Fabien Schang

Misunderstanding occurs between speakers when they disagree about the meaning of words in use. In the case of truth-values, Frege took these to be referents of sentences which consist of classes of accepted (i.e. “true”) or rejected (i.e. “false”) sentences. From this usual depiction of truth and falsity, a general algebraic framework is proposed to systematize the use of truth-values from a dialogical point of view of logic. A special attention will be paid to two radically opposed pseudo-speakers: Heraclites and Nagarjuna, according to whom truth-values respectively refer to everything or nothing. Finally, dialectical (pseudo-Hegelian) negation will be rendered as a very special function: an ontological object-forming operator, similar to the arithmetic successor-forming operator Sn+1(x) on integers and consistent within our generalized theory of truth-values as variable referents.

Quel message est apporté par le courant littéraire de la négritude, et comment procède-t-il pour le transmettre? C'est par le biais d'une écriture introspective que la diaspora noire a conquis sa dignité et dépassé le stade victimaire, par-delà le seul cadre de la communauté francophone. A travers l'histoire de la traite et de la colonisation, notre lecture procédera en trois phases: une phase locutoire, consacrée à un rappel chronologique du contexte noir dans l'Histoire; une phase illocutoire, où seront exposées les différentes réactions de l'intelligentsia noire face à la ségrégation et au passif colonial; une phase perlocutoire, qui conclura l'étude en observant l'impact de la négritude sur la réalité sociale du genre noir. Au-delà du courant historique francophone, l'idée de négritude incarne le problème des constructions d'identité et illustre parfaitement la difficulté de la condition humaine: être ce que nous voulons de ce que les autres veulent faire de nous.

An alternative semantic framework is proposed in the following to reconstruct and make sense of “Eastern logics”: a Question-Answer Semantics (thereafter: QAS), including a set of questions-answers and a finite number of ensuing non-Fregean logical values. Thus, meaning is provided by yes-no answers to corresponding questions about relevant properties. These logical values help to show that the saptabhaṅgī (and its dual, viz., the Buddhist Mādhyamaka catuṣkoṭi) is not a many-valued paraconsistent logic but, rather, a one-valued proto-logic: a constructive machinery that serves as a formal theory of judgment, rather than a Tarskian-like theory of consequence. Such an explanatory model of contradiction assumes a deep redefinition of logical values.

The paper deals with the main contribution of the Finnish logician Jaakko Hintikka: epistemic logic, in particular the 'static' version of the system based on the formal analysis of the concepts of knowledge and belief. I propose to take a different look at this philosophical logic and to consider it from the opposite point of view of the philosophy of logic. At first, two theories of meaning are described and associated with two competing theories of linguistic competence. In a second step, I draw the conclusion that Hintikka's epistemic logic constitutes a sort of internalisation of meaning, by the introduction of epistemic modal operators into an object language. In this respect, to view meaning as the result of a linguistic competence makes epistemic logic nothing less than a logic of unified meaning and understanding.

Aristotle’s philosophy is considered with respect to one central concept of his philosophy, viz. opposition. Far from being a mere side-effect of syllogistic, it is argued in the present paper that opposition helps to articulate ontology and logic through an account of what can be or cannot be in a systematic and structural way. The paper is divided into three main parts. In Section I, the notion of Being is scrutinized through Aristotle’s theory of categories. In Section II, the notion of Non-Being is connected to Aristotle’s theory of oppositions. In Section III, the notion of essence is revisited in order to bring about a holist theory of meaning by individuating through opposite properties. In conclusion, the legacy of Aristotle is depicted as balanced between a powerful reflection around Being and a restrictive ontology of substance.

Russell prétend qu’un examen des croyances est indispensable pour définir nos raisonnements quotidiens et comprendre ce que les philosophes entendent par la notion de vérité. Cela étant, l’auteur considère qu’une étude de ces croyances n’a aucun rapport avec la logique, laquelle concerne uniquement le vrai et le faux. En d’autres termes, Russell associe croyance et psychologie tout en réservant le domaine de la logique au thème de la proposition, vraie ou fausse par définition. Une certaine théorie de la vérité sous-tend son rejet primordial d’une logique épistémique ; si la croyance a un intérêt philosophique, c’est parce que Russell se sert de son examen pour discerner la théorie de la vérité que défendent plusieurs philosophes : la théorie de la vérité-cohérence est une cible principale du Britannique, qui défend pour sa part une théorie de la vérité-correspondance en caractérisant la proposition par sa relation de correspondance ou de non-correspondance avec un fait.

L’article qui suit a pour but de présenter un des aspects centraux de la contribution philosophique de Jaakko Hintikka : l’épistémologie formelle. Le thème choisi, le Paradoxe de Moore, permettra d’illustrer le mot d’ordre de la philosophie formelle, celui d’utiliser des outils logiques en vue de la clarification de problèmes philosophiques. Il s’agit également de mettre en évidence la nature pragmatique du discours épistémique, qui transparaît dans les résultats sémantiques de Hintikka et parle en faveur de la logique illocutoire.

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on affirmations and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3).

Nonism refers to the attitude of whoever is neither pro nor cons a given issue. Midway between affirmation and denial, or truth and falsity, the nonist says neither “yes” nor “no” and intrigues by his lack of clear answer to any related question. What does (s)he say, if any, and what is the sense of such an attitude? Through the special case of politics, three sorts of nonists are depicted in the following: the nonist by default, the nonist by interest, and the nonist by absurdity. The first cannot say anything else and the second does not want to, whilst the third paves a new way towards a refoundation of political discourse. The conditions of possibility of such a refoundation rely upon the dialectical relationship between two distinctive rationales, namely: the world of theoretical ideas, and the world of events. The resulting contradiction witnesses the crisis of political activity, and some output solutions will be exposed accordingly. Le ninisme désigne l’attitude de celui qui n’est ni pour, ni contre un thème donné. A mi- chemin entre l’affirmation et la négation, ou la vérité et la fausseté, le niniste ne dit ni « oui » ni « non » et intrigue par son absence de réponse claire à une question posée. Que dit-il au juste, et quel est le sens de son attitude ? A travers le cas précis du domaine politique, trois types de ninistes seront décrits dans ce qui suit : le niniste par défaut, le niniste par intérêt, et le niniste par l’absurde. Le premier ne peut se prononcer autrement et le deuxième ne le souhaite pas, tandis que le troisième ouvre la voie en vue d’une refondation du discours politique. Les conditions de possibilité de cette refondation dépendent du rapport dialectique entre deux logiques distinctes : le monde des idées théoriques et le monde réel des événements. La contradiction qui en résulte est à l’image d’une activité politique en crise, et quelques solutions de sortie seront envisagées.

The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation and semi-negations.

The paper proposes two logical analyses of (the norms of) justification. In a first, realist-minded case, truth is logically independent from justification and leads to a pragmatic logic LP including two epistemic and pragmatic operators, namely, assertion and hypothesis. In a second, antirealist-minded case, truth is not logically independent from justification and results in two logical systems of information and justification: AR4 and AR4¢, respectively, provided with a question-answer semantics. The latter proposes many more epistemic agents, each corresponding to a wide variety of epistemic norms. After comparing the different norms of justification involved in these logical systems, two hexagons expressing Aristotelian relations of opposition will be gathered in order to clarify how (a fragment of) pragmatic formulas can be interpreted in a fuzzy-based question-answer semantics.

An analogy is made between two rather different domains, namely: logic, and football. Starting from a comparative table between the two activities, an alternative explanation of logic is given in terms of players, ball, goal, and the like. Our main thesis is that, just as the task of logic is preserving truth from premises to the conclusion, footballers strive to keep the ball as far as possible until the opposite goal. Assuming this analogy may help think about logic in the same way as in dialogical logic, but it should also present truth-values in an alternative sense of speech-acts occurring in a dialogue. The relativity of truth-values is focused by this way, thereby leading to an additional way of logical pluralism.

La position résolument extensionaliste de Quine a été appuyée par des arguments de nature différente, dans ses multiples articles destinés à rejeter le projet de logique modale. On peut classer ces arguments en trois catégories : un argument naturaliste, où l’auteur tente de baser le langage scientifique sur une notation tâchée de décrire la “structure ultime de la réalité” ; un argument esthétique, où Quine fait allusion à des raisons de clarté et d’efficacité démonstrative pour privilégier la théorie des fonctions de vérité ; un argument pratique, dans la mesure où Quine défend la logique classique sur la base du “principe de mutilation minimum”. A travers une étude de ses écrits relatifs aux attitudes propositionnelles, nous montrerons que la philosophie de la logique de Quine a prolongé la partie épistémologique de son oeuvre, optant finalement pour une stratégie de réduction naturaliste des intensions, à l’image du mouvement engagé par Word and Object et prolongé par From Stimulus to Science. Ce projet se soldera par un échec relatif, et Quine résumera cette désillusion par un fossé entre les structures du langage et du monde : la thèse du “monisme anomal” de Davidson sera le dernier mot, amer, du défenseur acharné de la logique classique.

We present the Jaina theory of sevenfold predication as a 7-valued logic, in which every logical value consists in a 3-tuple of opinions. A question-answer semantics is used in order to give an intuitive characterization of these logical values in terms of opinion polls. Two different interpretations are plausible for the latest sort of opinion, depending upon whether "non-assertability" refers to incompleteness or inconsistency. It is shown hat the incomplete version of JL_{G} is equivalent to Kleene's logic K3, whereas the inconsistent version of JL_{M} is equivalent to Priest's Logic of Paradox LP. Finally, it is argued that the Indian logics depart from Western logics by conflating truth and justified belief: the different preconditions for belief ascription accounts for the difference between pluralist and skeptic logics.

One of the most prominent myths in analytic philosophy is the so- called “Fregean Axiom”, according to which the reference of a sentence is a truth value. In contrast to this referential semantics, a use-based formal semantics will be constructed in which the logical value of a sentence is not its putative referent but the information it conveys. Let us call by “Question Answer Semantics” (thereafter: QAS) the corresponding formal semantics: a non-Fregean many-valued logic, where the meaning of any sentence is an ordered n-tupled of yes-no answers to corresponding questions. A sample of philosophical problems will be approached in order to justify the relevance of QAS. These include: (1) illocutionary forces, and the logical analysis of speech-acts; (2) the variety of logical negations, and their characterization in terms of restricted ranges of logical values; (3) change in meaning, and the use of dynamic oppositions for belief sets.

Hugh MacColl is commonly seen as a pioneer of modal and many-valued logic, given his introduction of modalities that go beyond plain truth and falsehood. But a closer examination shows that such a legacy is debatable and should take into account the way in which these modalities proceeded. We argue that, while MacColl devised a modal logic in the broad sense of the word, he did not give rise to a many-valued logic in the strict sense. Rather, his logic is similar to a “non-Fregean logic”: an algebraic logic that partitions the semantic classes of truth and falsehood into subclasses but does not extend the range of truth-values.

A formal theory of oppositions and opposites is proposed on the basis of a non- Fregean semantics, where opposites are negation-forming operators that shed some new light on the connection between opposition and negation. The paper proceeds as follows. After recalling the historical background, oppositions and opposites are compared from a mathematical perspective: the first occurs as a relation, the second as a function. Then the main point of the paper appears with a calculus of oppositions, by means of a non-Fregean semantics that redefines the logical values of various sorts of sentences. A num- ber of topics are then addressed in the light of this algebraic semantics, namely: how to construct value-functional operators for any logical opposition, beyond the classical case of contradiction; Blanché's "closure problem", i.e., how to find a complete structure connecting the sixteen binary sentences with one another. All of this is meant to devise an abstract theory of opposition: it encompasses the relation of consequence as subalternation, while relying upon the use of a primary "proto- negation" that turns any relatum into an opposite. This results in sentential negations that proceed as intensional operators, while negation is broadly viewed as a difference-forming operator without special constraints on it.