In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s (...) minimally inconsistent Logic of Paradox with q-entailment as introduced by Grzegorz Malinowski. (shrink)

The following proposal explores and discusses the potential of Cartography as a methodological path in the development of research in Mathematics Education aimed at working with different groups that, in many cases, in addition to finding themselves in various situations of vulnerability and social neglect – taken in their potentiality of life –, are not necessarily linked to formal or informal academic training spaces, such as schools or universities. To this end, we begin with a general presentation of the doctoral (...) research carried out by five members of the research group Coletivo Cronopies+ (cronopiando.org) and, in addition, we invite the participants of the session to visit the first Hip Hop House in Brazil in Diadema/SP, which constitutes one of the settings that make up the fieldwork of one of the research projects presented. The research we share involves working with a Hip Hop cultural center in Piracicaba/São Paulo (SP), a Guarani-Kaiowá indigenous village in Coronel Sapucaia/Mato Grosso do Sul (MS), a traveling school in a Landless Workers’ Movement camp in Porecatu/Paraná (PR), a rural settlement school in Nova União/Rondônia (RO) and three collectives that operate with gender in the region of Rio Claro/SP. The construction of this proposal is methodologically based on Cartography, since the discussion aims to produce the field of this research and we propose “fieldwork”. (shrink)

Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain (in)validities concerning episodic imagination. They are not all equally plausible as principles of episodic imagination. The logic also does not model that the initial input of an imaginative episode is deliberately chosen.Stit-imagination logic models the imagining agent’s deliberate choice of the content of their imagining. However, the logic does not model the episodic nature of imagination. The present paper combines the two logics, thereby modelling imaginative episodes with deliberately (...) chosen initial input. We use a combination ofstit-imagination logic and a content-sensitive variably strict conditional à la Berto, for which we give a Chellas–Segerberg semantics. The proposed semantics has the following advantages over Berto’s: (i) we model thedeliberate choiceof initial input of imaginative episodes (in a multi-agent setting), (ii) we showframe correspondencesfor axiomatic analogues of Berto’s validities, which (iii) allows thepossibility to disregard axiomsthat might be considered not plausible as principles concerning imaginative episodes. We do not take a definite stance on whether theseshouldbe disregarded but give reasons for why one might want to disregard them. Finally, we compare our semantics briefly with recent work, which aims to model voluntary imagination, and argue that our semantics models different aspects. (shrink)

We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus $\mathtt{SC2Int}$ for the bi-intuitionistic logic $\mathtt{2Int}$. A distinctive feature of $\mathtt{SC2Int}$ is that it makes use of two kind of sequents, one representing proofs, the other representing refutations. The structural rules of $\mathtt{SC2Int}$, in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated through (...) two different negation connectives, the well-known implies-falsity negation and the less well-known coimplies-truth negation of $\mathtt{2Int}$. By assuming that the interaction rules have no impact on the identity of derivations, the concept of inherited identity between derivations in $\mathtt{SC2Int}$ is introduced and the notions of positive and negative synonymy of formulas are defined. Several examples are given of distinct formulas that are either positively or negatively synonymous. It is conjectured that the two conditions cannot be satisfied simultaneously. (shrink)

No detailed description available for "Negation".

Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number (...) of simple observations is made showing that the unwanted phenomenon exemplified by tonk in some logics also occurs in contexts in which tonk is acceptable. In fact, in any non-trivial context, the acceptance of arbitrary introduction rules for logical operations permits operations leading to triviality. Connectives that in all non-trivial contexts lead to triviality will be called non-trivially trivializing connectives. (shrink)

A version of strong negation is introduced into Categorial Grammar. The resulting syntactic calculi turn out to be systems of connexive logic.

Justification stit logic is a logic for reasoning about proving as a certain kind of activity, namely seeing to it that a proof is publicly available. It merges the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. In this paper, after recalling its language and basic semantical definitions, various ramifications and refinements of justification stit logic are presented and discussed: imposing natural restrictions upon the class of models under consideration, making (...) use of modalities that assert the existence of a proof, introducing a variant of justification stit logic based on a semantics introduced by M. Fitting, and adding variable-binding operators and extending the set of proof polynomials. (shrink)

Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about (...) the truth or falsity of atomic sentences, A always receives the top-element of a certain partial order on non-ontic semantic values as its value. The ordering in question is a told-true order. Analogously, a formula A is logically false just in case no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain told-false order as its value. Here, truth and falsity are pari passu , and it is the treatment of truth and falsity as independent of each other that leads to an informational interpretation of these notions in terms of a certain kind of higher-level information. (shrink)

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

Dans ce chapitre publié en 1894, Heinrich Waentig (1870-1943) ne présente pas Comte comme une victime qu’il s’agirait de défendre. Il essaie plutôt de marginaliser les critiques de Comte qui dominent l’espace académique germanophone à cette époque. Il insiste sur le « triomphe » annoncé de la méthodologie comtienne, répond aux critiques de Dilthey et reprend certains arguments de son maître de Leipzig, Wilhelm Wundt. Waentig rend hommage à la méthode comparative qui permet de dégager les faits typiques d’une (...) manière beaucoup plus pertinente que celle adoptée par l’économiste Carl Menger. Ce texte est donc aussi pour lui l’occasion de prendre position dans la querelle opposant Schmoller à Menger. (shrink)

Although it is not younger than other areas of non-classical logic, paraconsistent logic has received full recognition only in recent years, largely due to the work of, among others, Newton da Costa, Graham Priest, Diderik Batens, and Jerzy Perzanowski. A logical system Λ is paraconsistent if there is a set of Λ-formulas Δ ∪ {A} such that in Λ one may derive from Δ both A and its negation, and the deductive closure of Δ with respect to Λ is different (...) from the set of all formulas. If from Δ one may derive a formula and its negation, Δ is said to be syntactically inconsistent. But is every syntactically inconsistent set of formulas contradictory? In classical logic and many non-classical logics, every syntactically inconsistent set is unsatisfiable, that is, semantically inconsistent. If contradictoriness means semantical inconsistency, there is, up to logical equivalence, only one contradiction. In paraconsistent logics, there are usually many non-equivalent formulas representing the semantically unique contradiction in a non-paraconsistent logic. So when is a formula the contradiction of another formula, and, moreover, how does the notion of contradiction relate to the notions of contrariety and negation? (shrink)

PREFACE TO THE FIRST FEENCH EDITION. WHEN the Emperor Otho IIL visited the tomb in which had reposed for many years the mortal remains of Charlemagne, ...

Este ensayo se propone reconstruir la teoría aristotélica del tiempo en ocho pasos, a saber: 1. La movilidad como principal característica del ente; 2. la vida como praxis esencialmente vinculada al habla; 3. la relación expresa entre tiempo y experiencia del movimiento; 4. historia y movimiento natural, en el que se discute la relación y la diferencia entre éstos y el tiempo; 5. se busca mostrar cómo se genera propiamente el tiempo, recogiendo lo pensado en los pasos anteriores; 6. se (...) destaca la posibilidad lingüística de decir “ahora” como momento esencial de la comprensión de la generación del tiempo; 7 se intenta tematizar la relación que Aristóteles establece entre tiempo y número, y, por último; 8. la relación entre pasado y Tiempo. (shrink)

L’utilisation des données des plus grands catalogues électroniques des bibliothčques allemandes concernant les éditions des ouvrages de Franjo Petrić et leurs exemplaires permet d’arriver ŕ des résultats qu’il serait probablement impossible d’obtenir par d’autres moyens et instruments. Il existe de fortes indications qui montrent que la réception allemande de Petrić antérieure au XXe siecle diffčre sensiblement de sa réception dans d’autres pays . A ce stade-lŕ de réception, l’impact des ses Discussiones peripateticae et Militia romana est particuličrement évident. Les résultats (...) concernant l’impact des éditions de 1952 et postérieures different ŕ maints égards de ceux obtenus pour les éditions antérieures. Cet article est une étude de cas préliminaire utilisant, ŕ des fins de comparaison, des données puisées dans des sources britanniques et dans la banque de données AHCI. (shrink)

Cet ouvrage doit contribuer à renforcer l'assurance des éducateurs et soutient deux thèses : d'abord, l'important pour la pédagogie est la méta-théorie, ensuite, qui n'atteint pas le niveau de la méta-théorie reste volontairement dans la servitude. L'éducateur doit donc être intelligent et avoir toute liberté dans sa tâche.

Bei Gilles Deleuze findet man einen der seltenen Ansätze zu einem genuin philosophischen Verständnis der Linie. Er versucht eine Emanzipation der Linie nicht nur aus der Geometrie, sondern auch aus der Dominanz des Raumes. Die wichtigsten Motive, die ihn dabei leiten, hat er in dem Konzept der Fluchtlinie gebündelt. Dessen potentiell metaphorischer Status wird ebenso befragt wie seine Aussagekraft für das deleuzianische Verständnis von Philosophie überhaupt. The work of Gilles Deleuze is one of the rare cases in which a genuinely (...) philosophical understanding of the line is attempted. He not only tries to dissociate the line from geometry, but also to free it from the dominance of space. The most important motives behind his thinking about the line converge in the concept of the ›ligne de fuite‹. The text examines the potentially metaphorical status of this notion, as well as its significance for Deleuze’s view of philosophy in general. (shrink)

As the United States population ages, there is a growing group of aging, elderly, individuals who may consider "preemptive suicide"(Prado, 1998). Healthy aging patients who preemptively attempt to end their life by suicide and who have clearly expressed a desire not to have life -sustaining treatment present a clinical and public policy challenge. We describe the clinical, ethical, and medical-legal decision making issues that were raised in such a case that presented to an academic emergency department. We also review and (...) evaluate a decision making process that emergency physicians confront when faced with such a challenging and unusual situation. (shrink)