences containing connotative terms suggests that the expounded form is semantically primary. More importantly, however, even when he brings propositions with a connotative term under the common rubric where the predicate term stands for the same thing as the subject term does, Ockham spells that out in a special way. The import of "Sortes is white," he says, is that there is a whiteness in the same thing the subject term stands for.(47) It should be clear, I think, that if signifying is something Ockham thinks that both absolute and connotative terms do, it is not something which is explained by their being both categorematic terms. There is a fairly common perception among recent Ockham commentators that we lack a definitive interpretive theory about just what supposition is supposed to do in Ockham's system. I trust it will not be thought a purely negative contribution to suggest that we are not altogether better off when it comes to signification." (p. 33)

(47) Expositio in Librum Porphyrii de Praedicabilibus, ch. 1, # 6 (O. Ph., II: 25/ 57-65).
Bos, Egbert Peter. 1978. "Mental Verbs in Terminist Logic (John Buridan, Albert of Saxony, Marsilius of Inghen)." Vivarium no. 16:56-69.

"This essay deals with the field of medieval logic and semantics, especially that part which is usually designated as terminist logic or logica modernorum. It was here that, among other things, the theory of supposition— which originated in the theory of fallacies and twelfth-century grammar— was developed.(3)

The theory of supposition is a theory of the use of terms. In fourteenth-century logic (the period of our inquiry) supposition of terms occurs in propositions.(4)

(...)

"Supposition theory first and foremost is a theory of the reference of terms to individual things; the propositions are analysed primarily as to whether the constituent terms refer to individual things in the external world, in terms of which they are verifiable. Fourteenth-century logic is directed extensionally.(6)

In this paper I intend to present a survey and analysis of the behaviour of so-called intensional verbs and of the terms that are constructed with these verbs. I mean verbs like ‘intelligere’, ‘cognoscere’ , ‘appetere’ , ‘promittere’, i.e. verbs signifying a mental act . It appears, in medieval as well as in modem logic,(7) at the reference of the terms constructed with intensional verbs, is often not very transparent.(8)" (pp. 56-57)

3 L. M. de Rijk, Logica Modernorum. A Contribution to the History of Early Terministic Logic, 2 Vols. , Assen 1962-7.

4 L. M. de Rijk, The Development of "Suppositio naturalis” in Medieval Logic (I and II), in: Vivarium, 9 (1971). P- 91-107: 11 (1973). P- 43-9. especially p. 37ff. of the second part.

8 J. Pinborg, op. cit. ( cf . note 1), p. 127.

7 See section 4, p. 60.

8 The term ‘transparent’ , of course, is Quine’s. See e.g., his Word and Object, Cambridge (USA), 160 ; for this term and related notions and for the problem as such, esp. ch. 6.
———. 1997. "Speaking About Signs. Fourteenth-century views on suppositio materialis." Amsterdamer Beiträge zur älteren Germanistik no. 48:71-86.

"The principal questions in my paper are the following: How did the medieval semanticists indicate the autonymous use of words? Does the subject term in such a proposition express a linguistic item (itself, or its likes) because of the determination by the predicate? Or is it dependent on the will or intention of man, the voluntas utentium, as Ockham calls it?

Or is it a convention that determines the use of terms? Is a signum materialitatis (a sign, or mark, indicating material supposition) necessary? To what extent do the Medievals distinguish the autonymous use of language from other uses? Or is this kind of language meaningless?

There is hardly any secondary literature on this subject. (*)" (p. 75)

(*) M. Bochenski, Formale Logik (München 1970 (1956). 188-193; CA. Dufour, Die Lehre der Proprietates Terminorum. Sinn und Referenz in mittelalterlicher Logik (München/Hamden/Vv'ien 1989). 172-188. (Dufour tries to reconstruct the medieval theory of the properties of terms with the help of modern formal logic. This very interesting study did not obtain the attention it deserves, I feel). E. Karger, 'La supposition matérielle comme supposition significative: Paul de Venise, Paul de Pergola', in English Logic in Italy in the 14th and 15th Centuries. Acts of the 5th European Symposium on Medieval Logic and Semantics, Rome, 10-14 november 1980, ed. by A. Maierù (Napoli). 331-342. In a penetrating analysis, Karger discusses the difficulties arising from the 'mentioning' of terms in relation to the general semantical theory of a philosopher.
———. 2007. "Richard Billingham's Speculum puerorum, Some Medieval Commentaries and Aristotle." Vivarium no. 45:360-373.

Abstract: "In the history of medieval semantics, supposition theory is important especially in the twelfth and thirteenth centuries. In this theory the emphasis is on the term, whose properties one tries to determine. In the fourteenth century the focus is on the proposition, of which a term having supposition is a part. The idea is to analyse propositions in order to determine their truth (probare). The Speculum puerorum written by Richard Billingham was the standard textbook for this approach. It was very influential in Europe. The theory of the probatio propositionis was meant to solve problems both in (empirically oriented) scientific propositions such as used by the Oxford Calculators, and theological propositions, especially those about the Trinity. The book is original, concise, but not clear in every respect. Studying medieval commentaries may help us to understand Richard's book. In the present paper three commentaries are presented. The commentators discussed problems about the status of Richard's book, and about its doctrine: what is the relation between probatio and truth, what is the relation between probatio and supposition, what exactly are mediate and immediate terms (e.g.is the pronoun 'this' mediate or immediate?). The commentators sometimes criticize Richard. For example, one of them argues, against Billingham, that the verb 'can' ampliates its subject term and is therefore mediate."
———, ed. 2013. Medieval Supposition Theory Revisited: Studies in Memory of L. M. de Rijk. Leiden: Brill.

In Collaboration with H.A.G. Brakhuis, W. Duba, C. H. Kneepkens, and C. Schabel.

Acts of the XVIIth European Symposium for Medieval Logic and Semantics, held the University of Leiden, 2nd, 7th June. 2008.

Also published as Volume 51, 1-4 (2013) of Vivarium.

Contents: E. P. Bos: Preface 1; E.P. Bos and B.G. Sundholm: Introduction 3;

Early Supposition Theory in General

LM. de Rijk: Semantics and Ontology. An Assessment of Medieval Terminism 13; Sten Ebbesen: Early Supposition Theory II 60;

Arabic Philosophy

Allan Bäck: Avicenna’s Theory of Supposition 81;

XIIth Century

Luisa Valente: Supposition Theory and Porretan Theology: Summa Zwettlensis and Dialogus Ratii et Everardi 119;

XIIIth Century

Mary Sirridge: Supposition and the Fallacy of Figure of Speech in the Abstractiones 147; Julie Brumberg-Chaumont: The Role of Discrete Terms in the Theory of the Properties of Terms 169; Dafne Mure: Suppositum between Logic and Metaphysics: Simon of Faversham and his Contemporaries (1270-1290) 205;

XIVth Century

Costantino Marmo: Scotus on Supposition 233; Simo Knuuttila: Supposition and Predication in Medieval Trinitarian Logic 260; Laurent Cesalli: Richard Brinkley on Supposition 275; Alessandro D. Conti: Semantic and Ontological Aspects of Wyclif’s Theory of Supposition 304; Fabrizio Amerini: Thomas Aquinas and Some Italian Dominicans (Francis of Prato, Georgius Rovegnatinus and Girolamo Savonarola) on Signification and Supposition 327; Catarina Dutilh Novaes: The Role of ‘Denotatur’ in Ockham’s Theory of Supposition 352; Claude Panaccio: Ockham and Buridan on Simple Supposition 371; E. Jennifer Ashworth: Descent and Ascent from Ockham to Domingo de Soto: An Answer to Paul Spade 385; Ernesto Perini-Santos: When the Inference ‘p is true, therefore p’ Fails: John Buridan on the Evaluation of Propositions 411;

XV-XVI-XVIIth Centuries

Angel d’ Ors: Logic in Salamanca in the Fifteenth Century. The Tractatus suppositionum terminorum by Master Franquera 427; Stephan Meier-Oeser: The Hermeneutical Rehabilitation of Supposition Theory in Seventeenth-Century Protestant Logic 464;

Logic: Medieval and Modern

Sara L. Uckelman: A Quantified Temporal Logic for Ampliation and Restriction 485; Terry Parsons: The Expressive Power of Medieval Logic 511;

Index Locorum 525; Index Nominum 539; Manuscripts Mentioned 552-553.

"From June 2nd to June 7th, 2008, the XVIIth European Symposium for Medieval Logic and Semantics was held at the University of Leiden, The Netherlands.

The present volume contains the papers presented at the symposium by scholars from all over the world (the European Symposium extends beyond Europe in terms of its participants).

The general theme of the symposium was ‘The Rise and Development of Supposition Theory’. It seemed appropriate that a symposium in Leiden, held about 50 years after the publication of L.M. de Rijk’s Logica Modernorum (Assen 1962-1967), emeritus professor of the University of Leiden, should be devoted to medieval supposition theories. On June 30, 2012, De Rijk died at the age of 87 years." (Preface, p 1)
Braakhuis, Henk A.G. 1999. "Scientific knowledge and contingent reality. Knowledge, signification and (natural) supposition in Buridan's Questions on De generatione et corruptione." In The Commentary Tradition on Aristotle's De generatione et corruptione: Ancient, Medieval, and Early Modern, edited by Thijssen, J. M. M. H. and Braakhuis, Henk A.G., 131-161. Turnhout: Brepols.

"In view of the above, it will not come as a surprise to see that in the beginning of John Buridan’s Questions on De generatione et corruptione, the problem of the possibility of scientific knowledge of beings coming into being and passing away is brought into sharp focus. Whereas in the commentaries of both Giles of Rome and Giles of Orleans, the problem is discussed under two headings, namely by asking whether there can be scientific knowledge of corruptible things and whether, if something has passed away, there can remain scientific knowledge of it,(4) John Buridan devotes the first three questions of his commentary to this problem. Two questions which resemble those discussed by Giles of Rome and Giles of Orleans are here followed by a third question which asks whether a word signifies the same irrespective of whether the thing it signifies exists or has already passed away (utrum vox significet idem, re existente et corrupta). By introducing, into this context, a semantical issue which had been eagerly discussed in the late thirteenth century, namely whether a word can lose its signification, Buridan makes it clear that for him, the problem of scientific knowledge has an essentially semantic character.

In the present contribution, I shall discuss these first three questions of Buridan’s Questions on De generatione et corruptione(5) Although it will become apparent that Buridan’s views as expressed in these three questions do not differ considerably from those offered in similar questions to be found in his other works,(6) the questions he discusses here nevertheless add to a better understanding of his views and form a further testimony to the importance he attached to the semantic aspect of problems of scientific knowledge and to the role he assigned to a correct analysis of the propositions in which we express our scientific knowledge." (pp. 132-133)

(4) Cf. Aegidius Romanus, Commentaria in libros De generatione et corruptione (Venezia, 1505), fols. 2va-3vb and Aegidius Aurelianensis, Quaestiones super De generatione et corruptione (Kuksewicz), pp. 3-12.

(5) For a complete list of the questions of Buridan’s commentary, see the Appendix 1.

(6) These questions are mainly: (1) Johannes Buridanus, Quaestiones super decem libros Ethico-rum Aristotelis ad Nicomachum (Paris, 1513) VI, 6 , fols. 121vb-123rb: utrum omne scibile sit etemum. There is a translation of most of the text in Hyman e.a. Philosophy in the Middle Ages, pp. 705-710. (2) Johannes Buridanus, Summulae De suppositionibus (Van der Lecq), 4.3.4: De divisione suppositionis communis in naturalem et accidentalem, pp. 45-49. This new edition differs in important points from the older one in Reina, “Giovanni Buridano,” pp. 206-208. There is a translation of this text in Jean Buridan''s Logic (King), pp. 125-128. For a study of both these texts cf. in particular Scott, “John Buridan,” passim and De Rijk, “The Development,” pp. 47-68. (3) Johannes Buridanus, Questiones longe super librum Perihermeneias (Van der Lecq), I, qu. 2: utrum omne nomen significat aliquid, pp. 728-1438.

References

Johannes Buridanus, Jean Buridan’s Logic. The Treatise on Supposition, the Treatise on Consequences. Transi, by P. King. Dordrecht, 1985. (Synthese Historical Library, 27).

_________ . SophismataEd. T. K. Scott. Stuttgart etc., 1977. {Grammatica speculativa, 1).

_________ . Questiones longe super librum Perihermeneias. Ed. R. van der Lecq. Nijmegen, 1983.

M. E. Reina, “Giovanni Buridano: Tractatus de suppositionibus.” Rivista critica di storia della filosofia, 12 (1957), 175-208 & 323-352.

Logica Modernorum. A Contribution To The History of Early Terminist Logic. Ed. L. M. de Rijk. Vol. II, 1: The Origin And Early Development Of The Theory Of Supposition, II, 2: Texts and Indices. Assen, 1967.
Brown, Stephen F. 1972. "Walter Burleigh's Treatise De Suppositionibus and its influence on William of Ockham." Franciscan Studies no. 32:15-64.

"In the present article we will edit and study Burleigh's earlier treatise on supposition. Certainly it is the work of Burleigh. This is witnessed by the explicits of both manuscripts which contain it.(5) Also, as Boehner indicated, it has large parts in common with the De puritate. Furthermore, Burleigh in the De puritate speaks of an earlier treatise with its manifold divisions of supposition, and the De suppositionibus lives up to that description. It is most probably a very early work of Walter Burleigh. As both Boehner and Weisheipl indicated, unlike the De puritate it shows no sign of attacking Ockham at all.(6) Also in the De puritate Burleigh himself speaks of an earlier treatise on supposition as "written in my youth."(7) Finally, in the manuscripts it is located beside works written in 1301 and 1302, shortly after Burleigh became a Master in the Arts Faculty. We conclude therefore that it is certainly the work of Burleigh and most probably was written about 1302." (p. 16)

(5) London, British Museum, Royal 12 F XIX, f. i33va : " ...Et ideo valet quia arguitur a pluribus determinatis ad unum determinatum. Expliciunt suppositions datae a M. W. de Bourť. " Cambridge, Gonville et Caius 434/434, f. I9ra : " Et non, quia arguitur a pluribus determinatis ad unum determinatum. Expliciunt suppositiones datae a Magistro Waltero de Burley. "

(6) Walter Burleigh, De puritate..., XIII-XIV ; J. Weisheipl, "Ockham and Some Mertonians" in Mediaeval Studies, XXX (1968), 179.

7) 7 Walter Burleigh, De puritate..., 2 : " Plurimas divisiones suppositionis in iuventute mea memini me scripsisse...".
———. 1993. "Medieval Supposition Theory in Its Theological Context." Medieval Philosophy and Theology:121-157.

In appendix: Walter Chatton: Lectura in I Sent. 4.1.1-2 (pp. 135-157).

"In brief, although modern students of medieval supposition theory have, for the most part, based themselves on medieval logic treatises, there is a rich parallel source for studying the development of the theory of the supposition of terms to be found in theological writings.

For, especially in dealing with the Trinity and the Incarnation, theologians had to clarify their statements, explaining in each case whether they were speaking about the divine essence or about all or one of the divine persons, or whether they were speaking about Christ as God or Christ as man. Did they develop a certain consistency in their theory of reference or supposition? Did they find some logical principles that governed their use of language and could be applied to each proposition dealing with the Trinity? If they did, would such a theory also be applicable in statements concerning the Incarnate Son, where one is dealing with only one person, but a person with a divine and a human nature?"

(...)

"Our present task is a much more modest one. We are writing this essay as an introduction to a particular text of Walter Chatton. We will be looking at one particular theological case and showing how a small number of Chatton's predecessors dealt with that case and how they tried to develop a theory of supposition to handle it. The particular theological case is found in Lombard's Sentences 1.4 where, picking up the Alberic-Abelard debate of 1121 ]*], the Magister Sententiarum examines the truth of the proposition "Deus genuit Deum."

Since the Sententiae of Lombard became the official theology textbook at Paris and Oxford before the middle of the thirteenth century, and every medieval baccalareus had as one option to present a commentary on Lombard's work as a partial requirement for becoming a Master of Theology, the commentaries baccalarii wrote on distinction 4 contain an alternate source for their theories of supposition.(9)" (pp. 113-114)

[*] Peter Abelard Historia calamitatum (Monfrin [Paris: Vrin 1967] 84-765-85.769).

(9) For an introduction to the development of the theory of the supposition of terms in the medieval period according to logical works, see Brown, "Walter Burleigh's Treatise De suppositionibus and its Influence on William of Ockham," Franciscan Studies 32 (1972): 15-64.
———. 2009. "Gerald Odonis' Tractatus de suppositionibus: What is suppositio communicabilis?" Vivarium no. 47:205-220.

Abstract: "The Tractatus de suppositionibus, which is cited by Gerald Odonis in his commentary on the Sentences, probably dates from ca. 1315-25. In the Sentences commentary he refers to his treatment of 'suppositio communicabilis' and its species, indicating a type of supposition whose language seems new. This article attempts to find a source for it in contemporary authors and arrives at the conclusion that 'communicabilis' is simply a synonym for 'personalis', the most common form of supposition according to Odonis."
———. 2020. "Praepositinus of Cremona and William of Auxerre on Suppositio. Their Influence on the Summa Halensis." In The Summa Halensis: Sources and Context, edited by Schumacher, Lydia, 235-250. Berlin: de Gruyter.

Abstract: "Early medieval discussions of supposition begin with reflections on an early passage of the first chapter of St Augustine’s De Trinitate. Here Augustine is criticizing Sabellius and his followers who claimed that the Father had begotten himself, i. e. God begets deity, which gave rise to a kind of modalism. These words of Augustine show up in Peter Lombard’s Sentences, Book I, Distinction 4, and gave rise to a larger debate about the words that can properly apply to God which engaged the minds not least of Abelard and Alberic of Reims, culminating in Gilbert of Poitiers.

Praepositinus (1135–1210) and William of Auxerre (1140–1231) are the sources of a new trajectory in interpreting the supposition of the name ‘God’, which directly influences the Summa Halensis. This paper examines the nature of that influence and provides a translation of brief texts from Prepositinus and William that form its background."
Brumberg-Chaumont, Julie. 2013. "The Role of Discrete Terms in the Theory of the Properties of Terms." Vivarium no. 51:169-204.

Abstract: "Discrete supposition occurs whenever a discrete term, such as 'Socrates', is the subject of a given proposition. I propose to examine this apparently simple notion. I shall draw attention to the incongruity, within a general theory of the semantic variation of terms in a propositional context, of the notion of discrete supposition, in which a term usually has a single semantic correlate. The incongruity comes to the fore In those treatises that attempt to describe discrete supposition as a sort of personal supposition, although the same term cannot be in simple supposition in another propositional context, because it has no significate distinct from its suppositum. This shows a fundamental link between common signification, simple supposition and predicability, three notions that rely on the existence of a significate distinct and Independent from the suppositum of the term. The connection is to be seen especially in William of Sherwood's Introductiones, the only author of a terminist Summa who recognizes the existence of simple supposition for discrete terms."
Buridan, John. 1966. Sophisms on Meaning and Truth. New York: Appleton - Century - Crofts.

Translated and with an introduction by Theodore Kermit Scott.

Introduction; V. Buridan's Theory of Language. B. Supposition, 29-42.

"The theory of supposition is the core of terminist logic.(54) Signification is a function of terms and concepts taken in isolation, but supposition is a function of the predication of terms and concepts.(55) In at least one of its aspects, supposition differs from signification as using a term differs from knowing how to use it. It is treated as a property of terms, but only as they occur in propositions, and it is used both as the basis for a theory of truth and as a tool for the purely syntactical analysis of propositions.

It is this double function of supposition that has led astray most attempts to give a general characterization of the theory. It is in fact, not one theory, but two, and they require separate treatments. (56) The first, which can be called simply the doctrine of supposition proper, is a set of rules governing the reference of terms in propositions and is the basis of a theory of truth. The second, which I call the doctrine of modes of supposition, has no effect on the reference of terms, but is a set of rules for the syntactical analysis of propositions containing quantifying words and is thus the quantification theory of terminist logic." (pp. 29-30)

(54) The use of the term suppositio stems from the use of the verb (“to place under” or “to stand in place of”) made by both classical and medieval grammarians. The habit of grammarians of using the notion of standing for primarily in connection with pronouns helps explain the adaptation, for considerations of pronominal reference are inseparable from considerations of occasions and contexts of use, which is just what distinguishes supposition from signification in terminist logic. For a brief account of the history of the use of the term and of the doctrine, see Mullally, op. cit., [The Summulae Logicales of Peter of Spain (Notre Dame, Indiana, 1945)] pp. xlvi-xlvii.

(55) As in the case of signification, the supposition of a concept always matches that of the corresponding term, so that discussion can be confined to the supposition of terms.

(56) Whether Buridan is himself fully aware of the distinction is uncertain.

In his only general definition of “supposition,” at Chapter III, Remark i, he takes account of only one of the theories. But he does separate the two in practice, devoting the first six sophisms of Chapter III to the first and the last four to the second.
Burton, Patricia Shelby. 1990. "Suppositio Naturalis" and the Truth Conditions of the Propositions of Demonstrative Science, The University of Texas at Austin.

Available at ProQuest Dissertation Express. Order number: 9105524.
Cesalli, Laurent. 2013. "Richard Brinkley on Supposition." Vivarium no. 51:275-303.

Abstract: "This study comments on six notabilia found in the general observations (praemittenda) with which Brinkley begins his treatise on supposition in his Summa logicae: i) the logico-metaphysical explanation of the distinction between significatio and suppositio, ii) the ontic division principle of supposition, iii) the relationship between supposita and truth-makers, iv) what seems to be a late (and English) resurgence of natural supposition, v) a pragmatic suspension of the regula appellationum and vi) Brinkley’s apparently incompatible claims that there are communicable things and that there are only singular things, a position that is a medieval form of immanent realism. Based on the two manuscripts that contain the treatise on supposition, an appendix offers a provisional edition of part of Brinkley’s Summa, a collaboration between the author and Joël Lonfat."
Cesalli, Laurent, and Goubier, Frédéric. 2018. "Anton Marty on Naming (Nennen) and Meaning (Bedeuten): a Comparison with Medieval Supposition Theory." In Modern Views of Medieval Logic, edited by Kann, Christoph, Loewe, Benedikt, Rode, Christian and Uckelman, Sara L., 29-54. Leuven: Peeters.
Cocchiarella, Nino. 2001. "A Logical Reconstruction of Medieval Terminist Logic in Conceptual Realism." Logical Analysis and History of Philosophy no. 4:35-72.

Abstract: "The framework of conceptual realism provides a logically ideal language within which to reconstruct the medieval terminist logic of the 14th century. The terminist notion of a concept, which shifted from Ockham's early view of a concept as an intentional object (the fictum theory) to his later view of a concept as a mental act (the intellectio theory), is reconstructed in this framework in terms of the idea of concepts as unsaturated cognitive structures.

Intentional objects (ficta) are not rejected but are reconstructed as the objectified intentional contents of concepts.

Their reconstruction as intentional objects is an essential part of the theory of predication of conceptual realism. It is by means of this theory that we are able to explain how the identity theory of the copula, which was basic to terminist logic, applies to categorical propositions. Reference in conceptual realism is not the same as supposition in terminist logic. Nevertheless, the various "modes" of personal supposition of terminist logic can be explained and justified in terms of this conceptualist theory of reference."
Conti, Alessandro D. 2013. "Semantic and Ontological Aspects of Wyclif's Theory of Supposition." Vivarium no. 51:304-326.

Abstract: "The relationship between thought and reality was a focal point of Wyclif’s reflection.

On the one hand, Wyclif believed that thought was linguistically constrained by its own nature; on the other hand, he considered thought to be related to reality in its elements and constitution. Hence he deemed language, thought, and external reality to be of the same logical coherence. Within this context, the theory of supposition was intended to explain the different roles that terms can have in relation to language and the extramental world when they appear as extremes in propositions. Characteristically, his theory of supposition provides an account not only of the truth-values of a sentence, but also of its meaning; it is not therefore simply a theory of reference, but a sort of complex analysis of language viewed as a semiotic system whose unique interpretative model was reality itself. It gives clear evidence of Wyclif’s realist stance and of his conviction that any kind of linguistic and semantic features must be grounded on ontological structures."
Corcoran, John, and Swiniarski, John J. 1978. "Logical Structures of Ockham's Theory of Supposition." Franciscan Studies no. 38:161-183.

"There are two pervasive themes in this article. In the first place this article is a defense of Ockham against a baseless charge oferror, which, if left unanswered, might tend to diminish Ockham's reputation as a technically competent logician. Study of the sources of the charge reveal that two recent commentaries each attribute ingenious and interesting logical structures to Ockham's thought on supposition. Comparison of these two structures with each other and with Ockham's writings yields three results: first, that the two structures, though separately consistent, are inconsistent with each other; second, that neither of them square with Ockham's own statements and, third, that Ockham's thought does have a logical structure which, in several respects, is even more ingenious. Thus, the second theme of this article involves an attempt to articulate the logical structure of Ockham's theory of supposition and to compare this structure with two others that have been proposed." (p. 161)

(...)

"It is important to realize that this article in no way impugns either the Loux interpretation or the Priest-Read formalization. In regard to Loux's work, this article refutes two inferences made in the exposition of Ockham's theory but it in no way criticizes the interpretation on which the exposition is based. The interpretation contains several worthwhile observations. Moreover, the Priest-Read formalization per se is not criticized at all. This article implies, however, that the Priest-Read formalization is not a formalization of Ockham's theory and that it is not a formalization of the Loux exposition either. We should acknowledge that without the clarity and precision provided by the Priest-Read formalization the results of this article would have been much more difficult to obtain. Thus it can be said that this article builds on the works of Loux and of Priest and Read." (p. 163)

References

Loux, Michael J. [1974], Ockham's Theory of Terms: Part I of the Summa Logicae, translated and introduced by M. J. Loux, University of Notre Dame Press, Notre Dame and London.

Priest, Graham and Stephen Read [1977], "The Formalization of Ockham's Theory of Supposition," Mind, 86, 109-113.
Courtenay, William. 1984. "Force of Words and Figures of Speech: The Crisis over Virtus Sermonis in the Fourteenth Century." Franciscan Studies no. 44:107-128.

"On the Friday after Christmas in 1340 the Arts Faculty at the University of Paris, during the rectorship of Alain de Villa Colis, enacted a statute listing propositions and types of argumentation that should not be used in the schools by any master, bachelor, or scholar under pain of expulsion from the faculty forever.(1) Most of the articles in that statute concerned arguments employing the phrase de virtute sermonis, to the effect that propositions taken from authoritative sources should not simply be called false, de virtute sermonis." (p. 107)

(...)

"As far back as 1946 Boehner attempted to erase many of the misunderstandings about the meaning of the expression de virtute sermonis and shed light on Ockham's use of it.(5) The persuasiveness of his analysis was handicapped by his need for brevity (it was given as an aside in the context of another article), by a few unfortunate mistakes, and probably by the ad hominem assumption by many that Boehner had a vested interest in freeing Ockham from the taint of heresy. Yet when Boehner's analysis is considered on its own merits, it is essentially correct. It is only insufficient in the degree of attention given to the pre- and post-Ockhamist history of the phrase de virtute sermonis and the limitation of discussing it only in the context of supposition theory, leading to the mistaken inference that the expression de virtute sermonis was equivalent to and interchangeable with proper supposition, as opposed to improper supposition, or ex usu loquendi." (p. 108)

(1) Chartularium Universitatis Parisiensis, ed. H. Denifle and E. Châtelain, Vol. II (Paris, 1891), 505-07, n. 1042, henceforth cited as CUP.

(5) Boehner, [Ockham’s Theory of Supposition and the Notion of Truth, (1946) pp. 232-267, in] Collected Articles, 248-53.
Crimi, Milo. 2014. "Significative Supposition and Ockham’s Rule." Vivarium no. 52:72-101.

Abstract: "Paul Spade argues that there is a tension between Ockham’s descriptions of the various types of supposition at Summa Logicae (sl) I.64 and a rule he provides at sl I.65. In later papers, Spade proposes a solution: a term supposits significatively (i.e., personally) just in case it supposits for everything it signifies. I evaluate Spade’s proposal and explore some of its implications. I show that it successfully resolves the tension and that it suggests a way to more precisely describe material and simple supposition. I argue furthermore that Ockham is committed to the proposal by showing that uncontroversial features of his theory imply it. In doing so, I raise and refute three potential objections. Finally, I highlight and discuss a controversial result: self-signifying conventional terms can supposit materially. I argue that this result makes for a more satisfying theory."
———. 2013. "Logic in Salamanca in the Fifteenth Century. The Tractatus suppositionum terminorum by Master Franquera." Vivarium no. 51:427-463.

Abstract: "This paper looks into the contents of the Tractatus suppositionum terminorum by Master Franquera, in the context of the teaching of logic in Salamanca (and elsewhere in Spain) in the fifteenth century. Franquera’s work is characterised by its explicit realist bias and its rejection of Ockhamist theses, i.e., by its recognition of the existence of a natura communis or a universale in re, which is evident in all discussions related to suppositio simplex and the theory of significatio. But, apart from this, Franquera’s discussion of the theory of suppositio stands out as a strange mixture of different doctrines: some of them are derived from thirteenth-century (or earlier) analyses, others from fourteenth-century developments; realist goals are reached by means of instruments that, while not being nominalist, are definitely inspired by terminism. While upholding the theses of realist schools, Franquera adopts the definitions and rules of nominalist authors."
Dinneen, Francis P. 1990. "Suppositio in Petrus Hispanus. Linguistic Theories and Models." In De Ortu Grammaticae. Studies in Medieval Grammar and Linguistics Theory in Memory of Jan Pinborg, edited by Bursill-Hall, Geoffrey L., Ebbesen, Sten and Koerner, Konrad, 69-85. Amsterdam, Philadelphia: John Benjamins.

"Hispanus opposes Signification and Supposition much like sense and reference. Each is a technical term. For Hispanus, term (terminus) itself is a technical term. It is distinguished from word (dictio), locution (vox), or part of speech (pars orationis) because those expressions are appropriate when discussing multiple ordinary or grammatical functions, while term is reserved for discussing only two logical functions that a grammarian's word, locution, or part of speech may serve: that of being relatable to another term as subject or predicate oí a.proposition.

Hispanus is quite clear about this.

(...)

Hispanus is less clear in his definitions of Signification and Supposition as properties of a term. Technical terms should be precisely defined. But there are at least two different kinds of precision. One lists elements of composition positively, another indicates function or distinction negatively or relationally. Signification is positively defined as "conventional representation of a thing by a locution" (VI.2); Supposition as "acceptance of a substantive term for something" (VI.3). They are relatively defined because Supposition presupposes Signification: "Supposition and Signification differ because Signification is the imposition of a locution to signify a thing, but Supposition is the acceptance of that term, already significant of a thing, for something" (ibid.). Both are subcategorized and related, but the chief interest is in the sense and reference of common nouns, discussed as the Signification and Supposition of common terms. (pp. 70-71)

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