Fabien Schang

Cet ouvrage de philosophie du langage politique a pour but de mettre fin à deux idées reçues. D’une part, tout le monde sait que les communistes sont ‘de gauche’ ; mais personne ne semble admettre qu’il aurait pu y avoir des communistes de droite.
D'autre part, tout le monde pense que l’expression ‘extrême centre’ est absurde ; mais elle désigne une réalité politique.
Trois affirmations principales seront défendues, afin de corriger ces croyances de sens commun. (1) Gauche et droite sont des attitudes politiques basées sur des relations d’inférence morales. (2) L’espace politique peut être recomposée de façon impartiale, en redéfinissant les catégories supplémentaires de ‘centre’ et d''extrême’. (3) Le principal responsable de la crise politique contemporaine est identifiée sous le nom
d’‘extrême-centre’ : située en-deçà de la gauche et la droite, dénuée de tout contenu idéologique et de toute cohérence théorique, son unique objectif est de conquérir et préserver le pouvoir par le biais d’un discours dépourvu de sens.
Tous ces points seront expos´es dans le cadre d’une théorie générale du discours politique.

The present book wants to put an end to two received ideas about politics. The first is that the concepts of left and right have a proper content. The second is that the auxiliary concepts 'far' and 'center' are nothing but contradictories.
Three main statements will be upheld to correct these commonsensical beliefs. (1) Left and right are political attitudes based on moral relations of inference. (2) Political space can be recomposed in an impartial way, by redefining the additional categories of 'center' and 'extreme'. (3) The main culprit of political disillusion is identified by the name of 'far-center' standing below left and right, devoid of any ideological commitment and theoretical coherence, its only goal is to conquer and retain power through meaningless speech.
All this will be explained through a general theory about the meaning of political discourse.

Deux amis parlent de la philosophie. L’un est professeur de philosophie, l’autre pas. Le premier s’explique sur le sens de sa profession, et cela va les emmener jusqu’à une discussion concernant le sens des mots ‘gauche’ et ‘droite’. Le non-philosophe entame la conversation.

Une polémique a eu lieu récemment au Brésil, selon laquelle le nazisme serait une théorie politique de gauche. Contre cette polémique issue de "cercles de droite brésiliens" , l'opinion commune des "historiens sérieux" est que le nazisme n'est rien d'autre qu'une théorie d'extrême-droite. On peut considérer au moins deux analyses de cette polémique : factuelle, et morale. La seconde va être privilégiée et inclure un cas de reductio ad hitlerum, conduisant ainsi à une analyse aléthico-morale du discours politique. De façon générale, gauche et droite sont définis en termes de relations inférentielles entre des concepts politiques, ou sous-valeurs. Les conditions d'attribution de valeurs morales et les relations d'inférence entre des sous-valeurs vont produire une approche semi-formelle ou opérationnelle de la politique.

Misunderstandings occur whenever any two speakers disagree about the meaning of the words they use. In the special case of truth-values, Frege took these as the referents of propositions that are classes of sentences accepted ('true') or rejected ('false'). Starting from this usual depiction of truth and falsehood, a general algebraic framework ARmn is proposed in order to systematize the use of truth-values within a dialectical perspective of logic. A special attention is paid to two pseudo-speakers radically opposed, namely: Heraclitus, and Nagarjuna, according to whom truth-values refer to everything and nothing, respectively. In the end, a dialectical (pseudo-Hegelian) negation is sketched as a very peculiar function, namely: as an ontological object-forming operator, which is similar to the arithmetic successor-forming operator Sn+1(x) applied to integers and also matches with a generalized theory of truth-values as Millian or Kripkean proper names.

It is often assumed in the community of linguists that a formal logical treatment of negation is not able to account for negation in natural language. The present talk wants to argue that, on the contrary, a proper treatment should be able to render the plurality of negations –whether sentential or not, through a unique theory of basic speech-acts. Five main theses will be defended about the meaning of negation for this purpose, with the help of a formal semantics of questions-answers: Question-Answer Semantics (thereafter: QAS), inspired by Searle's speech-act theory while assuming a primary set of speech-acts: affirmation (yes-answer), and denial (no-answer). This formal device enlarges the meaning of negation beyond the usual criterion of incompatibility and endorses rejectivism: negation has to be explained in terms of a primary speech act of denial, rather than the contrary.

We propose hereby a pioneer essay in formal political philosophy, devoted to the area of International Relations Theory. The correspondig formalism is used as a method to explain friendly and hostile relations between states. A model is constructed to make sense of indirect relations between states, borrowing from Fritz Heider's balance theory in social psychology. Then a calculus is provided to assess these relations, together with an interpretation of them into Theorems I-V. Finally, it is argued that the essentially social aspect of IRT does not prevent one from applying a positivist method of analysis. Rather, our complementary defense of a post-positivist ontology with competing paradigms helps to maintain Ditlhey's distinction between explaining and understanding in theories. Two illustrations are supplied in the end, as a way to give more concrete instantiations of political ontologies (Appendix I) and invalid indirect relations (Appendix II).

We propose a 4-valued doxastic logic to make sense of some intuitive modal formulas. After recalling the decline of algebraic semantics, we argue that there is a way to capture these intuitive formulas in a many-valued semantics without falling under the grip of Dugundji's Theorem. For this purpose, a deviant logic AR4 and its modal extension AR4B are exposed and are intended to improve a similar attempt made by Béziau, namely, restore the philosophical relevance of algebraic semantics.

The present paper wants to develop a formal semantics about a special class of formulas: quantifying statements, which are a kind of predicative statements where both subject-and predicate terms are quantifier expressions like 'everything', 'something', and 'nothing'. After showing how talking about nothingness makes sense despite philosophical objections, I contend that there are two sorts of meaning in phrases including 'thing', viz. as an individual (e.g. 'some thing') or as a property (e.g. 'something'). Then I display two kinds of logical forms for quantifying statements, depending on how these 'thing's are ordered into a whole predication. Finally, an algebraic semantics is proposed for the finite set of quantifying statements to order these into a (fragmentary) dodecagon of logical relations. The corresponding Sub-Model Semantics (hereafter: SMS) aims to update the usual theory of opposition whilst leading to a research program for other kinds of statement like categorical and even modal propositions.

The concept of legal gap is tackled from a number of logical perspectives and semantic methods. After presenting our own goal (Section 1), a first introduction into legal logic refers to Bobbio’s works and his formalization of legal statements (Sections 2 and 3). Then Woleński’s contribution to the area is taken into account through his reference to the distinction between two juridical systems (viz. Common Law vs Civil Law) and the notion of conditional norms (Section 4). The notion of reason is also highlighted in the case of Raz’s legal logic, thereby leading to a future connection with von Wright’s logic of truth and an analogy made with an anti-realist reading of truth-values and norms (Section 5). Our personal contribution is introduced through a reflection on how logic should deal with the logical form of norms (Section 6), before entering a number of crucial definitions and distinctions for the concepts of norm, legal statement, and promulgation (Section 7). The final point is a proposed semantics for legal statements, which is both many-valued and gap-friendly (Section 8). A distinction between a number of requirements for permission and forbiddance leads to a set of non-classical juridical systems in which non-permission and forbiddance are not equivalent with each other any more; this does justice to Woleński’s former distinction between Common Law and Civil Law, also leading ultimately to a non-classical square of legal oppositions in which several legal operators may collapse into other ones (Section 9).

The present paper wants to develop a formal semantics about a special class of formulas: quantifying statements, which are a kind of predicative statements where both subject-and predicate terms are quantifier expressions like 'everything', 'something', and 'nothing'. After showing how talking about nothingness makes sense despite philosophical objections, I contend that there are two sorts of meaning in phrases including 'thing', viz. as an individual (e.g. 'some thing') or as a property (e.g. 'something'). Then I display two kinds of logical forms for quantifying statements, depending on how these 'thing's are ordered into a whole predication. Finally, an algebraic semantics is proposed for the finite set of quantifying statements to order these into a (fragmentary) dodecagon of logical relations. The corresponding Sub-Model Semantics (hereafter: SMS) aims to update the usual theory of opposition whilst leading to a research program for other kinds of statement like categorical and even modal propositions.

I propose a so-called Submodel Semantics (thereafter: SMS) that differs from both Bistring Semantics (Demey & Smessart 2018) and a recent Numbering Semantics (Schang & Falessi 2023). It deals with a number of statements including predicate negations, i.e. ancient statements and knowledge statements:
- ancient statements are categorical propositions including either affirmative or negative predications, e.g. (1) "Socrates is just", (2) "Socrates is not-just", (3) "Socrates is unjust", and (4) "Socrates is not just". (4) includes of external of sentential operator of negation and proceeds as Boolean complementation, whereas (2) and (3) are two cases of internal or predicate negations that are called infinite and privative negations respectively;
- knowledge statements are those statements introduced in Englebretsen (1969) that include one predicate of knowedge.
Both kinds of statements are explained according to SMS into increasing and partial submodels, and the logical relations between these statements are explained in terms of iterative opposite-forming operators (see Schang 2011, 2018) and a corresponding set of deduction rules. Thus any subaltern is a contradictory of a contrary, and any subcontrary is a contradictory of superaltern.
I will apply the above definitions to deduce most of logical relations between four kinds of matching statements, namely: ancient statements; knowledge statements; ancient knowledge statements; iterated ancient knowledge statements (e.g. privately infinite statements); individual negations will be eventually proposed in the line of SMS.
By defining the predicate negations by means of submodels that include additional possible worlds (for privative negation) or additional predicates (for infinite negation), my main thesis is that internal or predicate negations proceed as expanding models by means of successor functions that nicely echo with an interpretation of Hegel's dialectical negation or Aufhebung (Schang 2020).

The present paper wants to develop a formal semantics about a special class of formulas: quantifying statements, which are a kind of predicative statements where both subject-and predicate terms are quantifier expressions like 'everything', 'something', and 'nothing'. After showing how talking about nothingness makes sense despite philosophical objections, I contend that there are two sorts of meaning in phrases including 'thing', viz. as an individual (e.g. 'some thing') or as a property (e.g. 'something'). Then I display two kinds of logical forms for quantifying statements, depending on how these 'thing's are ordered into a whole predication. Finally, an algebraic semantics is proposed for the finite set of quantifying statements to order these into a (fragmentary) dodecagon of logical relations. The corresponding Sub-Model Semantics (hereafter: SMS) aims to update the usual theory of opposition whilst leading to a research program for other kinds of statement like categorical and even modal propositions.

In this paper, we propose an explication of the notion of emotional (pragmatic) truth due to defining performative propositions on non-Archimedean models [Formula: see text]. In these models, it is possible to fix an appropriate behavioral scenario for each atomic performative proposition. Meanwhile, each performative proposition [Formula: see text] has an appropriate form of cognitive bias [Formula: see text] changing the meaning of [Formula: see text], but this bias is the result or foundation for interaction with the outside world. Therefore, instead of the usual domain [Formula: see text] of realization of atomic informative propositions [Formula: see text], which can be finite, we always have an infinite domain [Formula: see text] of realization of performative propositions [Formula: see text], where [Formula: see text] is an informative proposition, distorted by some kind of cognitive biases [Formula: see text]. This semantics allows us to shift the focus from artificial intelligence (AI) to emotional artificial intelligence (EAI).

This article aims at providing some extension of the modal square of opposition in the light of Ockham’s account of modal operators. Moreover, we set forth some significant remarks on the de re-de dicto distinction and on the modal operator of contingency by means of a set-theoretic algebra called numbering semantics. This generalization starting from Ockham’s account of modalities will allow us to take into consideration whether Ockham’s account holds water or not, and in which case it should be changed.

Hugh MacColl is commonly seen as a pioneer of modal and manyvalued 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. Modalities and many-valuedness A preliminary attention to the notation is in order. MacColl’s Logic (hereafter: MCL) resorts to a symbolic language that is in accordance with the algebraic style of George Boole or Ernst Schröder. Mathematical signs are used to characterize operations between any propositions A and C. Thus, A + C stands for their sum, AC (or A×...

la position resolument extensionaliste de Quine a ete appuyee par des arguments de nature differente, dans ses multiples articles destines a rejeter le projet de logique modale. On peut classer ces arguments en trois categories : un argument naturaliste, ou l’auteur tente de baser le langage scientifique sur une notation tâchee de decrire la « structure ultime de la realite » ; un argument esthetique, ou Quine fait allusion a des raisons de clarte et d’efficacite demonstrative pour privilegier la theorie des fonctions de verite ; un argument pratique, dans la mesure ou Quine defend la logique classique sur la base du « principe de mutilation minimum ». A travers une etude de ses ecrits relatifs aux attitudes propositionnelles, nous montrerons que la philosophie de la logique de Quine a prolonge la partie epistemologique de son œuvre, optant finalement pour une strategie de reduction naturaliste des intensions, a l’image du mouvement engage par Word and Object et prolonge par From St...

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

The given volume is devoted to the life and work of Hugh MacColl (1837–1909), the Scottish mathematician, philosopher, novelist and eminent logician. The volume includes papers from the MacColl centenary meeting (9–10 October 2009) at Boulogne-sur-Mer, the city where MacColl lived from 1865 until his death in 1909. This meeting can be seen as the prosecution of the Colloquium Hugh MacColl and the Tradition of Logic, which took place in Greifswald (Germany) in 1998.2 There is a considerable amount of common participants in both events and there is the common idea that MacColl’s intellectual heritage comprises a plurality of directions, which is mirrored in the interdisciplinary approaches of the participants of both meetings. Undoubtedly, his contributions to logic were the most outstanding intellectual attainments of MacColl and consequently the starting point of the modern MacColl scholarship. However, it would give a one-sided picture of MacColl, if the research concerning his logical ideas would be not accompanied, as done in the meetings in Greifswald and Boulogne, by the appreciation of other intellectual domains of MacColl’s work, like mathematics or literature. The volume is opened (pp. 7–29) by the reprint of the paper A Survey of the Life of Hugh MacColl (1837–1909) by Michael Astroh, Ivor Grattan-Guinness and Stephen Read.3 The authors deliver in a concise way very interesting and detailed information about the personal and professional life of MacColl, which was unknown to a big extent before the first publication of this paper. While the first paper of the volume gives a biographical survey about the material and institutional life of MacColl, the second paper Outside the Intellectual Mainstream? The Successes and Failures of Hugh MacColl (pp. 31–53) by Stein Haugom Olson deals with the intellectual life of MacColl and its integration into the main intellectual developments starting from the second half of the nineteenth century. Olson underlines that MacColl in addition to his logical works wrote a short story, a poem, and a couple of novels, which can be characterized as belonging to a kind of cultural criticism. MacColl exposed in these works of literature his deep concern with two main topics of the intellectual life during the Victorian period: first the rising importance of science and its influence on the manner of thinking and second the decline of the importance of religion and religious thinking. Even concerning central questions of the Victorian period, the cultural criticism of MacColl had the same fate as his revolutionary ideas concerning logic: they were being widely ignored until very recently and without influence on the intellectual mainstream. Olson’s paper is focused on the question, why in spite of MacColl’s outstanding intellectual skills his cultural criticism found almost no attentiveness by his contemporaries and the following generation. As causes for the neglect of MacColl’s ideas, Olson identifies the way in which MacColl presents these ideas to the public and his outsider position in relation to the British society. There is on the one side his spatial distance from the center of British intellectual life, living far away from London in a little French provincial town without any contact with the metropolitan literature and cultural developments. This dividedness from the leading

It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern of oppositions that proceeds with colored diagrams and an increasing set of bitstrings

Our aim is to propose a non-referential semantics for the principle of logical charity: neither logical universalism (one logic, one way of thinking), nor logical relativism (several logics, several ways of thinking) afford an adequate conceptual framework to interpret the meaning of any speech act. But neither of them is totally wrong, either. The point is to know to which extent each of these views is partly right, thus leading to a more consensual but paradoxical-sounding "relative principle of charity". After recalling the theoretical background of logical charity, we suggest a four-valued logic of acceptance and rejection (hereafter: AR4); then we explain how such a non-referential semantics does justice both to the champions of logical charity and its opponents. While endorsing coherence as a precondition for rationality, we argue that such a criterion does not entail that classical logic is a necessary conceptual scheme to interpret the others' beliefs. A better...

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 œuvre, optant finalement pour une stratégie de réduction naturaliste des intensions, à l’image du mouvement engagé par Word and Object et prolongé par From St...

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

Fabien Schang National Research University, Higher School of Economics, Moscow (Russia) Abstract: The present talk is a combination of two main topics, i.e. a many-valued logic of justifications (Schang 2015) and the galaxies of logic (Bensusan, CostaLeite, De Souza (2015). A number of problems will be tackled in this respect: To what extent are any two logical systems opposed to each other? Are there several kinds of opposition between logical systems? Which basic logical relation characterizes such a relation of opposition: the relation of consequence, or the relation of opposition itself?

Aristotle's philosophy is considered with respect to one central concept of his philosophy, viz. opposition. Far from being a mere side-effect of syllogistics, my claim is that opposition helps to articulate ontology and logic through what can be or cannot be in a systematic and structural way. The paper is divided into three interrelated parts. In Section 1, the notions of Being and non-Being are scrutinized through Aristotle's theory of categories. In Section 2, the notion of existence is reviewed in its ontological and logical ambiguities. In Section 3, the notion of essence is revisited in order to bring about a holist theory of meaning by individuation 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.

An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown that the famous problem of existential import may be solved in two ways: with a model-adaptive strategy, in which the square of opposition is validated by restricting the models; with a language-adaptive strategy, in which the logical form of categorical propositions is extended in order to validate the square in every model. The latter strategy is advocated in the name of logic, which means truth in every model. Finally, the present paper needs some automatic process in order to determine the nature of logical relations between any pair of the available 256 categorical propositions. This requires the implementation of a programming machine in the style of Prolog.

Cahiers 22 Cahiers « Soyons logiques » est une invitation à double sens. Bien que la logique désigne couramment une disposition d'esprit partagée par tout un chacun, cette disposition prête à confusion dès lors que l'on s'interroge sur ses sources théoriques. Le présent volume propose treize articles de logique portant sur plusieurs aspects de la discipline logique et de ses méthodes, notamment le formalisme, la théorie des oppositions, la vérité mathématique et l'histoire de la logique. Ce volume a été préparé avec le souci pédagogique de parler au plus grand nombre des lecteurs de logique et de philosophie. " Let´s be Logical " is a double invitation. Although logic often refers to a disposition of mind that we all share, this disposition might be confused once its theoretical sources are questioned. The present volume offers thirteen articles that address various aspects of the discipline of logic and its methods, notably formalism, the theory of opposition, mathematical truth, and history of logic. This volume has been prepared with the pedagogical concern of making it accessible to a wide audience of logic and philosophy readers.

The talk is articulated around a reflexion between three main notions: being, existence, and essence. After recalling Aristotle's categories as a number of ways of being, Aristotle's theory of opposition is depicted as a way in which things cannot be. Then existence is introduced, which is not among the categories and seems to challenge Aristotle's oppositions through the case study of existential import. Not only is the latter settled through a distinction between counter-affirmation and denial. But also, Aristotle's theory of opposition can be extended into a general way of individuating objects through an indefinite range of predicates. The conclusion is not that existence results from essence, however; rather, the ancient distinction between primary and secondary substance is questioned and Aristotle's atomist ontology is replaced by a holist, opposition-friendly framework of structured objects. By doing so, the talk proposes an abstraction from Aristotle's oppositions between truth-values to a theory of Aristotelian-types oppositions between bitstrings.

Inspired by Kripke’s distinction between the concepts of analyticity and apriority though the auxiliary concept of necessity, the central thesis of the present paper is that there are more kinds of political attitudes than expected; the lack of some of these in the political spectrum comes from a deep confusion between the concepts of right and conservatism. Furthermore, the separation between two kinds of order – economical and moral, will justify the more original attitudes of ‘left conservatism’ and ‘right progressism’ whilst accounting for the more ambiguous notions of political centers and extremes. Finally, a comparison between political values and logical values – truth and falsity, will allow an explanation of the ambivalent attitudes ‘left and right at once’ and ‘neither left nor right’ either as cases of conceptual confusions or as a collapse of the political discourse into ‘extreme center’.

A rational interpretation is proposed for two ancient Indian logics: the Jaina saptabhangi, and the Madhyamika catuskoti. It is argued that the irrationality currently imputed to these logics relies upon some philosophical preconceptions inherited from Aristotelian metaphysics. This misunderstanding can be corrected in two steps: by recalling their assumptions about truth; by reconstructing their ensuing theory of judgment within a common conceptual framework.

La valeur d'une analyse logique reside dans sa capacite a resoudre des paradoxes et a comprendre l'origine de nos problemes conceptuels ; a ce titre, le role d'une logique epistemique est de traiter des paradoxes lies au concept de connaissance. On presente generalement la logique epistemique comme une analyse logique de concepts centraux en epistemologie : connaissance, croyance, verite, justification. Une autre approche sera proposee ici en vue de clarifier ce genre de discours, centree sur la notion d'assertion et decrite en termes d'enonciation. Parce que les modalites epistemiques expriment des attitudes, c'est l'intentionnalite du discours qui sera mise en valeur dans le cadre d'une logique modale illocutoire. Deux theses transversales parcourront l'ensemble du travail : les enonces declaratifs et epistemiques partagent la meme logique (logique assertorique) ; la pluralite des jeux de langages n'implique pas un pluralisme logique.

Avec Kazimierz Twardowski, Stanislaw Leśniewski et Alfred Tarski, le logicien et philosophe polonais Jan Łukasiewicz (1878-1956) est l’un des membres les plus importants de l’Ecole de Lvov-Varsovie.Celebre pour ses ouvrages consacres a Aristote, notamment sur le principe de non-contradiction et sur la syllogistique, il a egalement publie des articles majeurs sur la logique propositionnelle, la logique modale, l’intuitionnisme et les logiques multivalentes, dont il fut l’un des fondateurs. Enfin, il a contribue a faire reconnaitre l’importance des travaux en logique de l’ecole megarico-stoicienne, trop longtemps eclipses par ceux d’Aristote sur la syllogistique.Mais Łukasiewicz ne fut pas seulement un logicien et un historien brillant, il s’engagea aussi dans les polemiques philosophiques de son temps. Il defendit ainsi la methode logique en philosophie. Proche sur ce point des membres du Cercle de Vienne, il ne rejetait pas pour autant les questions metaphysiques, commecelle du dete...

Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness.

Quantifying statements, i.e. statements including the quantifier phrases "every", "some", and "no", are analyzed into a formal semantic of bitstrings (Bistring Semantics). It is shown that these statements make sense into a second order logic with quantifiers ranging over either individual or predicate variables, despite some philosophical objections to them. Then a formal semantics of bitstrings helps to determine the logical relations between these, displaying a logical dodecagon of quantifying statements.

A set of three overlapping answers are proposed to two initial questions (about what and how do leftists and rightists disagree with each other?)
(1) Intensional rigidity: Yes, left and right are rigid designators, but provided that these are not referring to concrete objects (individuals) but, rather, to abstract objects (properties). No, they aren’t if these must refer to individuals only.
(2) Faultless disagreement: Left- and right-wing agents are in disagreement whilst being correct with respect to discretionary, perspectival, Blackburn style expressivism (Blackburn 1984, 1993).
(3) Inferential roles: Left and right are better defined in logical terms of moral inference rules (Zangwill 1994, 2021), provided that: political concepts are thick concepts (Williams 1985); their descriptive use relies on a ‘lightweight’ truth (Wright 1993); equivocations (including the Frege-Geach Problem) are avoided by moral inferentialism (Hamblin 1987, Hallich 2014).

How to formalize the political discourse around populism? By proposing a translation of political concepts in terms of Boolean bitstrings. This needs to be motivated in terms of political science and political philosophy, beforehand.
What is meant by "populism", and what is meant by "left populism"? Although the classical distinction between people-as-demos and people-as-ethnos may throw some light upon the left-right versions of populism, they are taken to be insufficient or too coarse in the following.
Starting from both extensional and intensional considerations, a minimal definition is to the effect that populism is a theory of justification about political power and according to which the will of the rulers ought to be aligned on the will of the ruled. This leads to a critical analysis of related concepts whose essential occurrence makes the definition confusing. Against this confusion, a conceptual analysis is proposed in terms of relative identification and differentiation among lexical fields. First, populism belongs to a conceptual network including elitism and pluralism. Second, the left-right distinction will be viewed as a peripheral set of notions whose populist versions lead to two kind of political agents: populist-pluralists and populists-elitists, respectively. These expressions have nothing contradictory, once the logic of identification and differentiation makes room for more fine-grained combinations of political properties to characterize more than one form of populism.

Une polémique est apparue récemment au Brésil, selon laquelle le nazisme serait une théorie politique de gauche. Contre cette polémique issue de "cercles de droite brésiliens", l'opinion commune des "historiens sérieux" est que le nazisme n'est rien d'autre qu'une théorie d'extrême-droite. 
Qui dit la vérité, ici? Ma réponse est: personne. Ou plutôt: la question est mal posée, en raison de la nature même du contenu propositionnel mentionné ci-dessus.
Cette affirmation peut être expliquée à partir de trois thèses principales:
(1) Les concepts de gauche et de droite sont des propriétés relationnelles, non-cognitives et opérationnelles (sans contenu propre). Ces propriétés sont basées sur un ensemble de normes éthiques en vue de l'action collective. 
(2) Gauche et droite sont des conditions préalables à l'activité politique, mais elles devraient être pensées comme des objets structurés et non simples; leur structure  produit une position politique relative à partir des relations élémentaires d'amitié ou d'inimitié entre agents politiques. 
(3) Cette réflexion de nature politique se réclame du processos philosophique particulier de construction de concepts, relativement à ce que ces derniers "devraient" ou "pourraient" signifier.

This talk is the second part of a first presentation made in Pirenopolis (Brasil) in 2017, which was based on the critical analysis of the proposal made by Costa-Leite to declare the "end of the square", i.e., to reduce the Aristotelian square of opposition into an arithmetic line. After showing the limits of such a proposal, I showed that there was no such proper such end but, rather, some reasons to promote alternative views of the square of opposition. Thus, the present talk is a development of such a project.
The geometry of logic displayed by Demey & Smessaert relies upon a basic distinction between two kinds of relation, namely: opposition, and implication. Against this approach, the following wants to show three things: first, the above two relations can be reduced to a unique explanatory framework of logical relations, in terms of mappings; second, these mappings characterize any logical relations by adopting the case of partial functions; third, composition and product are two algebraic operations between mappings that help to make this unifying characterization. For instance, composition helps to show how subalternation can be viewed as a "contradictory of subcontrary" and why some "oppositional relations" do not appear as proper negations.
It results from this framework both a geometry and an algebra of logical relations: partitioned squares or graphs, in geometry; bistring semantics or many-valued mappings, in algebra.
A next work will be the analysis of non-standard (or many-valued) oppositions, in the light of the theory of truth-values as structured objects.

A general framework for translating various logical systems is presented: AR4O, where O = {A,N} is a set of partial unary operators of affirmation or negation. Despite its usual reading, affirmation is not redundant in any non-two-valued domain of values and whenever it does not behave like a total function (or application). After depicting the process of partial functions, non-classical logics are translated through a variety of affirmation operators and constant pairs of negations (Boolean, or Morganian). Such a result is made possible by two preconditions: the deconstruction of truth-values as ordered and structured objects, contrary to its mainstream presentation as a simple object;  the redefinition of the Principle of Bivalence as a set of four properties.

“Crise” (krisis, gr.) significa uma mudança geral de uma situação dada. Essa mudança pode ser justificada ou não, compreensível ou não. A pior forma de crise é essa que não pode ser evitada per falta de ferramentas conceituais. De qual crise Daesh ou Donald Trump são os nomes concretos, dado que aqueles são apresentados como manifestações atuais do mau? A palestra pretende que, se Trump incarne qualquer “pós-verdade” politicamente incorreta, tem um mau mais profunde e comum da nossa geração: o niilismo politico. Um corto retorno no passado é necessário para explicar essa origem da crise política.
A período que segou a fim do bloco soviético corresponde uma situação especial, isto é : a negação da crise politica através a “fim da historia”, em sentido que o mundo assistiria a uma período de estabilização das relações internacionais e, ao mesmo tempo, de racionalização da atividade política sob a sua aplicação tecnocrática. Uma manifestação desse “pensamento” pós-soviético é a onipresença do economicismo: a uniformização dos modelos de politica economia de tendência liberal, favorizando o mercado livre e o capitalismo financial. Uma consequência do economicismo se resumo no acrónimo TINA (“There is no alternative”, Não há alternativa). Um efeito do economicismo é uma versão baixa do pragmatismo politico: uma boa politica é uma politica que funciona (Deng Xiaoping, Tony Blair); ela implica a negação correlativa da distinção fundamental entre os valores politicas: esquerda, e direita.
Como ser nem esquerda nem direita, dado que essas duas direções parecem essenciais para fazer sentido da atividade politica em se mesma? Em vez de apoiar essa negação conceitual, a tesa central desta palestra é que o ninismo politico conduzi ao niilismo, isto é, a privação do pensamento politico. Sem a possibilidade de uma oposição ideológica autentica com ideias bem definidas, tal uma situação de globalização pós-moderna (verdade é inacessível, cada valor vale qualquer outra) aparece como uma forma de regime auto-justificativo que realiza as projeções conjuntas de Machiavel, Bentham e Orwell: uma sociedade uniformizada, sem qualidade visível, estabilizada a partir dum processo de controle panóptico da opinião publica.
Contra essa uniformização passiva e por uma defesa do processo ativo de crise politica, pensar politicamente se torna uma condição necessária (mas não suficiente) para se opor ao qualquer poder em atividade e, por entanto, satisfazer a vida democrática da sociedade civil. Por isso, essa palestra proponho:
(a) de voltar sobre os valores cardinais de esquerda e direita,
(b) de analisar seus significados através um processo histórico e critica, e
(c) de comparar diferentes modelizações do domínio politico com um trabalho de filosofia formal.
Se inspirando da distinção epistemológica entre os valores de verdade e de falsidade, trata-se de mostrar que o ninismo politico e nada mais do que uma estratégia de negar cada crise politica privando os meios teóricos do seu reconhecimento.
Por isso, a primeira ordem do cidadão responsável seria de lutar contra esse ninismo politico para compreender as “crises internacionais” do tempo presento (terrorismo, imigração politica, pauperizaçāo). Lutar contra crises se faz com ideias politicas, em vez de sua ausência ou impossibilidade pratica.

The talk consists of three sections.
(I) The foundations of the so-called theory of opposition are recalled [2]. It is a logical theory where some concepts like incompatibility and negation [10] prime over those of consequence and truth. Some illustrations of logical oppositions are given to show that these concern not only quantified sentences, but also any sort of object x in a finite language [1,2,4,6,9].
(II) It has been recently argued that the well-known square of opposition is a useless gathering that can be reduced to a one-dimensional figure, viz. an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets [5].
(III) Three main decision methods are then proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics [7], vectorial semantics [8], and combinatorial functions (see Appendix). In these three cases, an opposite of x (symbol: op(x)) proceeds as a multifunction mapping from an x into a subset P(x). The final result is a new sort of diagram of oppositions, viz. colored diagrams with an increasing set of bitstrings of length n. These 2D diagrams are not oriented graphs anymore, replacing vertices by areas in a logical place. They are squared whenever n is even, rectangular whenever n is odd.

According to logical pluralism, there is more than one way to say that a logic is correct. According to pluralist pluralism, there is more than one way to say that there is more than one way to say that a logic is correct.

I illustrate three dimensions of such a plural correctness: logical pluralism (about the meaning of logical constants, and logical consequence); epistemic pluralism (about the criteria of justification); axiological pluralism (about the meaning of logical values).

All the three purport to depict logic as a three-dimensional science of values, in the vein of Lukasiewicz.

The talk is articulated around a reflexion between three main notions: being, existence, and essence.

After recalling Aristotle's categories as a number of ways of being, Aristotle's theory of opposition is depicted as a way in which things cannot be.

Then existence is introduced, which is not among the categories and seems to challenge Aristotle's oppositions through the case study of existential import. Not only is the latter settled through a distinction between counter-affirmation and denial. But also, Aristotle's theory of opposition can be extended into a general way of individuating objects through an indefinite range of predicates.

The conclusion is not that existence results from essence, however; rather, the ancient distinction between primary and secondary substance is questioned and Aristotle's atomist ontology is replaced by a holist, opposition-friendly framework of structured objects.
By doing so, the talk proposes an abstraction from Aristotle's oppositions between truth-values to a theory of Aristotelian-types oppositions between bitstrings.

It is shown hereby that a doxastic interpretation of modalities can be achieved by means of a four-valued modal logic, following a recent work by Béziau and despite Dugundji's Theorem and the related objection to characterizing modal systems S1-S5 by finitely many-valued matrices.
After distinguishing the concepts of information and justification, an antirealist semantics is endorsed and leads to a non-normal logic of justification including (at least) four different doxastic attitudes marked by different constraints on epistemic justification. Then a translation function helps to validate the intuitive theorems of modal logic by giving special doxastic interpretations to necessity and possibility.
Finally, iterated modalities are also interpreted in a new way and validated (or not) according to the strength of nested attitudes.

Just as Hartley Slater famously questioned the meaning of paraconsistency, I want to do the same hereby with connexivity, i;e., to talk about about what "connexive logics" are taken to be the name of.

The talk consists of three parts.

Firstly, we consider in which sense connexive logics deal with connexivity in the four main "connexive theses" (two Aristotelian, two Boethian). Several logical concepts are related to these: implication, compatibility, consistency, soudness, contradiction, impossibility.

Second, we see in what sense this special class of formulas requires a special logic: (a) as theorems (or tautologies) of the form |- A -> B; (b) as semantic consequences of the form A |- B; (c) as denied inferences of the form A |-/ B. We claim that the first reading is too strong, the second is trivial for some cases, and the third is too weak.

Thirdly, we propose a logical system and its "modal" extension to validate the connexive theses. The first system is a four-valued logic of acceptance and rejection, AR4, which is a non-classical or deviant extension of Dunn-Belnap's FDE including a logical constant of strong implication. The second system is a doxastic logic AR4B, which includes at least four different sorts of epistemc agents with various criteria of justification. We show that one of these agents makes sense of connexive statements, thereby fulfilling the requirement (a) by a specific translation of the four connexive theses into AR4B. We also show that this belief operator behaves like the modal operator of necessity without falling into the net of Dugundji's Theorem (i.e., there is no finite characteristic matrix of any of the Lewis' systems between S1 and S5).

The final result is an interpretation of connexivity in a fourth sense (d), namely, as a set of valid theorems which rely upon a "non-normal" constant of implication. The difference with "normal" implication lies in the relation between inference rules and consequence as a truth-preserving relation: Modus Ponens is still a truth-preserving relation from premise to consequence in AR4, whereas Modus Tollens is a non-falsity preserving relation.

Two final appendices help to illustrate this added distinction, together with a square of belief oppositions that show the sound behavior of doxastic agents from a connexive perspective.

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.

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions, we argue that a proper account of conditional can be obtained by extending the logical notation of Frege’s Begriffsschrift. After discarding his Equivalence Thesis, according to which the denial of a sentence equates with the affirmation of its negation, it becomes possible to characterize the logical meaning of “if”, and only “if”. That is: without irremediably leading from entailment into formal implication, whilst sticking to a bivalent definition of conditional as a speech-act commitment. Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed in this new light.

At least two questions may be raised with respect to the well-known statement that " One can laugh about anything, but not with anybody " : Is it true? If so, why? The present paper wants to account for this statement through an illocutionary treatment of humour as proper speech-acts. Our analysis consists of three main steps. For one thing, a " Socratic " approach to the problem purports to investigate the proper conditions for a speech-act to be funny. Unlike Levinson's minimalist definition, according to which an act is said to humoristic if and only if it makes one laugh, we need an explication of what makes one laugh in such a statement. Rather than listing the different forms of humour in terms of cultures (English, Jewish, Belgian), styles (situation, gesture, word comics) or values (absurd, black, crude), we want a definition of humour just as Socrates wanted a definition of knowledge. We first claim that a given sentence p is humoristic if and only if: (i) p is funny; (ii) p is understood to be funny (i.e., brings about good humor by its incongruous content); (iii) p creates some connivance (between the speaker and the hearer(s)). Such a definition relies upon an analogy with the Socratic definition of knowledge as justified true belief after substituting humour for knowledge, funniness for truth, understanding for belief, and connivance for justification. (...)

I propose a formal framework for social epistemology, in which a number of various sorts of agents may obey alternative sets of acceptance and rejection conditions on sentences.

The talk consists of two main parts.
After making a difference between information and justification, I propose two sorts of logical systems within a common dialogical framework AR_m^n of question-answer games. The first system, AR4, is a four-valued logic of information analogous to Belnap’s FDE, with the notable exception that it includes a strong version of implication and depicts logical values as structured pairs of yes-no answers. The second system, AR4B, is a logic of justification including at least four belief unary and truth-functional operators on justification sentences.

A taxonomy of several kinds of agents is suggested, namely: rational, irrational, and intelligible agents. By this way, I construct a formal epistemology that develops some problem raised by Martin Kusch’s works (on the relations between pluralism, skepticism, and relativism) whilst relying upon two fundamental data: yes-, and no-answers.

Then the notions of agreement and disagreement between agents are reviewed in the light of two basic concepts: negation, and opposition.
On the one hand, the occurrence of partial or total (dis)agreements makes room for a distinction between (full) negation and two semi-negations.
On the other hand, oppositions are then defined not as a
relation between ontic truth-values but, rather, epistemic attitudes of agreement or disagreement. This results in a more fine-grained theory where any two agents can stand into different relations of opposition with respect to the same sentence. These ensuing, “non-standard” oppositions correspond to pairs <X,Y> of standard, Aristotelian
oppositions X and Y.

To conclude, a number of philosophical applications will be exposed to make sense of such issues as partial or complete disagreement.

Afer reminding the apparent inconsistency caused by the Tetralemma or "catuskoti" (a set of four denied statements), three questions are asked about it: How to make sense of it? Is the Jain "saptabhangi" (set of seven inconsistent statements) the dual of catuskoti? What are the logical properties of both?
Then it is claimed that the two Indian theories are duals with respect to their truth-values, provided that a non-standard explanation of these is given within a question-answer game. Finally, an extension of the catuskoti is proposed through the Hegelian-like case of dialectical negation. It is argued that Jains and Madhyamikas can accept and reject everything by admitting an indefinitely increasing set of semantic predicates for sentences.
Thus, the nature of truth-values is deeply reviewed by defining rationality in terms of possible answers.

A general framework of acceptance and rejection is proposed to compare four logical systems. On the basis of an epistemological approach to truth-values as data sources, a variety of agents is described according to their behavior with respect to arguments for or against the truth of a sentence. Beliefs and truth-values are clearly distinguished by unary belief operators, whose properties is to be analyzed between negation and modality.

The so-called Theory of International Relations (or International Relations Theory: IRT) is supposed to deal rationally with political objects as equally rational agents as mere individuals. One of these rational rules concerns the relations of agreement and disagreement, including Fritz Heider’s theory of social balance: any triadic relation is said to be “balanced” whenever the number of disagreements is even; it is “imbalanced”, otherwise. An application of this social rule to IRT is to the effect that “the enemy of my enemy is my friend”. To what extent does
such a statement hold, and how to account for its empirical failure? The objective of my talk is to address such an issue by a formal treatment of international relations. By doing so, my talk resorts to a formal philosophy whose task consists in applying formal methods to philosophical problems including political philosophy.
After turning back to the roots of IRT, several primary issues are in order to characterize the general relation R(a,b) between arbitrary agents a,b. The first question is: what is the nature of a and b in IRT? The second one is: what is the relation R holding between these? And the third one: what are the logical properties of R, if any?
Then a formal treatment of IRT is proposed to frame the whole debate, including a special focus on the previous case of enemies and friends between state-centered entities. Letting E and F be the relations of enmity and friendship, respectively, the point is to assess the value of the aforementioned statement:
          (EEF) For every x,y,z: (E(x,y) & E(y,z)) -> F(x,z)
The formal logic I developed for semantic purposes (Opposition-Friendly Logic: OF Logic) will be advocated to make sense of both the plausibility of (EEF) and its restrictions, in terms of opposite objects endowed with specific logical values (sequences of 0-1 values, or bitstrings). Thus each state is defined within a unique referential framework (that of the hegemon) by a set of features like military, economic, social and cultural values, and each of these combined values is marked with a proper strength coefficient. The resulting set of ordered values may help to assess the political relationship between any two states and to throw some light upon their variation through time.
More specifically, an abstract logic of opposition will be used to characterize the difference between friends and enemies in basic terms of compatible and incompatible sets of values. A number of statements will be defended in this formal philosophy of political relationships, both paralleling the results of [5] and developing the latter by means of logical operators:
(1) The relation of rivalry proceeds as an intermediary stage “between” friendship and enmity, corresponding to the logical relation of indifference (the same ordered values can be shared or not).
(2) The strength coefficient attached to each single value depends upon the political paradigm assumed by the corresponding state (liberal, realist, Marxist, transnational, or constructivist model of political relations) and may explain why two states can share common values while changing their behavior with respect to these through their history.
(3) The difference between direct and indirect relations between states also justifies the call for coefficients attached to states: the combination of physical distance and political difference (non-identity) may weaken the relation between two states x,z sharing a common enemy (or friend) y, thereby explaining the possible failure of (EEF) or its variant (EFE): “the enemy of my friend is my enemy.”
Finally, I conclude by returning to the “Great Debate” concerning the epistemological status of IRT: is the latter nothing but a set of maxims based on individual caution and experienced wisdom, or a scientific system of computable rules based on logic and statistics? My plea for OF Logic does not want to overcome Dilthey’s famous distinction between natural and social sciences in this respect. To the contrary, I will argue that the crucial role of paradigms does justice to the understanding of state-centered objects (unlike explaining their political decisions).

Quel point commun y a-t-il entre la classification des désirs chez Épicure, la théorie de la connaissance de Kant, et le clivage politique gauche-droite? Aucun dans leur contenu. Dans leur forme, en revanche, ces trois thèmes semblent partager une même représentation logique du discours qui les concerne.
La théorie des oppositions est un outil capable d'en rendre compte, et nous verrons en quoi les processus d'expansion et de contraction du discours peuvent modifier un champ lexical et, avec lui, notre représentation collective des idées.
Cette théorie peut apporter également un certain ordre à la question du désaccord dans le discours philosophique: sur quoi les philosophes sont-ils en désaccord; comment peut-on clarifier la distinction entre désaccord verbal (centré sur les "mots") et désaccord substantiel (centré sur les "choses"); la recherche de la vérité souffre-t-elle de ces conflits conceptuels, ou en est-elle le produit?

Quel point commun y a-t-il entre la classification des désirs chez Épicure, la théorie de la connaissance de Kant, et le clivage politique gauche-droite? Aucun dans leur contenu. Dans leur forme, en revanche, ces trois thèmes semblent partager une même représentation logique du discours qui les concerne.
La théorie des oppositions est un outil capable d'en rendre compte, et nous verrons en quoi les processus d'expansion et de contraction du discours peuvent modifier un champ lexical et, avec lui, notre représentation collective des idées.
Cette théorie peut apporter également un certain ordre à la question du désaccord dans le discours philosophique: sur quoi les philosophes sont-ils en désaccord; comment peut-on clarifier la distinction entre désaccord verbal (centré sur les "mots") et désaccord substantiel (centré sur les "choses"); la recherche de la vérité souffre-t-elle de ces conflits conceptuels, ou en est-elle le produit?

Quel point commun y a-t-il entre la classification des désirs chez Épicure, la théorie de la connaissance de Kant, et le clivage politique gauche-droite? Aucun dans leur contenu. Dans leur forme, en revanche, ces trois thèmes semblent partager une même représentation logique du discours qui les concerne.
La théorie des oppositions est un outil capable d'en rendre compte, et nous verrons en quoi les processus d'expansion et de contraction du discours peuvent modifier un champ lexical et, avec lui, notre représentation collective des idées.
Cette théorie peut apporter également un certain ordre à la question du désaccord dans le discours philosophique: sur quoi les philosophes sont-ils en désaccord; comment peut-on clarifier la distinction entre désaccord verbal (centré sur les "mots") et désaccord substantiel (centré sur les "choses"); la recherche de la vérité souffre-t-elle de ces conflits conceptuels, ou en est-elle le produit?

Il s’agit de montrer dans cet expos ́e l’opposition posée par Gilles-Gaston Granger entre deux catégories de négation: la négation "pure", d’un côté, et les négations "appliquées" de l’autre. Nous examinerons les propriétés de cette opposition, ainsi que les enseignements à en tirer pour la philosophie de la logique de Granger. Puis nous proposerons une théorie des valeurs logiques structurées, susceptible d'établir un lien entre la théorie de la négation de Granger et certains travaux de logique plus récents.

A formal semantics is used hereby to make sense of two ancient Indian "logics", namely: the Jain Saptabhangi and the Madhyamaka Catuskoti (Tetralemma). From a question-answer game, a new non-Fregean valuation helps to emphasize the dual behaviors of their two opposite statements.
Far from being "irrational", Indian logics depart from classical logic by different truth-ascriptions close to many-valuedness. Many-valued systems are not used in the present talk, however. To the contrary: Jain and Madhyamaka restrict their "rationality" to only one sort of statement in a skeptic or perspectivist sense of truth. The resulting sublogics (with domains of value restricted to a single one) lead to a one-valued logic, thus making sense of non-one-sidedness (no one knows the plain truth).
To those who would justifiably reply that one-valuedness is pointless in logic, the soteriological aim of Indian logic is recalled as an alternative, non-Tarskian view of logic.

Can doubt be doubted? From this Cartesian-minded question, a general reflection is proposed around the issue of "iterative verbs", i.e. those verbs which can be iterated in a statement (thinking that one things, knowing that one knows, and the like). It follows from it that a special class of verbs allow such an iteration, namely: psychological verbs having to do with awareness. The logical features of the latter is considered in the present talk.

A structural interpretation of oppositions is proposed. It is a functional calculus upon oppositional relations, based on the logical form of statements. Such a calculus primarily relies upon the application of proto-negations to one or several components of a given statement, and the result holds for any set of isomorphic statements: the validity of these results does not depend upon the contentual meaning of the components but merely comes from their structuration. The merits and limits of the whole method are considered, with a special emphasis on the peculiar case of the logical relation of independence.