Preliminary descriptions of medieval logic have first been attempted in the 1950ies by P. Boehner and by E. Moody. In the subsequent 75 years, various important works of medieval logicians such as P. Abelard, J. Buridan, W. Burley, R. Kilwardby, W. Ockham, or Paul of Venice have been edited and, and least partially, translated into English. Furthermore, in recent times several monographs on the philosophy and logic of some individual medieval thinkers have been published. Yet, until now, no comprehensive exposition of medieval logic appears to exist. This is very regrettable because the ideas of logicians especially from 13 th and 14 th century are of great interest also for contemporary discussions of, e.g., paraconsistent logic, relevance logic, and connexive logic. The aim of this tutorial is to give a survey of the most important findings in this area.

 1. The heritage of ancient logic and major medieval innovations

In the first part, I will sketch the background of medieval logic, as it had been developed in particular by Aristotle (with his theory of the syllogism) and by the Stoics (with their investigation of the basic laws of propositional logic). Furthermore, I will briefly deal with two issues of what Boehner called the “new elements of Scholastic logic”, namely, a systematic investigation of syncategorematic expressions, and of the properties of terms (in particular their theory of supposition and distribution). The other “new elements”, namely the investigation of sophisms and paradoxes, and the elaboration of the theory of consequences, will be dealt with in parts 2 and 3 of the tutorial.

2. Modal propositional logic

The second part of the tutorial offers a thorough analysis of the medieval theory of compound propositions. This theory comprises not only the truth-conditions for conjunctions, disjunctions, and implications, but also an investigation of the necessity, possibility, impossibility, and contingency of such “hypothetical” propositions. Moreover, the medieval theory of inferences (“consequentiae”) with the main distinctions between (i) formally valid inferences, (ii) “simply” or materially valid inferences, and (iii) inferences which are valid “as  of now” (“ut nunc”) will be explained.

3. Sophisms, paradoxes, and self-refuting propositions

Under the label “Sophismata”, medieval logic abounds with sophisticated discussions of (apparent or real) contradictions. Some of these sophisms may easily be resolved as mere fallacies; others serious challenge the foundations of “classical”, two-valued logic. On the one hand, the famous Liar paradox appears to constitute a proposition which is both false and true. On the other hand, there are many interesting propositions p which “refute themselves” in the sense that the assumption that p is true entails that p is false, but not conversely. Generally speaking, medieval logicians refused to accept the existence of real antinomies. The Liar and similar “insolubles” are considered to be necessarily false, since they entail their own negation; but the (provable) falsity of these propositions in conjunction with the fact that they maintain themselves to be false, is not taken as sufficient for concluding that they are therefore true. 

Many medieval logicians accepted, however, the existence of merely self-refuting propositions such as ‘Every proposition is false’, and they recognized that so-called “Aristotle’s Theses” (‘No proposition implies, or is implied by, both of two contradictory propositions’; ‘No proposition implies, or is implied by, its own negation’) holds only when restricted to possible antecedents and to non-necessary consequents. This result also follows from the principles “Ex impossibili quodlibet” and “Necessarium ad quodlibet”, the validity of which is safeguarded by the very definition of a true conditional (or a valid inference).

 References

P. Boehner, Medieval Logic, Chicago 1952.

W. Lenzen, Essays in Medieval Logic (with special emphasis on issues of connexive logic),

forthcoming.

E. Moody, Truth and Consequence in Medieval Logic, Amsterdam 1953. 

-------------------------------------------------------------------------------------------------------------------

The pertinent results have been published during the past few years in the following publications of mine:

(Book)

Abelards Logik, Paderborn: Brill 2021.

(Articles)

“Ockham’s Calculus of Strict Implication” (Logica Universalis Special Volume 2015)

“A Critical Examination of the Historical Origins of Connexive Logic” (History and Philosophy of Logic, 2020)

“Kilwardby’s 55th Lesson” (Logic and Logical Philosophy , 2020)

“What follows from the Impossible – Everything or Nothing?” (History and Philosophy of Logic 2022)

“Rewriting the History of Connexive Logic” (Journal of Philosophical Logic 2022)

“Abelard and the Development of Connexive Logic” (Logica Yearbook 2023)

“Buridan on ‘Ex impossibili quodlibet’, ‘Ex contradictione quodlibet’, and ‘Ex falso quodlibet’” (Inquiry 2024)

“Buridan’s Theory of Consequences” (History and Philosophy of Logic 2024)

““A Medieval Controversy about Entailments between Categorical and ‘Continuing’ Propositions” (History and Philosophy of Logic 2024)

“Even in Logic Laws may Admit of Exceptions – A Survey of some Important Medieval Insights” (Problemos 2024)

“Burleigh on Impossible Antecedents and a Generalisation of ‘Burleigh’s Paradox’” (Festschrift für Volker Peckhaus 2025)

“Paul of Venice’s Disjunction Theses” (History of Philosophy and Logical Analysis 2025).

“Albert of Saxony’s Variants of the Liar”. (Proceedings of the 24th European Symposium on Medieval Logic and Semantics, Parma 2024).

“The Pseudo-Scot on the Liar Paradox and on Aristotle’s Theses” (Proceedings of the Logica 2025 conference)