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Proofs of Propositions in 14th-Century Logic
Research Project: History and Philosophy of Logic and Mathematics
May 23 - May 24
Paul Spade complained in 2000 that four key components of late medieval logic were mysterious to modern scholars. Since then, much has been done to clarify two of them (obligations and supposition), but the other two (exposition and proofs of propositions) remain just as mysterious. The aim of this workshop is to reach a clearer understanding of the genre of ‘proofs of propositions’ (probationes propositionum) that came to characterize British logic in the second half of the 14th century. The workshop will also consider the earlier theories of ‘exposition’ that were subsumed into this new genre.
Tuesday 23 May
10:00 Graziana Ciola (Pisa) ‘Expositiones and Consequentiae in Marsilius of Inghen’
11:30 Mark Thakkar (St Andrews) ‘Wyclif’s Three Treatises on Proofs of Propositions’
14:00 Ota Pavlícek (Czech Academy of Sciences) ‘Alyngton, Tarteys and Wyclif: An Anonymous Treatise and a Commentary on Probationes Propositionum in MS Prague NK VIII F 16′
15:30 Harald Berger (Graz) ‘Helmoldus Zoltwedel and his Quaestiones Byligam, Prague c1390′
17:00 Martin Dekarli (Austrian Academy of Sciences) ‘Štepán of Palecz’s Notabilia Super Billingham: Another Witness to the Proofs of Propositions Tradition in Late Medieval Bohemia’
Wednesday 24 May
10:00 Egbert Bos (Leiden) ‘Henry of Coesfeld (?) as a Commentator on Billingham’s On the Tests of Terms, and the Expository Syllogism’
11:30 Joke Spruyt (Maastricht) ‘Henry of Coesfeld (?) on Gradation and Change’
14:00 Heresy Tour of St Andrews (Bess Rhodes)
15:30 Riccardo Strobino (Tufts) ‘Probatio and Expositio in Peter of Mantua’s Logic‘
17:00 Jenny Ashworth (Waterloo) ‘The Reception of Probationes in the Late 14th, 15th and Early 16th Centuries’
We gratefully acknowledge financial support from the Arché Research Centre, the Scots Philosophical Association, the St Andrews Institute for Mediaeval Studies, the Leverhulme Trust and the British Logic Colloquium.
Expositiones and Consequentiae in Marsilius of Inghen (Graziana Ciola)
I will focus on the second Book of Marsilius of Inghen’s Consequentiae (ca. 1369–1370), which deals with “consequences holding from exponentes to exposita” and offers an overview of “how all sentences in logic should be exposed” (II.1).
I will begin by contextualising Marsilius’ Consequentiae. Although his treatise is often listed – along with Buridan’s and Albert of Saxony’s – among those emblematic of the so-called Parisian or Continental tradition on consequentiae, it shows several relevant features typical of the contemporary English discussions on the subject. Furthermore, Marsilius’ text often happens to be transmitted in collections of mostly British logical works.
One interesting aspect of Marsilius’ Consequentiae is the insertion of a second book entirely devoted to expositions. We find a few chapters devoted to expositions within the sections on consequences in earlier systematic summae of logic (e.g. Ockham’s, Burley’s) and also in some later English authors (e.g. Billingham). However, these analyses of expositiones are neither as systematic nor as articulated as they are in Marsilius’ treatise. Furthermore, within the Parisian tradition, such examinations are either absent (e.g. Buridan’s Tractatus consequentiarum) or barely sketched (e.g. Albert of Saxony’s Perutilis logica IV). I am therefore going to examine the second book of Marsilius’ Consequentiae, by outlining its structure, some general features of the theory of expositiones as presented there, and how it connects to Marsilius’ theory of consequentiae tout court.
Wyclif’s Three Treatises on Proofs of Propositions (Mark Thakkar)
Wyclif’s three treatises on proofs of propositions (?c1370) have been obscured for over a century by the editio princeps, which buried them under the fictitious title ‘Logice continuacio’ and gave an inconsistent account of their structure. The resulting confusions continue to plague the scholarly literature, so I will begin by clearing them up. The main point of my talk, though, will be to raise the general question of what a probatio actually is. Contrary to the modern tendency to see it as an analysis or a test, I will argue that a probatio is in fact (surprise!) a proof.
Alyngton, Tarteys and Wyclif: An Anonymous Treatise and a Commentary on Probationes Propositionum in MS Prague NK VIII F 16 (Ota Pavlícek)
The unpublished treatise conserved in MS Prague Národní knihovna VIII F 16, named by František Šmahel “Collecta de probatione propositionum”, is part of the evidence for the reception of English logic in medieval Bohemia. The text is interesting from at least three points of view. First, it consists of several sub-treatises based largely on Wyclif’s and Tarteys’s logical tractates, which led to an understanding of the Collecta as a treatise based on these treatises. At the same time, the Collecta were also a subject to a commentary, and both of these texts betray the influence of Robert Alyngton. Second, the text is interesting for understanding the working method of the medieval author, i.e. what he borrowed from Wyclif and Tarteys (and Alyngton), what he decided to omit and what he decided to elaborate. Finally, there is a possibility that the author of the Collecta was Jerome of Prague, the famous propagator of Wyclif’s philosophy. In my paper, I will first summarise Šmahel’s findings on the structure of the Collecta. Next, based on my transcription of the text, I will show how the author works with Wyclif’s treatises, how he expands or limits Wyclif’s theories and what his other sources are. In particular, I will focus on the Collecta’s chapters related to the problematics of chapters 1–3 of the first treatise of Wyclif’s so-called Logicae continuatio in which Wyclif laid the foundations of his view on probationes propositionum. One of the reasons for this selection is that the commentary on the Collecta is related to the first of these chapters, i.e. the one relating to the primary and secondary significations of propositions. Finally, I will show the textual and doctrinal parallels between the Collecta and Jerome of Prague’s opus, and will try to discern if there are convincing proofs for ascribing the Collecta to Jerome. As we will see, there is a non-negligible connection between Jerome of Prague, John Wyclif, Robert Alyngton, and the Collecta with its commentary.
Helmoldus Zoltwedel and his Quaestiones Byligam, Prague c1390 (Harald Berger)
Helmoldus Gledenstede de Zoltwedel (†1441) is a very interesting figure in the scientific community of the late 14th and early 15th centuries. He was a graduate of the faculties of arts, medicine, and theology, and he was active as such at the Prague and Leipzig universities. In this talk, I shall firstly present Helmold’s life and works. These works are valuable sources for the history of logic and philosophy at the end of the 14th century, because Helmold quotes many authors of his times by name.
Helmold’s Quaestiones parvorum logicalium, composed at Prague in around 1390, are probably the most comprehensive work of the genre, with regard to both parts and pages: the work comprises nine parts and fills some 200 leaves in folio. The seventh part is devoted to the liber Byligam and comprises 20 questions. I shall focus on the relation of the scientia Byligam to the scientia sophistriae (qq. 1–2) and on the termini exponibiles (qu. 12).
Štepán of Palecz’s Notabilia Super Billingham: Another Witness to the Proofs of Propositions Tradition in Late Medieval Bohemia (Martin Dekarli)
The majority of historians consider the oeuvre of John Wyclif (d. 1384) as one of the most important sources imported from England to the milieu of Prague University. After 1385, Wyclif’s treatises received vast acclaim from Czech realists such as Stanislaus of Znojmo (d. 1414), Štepán of Palecz (d. 1422), Jan Hus (d. 1415) and Jerome of Prague (d. 1416). However, from the late 1360s, several English logical treatises by Richard Brinkley (d. ca. 1350), Richard Kilvington (d. 1361), Richard Billingham (d. ca. 1361) and William Heytesbury (d. 1372/3) had already been studied by generations of Prague masters. One of the frequently used handbooks and tools employed for teaching purposes in Prague during the late Middle Ages was Billingham’s De probatione terminorum. The impact of this work on the universities’ logic curricula during the 14th century, including that of Prague University, has been thoroughly studied for several decades thanks to A. Maierù, L. M. de Rijk, E. P. Bos and other scholars.
Another text belonging to the late medieval proofs of propositions tradition is preserved in MS Prague NK X H 9, ff. 101r–108v, under the title Notabilia super Billingham. This short tract was compiled sometime around the mid-1390s and its authorship can be attributed to the Czech realist Štepán of Palecz. The aim of my talk is to present the content of this work and to provide its contextualization into Prague’s late medieval proofs of propositions tradition, i.e. to retrace further the influence of English logic on the European continent.
Henry of Coesfeld (?) as a Commentator on Billingham’s On the Tests of Terms, and the Expository Syllogism (Egbert Bos)
In this paper I would like to announce an edition prepared by Joke Spruyt and myself of a commentary on Richard Billingham’s handbook De probationibus terminorum (‘On the tests of terms’). The commentary is ascribed to a certain Henry of Coesfeld, probably living in the second half of the fourteenth century in the eastern part of Holland. Which are the manuscripts, how are they related? To give an impression of the nature of this commentary I have selected Henry’s comments on Richard’s remarks on the expository syllogism, both affirmative and negative.
Following Richard’s text, Henry starts with a discussion of the affirmative expository syllogism. This kind of syllogism is one of the main points of interest in both Billingham’s and Henry’s work. According to them it is the basis of all syllogistic reasoning. It is in the context of this kind of syllogism that 1) the part played by singular terms is investigated, and, 2) in logical connection on occasion of the Trinitarian syllogism ‘Iste Deus est pater, et iste Deus est filius, ergo filius est pater’, the question is considered in how far syllogistic reasoning is universally formal. Henry elaborates and clarifies Richard’s view on both points and solves the problem of the Trinitarian syllogism by introducing the formula ‘omne quod est’, thus reducing it to the ‘dici de omni et nullo’ principle. Henry says: ‘Ergo non sequitur “Iste Deus est pater, iste Deus est filius, ergo filius est pater”, quia non sequitur “Iste Deus est pater, ergo omne quod est iste Deus est pater”, quia antecedens est verum et consequens falsum’. So, in his opinion, singular theological propositions should in this case be universalized.
As to the negative expository syllogism, Henry corrects Billingham’s account on the topic of its foundation. He notes that to test the truth of a negative expository syllogism, three more conditions are required than the ones listed by Billingham with regard to the affirmative one.
Henry of Coesfeld (?) on Gradation and Change (Joke Spruyt)
The commentary on Richard Billingham’s De probationibus terminorum presumably written by Henry of Coesfeld pays ample attention to propositions with expressions indicating comparison and change. While Billingham’s explanations of some of those expressions are quite brief and not always clear, Coesfeld makes distinctions and goes more deeply into the complications that arise when several expressions come together in one sentence.
In that regard, Coesfeld’s comments on expressions featuring the superlatives ‘primum’ and ‘ultimum’ are interesting to look at. He starts off with Billingham’s exposition of the sentence ‘hoc erit primum istorum’. Billingham pronounces that this expression should be analysed as follows: ‘hoc erit pridem istorum, vel pridem inter istos, et nullus istorum erit prior isto, sed aliqui istorum erunt posteriores eo, igitur hoc erit primum istorum.’ Coesfeld adds that the master also says that this exposition applies whether or not something is added to ‘primum’, so that we should analyse a sentence like ‘Sortes erit primus istorum qui venient’ in the same way.
But Henry is not altogether satisfied with Billingham’s analysis, and comes up with a list of dubia to illustrate his point that matters are somewhat more complex than the auctor makes them out to be. What to say of propositions featuring the combinations ‘primum instans’ and ‘ultimum instans’, for example? Coesfeld takes this opportunity to embark on a more elaborate conceptual analysis of physical phenomena.
Probatio and Expositio in Peter of Mantua’s Logic (Riccardo Strobino)
Peter of Mantua’s (d. 1399) Logica has attracted attention over the past few years for its original way of combining elements and views borrowed from the two main logical traditions of the 14th century, the English and the Continental, which reflects a high sophisticated level of reception and interpretation of materials in the logica moderna roughly a generation before Paul of Venice, whom orthodox scholarship used to regard until recently as the first and main representative of this Italian tradition of assimilation and appropriation.
An unexplored area of Peter of Mantua’s vast and advanced logic textbook includes a number of treatises on probatio, in particular one on the proof of the universal proposition, one on the proof of the propositio exclusiva and one on proof of the propositio exceptiva. The purpose of this paper is to offer a first account of the text and doctrine of these treatises and their role in Peter’s logic alongside other chapters on the expositio of canonical types of propositions such as the reduplicative and of standard syncategorematic terms.
The Reception of Probationes in the Late 14th, 15th and Early 16th Centuries (Jenny Ashworth)
Treatises on proofs of terms seem to have developed from texts on syncategoremata, abstractiones, and sophismata, and they seem to have been replaced by texts on exponibilia, which themselves disappeared during the sixteenth century. In this paper I will look at some English texts on proofs of terms, especially those that were printed in England, and I shall consider their relationship with some Italian logicians. I shall focus on resoluble propositions and the distinction beween immediate and mediate terms, since the treatment of these notions seems to have been peculiar to texts on the proofs of terms.
Other events in History and Philosophy of Logic and Mathematics
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