The aim of this paper is to make sense of the Keynes–Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show how this structure is to be handled by means of a semantics of partition, thus computing logical relations between matching formulas with a semantic method that combines model theory and Boolean algebra.

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...) import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

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. (shrink)

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. (shrink)

A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and structured (...) objects, unlike its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality. (shrink)

A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences (...) in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth. (shrink)

An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.

It is claimed hereby that, against a current view of logic as a theory of consequence, opposition is a basic logical concept that can be used to define consequence itself. This requires some substantial changes in the underlying framework, including: a non-Fregean semantics of questions and answers, instead of the usual truth-conditional semantics; an extension of opposition as a relation between any structured objects; a definition of oppositions in terms of basic negation. Objections to this claim will be reviewed.

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 application of charity should take account of the questions implicitly asked by a statement, and we bring these questions out in replacing Quine's truth-functions by Quine’s verdict functions while emphasizing upon their varying degrees of strength. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

Nous proposons une logique épistémique quadrivalente AR4.

A rational interpretation is proposed for two ancient Indian logics: the Jaina saptabhaṅgī, and the Mādhyamika catuṣkoṭi. 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.

An argument for the rationality of religious belief in the existence of God is defended. After reviewing three preconditions for rational belief, I show reasons to privilege the criterion of consistency. Taking the inconsistency of the religious belief in God and the belief in the scientific world picture as the impediment to a rational belief in God, I propose that we can overcome this objection by assuming, firstly, that God is a universal class. This allows us to put the problem (...) of God in set-theoretic terms, such that the antinomy that follows from such an assumption can be overcome by assuming that God is not a subject but a strict class that cannot be individuated. I conclude that that the self-contradictory nature of God does not prevent the believer from making a rational, ethical assessment that the contradiction resides in the possibility of using language to explain his existence, but that this does not make belief in the existence of God unjustifiable – on the contrary. In this way, we can say statements that claim God exists are justifiable. (shrink)

Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz's mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhangi, i.e. the theory of sevenfold predication. Before arguing for this formalist approach to (...) philosophy, let us return to the reasons to be reluctant at it. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

L'article s'intéresse aux obstacles épistémologiques qui empêchèrent Wittgenstein d'admettre l'idée moderne de logique modale et, en particulier, les logiques d'attitudes propositionnelles. Tout en proposant un aperçu rétrospectif de la logique des modalités épistémiques, nous verrons que ces obstacles reposent avant tout sur la nature de l'espace logique présenté dans le Tractatus Logico-Philosophicus et le statut métaphysique du sujet. Des passages éclairants seront rappelés pour justi.

Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: a review of the main concepts involved in the definition of logical negation; an explanation of the epistemological obstacles against the introduction of non-classical negations within diagrammatic logic.

Un paralogisme semble commis dans la démonstration par Aristote du principe psychologique de non-contradiction : à partir d’un principe performatif d’assertion (dire quelque chose, c’est le croire), une approche moderne nous incline à prétendre qu’Aristote présuppose une transparence référentielle des contextes opaques de croyance afin de corréler les versions psychologique et logique. Nous tenterons de restituer la preuve du principe (I). Au moyen de la formalisation moderne, nous appliquerons cette explication à quelques paradoxes (II). Nous en conclurons la nature de (...) la non-contradiction (III), avant de proposer une "dissolution" syntaxique du problème d'opacité des contextes d'attitudes propositionnelles. Cette dissolution exprimera un certain scepticisme face aux approches formelles de l'intentionnalité. (shrink)

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. (shrink)

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). (shrink)

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. (shrink)

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. (shrink)

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 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. (shrink)

A analysis of some concepts of logic is proposed, around the work of Edelcio de Souza. Two of his related issues will be emphasized, namely: opposition, and quasi-truth. After a review of opposition between logical systems [2], its extension to many-valuedness is considered following a special semantics including partial operators [13]. Following this semantic framework, the concepts of antilogic and counterlogic are translated into opposition-forming operators [15] and specified as special cases of contradictoriness and contrariety. Then quasi-truth [5] is introduced (...) and equally translated as a product of two partial operators. Finally, the reflections proposed around opposition and quasi-truth lead to a third new logical concept: quasi-opposition, borrowing the central feature of partiality and opening the way to a potential field of new investigations into philosophical logic. (shrink)

This paper discusses the philosophical and logical motivations for rejectivism, primarily by considering a dialogical approach to logic, which is formalized in a Question–Answer Semantics. We develop a generalized account of rejectivism through close consideration of Mark Textor's arguments against rejectivism that the negative expression ‘No’ is never used as an act of rejection and is equivalent with a negative sentence. In doing so, we also shed light upon well-known issues regarding the supposed non-embeddability and non-iterability of force indicators.

What's wrong with modalities in (Wittgenstein 1922)? In (Suszko 1968), the writer argued that "Wittgenstein was somewhat confused and wrong in certain points. For example, he did not see the clear-cut distinction between language (theory) and metalanguage (metatheory): a confusion between use and mention of expressions". Furthermore, a modal logic was proposed in (von Wright 1986) as depicting Wittgenstein's bipolarity thesis in a S5 frame. -/- The aim of the present paper is to deal with the specific case of epistemic (...) modal logic: such a logic of propositional attitudes assumes a philosophy of language that would violate Wittgenstein's two main assumptions. (shrink)

In this paper, it is argued that there can be necessary and non-natural desires. After a discussion about what seems wrong with such desires, Epicurus’ classification of desires is treated similarly to Kripke’s treatment of the Kantian table of judgments. A sample of three cases is suggested to make this point.

Assuming that a paralogism is an unintentionally invalid reasoning, we give an exampli.

Can international relations (IR) be a distinctive discipline? In the present paper I argue that such a discipline would be a social science that could be formulated within the perspective of comparative paradigms. The objections to scientific methods are thus overcome by the logic of international oppositions, in other words a model takes several paradigms into account and considers three kinds of foreign relation (enemy, friend, and rival) in the light of three main questions: what is IR about (ontology); what (...) does relate therein (epistemology); and how to assess such a relation (logic). (shrink)

Il s’agit de comprendre dans cet article l’opposition formulée par Gilles-Gaston Granger entre deux types de négation : la négation « radicale », d’un côté, et les négations « appliquées » de l’autre. Nous examinerons les propriétés de cette opposition, ainsi que les enseignements à en tirer sur la philosophie de la logique de Granger. Puis nous proposerons une théorie constructive des valeurs logiques considérées comme des objets structurés, consolidant à la fois l’unité de la théorie logique de Granger et (...) son pluralisme philosophique. (shrink)

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. (shrink)

The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition.

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. (shrink)

The relevance of any logical analysis lies in its ability to solve paradoxes and trace conceptual troubles back; with this respect, the task of epistemic logic is to handle paradoxes in connection with the concept of knowledge. Epistemic logic is currently introduced as the logical analysis of crucial concepts within epistemology, namely: knowledge, belief, truth, and justification. An alternative approach will be advanced here in order to enlighten such a discourse, as centred upon the word assertion and displayed in terms (...) of utterance. Insofar as epistemic modalities express some attitudes, the intentionality of discourse will be emphasized within an illocutionary modal logic. Two large views will range over the whole study: declarative and epistemic sentences have one and the same logic (assertion logic); the plurality of languages games doesn’t entail any logical pluralism. -/- La valeur d'une analyse logique réside dans sa capacité à résoudre des paradoxes et à comprendre l'origine de nos problèmes conceptuels ; à ce titre, le rôle d'une logique épistémique est de traiter des paradoxes liés au concept de connaissance. On présente généralement la logique épistémique comme une analyse logique de concepts centraux en épistémologie : connaissance, croyance, vérité, justification. Une autre approche sera proposée ici en vue de clarifier ce genre de discours, centrée sur la notion d'assertion et décrite en termes d'énonciation. Parce que les modalités épistémiques expriment des attitudes, c'est l'intentionnalité du discours qui sera mise en valeur dans le cadre d'une logique modale illocutoire. Deux thèses transversales parcourront l'ensemble du travail : les énoncés déclaratifs et épistémiques partagent la même logique (logique assertorique) ; la pluralité des jeux de langages n'implique pas un pluralisme logique. (shrink)