I study Aristotle’s logic, reading in particular his syllogistic with the context of dialectical debates as the historical and cultural background.

I defended my PhD dissertationin 2021, “Aristotle, Science and the Dialectician’s Activity. A Dialogical Approach to Aristotle’s Logic” which was recognized as one of the best dissertations in mathematical logic and foundations of exact sciences by the DVMLG (Colloquium Logicum 2022, Konstanz).

Shahid Rahman, Zoe McConaughey, Ansten Klev, Nicolas Clerbout (Springer)

This monograph develops a variant of Lorenzen and Lorenz’s « dialogical logic ».

« Dialogical logic » is an interaction-based, pragmatist framework that can express many different logics with dialogues (intuitionist, classical, modal, syllogistic logics among others). The framework is dynamic and pluralistic. Part of the monograph consists in presenting step by step the standard framework, with examples and exercises with solutions.

The variant « Immanent Reasoning » integrates the notation from Per Martin-Löf’s « Constructive Type Theory » in order to explicit reasons backing a statement within the object-language. The central idea behind « Immanent Reasoning » is that a player (the proponent) builds the formal reason backing his initial statement through the interaction with the other player (the opponent), so that the justification for a statement is immanent to the argumentative dialogue with a partner. The « equality in action » refers to the fact that the proponent’s best reason backing a statement is that the opponent herself just said so: the equality between statements is produced through interaction in the dialogue.

This entry presents the framework of « dialogical logic » in the initial Lorenzen and Lorenz tradition. The rules for the game and for building strategies are provided with step by step examples, helping the reader understand how the dialogue tables reflect a dynamic process of interaction between the players. Various logics are presented within this pluralistic framework: intuitionist logic, classical logic, and modal logics, with references to various other logics.

In a second part of the entry, objections against the framework are considered, together with answers provided by the « Immanent Reasoning » variant, which stays within the Lorenzen and Lorenz tradition, and by the « Built-In Opponent » variant first developed by Catarina Dutilh Novaes, which develops a different dialogical tradition.

Michel Crubellier, Mathieu Marion, Zoe McConaughey, Shahid Rahman (HPL)

This collective paper develops a historical and a logical approach to propose a new interpretation of Aristotle’s « ecthesis » and the role of the « dictum de omni » in the Prior Analytics. The first part of the paper examines what « ecthesis » has been taken to be in the literature, while the second part develops a dialogical interpretation of this notion (understood as a procedure and as a step within that procedure), inspired by the dialogical framework of Lorenzen and Lorenz and based on Aristotle’s texts. A third and final part of the paper then reconstructs part of Aristotle’s assertoric syllogistic within the dialogical « Immanent Reasoning » framework, which is based on the understanding previously expounded that « ecthesis » is the procedure for carrying out the meaning explanation of quantification found in the « dictum de omni », and thus lies behind every syllogistic figure and every proof. The formal reconstruction explicits this interpretation of « ecthesis » and the « dictum de omni », and its dialogical structure gives external ground for drawing the Prior Analytics closer to the Topics.

Note: the formal reconstruction in this paper reflects an early stage of my PhD studies; though the framework remains the same, the formal reconstruction found in my PhD dissertation is slightly different and more robust in the sense that it can account for all of Aristotle’s assertoric syllogistic (conversion, figures, ecthesis, indirect deduction, reduction to the first figure, middle term, invalid moods).

« This book is a collective work built on the efforts of 62 women, including authors, reviewers, and editors. It features ten original contributions to different fields of ancient and medieval philosophy, all of which have been peer-reviewed in a double-anonymous process. Each contribution is accompanied by one or two response-and-discussion papers by scholars, thus opening new perspectives and engaging in further reflections on the matters at hand. Such a model provides the reader with a broader philosophical discussion of the topics addressed by the articles » (taken from the editors’ preface).

The volume is an offspring of the three-day « Symposium in Ancient and Medieval Philosophy—Feminine* Perspectives » which was held in Montreal in 2018. The same spirit was kept for the volume: we wanted contributions from women scholars on any topic in ancient and medieval philosophy, and we added the extra criterion that the peer-reviewers should also be women. In order to make the volume more dynamic, we included one or two response-and-discussion papers, making each topic the subject of discussion.

By focusing on the law of excluded middle, this paper addresses one of the main philosophical problems underlying logical systems, namely, the problem of clearly demarcating the notions of truth, proof, and meaning. The main contention of the paper is that the dialogical framework of Lorenzen and Lorenz has the philosophical means for distinguishing these three notions and defining them in a non-circular way (see part 2 of the paper). I argue in the first part that in his « intuitionistic period » of the 1920s, Hermann Weyl developed many philosophical considerations on these three notions and their relation, in particular with regard to the law of excluded middle, but he did not formalize these ideas within a logical system. The second part of the paper shows that the dialogical framework provides a formal framework adapted to Weyl’s philosophical considerations.