Dutilh Novaes, Catarina. 2000. A Study of William of Ockham's Logic - From Suppositio to Truth Conditions, , University of Amsterdam.

Available at the University of Amsterdam.

Abstract: "This work is the result of my attempts to combine my Philosophy background with the Mathematical Logic inclinations of the institution within which this research was developed. In fact, this twofold character is noticeable in many features thereof; I shall now outline some of them.

The project has two main purposes: the less risky one is to provide an account of William of Ockham's logical thinking, with focus on its aspects which bear a relation with the contemporary issues of intensional logics and possible-world semantics. The more risky one consists of investigating the possibilities of developing a purely extensional treatment of intensional contexts, such as tense and modalities. For the latter, some other extensional/nominalistic systems could have played the role of `experimental sample', but there seemed to be something intriguing about Ockham, as one wonders whether a philosopher from the XIVth century would have something relevant to add to our present logical issues. Moreover, he is considered to be the founder of nominalism, so the historical interest of such enterprise was self-evident - therefore, the legitimacy of the first purpose.

I shall try to comply with two very distinct kinds of expectations: those which are the desiderata for a History of Philosophy work, and those of logicians, who are interested in the formal correcteness of the system hereby presented. The criteria of excellence of these two lines are almost incompatible, and one wonders if it is not a suicidal enterprise to try to combine them. On the one hand, an Ockham scholar may be discontent with the absence of a few important aspects of Ockham's logic, since I deliberately priorize those related to contemporary logic. On the other hand, a logician may be bothered by the presence of too many `antiquities', perhaps hindering logical clarity. So, at the risk of displeasing everybody, I nevertheless maintain that such a combination may turn out to be fruitful and informative to both sides.

Chapter 1 will display some fundamental aspects of Ockham's logic and semantics, in a rather historical approach. However, even this part is developed taking into account what I later shall want to establish as my version of an `ockhamist system'. I consider it to be the flaw of many such reconstructions that they do not undertake a serious analysis of the underlying concepts; alternatively, some which did rely on such an analysis have reached very interesting results.

Chapter 2 relates some apparently less central (when compared to supposition theory, for example) issues of Ockham's theory to relevant topics of Contemporary Philosophy, such as possible worlds, designation, demonstratives etc... In this chapter I also introduce conceptual tools which I will make use of for the reconstruction undertaken in chapter 3. Finally, Chapter 3 is an attempt to provide truth conditions for quantified, modal and tense propositions, based on the truth of singular propositions.

I hereby hope to reach a rather broad account of Ockham's thinking, even though my main target is to build a coherent and correctly structured reconstruction of his theory of propositions."
———. 2004. "The Buridanian Account of Inferential Relations between Doubly Quantified Propositions: a Proof of Soundness." History and Philosophy of Logic no. 25:225-243.

Abstract: "On the basis of passages from John Buridan’s Summula Suppositionibus and Sophismata, E. Karger has reconstructed what could be called the ‘Buridanian theory of inferential relations between doubly quantified propositions’, presented in her 1993 article ‘A theory of immediate inference contained in Buridan’s logic’.[*]

In the reconstruction, she focused on the syntactical elements of Buridan’s theory of modes of personal supposition to extract patterns of formally valid inferences between members of a certain class of basic categorical propositions. The present study aims at offering semantic corroboration—a proof of soundness—to the inferential relations syntactically identified by E. Karger, by means of the analysis of Buridan’s semantic definitions of the modes of personal supposition. The semantic analysis is done with the help of some modern logical concepts, in particular that of the model. In effect, the relations of inference syntactically established are shown to hold also from a semantic point of view, which means thus that this fragment of Buridan’s logic can be said to be sound."

[*] in: Klaus Jacobi (ed.), Argumentationstheorie. Scholastische Forschungen zu den logischen und semantischen Regeln korrekten FolgernsI, Leiden: Brill 1993, pp. 403-429.
———. 2007. "Theory of Supposition vs. Theory of Fallacies in Ockham." Vivarium no. 45:343-359.

Abstract: "I propose to examine the issue of whether the ancient tradition in logic continued to be developed in the later medieval period from the vantage point of the relations between two specific groups of theories, namely the medieval theories of supposition and the (originally) ancient theories of fallacies. More specifically, I examine whether supposition theories absorbed and replaced theories of fallacies, or whether the latter continued to exist, with respect to one particular author, William of Ockham. I compare different parts of Ockham's Summa Logicae, namely III-4 (on fallacies), and the final chapters of part I and first chapters of part II (on supposition). I conclude that there is overlap of conceptual apparatus and of goals (concerning propositions that must be distinguished) in Ockham's theories of supposition and of fallacies, but that the respective conceptual apparatuses also present substantial dissimilarities. Hence, theories of supposition are better seen as an addition to the general logical framework that medieval authors had inherited from ancient times, rather than the replacement of an ancient tradition by a medieval one. Indeed, supposition theories and fallacy theories had different tasks to fulfil, and in this sense both had their place in fourteenth century logic."
———. 2007. Formalizing Medieval Logical Theories: Suppositio, Consequentiae and Obligationes. New York: Springer.

Contents: Introduction I-XII; 1. Supposition theory: algorithmic hermeneutics 7; 2. Buridan's notion of Consequentia 79; 3. Obligationes as logical games 145; 4. The philosophy of formalization 215; Conclusion 293; References 301; Index of names and topics 310.

"From a modern perspective, the medieval writings in logic are incomprehensible. Not only is the language (Latin) a barrier; medieval logic was embedded in a complex conceptual framework, with constant use of highly technical jargon. But the most serious obstacle may be the modern tendency to express logical theories in especially devised notations, and with a certain axiomatic structure, which are not to be found in the medieval writings. Either way, it is clear that one way of establishing such a dialogue between these two traditions is to formalize fragments of medieval logic. And this is precisely what I set out to do. In particular, the objects of formalization in the present study are three topics from medieval logic, namely supposition, consequentia and obligationes; each can be seen as a case study demonstrating the fruitfulness of formalizing medieval logic." (pp. 2-3)

(...)

"The concept of supposition was already the topic of my master thesis, where I dealt with Ockham’s truth conditions for the main propositional forms, leaving aside the different kinds of supposition that are my concern here. Besides, supposition is a crucial concept in the medieval semantic framework, so it seemed appropriate to treat of it in the present context – even more so since supposition remains an unfinished topic within medieval scholarship. My main tenet is that, contrary to the accepted view, theories of supposition should not be compared to modern theories of reference.

Within the modern framework, they are best seen as theories of meaning, more specifically as theories for the algorithmic generation of the meanings that a certain body of propositions may carry. This insight came to me from a switch of perspective: theories of supposition should not be seen as static, but rather as procedural, in a sense that has recently become influential in logic." (p. 5)
———. 2008. "An Intensional Interpretation of Ockham's Theory of Supposition." Journal of the History of Philosophy no. 46:365-394.

"I have argued elsewhere that there are significant dissimilarities between theories of supposition and theories of reference, to the extent that the assimilation of the former to the latter becomes unfounded and misleading.(3) In fact, attributing the title of ‘theory of reference’ to any pre-Fregean theory is, to say the least, debatable.

Here, I argue that, if supposition theories are to be compared to a group of modern theories at all, it seems to be more fruitful to view them as theories of (propositional) meaning—insofar as they aim at the generation of the possible readings of (certain) propositions—and that this is true in particular of William of Ockham’s theory of supposition. To be sure, I am not contending that supposition is not fundamentally a property of terms in propositions; rather, what I claim is that, by establishing the possible supposita (i.e., the object[s] it may stand for) of a term in a proposition, Ockham intended to generate the possible meanings of the proposition in question. In other words, Ockham’s supposition theory does indeed concern this particular property of terms, their supposition, but it is in fact part of a larger program of propositional hermeneutics.

The conclusion I will draw from the textual, historical, and conceptual analysis to follow is that Ockham’s theory of supposition can be seen as a formal method for the semantic analysis of (certain) propositions, generating their possible readings. That is, the theory as formulated by Ockham is essentially intended to interpret propositions; it is a project of hermeneutics, but not in the sense that it relies on the subjective skills of the interpreter. Rather, it contains a set of rules that could be applied mechanically, in some senses resembling what is now known as computational semantics. Very important for this interpretation of supposition theory is its procedural nature, as these rules are viewed as a set of instructions to be carried out." (pp. 365-366, some notes omitted)

(3) C. Dutilh Novaes 2005, Formalizing Medieval Logical Theories—Suppositio, Consequentia and Obligationes [Formalizing] (Berlin: Springer, 2007), ch. 1.
———. 2008. "Logic in the 14th Century after Ockham." In Handbook of the History of Logic Vol. 2: Mediaeval and Renaissance Logic, edited by Gabbay, Dov and Woods, John, 433-504. Amsterdam: Elsevier.

"This chapter is meant to complement the previous chapter on Ockham’s and Buridan’s respective semantic systems, and the chapters on modalities, on self-referential paradoxes and on supposition in this volume. Here, I intend to cover for as much as possible the important material from the 14th century that is not covered by these other chapters."

(...)

"As any list of 14th century authors and texts (such as in [Spade, [Thoughts, Words and Things. Available at www.pwspade.com[ 1996, 329]) will show, the main logical topics treated in that period were: insolubilia (paradoxical propositions); modal propositions; supposition; the analysis (‘proof’) of propositions; obligations; and consequence."

(::.)

"As for the first two topics of this list, insolubilia and modal propositions (two of the main topics in 14th century logic), they are treated in detail elsewhere this volume, so I will not approach them here. We are thus left with the other four prominent logical genres in the 14th century: supposition, the analysis (‘proof’) of propositions, obligationes, and consequence. Indeed, this chapter is composed of three main parts, each of them dedicated to one of these topics – under the common heading of ‘semantics’, I treat supposition and, briefly, the theory of proofs of propositions. But before I move to the study of these three topics, in a preliminary section I give an overview of names, dates and places, so as to provide the reader with some of the historical background before we proceed to the conceptual analysis. The reader may also choose to turn directly to the thematic sections, if the historical aspects are not her main interest." (pp. 433-434)
———. 2011. "Ockham on Supposition and Equivocation in Mental Language." Proceedings of the Society for Medieval Logic and Metaphysics no. 3:47-64.

Abstract: "In my previous work on Ockham's theory of supposition, I have argued that it is best understood as a theory of sentential meaning, i.e., as an apparatus for the interpretation of sentences. In this paper, I address the challenge posed to this interpretation of Ockham's theory by the (presumed) existence of different kinds of supposition in mental language through the lenses of Ockham's theory of angelic communication. I identify two potentially problematic implications of Ockham's account of mental language as allowing for different kinds of supposition: the existence of non-significative supposition In mental language; and the possibility of ambiguous mental sentences. I then turn to angelic communication and examine these two issues from that point of view, concluding that there cannot be non-significative supposition in mental language, but also that there may still be room for sentential ambiguity in mental language."
———. 2012. "Ockham on Supposition Theory, Mental Language, and Angelic Communication." American Catholic Philosophical Quarterly no. 86:415-434.

Abstract: "In my previous work on Ockham's theory of supposition, I have argued that it is best understood as a theory of sentential meaning, i.e., as an apparatus for the interpretation of sentences. In this paper, I address the challenge posed to this interpretation of Ockham's theory by the (presumed) existence of different kinds of supposition in mental language through the lenses of Ockham's theory of angelic communication. I identify two potentially problematic implications of Ockham's account of mental language as allowing for different kinds of supposition: the existence of non-significative supposition in mental language; and the possibility of ambiguous mental sentences. I then turn to angelic communication and examine these two issues from that point of view, concluding that there cannot be non-significative supposition in mental language, but also that there may still be room for sentential ambiguity in mental language."
———. 2012. "Form and Matter in Later Latin Medieval Logic: The Cases of Suppositio and Consequentia." Journal of the History of Philosophy no. 50:339-364.

"Here, I would like to focus on a particular aspect of the Aristotelian metaphysical framework and its logical applications, namely uses of the form vs. matter distinction in logic. It is well known that Aristotle does not apply the form vs. matter distinction anywhere in his logical writings; in this respect, there is only a brief passage in Physics 195a18–19, and an almost identical passage in Metaphysics 1013b19–20. There he observes without much elaboration (in the context of a discussion of the four causes) that the premises (hypotheses) are matter for the conclusion (of an argument) “in the sense of ‘that from which,’” which is a familiar formulation for the notion of material cause. At first sight, this may seem surprising for two reasons: firstly, Aristotle applies the form vs. matter distinction in a wide variety of contexts, but not with respect to logic; secondly, subsequent traditions have made extensive use of this distinction in logic, so much so that the hylomorphic terminology is still ubiquitous in current (philosophy of) logic.

I shall focus on two specific Latin medieval applications of hylomorphism in logic: to the concepts of supposition and consequence. Significantly, these are among the most important topics of the logica modernorum tradition, and this lends support to the main thesis of the present contribution, namely that the assimilation of some elements of Aristotelian metaphysics into logic is a significant factor in the development of this tradition." (p. 340, a note omitted)
———. 2013. "The Role of 'Denotatur' in Ockham's Theory of Supposition." Vivarium no. 51:352-370.

Abstract: "In the scholarship on medieval logic and semantics of the last decades, Ockham’s theory of supposition is probably the most extensively studied version of such theories; yet, it seems that we still do not fully understand all its intricacies. In this paper, I focus on a phrase that occurs countless times throughout Ockham’s writings, but in particular in the sections dedicated to supposition in the Summa logicae: the phrase ‘denotatur’.

I claim that an adequate understanding of the role of the concept of denotatur within Ockham’s supposition theory shall yield a deeper understanding of the theory as a whole. Here, I first examine a few uses of the term ‘denotatur’ and its variants by other authors. I then turn to Ockham: first I briefly mention some uses of the term in contexts other than his theory of supposition. Following that, I focus on his supposition theory, in particular on how ‘denotatur’ allows him to deal with two crucial puzzles, namely the supposition of empty terms and the supposition of terms in false affirmative propositions.

The treatment of these two puzzles suggests that Ockham’s theory of supposition must be understood as a theory chiefly intended for the generation of the meanings of propositions."
———. 2015. "The Formal and the Formalized: The cases of Syllogistic and Supposition Theory." Kriterion no. 131:253-270.

Abstract: "As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied (i.e. theories of formalization). Regrettably, we now tend to view logic ‘proper’ exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss two historical theories of argument formalization: Aristotle’s syllogistic theory as presented in the “Prior Analytics”, and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments (i.e. the second sub-project). In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize."
———. 2018. "Ockham’s Supposition Theory as Formal Semantics." In Modern Views of Medieval Logic, edited by Kann, Christoph, Loewe, Benedikt, Rode, Christian and Uckelman, Sara L., 85-110. Leuven: Peeters.

"In what follows, I intend to show that William of Ockham’s theory, besides concerning the interpretation of propositions, is also essentially formal: it provides a procedure for the analysis of propositions that could be mechanically applied by anybody (or even by a machine), always yielding the same results. In this sense, his theory contrasts with traditional hermeneutical methods, which typically rely on the subjective skills of the interpreter. Moreover, Ockham’s supposition theory abstracts from the specific content of each particular proposition (since the meaning of propositions is precisely what is to be established), as it is based on a finite, small number of propositional schemata; what determines the schema to which a given proposition belongs – and thus the reading(s) it allows for – are (quasi-)formal features such as the semantic kind of its terms and the presence/absence of syncategorematic terms5, and not the particular meanings of its terms.

In order to spell out the formal, algorithmic character of Ockham’s supposition theory, I present here a non-symbolic reconstruction of it. Elsewhere(7), I have outlined this aspect of the theory by means of a formalization. But symbolization and formalization are not pre-conditions for formality: as I hope to show here, the formal character of Ockham’s theory can also be captured in ‘plain’ words. This reconstruction presents the theory as a formal procedure to generate the possible readings of some propositions, based on the relation between words and what they stand for." (pp. 85-86, som notes omitted)

(7) 7Part 1 of Dutilh Novaes (2007a). See also Parsons (2014) for a more recent formal treatment of medieval logical theories.

References

Dutilh Novaes, C. (2007a). Formalizing Medieval Logical Theories: Suppositio, Consequentiae and Obligationes. Springer, Berlin.

Parsons, T. (2014). Articulating Medieval Logic. Oxford University Press, Oxford.
———. 2020. "Supposition Theory." In Encyclopedia of Medieval Philosophy: Philosophy Between 500 and 1500. Second Edition, edited by Lagerlund, Henrik, 1819-1827. Dordrecht: Springer.

Abstract: "Supposition theory is one of the most important later medieval semantic theories (in the Latin tradition). Supposition is the property of terms (occurring in propositions) of standing for things, so that these things can be talked about by means of propositions, and supposition theory (in its different versions) is a theory codifying the different uses of terms in propositions, based on the idea that one and the same term can stand for different things when occurring in different propositional contexts. The different kinds of supposition are attempts to capture the phenomenon of semantic variation prompted by different propositional contexts.

The theory emerged in the twelfth century, and the two main traditions contributing to its development were the tradition of commentaries on Aristotle’s Sophistical Refutations and the tradition commenting on the fourth-century grammarian Priscian. Supposition theory acquired its first mature form in the thirteenth century, with the terminist/summulist tradition (in the works of William of Sherwood, Peter of Spain, Roger Bacon, and Lambert of Lagny/Auxerre), and was further developed in the fourteenth century by authors such as Walter Burley, William of Ockham, and John Buridan."
Ebbesen, Sten. 1979. "The Dead Man is Alive." Synthese no. 40:43-70.

"One of the thirteen fallacies treated by Aristotle in the Sophistici Elenchi turns on "something being said absolutely or in a certain respect" (in Latin: secundum quid et simpliciter). The false move in paralogisms falling under this fallacy consists in neglecting the difference between a qualified predicate and the same predicate unqualified.

In a short late 13th century Latin companion to the Elenchi we read(1) : "Secundum quid et simpliciter [ . . . ] The first mood of this fallacy is when there is an oppositio in adiecto, as in 'dead man'". The sophism referred to runs 'This is a dead man, therefore this is a man'. It is not mentioned in the Elenchi but Aristotle briefly alludes to it in De Interpretatione c. 11 21a21 which Ackrill (1963) translates: "When in what is added some opposite is contained from which a contradiction follows, it is not true but false (e.g. to call dead man a man)"." (p. 43)

(...)

"The 13th century knew two fundamentally different approaches to logical semantics, one concentrating on deducing the meaningof a sentence from the meaning of its terms. Roughly speaking this approach leads to intensional semantics. The other approach leads to an extensional semantics concentrating on the kind of meaning of a sentence that consists in its method of verification. Starting from the observation that people will and can communicate facts about the world to each other and do so by means of sentences consisting of words, the logician who chooses this approach studies the way this is conventionally done striving especially to discover the formal devices by means of which people indicate which comer of the world they are speaking about. Having formulated his discoveries in rules the logician is able for every" actual sentence to explain where one ought to look for verification of falsification of it."

(...)

"The notion of supposition is a genuinely Western invention. It has no counterpart in Greek scholasticism, although a series of Stoic problems which had been treated or mentioned by Porphyry in his major commentary on the Categories and which had passed from there into works the Westerners knew, viz. Boethins' commentary on the Categories and "Alexander's" on the Elenchi, played an important role in stimulating this kind of approach to logical semantics.(9)" (p. 46)

(1) Anonymus Bavaricus, Comm. in SE, f. 6vA: "Secundum autem quid et simpliciter [ . . . ] est primus modus quando est oppositio in adiecto, ut 'homo mortuus' vel quando est determinatio deminuens de ratione entitatis, ut 'opinabile' deminuit de entitate."

(9) For exatnple, the Stoic sophisms of the type called 'outis' passed through Porphyry and 'Alexander' to the West. Cf. Ebbesen (1976a, p. 155).

Refeences

Aekrill, J.L.: 1963, Aristotle's Categories and De lnterpretatione. Translated with Notes, Clarendon Press, Oxford.

Ebbesen, S.: 1976a, 'Anonymus Aurelianenis II, Aristotle, Alexander, Porphyry and Boethius. Ancient Scholasticism and 12th Century Western Europe', Universitéde Copenhague. Cahiers de l'lnstitut du Moyen-Age grec et latin 16.
———. 1981. "Early Supposition Theory (12th-13th Century)." Histoire, Épistémologie, Langage no. 3/1:35-48.

Reprinted in: S. Ebbesen, Topics in Latin Philosophy from the 12th-14th Centuries. Collected Essays Volume 2, Aldershot, Ashgate, 2009, pp. 1-14.

"The theory of supposition with the associated theories of copulatio (sign-capacity of adjectival terms), ampliatio (widening of referential domain), and distributio constitute one of the most original achievements of Western medieval logic. There is nothing really similar in any ancient text the medievals knew -though surely some Stoic writings once contained investigations of the problems these theories deal with -- nor had contemporary Byzantium anything similar.

The twelfth century produced a considerable harvest of rules about the referential range of terms in various contexts. When the 13th century arrived, a standard terminology had prevailed with such names as suppositio confusa and suppositio determinata for some particularly important types of referential range and a chapter on supposition had become a standard feature of Introductions to Logic (summulae). But then the development of the theory stopped. It appears that at least on the Continent, the chapter on supposition in the summulae became one that young students would be taught very early in their career, perhaps before entering university; and then forget all about through the rest of their student career.

In this paper I shall refrain from listing treatises 'de suppositionibus'; I shall on the whole refrain from following the developments of terminology and systematics. The spade-work in those fields has been done by De Rijk in his Logica Modernorum.

I will try to point to and explain some characteristic features of 12th and early 13th speculation about supposition without going into details and without paying much attention to the opinions of individual authors, not even when they protest they disagree with something I say they thought. I am not looking for the particular, but for general attitudes and patterns of thought underlying their investigation of suppositio." (p. 2 of the reprit)
———. 2013. "Early Supposition Theory II." Vivarium no. 51:60-78.

Abstract: "In 1981 I published an article called Early Supposition Theory.[*] Then as now, the magisterial work on the subject was L.M. de Rijk’s Logica Modernorum, and then as now any discussion of the topic would have to rely to a great extent on the texts published there.

This means that many of the problems that existed then still remain, but a couple of important new studies and several new texts have been published in the meantime, so it may be time to try to take stock of the situation. I will first look at the origin of the term suppositio and then at the chronology of our source texts. " (...)

"Conclusion

A host of questions concerning the dates of the relevant texts remain unresolved, but this is what I think the available evidence points to at this moment:

The main outlines of the story about supposition remain as in 1967, but the dates change. First, the birth of supposition theory took place in the very late twelfth century. The first signs of what was to come appear in the 1170s, but in logic centered round the notion of appellation, while supposition was becoming a key notion in theology.(43) A stage with a fairly developed terminology for types of supposition is not reached till about the 1190s, when also suppositio begins to outmanoeuvre appellatio, though this was to be a slow process. The majority of our early texts that teach or employ supposition, English and continental alike, were composed in the thirteenth century.

Finally, I think that although some authors may have had very clear ideas of which of the many uses of supponere was relevant in each particular context, they would generally be influenced both by the grammatical ‘putting as a subject’- tradition, the logical one of saying that what may be subsumed under a term supponitur under it, and the metaphysical thesis that bearers of forms supponuntur under their forms." (pp. 72-73)

(43) I am inclined to think that the Summa Zwettlensis is a work from about the 1170s. Häring’s date ‘before 1150’ rests on his very doubtful attribution of the work to one Peter of Poitiers/Vienna. See Valente (2008a), 25. If I am right, the Summa is approximately contemporary with Peter of Poitiers’ Sententiae, in which supponere is used in a relevant way, but without any developed system of types of supposition.

References

[*] Ebbesen, S. (1981), ‘Early Supposition Theory (12th-13th cent.)’, in: Histoire épistémologie langage 3, 35-48 (repr. in Ebbesen (2009)).

Ebbesen, S. (2009), Topics in Latin Philosophy from the 12th-14th centuries: Collected Essays of Sten Ebbesen, II (Aldershot 2009)

Valente, L. (2008), Logique et théologie. Les écoles parisiennes entre 1150 et 1220 (Sic et non; Paris 2008)
Eco, Umberto. 1984. "Signification and Denotation from Boethius to Ockham." Franciscan Studies no. 44:1-29.

"Prima facie, Ockham has little to say about the tortured story of the term "denotation." Baudry's Lexicon does not mention it. As far as I know- and in any case in his crucial texts on signification and supposition, Ockham does not use "denotation" but at most "denotari," in the passive form. However in this paper I shall try to provide some evidences for a further history of the term "denotation" and I shall suggest that this term started to shift from the intensional side to the extensional one just with or after Ockham." (p. 1)

(...)

"In its more mature formulation, supposition is the role played by a term, when inserted into a proposition, in order to refer to extra- linguistic things. From the first vague notions of "suppositum" to the most elaborate theories, such as the one of Ockham, the way was a long one, and there is a consistent literature on this topic (see de Rijk 1967 and 1982).(8) With the theory of supposition, the cognitive approach was over- whelmed by the extensional one and "reference and denotation was far more important than the more abstract notion of signification. What is primarily meant by a term is the concrete individual object the term can be correctly applied to" (de Rijk 1982:167)." (p. 12)

(8) It would be interesting to follow step by step the rise of a different idea of the relationship between a term and the external thing, where the notion of signification (as the relationship between words and concepts, or species, or universais, or definitions) becomes less and less important. See for instance in de Rijk (1982:161 ff.) how the followers of Priscian spoke of names as signifying a substance together with a quality, where the latter was undoubtedly the universal nature of the thing, but the former was the in- dividual thing (163): "so we find as early as the twelfth century 'supponere' (to supposit) as an equivalent for lignificare substantiam,' i.e. to signify the individual thing" (164). It is true that authors as William of Conches insist that names do not signify substance and quality but only the universal na ture and not the actual existence (168), and that during the whole twelfth century there is still a constant distinction between signification (of concepts and species) and nomination and appellation (denotation of concrete individual things- see for instance the Ars Meliduna).

References

De Rijk, L. M., ed., 1967. Logica modernorum, II,1. Assen: Van Gorcum.

De Rijk, L. M., 1982. "The Origins of the Theory of the Property of Terms." In N. Kretzmann et al., eds., The Cambridge History of Later Medieval Philosophy. Cambridge: Cambridge U. P., 1982.
———. 1989. "Denotaton." In On the Medieval Theory of Signs, edited by Eco, Umberto and Marmo, Costantino, 43-77. Amsterdam: Benjamins Publishes.

"Semioticians, linguists and philosophers of language frequently meet the term 'denotation'. Denotation (along with its counterpart, 'connotation') is alternatively considered as a property or function of (i) singular terms, (ii) declarative sentences, (iii) noun phrases and definite descriptions. In each case one has to decide whether this term has to be taken intensionally or extensionally: is 'denotation' tied to meaning or to reference? Does one mean by 'denotation' what is meant by the term or the named thing and, in case of sentences, what is the case.

As far as 'connotation' is concerned, if denotation has an extensional scope, it becomes the equivalent of intension, that is, of meaning as opposed to referent. If on the contrary denotation has an intensional scope, then connotation becomes a sort of further meaning depending on the first one." (p. 43)

(,,,)

"In the course of this paper I am interested in: (i) ascertaining what happened to the term significatio; (ii) when denotatio (along with designatio) occurs in connection with significatio and when it occurs as opposed to it.

As far as denotatio is concerned I am interested in registering its occurrence in one of the following three senses: (i) strong intensional sense (denotation is related to meaning); (ii) strong extensional sense (denotation is related to things or states of affairs); (iii) weak sense (denotation remains uncommitted between intension and extension with good reasons to take it intensionally).

We shall see that the weak sense predominates at least until the fourteenth century." (p. 49)
Fitzgerald, Michael Joseph. 1978. "Ockham's Implicit Priority of Analysis Rule?" Franciscan Studies no. 37:213-219.

"Some philosophers have doubted that Ockham intended his logical descent to singulars to be an analysis of quantified propositions.

Matthews has argued that fully descended propositions do not entail undescended ones because certain scope problems arise for the quantifiers when O propositions are analyzed.(1) Swiniarski has even provided us with a counterexample to descent as analysis.(2)"

(...)

"It is important to note, however, that neither Swiniarski nor Matthews has provided any textual support from Ockham's writings to show that he would allow the process of descent to begin with the predicate term prior to the subject term.

Now it seems to me that there are two distinct issues which are being blurred in their discussion of descent. The first issue is whether or not Ockham intended his descent to singulars to be an analysis of quantified propositions, snd the second is whether or not Ockham would allow the process of descent to begin with the predicate term.

Only if the process of descent begins under the predicate term, prior to the subject term, d o scope difficulties and possible counterexamples arise. Now, if it can be shown that Ockham would have rejected a case where descent begins with the predicate term, then the scope difficulties and counterexamples would not arise. If these scope difficulties do not arise, then one has no reason not to suppose that Ockham intended descent to be an analysis of quantified propositions.

What I would like to argue is that Ockham did intend for descent to be an analysis of quantified propositions, but he did not intend to allow descent to begin with the predicate term." (pp. 213-214)

(1) G. B. Matthews, "Supposition and Quantification in Ochham," Nous, VII (1973) 1 3-23.

(2) John Swiniarski, "A New Presentation of Ockham's theory of Supposition with an Evaluation of Some Contemporary Criiticism," Franciscan Studies, 30 (1970), 181-217.
———. 1982. Supposition and Signification: An Examination of Ockham's Theory of Reference, Rutgers University.

Unpublished Ph.D thesis, available at ProQuest Dissertation Express. Order number: 8221663.
———. 1984. "An Interpretative Dilemma in Burlean Semantics." Franciscan Studies no. 44:181-192.

"In his discussion of the debate between Walter Burley and William of Ockham, concerning the theories of signification and supposition, P. V. Spade has left us with a dilemma in interpreting Burlean semantics. Spade claims that the semantic relations between the notion of signification and the notion of supposition, in Burley's writings, clearly reflect the theory of cognition of the Arab-Aristotelian tradition where "understanding is of universals and sensation is of particulars."(1)

St. Thomas subscribed to such a theory, and argued that the intellect has an indirect knowledge of sensible particulars via a process he calls 'abstraction'." (p. 181)

(...)

"More precisely, Spade's dilemma can be formulated as follows:

1) If Burley allows simply supposing terms to indicate species, then he accepts the abstraction theory of cognition; and if he allows for a direct cognition of particulars by the intellect, then his epistemological theory does not reflect his semantic theory of proper supposition.

2) Either Burley allows for simply supposing terms to indicate species, or he allows for a direct cognition of particulars.

3) Therefore, either Burley accepts the abstraction theory of cognition, or his epistemological theory does not reflect his semantic theory of proper supposition.

This paper will undertake to grab this "bull" by the horns, and show the conjuctive premiss of the dilemma to be false. Burley does allow for the direct cognition of particulars by the intellect, yet simply supposing terms, for him, indicate species. Further, even though he allows for the direct cognition of particulars by the intellect, it does not follow that his epistemology is not reflected in his semantic theory of proper supposition." (pp. 182-183)

(1) Paul Vincent Spade, "Some Epistemological Implications of the Burley-Ockham Dispute," Franciscan Studies, 35 (1975): 221.
———. 2012. "Unconfusing Merely Confused Supposition in Albert of Saxony." Vivarium no. 50:161-189.

Abstract: "In this essay I argue that Albert would reject the need for a separate fourth mode of common personal supposition, and that his view of merely confused supposition has not been fully explicated by modern scholars. I first examine the various examples of conjunct descent given by modern scholars from his Perutilis logica, and show that Albert clearly adopts it in resolving the sophistic examples involved. Second, I explicate the view of merely confused supposition that Albert defends in his Sophismata, and then attempt to answer the question: which view of merely confused supposition was his final view, the view articulated in the Perutilis logica or the view in the Sophismata? I conclude that based upon his Sophismata view of merely confused supposition, Albert came to realize the logical strength his revised theory of personal supposition afforded, and consequently, that he is one of the earliest 14th-century logicians to adopt conjunct terminal descent to resolve various sophisms, a move which gave his theory of personal supposition a logical symmetry having two sorts of propositional descents to singulars, and two sorts of terminal descents to singulars."
Freddoso, Alfred J. 1979. "O-Propositions and Ockham's Theory of Supposition." Notre Dame Journal of Formal Logic no. 20:741-750.

"In their recent article "The Formalization of Ockham's Theory of Supposition" Priest and Read [4] make the following two claims:

1. In propositions(1) of the form of '(∃x)(P₁x & ∼ P₂x)' the predicate term, in this case P, has merely confused supposition, although Ockham mistakenly thought it to have confused and distributive supposition.

2. Contrary to the opinion of those who, like Geach, maintain that merely confused supposition is superfluous, there is at least one type of propositions (viz., negative indefinite exclusive propositions such as 'Only pigs don't fly') in which both the subject and the predicate have merely confused supposition, and in dealing with them the notion of merely confused supposition is ineliminable.

I will try to show in what follows that both of these claims are false.

Further, in my discussion of the first claim I will construct an alternative, though Ockhamistic, account of the supposition of the predicate in a particular negative proposition (O-proposition). I will then use this account in constructing an explication of negative indefinite exclusive propositions without recourse to the notion of merely confused supposition. Since my purpose is not explicitly to discuss or evaluate the formalization of Ockham's theory proposed by Priest and Read, I will make use instead of the sort of schematization employed by Loux in "Ockham on Generality" ([3], pp. 23-46). Thus, '{AD/'A'}' will stand for the appellative domain of A, i.e., for all those things which A can supposit for in a present-tense non-modal proposition. Also, the symbol v will be used as both a terminal and propositional connective, with the context of its occurrence making clear which use is intended. Finally, although I agree with Priest and Read that an adequate formalization of Ockham's theory must be given in an infinitary language, that issue is not germane to the points I wish to make here. So I will simplify the following discussion by treating the appellative domains of general terms as finite." (p. 741)

References

[3] Loux, M. J., ed. and trans., Ockham's Theory of Terms, University of Notre Dame Press, Notre Dame, Indiana, 1974.

[4] Priest, G. and S. Read, "The formalization of Ockham's theory of supposition," Mind, vol. 86 (1977), pp. 109-113.
Geach, Peter Thomas. 1956. "The doctrine of distribution." Mind no. 65:67-74.

"The doctrine of distribution occupies a peculiar position in logic.It is integral to the ' Aristotelian,' doctrine of categoricals and syllogisms; but it was quite unknown to Aristotle. Aristotle never uses rules like the modern rules about distribution to determine the validity of conversions and syllogisms; his whole procedure is different." (p. 67)

(...)

"We need only look at the traditional doctrine with a little carein order to see its deficiencies." (p. 67)

(...)

"The traditional doctrine is naturally popular; it is easy to apply mechanically, and it sounds intelligible. But we cannot really understand it without first reconstructing the logical edifice in which it is at home-- as it is not in contemporary class-logic.

We have already looked at one foundation of the edifice; we have seen how general terms are taken to be names, indeed as similated to proper names. (" Man " would then be a name of each man, not of the class of all men.) Another foundation is the identity theory of predication: viz. that in an affirmative categorical we have two names joined by a sign of identity, the predication being true if one and the same thing does indeed bear the two names. In " a dog is white ", " a dog " stan~s for ,a dog, " white " stands for something white, " is " is a sign of identity, and the whole is true if indeed one and the same thing is called both" a dog" and "white ".-Now the name-theory of general terms and the identity theory of predication are easily accepted even when they are explicitly formulated; still more so, when they are tacitly assumed.

In the Middle Ages many logicians explicitly held these two ·theories. Starting out from such simple-minded assumptions, they had to devise a complicated technical apparatus in order to fit the facts. This apparatus was the doctrine of suppositiones of terms. They were too acute to explain the varying inferential force of categoricals by the same term's signifying different objects - -"man" e.g. signifying now all men, now only some men -- -so they assumed instead variations in the modus significandi of a term, in what they called its suppositio." (pp. 70-71)
———. 1962. Reference and Generality: An Examination of Some Medieval and Modern Theories. Ithaca: Cornell University Press.

Second emended edition 1968; third revised and expanded edition 1980.

"The medieval term for what I call the mode of reference of a referring phrase was" suppositio". Apparently in origin this is a legal term meaning "going proxy for"; Aquinas and Ockham say quite indifferently that a term has suppositio for (supponit pro) and that it stands for (stat pro) one or more objects. In paraphrasing medieval writers I shall quite often tacitly use "mode of reference" for their" suppositio"." (p. 84 of the third edition)

(...)

"The medievals called the mode of reference of "any A" confused and distributive, that of "some A" determinate.

The point of the second epithet is that "f(some dog)" will be true iff some determinate interpretation of "x" in "f(x)" as the name of a dog makes "f(x)" true; a blurred awareness of this was what led to the untenable views that we studied in Chapter One, about the reference of "some man" to some man. For the epithet "confused and distributive" I shall generally substitute "distributive".

The doctrine of distributed terms is in fact originally a muddled memory of the mcdieval suppositio confusa et distributiva.

Distributive suppositio was called "confused and distributive" because of a supposed resemblance to another mode of reference (which we shall come to presently) called "merely confused"; but since I can see no specially important feature common to these two modes of reference rather than any other two, I shall for simplicity just call them the distributive and the confused mode of reference or suppositio." (p. 90)

(...)

"This concludes my treatment of the doctrine of suppositio.

The reader may well suppose that, in spite of the errors of detail into which Russell and the medievals fell, the theory must be essentially sound -- that something on these lines is needed, to deal with definite fallacies. I shall now try to show that the doctrine of suppositio is radically inconsistent, though less obviously so than the doctrine of distribution, and that we need to start all over again on new lines. Of course the fallacies which the doctrine of suppositio tried to eliminate are fallacies, and we shall have to give some account of them; but this no more justifies the doctrine of suppositio than the fallaciousness of syllogisms with an 'undistributed middle' is a ground for accepting the doctrine of distribution." (p. 104)
———. 1976. "Distribution and Suppositio." Mind no. 84:432-435.

"The doctrine of distribution is historically a simplified, indeed muti-lated, form of the medieval suppositio theories; in these theories the maindivision is made not between distributed and undistributed terms, butbetween confused and determinate suppositio." (p. 433)

(...)

"Some recent articles betray a confusion of mind as to the relation between medieval suppositio theories and the doctrine of distribution.

What is distinctive of the latter doctrine is its making fundamental the division between distributed and undistributed terms; in modern presentations of the doctrine, the terms possessing (to use medieval language) determinate suppositio and suppositio confusa tantum are indiscriminately called undistributed terms. In medieval theories, on the other hand, the main division is between suppositio confusa and determinate suppositio, and terms that are said to be distributed form one sub-class of terms having suppositio confusa: technically, they have suppositio confusa et distributiva mobilis. In 'Every nobleman possesses a dog', the prenex 'every' would be held to exert the power of giving confused suppositio (vim confundendi) as regards both following terms: the second has suppositio confusa tantum, the first has suppositio confusa et distributiva mobilis. Though it is not quite clear what common feature of terms suppositio confusa is here supposed to be, this doctrine is manifestly different from the doctrine of distribution in its standard modern presentation; and that doctrine is not to be read back into medieval authors merely on the ground that terminus distributus in medieval syllogistic rules extensionally coincides with the modern distributed term so far as terms occurring in ordinary syllogisms are concerned." (pp. 433-434)
Gordon, Alec. 2008. "Philosophical Translation, Metalanguage, and the Medieval Concept of Supposition." Medieval Philosophy no. 14:45-71.

Abstract: "In his Welcome Message for the XXII World Congress of Philosophy hosted by Seoul National University in August 2008 the President of the International Federation of Philosophical Societies (FISP), Peter Kemp, said that—inter alia—it will be an occasion “for rethinking the great philosophical questions.” Amongst there questions how we in the present understand the philosophical past is surely a perennial query before us. In this short paper I will refer to the endeavor of understanding past philosophical thought on its own terms or as presented in a current idiom as “philosophical translation.” The latter can take three forms: logical, analytical, or hermeneutic. This paper will briefly discuss all three forms vis-à-vis modern attempts to understand the medieval concept of “supposition” with special regard to the role metalanguage plays in philosophical translation."
Goubier, Frédéric. 2017. "The Role of the Speaker in Roger Bacon and William of Ockham's Supposition Theories: A Contrast." In The Language of Thought in Late Medieval Philosophy: Essays in Honor of Claude Panaccio, edited by Pelletier, Jenny and Roques, Magali, 169-182. Cham, Switzerland: Springer.

"While supposition theory is perhaps the closest thing medieval logicians have to a formal approach to semantics, it grants speakers a role. This role varies in importance from one logician to another. If we were to place the different positions on an axis stretching from the most semantic to the most pragmatic, William of Ockham and Roger Bacon would likely occupy the two extremes. On the semantic side, we would find William of Ockham and his apparent willingness to propose a system that seeks to determine sentences’ truth conditions as formally as possible.

On the pragmatic side and a few decades before Ockham, we would find Roger Bacon and his attempt to translate supposition theory into an intensional semantics of signification, so that the central importance of speakers is better described. This paper will rely on Claude Panaccio’s work on Ockham’s semantics and attempt to show that, in spite of the considerable differences that oppose the two theories, they share some fundamental ideas about the speakers’ involvement in the semantic processes."
Goubier, Frédéric, and Perini-Santos, Ernesto. 2015. "When the World is Not Enough: Medieval Ways to Deal with the Lack of Referents." Logica Universalis no. 9:213–235.

Abstract: "According to several late medieval logicians, the use the universal quantifier ‘omnis’ creates the requirement that the sentence refers to at least three items—the principle of sufficientia appellatorum. The commitment is such that, when the quota is not fulfilled, one has to import the missing items from the realm of the nonexistent. While the central argument for this principle, whose origin is Aristotle’s De Caelo, stems from the contrast between unrestricted universal quantifiers and binary quantifiers, the discussion is often mixed with another issue, concerning the requirement of a plurality of referents for universals. In this paper, we try to distinguish those different issues and map the reactions of xiiith authors to the principle of sufficientia appellatorum."
Henry, Desmond Paul. 1963. "The Early History of Suppositio." Franciscan Studies no. 23:205-212.

"The origins of the doctrine of suppositio are "shrouded in darkness" (BML p. 27) and it has not hitherto been possible to trace the details of its development (KDL p. 246). In BML (p. 27), however, the late Fr. Philotheus Boehner did conjecture that its roots might well stretch back to St.Anselm, but he added no further detail, the note accompanying this remark merely referring the reader to MSL, which contains no mention of St. Anselm. Hereunder, by selecting certain aspects of the Burleigh-Ockham debate on suppositio it is shown not only that the same issues were being debated by Anselm in the eleventh century, but also that they were being resolved by means of distinctions in ways of signifying, thereby confirming Fr. Boehner's conjecture. The sigla used are detailed at the close of this paper." (p-205)

Sigla

BML = Ph. Boehner, Medieval Logic,1952.

KDL = W. & M. Kneale, Development of Logic, 1962.

MSL = J. P. Mullally, The Summulae Logicales of Peter of Spain, 1945.
———. 1964. "Ockham, Suppositio, and Modern Logic." Notre Dame Journal of Formal Logic no. 5:290-292.

"In a discussion (Philosophical Review, Jan. 1964) of the alleged difficulties of rendering the descensus of Ockham's suppositio-doctrine in terms of modern logic, G. B. Matthews is concerned with the inferences corresponding to the following theses:

.1 If some man is animal, then this man is animal or that man is animal or

.2 If all men are animal then each man is either this animal or that animal or

.3 If some man is animal then some man is this animal or some man is that animal or

.4 If all men are animal then this man is animal and that man is animal and

.5 (3x)(Fx . Gx) ⊃ (Fx_{w .} Gx_q . v Fx₂ . Gx₂ . v........ )

It will be more convenient to continue the discussion in terms of such theses, rather than in terms of the corresponding inferences, but this, of course, has no material effect on the points at issue. The first of these is

whether (as alleged by P. Boehner in his Medieval Logic)(5) is a proper modern logical rendering of the form of .1 as understood by Ockham. That it cannot be is then shown by pointing out that the consequent of .5 would also have to be the prima facie modern rendering of the consequent of .3, thereby missing Ockham's point that there is a difference here. More complex renderings in terms of predicate calculus enriched by identity are suggested, but rejected on account of their involving double quantification over nominal variables and a "wastage of disjuncts" (or conjuncts) in that a consequent such as that of .5 must range over all the all the x's and not just all the men, as does the consequent of .1. The second issue is whether Boehner's reason for alleging that modern logic and Ockham's part company because the former has nothing parallel to .2 is adequate; the conclusion reached, after an attempt to render the consequent of .4 in terms similar to those earlier applied in respect of that of .3, is that in all the cases in question, i.e. .1 to .4, the basic trouble is that "Ockham quantifies over terms, whereas modern logicians quantify over variables"; ergo modern logic is here inadequate." (p. 290)
———. 1981. "Suppositio and Significatio in English Logic." In English Logic and Semantics from the End of the Twelfth Century to the Time of Ockham and Burleigh, edited by Braakhuis, Henk A.G. and Kneepkens, Corneille Henry, 361-387. Nijmegen: Ingenium Publishers.

"It is well-known(1) that there is a difference of opinion between Walter Burleigh and William of Ockham on the subject of suppositio simplex. Both agree that a term having suppositio personalis stands for individual objects,(2) and that, for example, in "Homo est species" the "homo" is a term having suppositio simplex.(3) Their disagreement centres on Ockham's in effect making suppositio personalis the model for his basic sense of significatio.(4) For him terms having suppositio personalis are used significatively: they then stand for (supponunt pro) what they signify, whereas terms having suppositio simplex do not do so; they stand for mental concepts.(5)

Burleigh, on the other hand, is clearly attempting to avoid a sense of "signify" which amounts to "standing for" in the suppositio personalis manner: contrary to Ockham he holds that suppositio personalis does not involve a term's standing for what it signifies. He is, however, prepared to say that this "standing for what it signifies" occurs when a term has suppositio simplex.(6)

It all depends, of course, on what is meant by "signify"." (p. 361)

(1) BML pp. 48-9, KDL pp. 267-272, SEI, SOS, SAC, HES, HL § 3.4.

(2) 0 I, Ch. 64, 69, B p. 3.

(3) 0 I, Ch. 64, 68, B p. 7.

(4) 0 I, Ch. 33.

(5) 0 I, Ch. 64, 68.

(6) B p. 3, p. 7; cf. HES pp. 205-7, HL § 3.40.

Sigla

B = Burleigh, W., De Puritate Artis Logicae (ed. P. Boehner, 1955)

BML = Boehner, P., Medieval Logic (Manchester U.P. 1952)

HES = Henry, D.P., "The early History of Suppositio" (Franciscan Studies 23, 1963)

HL = Henry, D.P., The Logic of St. Anselm (Oxford, Clarendon 1967)

KDL = Kneale, W. and Kneale M., The Development of Logic (Oxford, Clarendon 1962)

0 I = Ockham, Wm. of, Summa Logicae, Pars Prima (ed. P. Boehner 1957)

SAC = Spade, P. V., "Ockham' s Distinction between Absolute and Connotative Terms" (Vivarium XIII, 1975)

SEI = Spade, P.V., "Some Epistemological Implications of the Burley Ockham Dispute" (Franciscan Studies 35, 1975)

SOS = Spade, P. V., "Ockham' s Rule of Supposition: Two Conflicts in his Theory" (Vivarium XII, 1974)
Hoenen, Maarten J.F.M. . 2022. "Grammar, Logic, and Cognition: Magnus Hundt (1449-1519) and the Notion of Material Supposition." Mediaevalia. Textos e estudos no. 41:73-92.

Abstract: "In a number of late medieval treatises, the question is raised whether material supposition should be treated in logic or in grammar. Traditionally, this kind of supposition was dealt with in logic. However, some late medieval authors argued that it should rather be treated in grammar. At first glance, this debate may seem to be a fruitless scholastic exercise. Upon closer inspection, however, this issue sheds fundamental light on the different ways in which late medieval scholastics understood the relationship between thoughts, terms, and things.

In my paper I will focus mainly on the position of Magnus Hundt, who taught the arts at the University of Leipzig towards the end of the fifteenth century. He is not often mentioned in the modern literature. His position, however, is highly remarkable. As will become clear, Hundt’s rejection of material supposition as belonging to the field of logic is illustrative of his strategy of separating logic from grammar, in order to bring it closer to the science of metaphysics."
Hülsen, Reinhard. 2000. "Understanding the Semantics of "Relativa Grammaticalia". Some medieval logicians on anaphoric pronouns." In Reference and Anaphoric Relations, edited by Heusinger, Klaus von and Egli, Urs, 31-46. Dordrecht: Kluwer.

"When in the early nineteen-sixties Geach presented his by now well known theory of the semantic roles of anaphoric pronouns, he did something quite unusual in those days: time and again he critically referred to certain medieval approaches to the same subject. He thought, apparently, that these sophisticated approaches showed the enormous difficulties a coreferential approach was bound to lead into. Geach (1960) even went so far as to claim sweepingly that "the medievals who discussed relativa - pronouns with antecedents - were groping in the dark despite all their ingenuity." It is one of the ironies of the history of philosophy that one such medieval theory - to be found in the fourteenth-century philosopher Buridan and his pupils (though foreshadowed a century earlier) - has now raised his head again in the work of Gareth Evans - this time against Geach.

Geach was mainly thinking of logicians and philosophers working in the thirteenth and fourteenth centuries (virtually all the names he drops are from this period). However, interest in relativa grammaticalia - this is the complete title for expressions called "anaphoric" nowadays to separate them from "logical" relatives, expressions such as 'father' and 'master' - can be found already in twelfth-century writers such as Peter Abelard, William of Conches or their pupil John of Salisbury." (p. 31)
Ile, Vlad-Lucian. 2016. "Some Remarks on Peter of Spain`s Theory of Suppositio." Philobiblon no. 22:75-92.

Abstract: "The present paper aims to reconsider our approaches to the suppositio theory (in the particular case of Peter of Spain’s Summaries of logic) in light of a new hypothesis of the double nature¹ of medieval logic. Starting from the existing points of view, i.e. the theory of suppositio as a theory of reference and suppositio as a theory of an untranslatable, this paper will examine their underlying commitments to the nature of medieval logic. Such an analysis will entail for the former approach a commitment to a formal nature, while for the latter to a non-formal one. The possibility of a new approach emerges when both natures can be traced in Peter’s theory."
Kann, Christoph. 2016. "Supposition and Properties of Terms." In The Cambridge Companion to Medieval Logic, edited by Novaes, Catarina Dutilh and Read, Stephen, 220-244. Cambridge: Cambridge University Press.

"Probably the most prominent among the new topics were the doctrines of the so- called properties of terms (proprietates terminorum), which are generally considered the basis for later medieval semantic theorising and adjacent issues.

Terms (termini) in the technical sense presupposed here (and pointing to the “terminist” tradition) are descriptive words which function as subject or predicate in a proposition. The basic idea of the “properties” (or terministic) approach is that an analysis of the semantics of (compound) linguistic expressions should proceed by analysing the semantic properties of the terms occurring in it.

In handbooks of logic from the later Middle Ages, the treatment of the properties started with signification (significatio), the capacity of terms to function as signs; supposition (suppositio), the property

of terms functioning as subject or predicate in propositions, was its centrepiece, but the framework also covered related properties like copulation, appellation, ampliation, restriction, and distribution." (p. 220)
Karger, Elizabeth. 1984. "Modes of Personal Supposition: The Purpose and Usefulness of the Doctrine within Ockham's Logic." Franciscan Studies no. 44:87-106.

"The so-called "theory of modes of personal supposition," in particular Ockham's version of it, has been a recurring source of perplexity to recent commentators. One especially persistent worry has been that of determining whether and how the doctrine could be reformulated in modem logic." (p. 87)

(...)

"However no textual evidence was offered in favor of the basic hypothesis that the purpose of TM [theory of modes] is to operate such wholesale reductions of general sentences. For my part, I have been unable to discover a text which would confirm it. Consequently proposed "formalizations' of TM so interpreted ought, I think, be regarded with some suspicion, it being far from established that what has been formalized should be identified with TM at all." (p. 88)

(...)

"I conclude that the contribution which TM makes to Ockham's logic as a whole is a major one: although, by lack of the required concept of sentential form, Ockham himself would not have described the matter in such terms, TM alone provides the means of dealing, albeit in a limited way, with the logic of categorical sentences other than A-O form sentences. It must not be forgotten however that TM is essentially a semantical doctrine lacking a syntactical foundation, such as an adequate analysis of categorical sentences, leading to an enumeration of the logical forms involved, would have provided. Where such a basic requirement fails to be met, the doctrine is unavoidably imperfect, and the existence of such flaws as those we drew attention to in a footnote 25 should come as no surprise. What is surprising rather is that the doctrine nevertheless works as well as it does." (p. 106, notes omitted)
———. 1993. "A Theory of Immediate Inferences Contained in Buridan’s Logic." In Argumentationstheorie. Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns, edited by Jacobi, Klaus, 407-429. Leiden: Brill.

"Within scholastic logic however these rules [of subalternation and conversion] are derivable from more general rules or principles, capable of determining which inferences are formally valid within a much more inclusive set of inferential forms, forming thereby a more powerful theory. Let us call this theory "the generalized theory of subalternation and conversion", for short "the generalized SC-theory". This is a theory which requires the apparatus of' "modes of personal supposition'', the purpose of which, as I have argued elsewhere,(2) it reveals.

Among the logicians in whose writings this theory is to be found is Buridan. The principles in which the theory consists are formulated, more or less completely, in different places, notably in his Tractatus de Suppositionibus (hereafter "De Suppositionibus"), in his Sophismata and in his Tractatus de Consequentiis (hereafter "De Consequentiis"), Book 1, Chapter 8, where they form the 9th, l0th and 11th "conclusion''.

(...)

"This paper falls into four parts, two of which are preliminary to its main task. In part I, the framework within which the generalized SC-theory will be reconstructed is defined and the basic concepts introduced which the theory requires. Part II provides, within this framework, syntactical characterizations of the modes of personal supposition. In part III the principles of the generalized SC-theory are represented within the same framework and examples are given demonstrating the scope of their application. In part IV a parallel is drawn between the theory thus reconstructed and the logic of doubly quantified sentences." (pp. 407-408)

(2) Cf. E. Karger, "Modes of Personal Supposition: the purpose and usefulness of the theory within Ockham's Logic", Franciscan Studies 44, 1984, 87-106. I am indebted to Ned Markosian, a student of Gareth Matthews, for a very lucid criticism of that paper which has in part motivated the present reworking of the theory of immediate inferences based on the doctrine of modes of personal supposition, cf. Ned Markosian, "On Ockham's Supposition Theory and Karger's Rule of Inference", Franciscan Studies 48, 1988, 40-52. I would recommend any reader of the earlier paper to substitute the rule labelled here '' P2'' for the rule referred to in that paper as the "non-reciprocal TM rule" -Cf. also the article by Paul Spade on the subject of the theory of modes of personal supposition: "The Logic of the Categorical: The Medieval Theory of Descent and Ascent", in Meaning and Inference in Medieval Philosophy, ed. N. Kretzmann, Dordrecht: Kluwer, 1988, 187-224.
———. 1997. "Some 15th and Early 16th Century Logicians on the Quantification of Categorical Sentences (*)." Topoi.An International Review of Philosophy no. 16:65-76.

(*) This paper deals not with supposition theory, but with a syntactical theory which, in late medieval logic, underlies the theory of supposition.(...)

"The focus of this paper is on a late development of medieval logic, namely the recognition of multiply quantified categorical sentences. I shall be drawing mostly on authors who were active in the 15th or early 16th century. They are not, to be sure, household names.

One author even has the misfortune of not having had his name recorded: he is the anonymous author of a 15th century logical treatise sometimes referred to as the “Hagenau commentary”, because it purports to comment on works by earlier logicians, and because its second printing was made in Hagenau.(1) I shall refer to him as to the author of the Hagenau commentary. I shall also draw on the Summulae of the Spaniard Dominicus Soto(2) and on a work by the Flemish Judocus Clichtoveus who, though a humanist, wrote a remarkably clear exposition of scholastic logic. This useful book is an exposition and commentary of a summary of logic, called the “Introductiones Artificiales”, written by his friend Jacques Lefèvre d’Etaples, a noted theologian.(3) These three men had, at some time of their career at least, lived in Paris, for a logician and philosopher undoubtedly a very stimulating place to be, in those days. I shall also draw on earlier authors, to whom those I just mentioned, “our authors” as I shall call them, were heavily indebted.

These earlier authors, who had also been active in Paris, include the first rate logician and commentator on John Buridan, John Dorp, a late 14th century author and, of course, their common spiritual father, John Buridan himself." (p. 65)

(1) The treatise in question bears as title “Commentum in primum et quartum tractatum Petri Hispani et super tractatibus Marsilii de suppositionibus, ampliationibus, appellationibus et consequentiis”(hereafter “Comm.”), Hagenau; “1495, reprint Minerva, Frankfurt, 1967. On the printings of this treatise, see S. Read, “Thomas of Cleves and Collective Supposition”, in Vivarium vol. 29, 1991, 50–84, p. 79.

(2) Summulae (hereafter “SL”), third revised edition, Salamanca, 1554, reprint Olms, Hildesheim-New York, 1980. The first edition of this treatise was published in 1529.

(3) Jacobi Fabri Stapulensis artificiales nonnullae introductiones, per Judocum Clichtoveum in unum diligenter collectae, familiarique commentario per eumdem declaratae (hereafter “IA”), Paris, 1535 (already published in 1500). On the milieu to which this author belonged, see E. J. Ashworth, Language and Logic in the Postmedieval Period, Dordrecht, 1974, p. 10.
Kaye, Sharon. 1997. "Later Medieval Nominalism and the Politics of Supposition." Eidos.The Canadian Graduate Journal of Philosophy no. 14:29-50.

Abstract: "The salient dispute between realists and nominalists of the fourteenth century concerns the metaphysics of supposition. Do general terms stand for extra-mental universals or not? By answering in the affirmative, Walter Burley loses his ability to provide a plausible account of indefinite promises such as "I promise you a horse." By answering in the negative, Ockham not only explains indefinite promises, but also paves the way for a conception of the faith community more revolutionary than Protestantism. In the Bible, Jesus promises his disciples that he will be with them "always, to the end of the age." In Ockham's view, this is an indefinite promise parallel to the case of the horse; it means "I promise you a Christian." According to this analysis, the universal church can survive in a single, unlikely, and even unknown, individual. Ockham thereby undermines the doctrine of papal infallibility as well as institutional religion itself."

Skip to the top