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Medieval Logic and its Contemporary Relevance

30th April 2018

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Edgecliffe: the Philosophy Department


George Santayana once observed that those who do not remember the past are doomed to repeat it. Of course, history can be studied for many reasons, even for its own sake. But studying medieval logic, in particular, can make us aware of the consequences of certain ideas in at least two ways. First, the problems that medieval logicians were tackling are in many cases still with us today and still unresolved, more so than in some more recent periods. Secondly, though medieval academia was small in comparison to its modern counterpart, logic played a key role in the medieval curriculum and was the object of close attention by some remarkably perceptive thinkers. So the study of medieval logic has particular contemporary relevance and can yield many insights into contemporary puzzles in philosophy of logic. The object of the workshop is to encourage investigation into these connections and to showcase notable examples.

Enquiries about the workshop and registration should be addressed to arche@st-andrews.ac.uk. Registration is free, to include tea/coffee. Lunch on the workshop days, and dinner on 30 April and 1 May are available as options. Registration is now closed. The closing date for registration was 16 April.

For those staying in St Andrews after the end of the workshop on Wednesday afternoon, there will be an opportunity to join a free optional excursion: a walking tour of St Andrews following the Martyrs Sites from both sides in the Reformation (15th and 16th centuries). The tour will last about one hour or so. (Unfortunately, it has not been possible to arrange the visit to Special Collections, mentioned earlier.) 


Monday 30 April 2018 Tuesday 1 May Wednesday 2 May
9.30 Enrico Donato (Geneva), ‘Peter Abelard on Truthmaking and Events 9.30 Barbara Bartocci (St Andrews), ‘Topical Arguments in the Middle Ages and Today
10.30 Coffee 10.30 Coffee 10.30 Coffee
11.00 Stephen Read (St Andrews), ‘Swyneshed, Paradox and the Rule of Contradictory Pairs 11.00 Graham Priest (CUNY Graduate Center), ‘Some Contemporary Solutions to Some Medieval Problems about the Instant of Change 11.00 Graziana Ciola (UCLA), ‘Inferences, Entailments, Consequences and Conditionals (John Buridan, Albert of Saxony, Marsilius of Inghen)
12.00 Break 12.00 Break 12.00 Break
12.15 Catarina Dutilh Novaes (Amsterdam), ‘A Genealogy of Logical Hylomorphism 12.15 Lu Jiang (Sun Yat-sen University, Guangzhou), ‘Ockham’s Model of Time and His Solution to the Problem of Future Contingents 12.15 Bianca Bosman (Groningen), ‘What medieval containment logics can tell us about the notion of logical consequence
13.15 Lunch 13.15 Lunch 13.15 Lunch
14.15 Joshua Mendelsohn (Chicago), ‘Robert Kilwardby on the relationship between logical theory and logical methodology 14.15 Hanoch Ben-Yami (Central European University), ‘An Application of the Quantified Argument Calculus to the Study of Buridan’s Modal Logic 14.15 End of Workshop: followed an optional Excursion: Martyrs Sites (see above).
15.15 Break 15.15 Break
15.30 Sara Uckelman (Durham), ‘The Ways in which we can Learn from Medieval Logic 15.30 Mikko Yrjönsuuri (Jyväskylä), ‘Valid on Formal Grounds: Burley, Ockham and Buridan
16.30 Tea 16.30 Tea
17.00 Tomi Francis (Oxford), ‘Obligationes in Non-Classical Logics 17.00 Spencer Johnston (Cambridge), ‘Using Medieval Logic as an Inspiration for Relational Syllogistics
18.00 End 18.00 End
 19.30 Dinner at Forgan’s  19.30 Dinner at the Links Clubhouse


We are grateful to the British Society for the History of Philosophy, to the Leverhulme Trust, to the Scots Philosophical Association and to the University of St Andrews for financial support.

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Barbara Bartocci (St Andrews)

Title: ‘Topical Arguments in the Middle Ages and Today’

Abstract: TBA

Bianca Bosman (Groningen)

‘What medieval containment logics can tell us about the notion of logical consequence’

Abstract: An important recent development in contemporary relevant logics is the Routley-Meyer semantics, which proposes a ternary relation R between what they call “set-ups”. While these semantics are pragmatically very successful, it leaves an important question unanswered: what kinds of things does the relation hold between, and what does it mean for these things to stand in relation R to one another. A number of answers has been proposed, among which information-based approaches and truthmaker approaches. The information-based approaches suggest that the relation holds between pieces of information, whereas a truthmaker approach suggests that the relation holds between facts, states of affairs, or whatever one considers to be a truthmaker. We encounter a parallel problem in medieval logic.

Medieval logicians use several different criteria of validity for consequences. One of these criteria is known as the containment criterion. It states that a consequence is good or valid iff the antecedent contains the consequent. In this presentation, I will analyse some thirteenth-century uses of this criterion, and show that the notion of containment is used in three different ways. It may be (1) metaphysical: the property or thing signified by the consequent is contained in the nature or essence of the thing signified by the antecedent, (2) semantic: the meaning of (the term(s) in) the antecedent contains the meaning of (the term(s) in) the consequent, or (3) epistemic: if someone hears/thinks/believes the antecedent, he will also hear/think/believe the consequent. Usually, it is a combination of two or three of these notions. Using these findings, I will suggest a solution for the contemporary problem: one should, in fact, combine the information-based and truthmaker approaches.

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Graziana Ciola (UCLA)

‘Inferences, Entailments, Consequences and Conditionals (John Buridan, Albert of Saxony, Marsilius of Inghen)’

Abstract: This talk focuses on the ontology of consequences (consequentiae) and their relation to conditionals (propositiones hypotheticae conditionales) in some 14th century Parisian accounts, namely John Buridan’s, Albert of Saxony’s and Marsilius of Inghen’s.

According to an enduring interpretation, Medieval Logic could not distinguish between consequences and conditionals. Supposedly, this claim would be supported by definitions such as Buridan’s, describing consequentiae as propositiones hypotheticae (hypothetical sentences) that can be indifferently true (consequentia vera) or valid (consequentia bona or that tenet i.e. holds). By analysing Buridan’s, Albert’s and Marsilius’ quod sit definitions of consequence and their accounts of the equivalence between consequentiae and conditionals, I will show that this interpretation is patently wrong – at least for this group of Parisian theories.

I am going to suggest that Buridan’s conception of consequentia should be interpreted as an inference performed by a mind, rather than as a propositional relation. With this reading, along with Buridan’s propositional tokenism, we can offer an interpretation of Buridan’s quod sit definition of consequentia that maintains a conceptual distinction between consequences and conditionals while accounting for his terminological shifts. Furthermore, I am going to contrast Buridan’s theory with Marsilius of Inghen’s and Albert of Saxony’s. Marsilius seems to think of consequentiae as strong relations of propositional entailment. Since Marsilius holds (a) that only a valid consequence is a consequence, (b) that there is no such thing as a consequentia ut nunc (as-of-now), and (c) that consequentiae are equivalent to conditionals, his treatment of conditionals shows some peculiarities – namely, (d) that there are no false conditionals. Albert of Saxony’s take on consequentiae seems to be intermediate between Buridan’s and Marsilius’, which gives his theory some interesting features while also yielding some peculiar issues.

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Catarina Dutilh Novaes (Amsterdam)

‘A genealogy of logical hylomorphism’

Abstract: The idea that logic is formal, and that the notion of ‘logical form’ is essential for logical theorizing, are among the cornerstones of how logic is conceived of by 21st century philosophers and logicians. But where does this conceptualization come from? Has logic always been conceived of in this way? In my talk, I will present a genealogy of logical hylomorphism, going back to Aristotle and the ancient commentators, but focusing more extensively on the Latin medieval period. I emphasize the aspects of continuity as well as of change in these developments, based on the method of genealogical analysis described in (Dutilh Novaes 2015). The conclusion will be that knowledge of the history of logical hylomorphism, in particular in the Latin medieval period, is essential for a better grasp of current conceptions of logic, including of the contingent and potentially misguided focus on so-called logical constants.

(Since Catarina cannot be present in person, she will give her talk by Skype.)

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Spencer Johnston (Cambridge)

‘Using Medieval Logic as an Inspiration for Relational Syllogistics’

Abstract: The aim of this talk is to critically assess the proposal that formalising aspects of medieval logic can provide a fruitful location for thinking about decidable and tractable fragments of first-order (modal) logic. In this, we will focus our attention on Buridan’s extensions of the theory of syllogisms with oblique terms and non-normal terms. Starting with contemporary formal studies by Pratt-Hartmann and Moss on relational syllogisms and various extensions to these, we will show how Buridan’s theories suggest a number of more expressive extensions to these theories.

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Lu Jiang (Sun Yat-sen University, Guangzho)

‘Ockham’s Model of Time and His Solution to the Problem of Future Contingents’

Abstract: The ‘Sea-battle problem’ in Aristotle’s Perihermeneias consists in the aporia that the truth of a proposition concerning future contingent events will lead necessarily to the factual realization of these events, if we accept the principle that a proposition is necessarily true, when it is true. This principle is however only valid in a logical model where there is no alternative world, or each world has only access to itself. The Christian worldview allows alternative worlds, but through God’s predestination anything pre-known by God will be inevitably realized in the course of time. Duns Scotus tried to describe the contingency of future events by their alternatives in other worlds. William of Ockham shuns this solution as un-Aristotelian and tried to describe future contingency without counterfactuals. I shall show in my paper that Ockham’s modes of time are also modalities. His conception of propositions differs to that in modern propositional logic, for him each proposition is relative to the time. A certain proposition about a future contingent event becomes necessary, when the particular event is already realized, because the proposition, which can be formalized in the form F(A) (F: it will be the case that…) relative to any time point before the time point of the realization of A in the time, should be formalized as PF(A) (it was the case that it will be the case that…), when taken relatively to any time point after the realization of A, because it is senseless to speak of the future when the event concerned has already taken place. Basing on the common sense intuition that history is necessary, Ockham ascribes to any true proposition in the past sense the modality of necessity, accordingly a true proposition in the form of PF(A) is necessary.

This paper therefore endeavors to illustrate a model which explains modalities within an ontology basing on a lineal time flow, within which Ockham’s theory and solution to the problem of future contingency and predestination can be explained convincingly. It will be shown however, that Arthur Prior’s so called ‘Ockhamist’ branching time model doesn’t really illustrate what Ockham had in mind. Though borrowing the latter’s name, this model doesn’t illustrate a most central intuition of Ockham that any future event will become determined and necessary during the cause of the time. In this paper I shall therefore provide a diagram which is in my judgment a more adequate model to explain Ockham’s conception of time and modality. Without going too much into technical details, this paper shall provide a thorough and careful text analysis of Ockham’s Tractatus de praedestinatione et de praescientia dei respectu futurorum contingentium and his Commentary of Aristotle’s Perihermeneias, in order to provide sufficient support for my thesis and my proposal of a temporal diagram different to that of Prior. It shall serve as a basis for a future technical formalization of a modal-temporal model according to Ockham’s understanding of modality and temporality.

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Graham Priest (CUNY Graduate Center)

‘Some Contemporary Solutions to Some Medieval Problems about the Instant of Change’

Abstract: The Medievals inherited a number of problems about the instant of change from Aristotle. These were partly to do with physics, and partly to do with the logical analysis of the syncategorematic terms `begins’ (incipit), and `ceases’ (desinit). In this paper, we will look at some of the solutions they came up with, and some contemporary dialetheic solutions to the same problems.

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Stephen Read (St Andrews)

‘Swyneshed, Paradox and the Rule of Contradictory Pairs’

Abstract: Roger Swyneshed, in his treatise on insolubles (logical paradoxes), dating from the early 1330s, drew three notorious corollaries of his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict the Rule of Contradictory Pairs, which requires that in every such pair, one must be true and the other false. Looking back at Aristotle’s treatise {\em De Interpretatione}, we find that Aristotle himself, immediately after defining the notion of a contradictory pair, gave counterexamples to the rule. Thus Swyneshed’s solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation.

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Sara Uckelman (Durham)

Title: ‘The Ways in which we can Learn from Medieval Logic’

Abstract: TBA


Mikko Yrjönsuuri (Jyväskylä)

‘Valid on Formal Grounds: Burley, Ockham and Buridan’

Abstract: This paper argues that the early fourteenth century distinction between formally and materially valid consequences is best understood in modern terms as distinguishing between kinds of grounds for validity. The main authors discussed are Walter Burley, William Ockham and John Buridan. Modern scholarship has distinguished between “Parisian” and “English” traditions in understanding the concept “formally valid”. This paper shows how these traditions do not disagree on the nature of formally valid consequences, but on what exactly they are grounded on.

Burley, Ockham and Buridan all accept the identification of consequence as a truth preserving relation between sentences. When compared to, e.g., John Etchemendy’s discussion (Etchemendy 1990), it seems clear that these medieval authors had in mind something very much like what Etchemendy calls variably as “ordinary”, “natural”, or “genuine” consequence relation. That is, the medieval logicians cannot be seen as taking a stance between syntactic and semantic understanding of consequence in the way Etchemendy describes these two technical accounts. Instead, medieval logicians sought to identify various ways to ground properly the core inferential relation that results in truth preservation.

Three main types of grounds are separated by Burley and Ockham, and Buridan’s discussion too recognizes the three types. First, the validity of the logically core group of consequences are grounded on syntactic structures of the premises and the conclusion, in a manner closely reminiscent of our current understanding of logical form. Second, a further group is grounded on what would currently be characterized as analytic truth (eg. “a human exists, therefore, an animal exists”). And third, in some cases truth preservation is grounded on the simple fact of a premise being impossible (or ut nunc false) or the conclusion necessary (or ut nunc true). This paper shows how each of the three discussed authors dealt with the three cases.

From this perspective, it appears clear that the so called “Parisian tradition” was adopted by all three authors considered. All of them emphasized that the logically core type of validity is grounded on syntactic features of the premises and the conclusion. These syntactic features are captured by rules of inference that can be used for warrant. Thus, all three authors appear to take logic as a discipline that concerns language and the rules governing its usage.

The so called “English tradition” relied on the principle that for formal grounding of validity the conclusion must be “included in the understanding” of the premises. While this does not, either, ground validity directly on real natures of things, it does rely on conceivability. Logically interesting types of validity are, in this tradition, grounded on intelligibility rather than syntactic features of language. As an excursion, this paper considers how such an understanding of truth preservation fits to what are now called counterfactual conditionals  – which were also taken into account by some medieval logicians but never accepted as valid inferences in the sense to be discussed in logic.
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30th April 2018


Stephen Read
Barbara Bartocci


Edgecliffe 104
University of St Andrews
St Andrews, United Kingdom
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