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Cette thèse se rapporte à la notion de contradiction, entendue en son sens logique ou formel. Plus précisément, elle vise à dégager une conception de la contradiction chez un philosophe qui, du point de vue chronologique, précède l’avènement de la syllogistique et de la logique : Platon. À partir de l’examen des dialogues réfutatifs de Platon, il s’agira de mettre en lumière la forme des propositions contradictoires, de déterminer la terminologie et les métaphores utilisées par Platon pour nommer et décrire la contradiction et d’évaluer le contexte dans lequel avait lieu la réflexion platonicienne. L’analyse révélera que Platon se faisait une idée somme toute assez précise de la contradiction logique et qu’il a même eu une influence sur Aristote lorsque ce dernier élabora son célèbre principe de non-contradiction. / This thesis examines the notion of contradiction understood in its logical or formal sense. Specifically, it seeks to study that notion in a philosopher who, chronologically speaking, precedes the advent of syllogistic or logic: Plato. Based on an analysis of Plato’s refutative dialogues, this thesis will determine the form given by Plato to contradictory propositions, unveil the terminology and metaphors used by Plato to name and describe contradictions and evaluate the context in which Plato reflected upon contradiction. The analysis will reveal that Plato had a very clear idea of what is a logical contradiction and that he even had an influence on Aristotle when the latter defined his famous principle of non-contradiction.

Il s’agit d’une thèse sur le traité De duobus communissimis principiis scientiarum de Gérard Odon (vers 1320). Dans la première partie, nous faisons l’analyse du texte en nous centrant sur la notion d’« ens tertio adiacens ». Il s’agit de l’étant signifié par la totalité de la proposition et son vérifacteur ; il est univoquement comment à l’ens reale et à l’ens rationis et pour cette raison Odon l’identifie au sujet des principes de non-contradiction et du tiers exclu. L’ens tertio adiacens correspond aussi au premier objet adéquat de l’intellect et au sujet de la logique, entendue comme la science première. Dans la deuxième partie, nous plaçons Odon dans deux débats historiographiques : celui du réalisme propositionnel (à côté de Walter Burley, Grégoire de Rimini et Jean Wyclif) et celui des avancements de la doctrine des surtranscendantaux (à côté de Nicolas Bonet, François de la Marche et d’autres), lequel émerge de la distinction des deux sens de « res » chez Henri de Gand et ensuite chez Duns Scot. / This thesis deals with Geraldus Odonis’ treatise De duobos communissimis principiis scientiarum (ca. 1320). In the first part, we analyze the text by focusing on the concept of "ens tertio adiacens". It is the being signified by the totality of the proposition and its truthmaker; it is univocally common to ens reale and ens rationis, for this reason Odonis identifies it to the subject of the principle of non-contradiction and the principle of excluded middle. The ens tertio adiacens also corresponds to the first adequate object of the intellect and to the subject of logic, which is understood as the first science. In the second part, we place Odonis in two historiographical debates: the propositional realism (alongside Walter Burley, Gregory of Rimini and John Wyclif) and the advancements of the doctrine of supertranscendentals (alongside Nicolas Bonetus, Francis of Marchia and others), which emerges from the distinction between the two senses of "res" in Henry of Ghent and in Duns Scotus .

En mathématiques et en logique classiques, on démontre que {P,¬P}├Q. C’est le fameux ex contradictione sequitur quodlibet, nommé également principe d’explosion. Si une théorie contradictoire est condamnée à exploser, c.à.d. à devenir triviale et à perdre tout intérêt pour la science, il faut à tout prix éviter la contradiction qui, pour ainsi dire, joue le rôle de détonateur. Dès lors, il devient impératif de nier toute conjonction d’une formule et de sa négation. C’est le principe de non-contradiction (PNC) symbolisé par ¬(P^¬P), une tautologie en logique mathématique classique. Aristote, déjà, dans l’antiquité, avait explicitement formulé le PNC qui, depuis, a été élevé au rang de principe définitif et absolu. Quelques rares mais irréductibles détracteurs, toutefois, ont mis en cause le statut absolu de ce principe. La présente thèse est une rediscussion du PNC -de son statut, de sa validité, de sa valeur- qui s’appuie sur le travail du logicien J. Łukasiewicz. Il sera établi que la mise en cause de l’absoluité du PNC proposée par le logicien n’est pas un prolongement des thèses sophistes antiques. Ses critiques s’inscrivent dans le cadre d’une Gegenstandstheorie twardowsko-meinongienne. La combinaison des éléments hérités de la théorie des objets et d’une analyse originale usant des outils de l’algèbre de la logique dans l’interprétation des textes anciens a permis au logicien de dégager l’idée cardinale selon laquelle on peut récuser l’absoluité du PNC sans tomber dans le trivialisme. Il sera démontré que ses travaux contiennent, pour la logique, l’esquisse d’un nouveau paradigme fondé sur la désabsolutisation du PNC, par sa dissociation d’avec le principe d’explosion. / In mathematics and classical logic, one proves that {P,¬P}├Q. This is the celebrated ex contradictione sequitur quodlibet, also named the principle of explosion. If a contradictory theory is condemned to explode, that is to become trivial and to lose all interest from a scientific point of view, one must at all costs avoid any contradiction which plays the role of detonator. Consequently, it is necessary to deny any conjunction of a formula and its negation. This is the principle of non-contradiction (PNC) symbolised by ¬(P^¬P), a tautology in classical mathematical logic. Already in antiquity, Aristotle had explicitly formulated PNC which, since, has been elevated to the status of a definitive and an absolute principle. However, a few obstinate critics have questioned the absolute status of this principle. The present thesis is a reappraisal of PNC -of its status, its validity, its value- which builds on the work of the logician J. Łukasiewicz. It will be demonstrated that the critique of absoluteness attributed to PNC proposed by Łukasiewicz is not a continuation of the theses of the ancient sophists. His criticisms can be placed in the framework of a Twardowskian-Meinongian Gegenstandstheorie. The combination of elements from a theory of objects and an original analysis using the tools of the algebra of logic in the interpretation of ancient texts has enabled Łukasiewicz to discern an essential idea according to which one can challenge the absoluteness attributed to PNC without sinking into triviality. It will be shown that his works contain, for logic, an outline for a new paradigm based on the disabsolutization of PNC, by dissociating it from the principle of explosion.

[pt] A dissertação tem como objetivo apresentar uma defesa do princípio de nãocontradição, uma defesa sustentada por dois argumentos. No primeiro argumento, coloca-se em destaque a relação entre a validade do princípio de não-contradição e a determinação do sentido das expressões linguísticas, em particular, a determinação do sentido dos termos gerais usados como predicados em frases singulares. Utilizar uma frase para dizer de um objeto que ele possui e, sob o mesmo aspecto, não possui uma mesma característica resultaria na indeterminação do sentido, a saber, que nada seria dado a entender pela frase. O segundo argumento pretende estabelecer uma relação entre uso de instâncias do princípio de não contradição e a capacidade de identificar objetos particulares. Para se referir determinadamente a um único particular, de tal maneira que seja possível pensar sobre este como sendo um sujeito de predicações, é preciso que se identifique esse particular através de um termo sortal e não simultaneamente através de um sortal oposto. Mais especificamente: tentar se referir a algo como sendo e não sendo de um certo tipo resultaria na indeterminação da referência, viz. não haveria identificação de um único objeto. / [en] The dissertation aims to present a defense of the principle of noncontradiction, a defense supported by two arguments. In the first argument, it is emphasized the relation between the validity of the principle of non-contradiction and the determination of the sense of linguistic expressions, in particular, the determination of the sense of general terms used as predicates in singular sentences. To say of an object that it has and, in the same respect, does not have a certain characteristic would result in the indetermination of sense, namely that nothing would be understood by the sentence. The second argument seeks to establish a relation between the use of instances of the principle of non-contradiction and the ability to identify particular objects. To refer specifically to a single individual, in such a way that it can be thought of as a subject of predication, it is necessary to identify this individual by means of a sortal term and not simultaneously through an opposite sortal. More precisely: trying to refer to a thing as being and not being of a certain sort would result in the indetermination of the reference, viz. no single object would be identified.