This is a critical examination of Antoine Arnauld's Logic or the Art of Thinking (1662), commonly known as the Port-Royal Logic. Rather than reading this work from the viewpoint of post-Fregean formal logic or the viewpoint of seventeenth-century intellectual history, I approach it with the aim of exploring its relationship to that contemporary field which may be labeled informal logic and/or argumentation theory. It turns out that the Port-Royal Logic is a (...) precursor of this current field, or conversely, that this field may be said to be in the same tradition. (shrink)

The Port Royal Logic Logic or the Art of Thinking, commonly known as The Port Royal Logic, was written by Antoine Arnauld and Pierre Nicole and first published in 1662. Although it was a textbook containing much worked-over material, the Logic was extremely influential, certainly the most important textbook in logic for the next two … Continue reading Port Royal Logic →.

The Logic of Port-Royal, first published in 1662 by the Jansenists Antoine Arnauld and Pierre Nicole, is a work that underlines the inadequacies of the traditional logic. Traditional logic, which included the texts of Aristotle's Organon and the works of the scholastics, was experiencing a mild renaissance in the seventeenth century following its outright and brutal discrediting by the humanists of the previous two centuries. Arnauld and Nicole introduce a fairly original system of logic (...) that attempts to remedy the shortcomings of the revived tradition; they dismiss the Aristotelian "Categories", "Predicables", and "Topics", ignore the scholastic "Doctrine of Terms and Consequence", and suggest a single "General Principle" by means of which the validity of all arguments can be decided. The Principle is based on a notion of containment, divided into entendue and comprehension , which applies to all terms. Because the notion of containment is linked to the objective reality of Cartesian ideas, the authors can claim that their system of logic properly describes reality. The General Principle also suggests that terminist logic is logically and epistemologically prior to sentential logic because, Arnauld and Nicole claim, it governs the Dictum de Omni et Nullo and the Nota Notae. The self-evidence of the two dicta confirmed the validity of all syllogisms of the first figure; furthermore, all syllogisms of other figures could be reduced to one of the first figure. With the General Principle, however, there is no need for such reduction to the first figure. This additional result makes the theorem of sentential logic, "$\supset$r)$\approx$$\supset$-q)", which was needed for the reductions of Baroco and Bocardo, unnecessary. The fact that no theorem of sentential logic is needed to underline term logic guarantees the autonomy of the latter. (shrink)

This book sets out for the first time in English and in the terms of modern logic the semantics of the Port Royal Logic of Antoine Arnauld and Pierre Nicole, perhaps the most influential logic book in the 17th and 18th centuries. Its goal is to explain how the Logic reworks the foundation of pre-Cartesian logic so as to make it compatible with Descartes' metaphysics. The Logic's authors forged a new theory of (...) reference based on the medieval notion of objective being, which is essentially the modern notion of intentional content. Indeed, the book's central aim is to detail how the Logic reoriented semantics so that it centered on the notion of intentional content. This content, which the Logic calls comprehension, consists of an idea's defining modes. Mechanisms are defined in terms of comprehension that rework earlier explanations of central notions like conceptual inclusion, signification, abstraction, idea restriction, sensation, and most importantly within the Logic's metatheory, the concept of idea-extension, which is a new technical concept coined by the Logic. Although Descartes is famous for rejecting "Aristotelianism," he says virtually nothing about technical concepts in logic. His followers fill the gap. By putting to use the doctrine of objective being, which had been a relatively minor part of medieval logic, they preserve more central semantic doctrines, especially a correspondence theory of truth. A recurring theme of the book is the degree to which the Logic hews to medieval theory. This interpretation is at odds with what has become a standard reading among French scholars according to which this 16th-century work should be understood as rejecting earlier logic along with Aristotelian metaphysics, and as putting in its place structures more like those of 19th-century class theory. (shrink)

The Port-Royal Logic includes a brief discussion of modal propositions, containing several mnemonic devices for rules of equivalence governing the possibility, necessity, impossibility, and contingency of propositions. When the mnemonics are decoded, it can be seen that these rules treat possibility and contingency as formally equivalent modes. The aim of this paper is twofold: to show that this identification of possibility and contingency follows from the Logic’s formal treatment of those modes; and to show that such (...) a treatment of these modes conflicts with claims the authors make in other contexts. In particular, the equivalence of possibility and contingency conflicts with the Cartesian principle that whatever is clearly and distinctly conceivable is possible—a principle that Arnauld and Nicole explicitly endorse elsewhere in the Logic. Why, then, would the authors adopt such equivalence rules? The paper concludes with a discussion of the historical precedents for these rules: they were a standard feature of Scholastic logic textbooks in seventeenth century France. It is likely that Arnauld and Nicole simply reproduced the rules for this reason, without recognizing that they were a poor fit for a Cartesian logic textbook like the Port-Royal Logic. (shrink)

The paper discusses the place and the status of fallacies in Arnauld and Nicole’s Port-Royal Logic, which seems to be the first book to introduce a radical change from the traditional Aristotelian account of fallacies. The most striking innovation is not in the definition of a fallacy but in the publication of a new list of fallacies, dropping some Aristotelian ones and adding more than ten new ones. The first part of the paper deals with the context (...) of the book’s publication. We then show the influence of Cartesian and Augustinian/Pascalian philosophy on the whole book, especially their common critical views about logic, dialectic and their traditional academic teaching. The third part of the paper discusses the two chapters on fallacies. It focuses on their place in the book and their relation with its general orientation, before turning to their content, closely connected with some major concerns of the time. (shrink)

The paper shows that in the Art of Thinking (The Port Royal Logic) Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and (...) others, the truth-conditions do not require the introduction of a new concept of ‘indefinite’ term restriction because the notion of conservative quantifier is formulated in terms of the standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in an analysis of truth because it is explained in terms of entailment, and entailment in terms of truth. By abstracting from semantic identities that underlie distribution, the new concept of distributive term is definitionally prior to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic’s truth-conditions for the categorical propositions are stated solely in terms of (1) universal (distributive) term, (2) conservative quantifier, and (3) affirmative and negative proposition. It is explained why the Cartesian notion of extension as a set of ideas is in this context equivalent to medieval and modern notions of extension. (shrink)

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A note correcting some technical terminology from linguistics found in ‘Distributive Terms, Truth, and The Port Royal Logic’, this journal, Jan. 17, 2013, 133–54.

One of the most popular textbooks on logic, La Logique ou l’art de penser (better known as the Port Royal Logic), was written by Antoine Arnauld and Pierre Nicole and it was first published in 1662...

La Logique ou L'Art de Penser (LAP), also known as the Port-Royal Logic, is generally presented as a "logic of ideas" in which the idea, the central epistemological entity, is the starting point of this logic based on Cartesian ontology. Structured around the four main operations of the mind - conceiving, judging, reasoning and ordering - the first part of the LAP contains "reflections on ideas". The idea, "the form by which we represent things [objects]", (...) thus takes the place of the concept in Aristotelian-inspired logic. Some of the chapters in this first part deal with the problems raised in scholasticism by the theory of _proprietates terminorum_, which means that it is also a semantics of terms. The word 'term' itself must be understood in its logical and grammatical dimensions. The analyses of the 'Messieurs' of Port-Royal often have a logico-grammatical character, because, according to the anthropology of the authors, men need to make their thoughts heard by one another through language (institutional signs) and, therefore, "it is necessary in logic to consider ideas joined to words, and words joined to ideas". In this text, we shall endeavour to show the importance and innovative character of the semantics of terms in this logic of ideas which makes LAP a pivotal moment in the evolution of the language sciences, reviving the tradition and allowing dialogue with future developments (extension vs. comprehension, explanation, determination of terms, etc.). We will pay particular attention to the chapters on definition, "a remedy for the confusion that arises in our thoughts and speech from the confusion of words". (shrink)

The long-lasting and debatable claim that in the seventeenth century, logic did not attract the attention of the best minds, with the exception of Leibniz, is reassessed in current research in the...

The aim of this paper is to analyse and to discuss the philosophical reflexions on Geometry due to Blaise Pascal, Antoine Arnauld and Pierre Nicole. All of them were linked to the Jansenism, religious movement whose centre was at the Port Royal abbey. Our theses is that their philosophical thoughts on Geometry as well as their criticism of Euclid’s Elements were rooted not only in the works of the geometers and Element’s translators and commentators of the sixteenth century (...) but also on their particular conceptions about human knowledge and soul. Our text is divided into five parts. In the first part we examine the place of Geometry in the culture of the seventeenth century. After that, in the second part, we discuss the standard criticism directed against Euclid’s Elements. In the third part we analyse three works of Pascal: The spirit of geometry, The art of persuasion and some fragments that have survived of a text entitled Introduction of Geometry. In the fourth part we discuss the critical remarks of the Logic of Port Royal on the geometrical works, especially on the Elements. The fifth part of our work is devoted to Arnauld’s reconstruction of plane elementary Geometry in his New Elements of Geometry. The conclusions are set forth in the sixth part. (shrink)

In this study, I intend to show how and why, in the Port-Royal Logic, a singular term can reveal the nature of the logical judgment in the handbook. As I argue, the treatment given to one of thee singular terms, namely, the defined descriptions, in the terminology introduced by Russell, leads to an opening to langage that sounds unexpected and unjustified. Considering the privilege of thinking over langage and also that judgment is the mental act that defines (...) logic, however, we may understand how the authors regard langage, in relation to the epistemic constituents, namely, the mental acts within the terms. In doing so we are compelled to recognize the implications of this step towards pragmatism in fixing the meaning of defined descriptions to the nature of judgment in the handbook. This opening to langage reveals the conception of judgment as a twofold mental act: a formal and a practical (moral and theological) one. (shrink)

In the XVIIth century the conflict which opposed the jansenists to the jesuits involved the problem of the due process in theological matter. The jesuits heralded the thesis that the infallibility of the Church has to be extended from dogmatics (‘quaestio iuris’) to the historical facts (‘quaestio facti’). On the opposite side Arnauld maintained that such an opinion was ‘monstruous’: also in religious matters the ‘fact’ has to be proved according to the principles of a due process, and not by (...) authority. In this article the thesis pleaded by the jansenists is considered in connection with the model of argumentative procedure offered by the Port-Royal logic.The Logique ou Art de penser (1622) by Antoine Arnauld and Pierre Nicole seems to have rediscovered the classical principles of the theory of argumentation: from the burden of proof to the idea of probable truth. But really a new model of adversary-system has been introduced into the modern mind, which is very different in concept from the topical tradition. The basic metaphor of combat, implying that the truth will prevail in the fight, is compatible with the epistemological premises of the modern logic (as the separation between ‘fact’ and ‘value’). Therefore the problem of the fact-finding seems to be attracted into the area of the logic of information, and not of the theory of argumentation. (shrink)

L'histoire critique des textes bibliques a été conçue par Richard Simon comme un art de juger, selon des règles strictes, des meilleures leçons à conserver. Cette méthode, qui impose dans la traduction de l'Écriture une règle d'uniformité textuelle, aurait fait défaut selon lui dans la version du Nouveau Testament donnée à Port-Royal « selon la Vulgate, avec les différences du grec ». La critique à la manière de Richard Simon n'est cependant pour Antoine Arnauld, qui préfère l'uniformité du (...) sens à celle du texte, qu'un art sans jugement : c'est de l'extension de l'art de penser à une logique pour le contingent, que dépend à ses yeux une définition véritablement générale de la critique. The critical history of biblical texts was conceived by Richard Simon as an ars judicandi, whose rules had to be applied to the discrimination between true and false lessons. Concerning translation, this method required in his view a principle of textual uniformity, so he thought defective the Port-Royal version of The New Testament . Antoine Arnauld, however, gave preference to the semantic uniformity over the literal one, and stated that a real definition of critique in its logical generality ought to be supplied by the extension of the art of thinking to the case of contingent truths. (shrink)

L’addition, dans la cinquième édition en 1683 de La Logique ou L’Art de penser, d’un chapitre consacré à la définition générale du signe et de plusieurs chapitres relevant spécifiquement d’une analyse des signes linguistiques, a été parfois interprétée comme une apparition tardive du “problème du langage” dans le traité d’Arnauld et Nicole. Parce que la plupart de ces chapitres supplémentaires sont la transposition de passages auparavant destinés dans la Perpétuité de la foi (1669-1674) à réfuter le sens calviniste de Ceci (...) est mon corps, on a été enclin à attribuer l’importance de la question du signe et du “problème du langage” dans l’édition de 1683 à une origine théologique. J’essaie au contraire de montrer que, dès la première édition de L’Art de penser en 1662, la problématisation des écarts des expressions linguistiques avec une correspondance terme à terme entre les mots et les idées a été indissociable pour Port-Royal de l’analyse des opérations de l’esprit. Selon moi, dans la Perpétuité de la foi, la critique du sens calviniste de la formule eucharistique constitue elle-même une application de cette analyse logique du langage : les passages incorporés ensuite dans L’Art de penser sont dans le prolongement des réflexions de 1662 sur les difficultés d’adéquation entre le dire et le vouloir-dire. Je montre pour finir que la définition générale du signe à Port-Royal suppose une restructuration de la définition augustinienne du De doctrina christiana, et fonde en 1683 une identification de la relation de signification linguistique à un rapport de représentation des mots aux idées, qui vient redoubler le rapport de représentation des idées aux choses établi en 1662. (shrink)

This article offers to outline a direction for a decolonial political theory based on Aimé Césaire’s and Frantz Fanon’s thoughts. In doing so, I will first discuss some work of comparative political theory that could be associated with an attempt to decolonize political theory. Rather than a systematic critique of these works, this article aims to outline some of their limits from a decolonial perspective, such as their embedment in a continental ontology/logic, and their over-emphasis on methodology that can (...) lead to an instrumental account of politics. In contrast, I will argue for a decolonial existential political theory that grounds its investigation in what Frantz Fanon called ‘the zone of nonbeing’ and that takes politics as first philosophy. To make my point, I will discuss Aimé Césaire’s Letter to Maurice Thorez and Frantz Fanon’s Political Theory of the Damnés. (shrink)