In this historical article, Newton da Costa discusses Francisco Miró Quesada’s philosophical ideas about logic. He discusses the topics of reason, logic, and action in Miró Quesada’s work, and in the final section he offers his critical view. In particular, he disagrees with Miró Quesada’s stance on the historicity of reason, for whom “reason is essentially absolute”, whereas for da Costa it “is being constructed in the course of history”. Da Costa concludes by emphasizing the (...) importance of Miró Quesada’s theory of logic and reason, despite it still being incomplete. -/- Historical article by Newton da Costa, annotated and translated by J. C. Cifuentes and L. F. Bartolo Alegre. (shrink)

The aim of this paper is to show the relevance of paragraph 308 of "On Certainty" to consider a wittgensteinian contribution to the epistemological thought. Given that Wittgenstein's concerns turn, in "On Certainty", to major epistemological problems - namely, the problem of doubt, certainty, knowledge and justification - I set forth some relevant results of his "visit" to Epistemology through the exegesis of paragraph 308, which sistematize the problems faced throughout the book. By doing so, three main themes of Wittgenstein's (...) Epistemology are explored: the categorical distinction between "knowledge" and "certainty", the logical role of "doubt" and the grammatical role of some empirical propositions. (shrink)

In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da (...) Costa logic is examined and employed to pinpoint the maximal non-classical extension of both daC and Heyting-Brouwer logic HB . Finally, the relationship between daC and Logics of Formal Inconsistency is examined. (shrink)

Capítulo de livro publicado em "Uma introdução à filosofia do direito" Itamar Luís Gelain (Org.) .- Ijuí: Ed. Unijuí, 2015. - 368 p. - (Coleção direito, política e cidadania; 37). . ISBN 978-85-419-0 I 75-8.

Based on the notion of proem as exposed in Aristotle’s Rhetoric, we examine in detail Metaph. A1. Our goal is to understand the argument contained in this chapter, as we also endeavour to show how the Stagirite introduces with uttermost caution the theme of wisdom [σοφία], that which is the incarnation of the preeminent science in the first book of the Metaphysics. The attention we devote to the proem of this work is explained by the importance we attribute, unlike much (...) of contemporary scholars, to σοφία, that is, the science of first causes and principles, which we consider to be, ultimately, the pivotal formulation of the supreme science in the Metaphysics. (shrink)

The article will expose the problem of the nature of reality stablished in the first sections of Wittgenstein"s “Tractatus Logico-Philosophicus”, especially the aphorisms 1 to 2.063 seeking to show points of contact between the Aristotelian-Thomistic and Suarezian thought. Initially, (I) a distinction is made between metaphysics and ontology in order to understand why Wittgenstein, notorious for his anti-metaphysical thought, actually ends up producing a theory of reality. Subsequently, (II) the relationship between reality and language will be drawn from the characteristic (...) isomorphism of the Tractatus in which a structural similarity will appear with the Aristotelian-Thomistic thought. This relationship will be the basis for (III) the construction of an ontological image of reality as the condition of possibility for a meaningful language. With this outlook, the (IV) hypothesis of the influence of Francisco Suárez"s thought as the content behind this Wittgensteinian description of reality will be advanced. (shrink)

The article examines the following interpretive hypothesis: from the formulation of the concept of “precariousness” in Precarious Life (2004), Judith Butler's thought undergoes a inflection towards a ethical-political foundation normatively understood and previously rejected by the author as evidenced in her debate with Nancy Fraser and Seyla Benhabib in the 1990s. It is therefore a matter of questioning the impact of this theoretical mutation on the notions of universal and subject that are embedded in the argumentative lines of the author’s (...) texts, thus establishing “precariousness” and “co-dependence” as ethical-political conditions that should guide political guidelines aimed at making life possible and viable. The article is divided into three moments: 1) the universal denied in form and content; 2) The universal affirmed in its form, but denied in its content; 3) the universal materially and formally affirmed. It will also address the different notions of subject that emerge from each of these three understandings of universal. (shrink)

With the ageing of the Portuguese population, there are more people in dependency situations and needing long-term care (LTC). In this context, it is important to ensure the quality of life (QoL) of those individuals, and that quality can be measured through their health-related quality of life (HRQoL) and overall well-being. Also, understanding how perceived service quality (PSQ) can be related to how people perceive their QoL is pertinent since service quality is an important factor to achieve patient health outcomes. (...) To develop this project, a LTC unit located in the district of Lisbon was chosen, the LTC unit of Arruda dos Vinhos. The main objective was to assess the relation between the PSQ, the HRQoL and the overall well-being of patients receiving LTC at the LTC unit of Arruda dos Vinhos. A project based on a case study was performed, through interviews based on the items of the SERVPERF, EQ-5D and ICECAP-O questionnaires, which were then analysed through content analysis. Results showed there is a relation between PSQ and HRQoL and between HRQoL and overall well-being. It was also possible to realise that to better evaluate the quality of this specific service, other subjects as the activities performed at the LTC unit, the physiotherapy service and the food provided, should be taken in consideration. Concluding, there is a relation between PSQ and the QoL of the patients receiving LTC at the LTC unit of Arruda dos Vinhos, when quality of life is measured through HRQoL. (shrink)

This article theorizes the relationship between three fundamental categories for bell hooks' formulations regarding cultural critique and subjectivity - keeping in mind that hooks' thought establishes a fractal system - oppositionality, affectability and radical black subjectivity. From this, we establish the main objective of this text: to think with hooks about the importance of the positionality of the body (subject) in the construction of knowledge and of itself, from its capacity to be affected (affectability) and to affect people, as being (...) primordial stages of the fertile context for the emergence of radical black subjectivity. For this analysis, this article will address the following questions: 1) the construction and role of radical black subjectivity in bell hooks; 2) the recovery of the body and affectability in the production of knowledge; and 3) the centrality of the oppositional gaze and the potency of imagination in the displacement of binaries towards new consciousnesses and new worlds. (shrink)

Partindo do cenário atual das sociedades de inimizade, tal como teorizado por Achille Mbembe, este texto segue os argumentos de bell hooks para pensar em uma política do amor que possa aparecer como um antídoto para os males causados pelas sociedades da inimizade que se sustentam em uma imagem da alteridade experimentada desde a figura do inimigo a ser combatido, mortificado, morto. Ao valorizar o amor como uma prática - e não somente como sentimento - que envolva o cuidado, a (...) responsabilidade, afeto, reconhecimento, confiança, respeito, comunicação franca, sustentamos a necessidade da construção de outro modelo de sociedade guiado pela prática do amor, as sociedades do amanhã, que apresente para a experiência das pessoas negras, rotineiramente violada pelo racismo, outro jeito de estar no mundo, considerando o espírito, entendido por Sobonfu Somé como dimensão da existência que necessita do caráter coletivo das relações, como pilar incontornável. (shrink)

Esta coletânea reúne, organizados na forma de capítulos, sete artigos que exploraram uma ideia central: a de que, subjacente à Lógica de Hegel, há uma mathesis, isto é, uma estruturação matemática que organiza as ideias dessa Lógica, mathesis de que Hegel faz uso, de modo implícito, ao longo do texto da "Ciência da Lógica".

This is a review of: Newton C.A. da Costa, Logiques Classiques et Non Classiques. Essai sur les Fondements de la Logique. Translated from the Portuguese by Jean-Yves Béziau (with two appendices by the translator) Culture Scientifique, Masson, Paris, 1997, 276p. ISBN 2-225-85247-2.

In "Godel es Way" diskutieren drei namhafte Wissenschaftler Themen wie Unentschlossenheit, Unvollständigkeit, Zufälligkeit, Berechenbarkeit und Parakonsistenz. Ich gehe diese Fragen aus Wittgensteiner Sicht an, dass es zwei grundlegende Fragen gibt, die völlig unterschiedliche Lösungen haben. Es gibt die wissenschaftlichen oder empirischen Fragen, die Fakten über die Welt sind, die beobachtungs- und philosophische Fragen untersuchen müssen, wie Sprache verständlich verwendet werden kann (die bestimmte Fragen in Mathematik und Logik beinhalten), die entschieden werden müssen, indem man sich anschaut,wie wir Wörter in bestimmten (...) Kontexten tatsächlich verwenden. Wenn wir klar werden, welches Sprachspiel wir spielen, werden diese Themen als gewöhnliche wissenschaftliche und mathematische Fragen angesehen, wie alle anderen auch. Wittgensteins Einsichten wurden selten übertroffen und sind heute so treffend wie vor 80 Jahren, als er die Blauen und Braunen Bücher diktierte. Trotz seiner Versäumnisse – wirklich eine Reihe von Notizen statt eines fertigen Buches – ist dies eine einzigartige Quelle für die Arbeit dieser drei berühmten Gelehrten, die seit über einem halben Jahrhundert an den blutenden Rändern von Physik, Mathematik und Philosophie arbeiten. Da Costa und Doria werden von Wolpert zitiert (siehe unten oder meine Artikel über Wolpert und meine Rezension von Yanofskys 'The Outer Limits of Reason'), da sie auf universelle Berechnung schrieben,, und unter seinen vielen Errungenschaften ist Da Costa ein Pionier in Parakonsistenz. Wer aus der modernen zweisystems-Sichteinen umfassenden, aktuellen Rahmen für menschliches Verhalten wünscht, kann mein Buch "The Logical Structure of Philosophy, Psychology, Mindand Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019) konsultieren. Diejenigen,die sich für mehr meiner Schriften interessieren, können 'Talking Monkeys--Philosophie, Psychologie, Wissenschaft, Religion und Politik auf einem verdammten Planeten --Artikel und Rezensionen 2006-2019 3rd ed (2019) und Suicidal Utopian Delusions in the 21st Century 4th ed (2019) und andere sehen. (shrink)

En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...) y lógica), que necesitan decidirse por unt cómo realmente usar palabras en contextos concretos. Cuando tenemos claro sobre qué juego de idiomas estamos jugando, estos temas son vistos como preguntas científicas y matemáticas ordinarias como cualquier otra. Las percepciones de Wittgenstein rara vez se han igualado y nunca superado y son tan pertinentes hoy como lo fueron hace 80 años cuando dictó los libros azul y marrón. A pesar de sus fallas — realmente una serie de notas en lugar de un libro terminado —, esta es una fuente única de la obra de estos tres eruditos famosos que han estado trabajando en los bordes sangrantes de la física, las matemáticas y la filosofía durante más de medio siglo. Da Costa y Doria son citados por Wolpert (ver abajo o mis artículos sobre Wolpert y mi reseña de ' los límites de la razón ' de Yanofsky) desde que escribieron en el cómputo universal, y entre sus muchos logros, da Costa es pionera en paraconsistencia. Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna dos sistemas punto de vista puede consultar mi libros Talking Monkeys 3ª ed (2019), Estructura Logica de Filosofia, Psicología, Mente y Lenguaje en Ludwig Wittgenstein y John Searle 2a ed (2019), Suicidio pela Democracia 4ª ed (2019), La Estructura Logica del Comportamiento Humano (2019), The Logical Structure de la Conciencia (2019, Entender las Conexiones entre Ciencia, Filosofía, Psicología, Religión, Política y Economía y Delirios Utópicos Suicidas en el siglo 21 5ª ed (2019), Observaciones sobre Imposibilidad, Incompletitud, Paraconsistencia, Indecidibilidad, Aleatoriedad, Computabilidad, Paradoja e Incertidumbre en Chaitin, Wittgenstein,. (shrink)

Dans 'Godel’s Way', trois éminents scientifiques discutent de questions telles que l’indécidabilité, l’incomplétude, le hasard, la calculabilité et la paraconsistence. J’aborde ces questions du point de vue de Wittgensteinian selon lesquelles il y a deux questions fondamentales qui ont des solutions complètement différentes. Il y a les questions scientifiques ou empiriques, qui sont des faits sur le monde qui doivent être étudiés de manière observationnelle et philosophique quant à la façon dont le langage peut être utilisé intelligiblement (qui incluent certaines (...) questions en mathématiques et en logique), qui doivent être décidés en regardant un comment nous utilisons réellement des mots dans des contextes particuliers. Lorsque nous obtenons clair sur le jeu de langue que nous jouons, ces sujets sont considérés comme des questions scientifiques et mathématiques ordinaires comme les autres. Les idées de Wittgenstein ont rarement été égalées et jamais dépassées et sont aussi pertinentes aujourd’hui qu’elles l’étaient il y a 80 ans lorsqu’il a dicté les Livres Bleus et Brown. Malgré ses défauts, vraiment une série de notes plutôt qu’un livre fini, c’est une source unique du travail de ces trois savants célèbres qui travaillent aux confins de la physique, des mathématiques et de la philosophie depuis plus d’un demi-siècle. Da Costa et Doria sont cités par Wolpert (voir ci-dessous ou mes articles sur Wolpert et mon examen de Yanofsky 'The Outer Limits of Reason') depuis qu’ils ont écrit sur le calcul universel, et parmi ses nombreuses réalisations, Da Costa est un pionnier dans la paraconsistence. -/- Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deux système peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 » 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2019) et autres. (shrink)

In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking (...) at how we actually use words in particular contexts. When we get clear about which language game we are playing, these topics are seen to be ordinary scientific and mathematical questions like any others. Wittgenstein’s insights have seldom been equaled and never surpassed and are as pertinent today as they were 80 years ago when he dictated the Blue and Brown Books. In spite of its failings—really a series of notes rather than a finished book—this is a unique source of the work of these three famous scholars who have been working at the bleeding edges of physics, math and philosophy for over half a century. Da Costa and Doria are cited by Wolpert (see below or my articles on Wolpert and my review of Yanofsky’s ‘The Outer Limits of Reason’) since they wrote on universal computation, and among his many accomplishments, Da Costa is a pioneer in paraconsistency. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking (...) at how we actually use words in particular contexts. When we get clear about which language game we are playing, these topics are seen to be ordinary scientific and mathematical questions like any others. Wittgenstein’s insights have seldom been equaled and never surpassed and are as pertinent today as they were 80 years ago when he dictated the Blue and Brown Books. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

在《哥德尔之路》中,三位杰出的科学家讨论了不可解性、不完整性、随机性、可估计性和副一致性等问题。我从维特根斯坦的观点出发来处理这些问题,即有两个基本问题有着完全不同的解决方案。有科学或经验问题,这是关 于世界的事实,需要研究观察和哲学问题,如何使用语言可理解(其中包括数学和逻辑中的某些问题),需要通过查看我们在特定上下文中实际使用单词的方式来决定。当我们清楚要玩哪种语言游戏时,这些话题就像其他话题一 样被视为普通的科学和数学问题。维特根斯坦的见解很少被平等,也从未被超越,今天和80年前他口述《蓝书》和《棕色书》时一样具有现实意义。尽管它的失败——实际上是一系列笔记,而不是一本已完成的书——这是这三 位著名学者作品的独特来源,他们半个多世纪以来一直在物理学、数学和哲学的流血边缘工作。达科斯塔和多里亚被沃尔珀特引用(见下文或我的文章沃尔珀特和我对亚诺夫斯基的"理性的外在极限"的评 论),因为他们写了通用计算,在他的许多成就中,达科斯塔是先驱参数一致性。 那些希望从现代两个系统的观点来看为人类行为建立一个全面的最新框架的人,可以查阅我的书《路德维希的哲学、心理学、Mind 和语言的逻辑结构》维特根斯坦和约翰·西尔的《第二部》(2019年)。那些对我更多的作品感兴趣的人可能会看到《会说话的猴子——一个末日星球上的哲学、心理学、科学、宗教和政治——文章和评论2006-201 9年第3次(2019年)和自杀乌托邦幻想21篇世纪4日 (2019) .

This article introduces some concepts that help exploring the ontological import of universal logic. It studies the notions of an antilogic and counterlogic associated to each logic and shows some of their properties. It presents the notion of galaxy, as the class of possible worlds compatible with a given logic.We explore some consequences of these developments.

Nous proposons une logique épistémique quadrivalente AR4.

In the debate about Christian attitudes to other religions, a threefold typology has emerged depicting differing Christian responses: pluralism, inclusivism and exclusivism. (This typology is not restricted to the Christian debate alone.) Traditionally, pluralism is opposed to exclusivism, the former claiming that it is arrogant and untenable to make exclusive truth claims, and that all religions are potentially equal paths to salvation and truth. In contrast, I argue that pluralism must always logically be a form of exclusivism and that nothing (...) called pluralism really exists. The main purpose of my paper is to show that there is no high-ground in the pluralist position, for in principle its logic is no different from the exclusivist position. If this is established, then the debate can proceed with more substantial issues regarding the justification and clarification of truth claims. (shrink)

Departing from basic concepts in abstract logics, this paper introduces two concepts: conjunctive and disjunctive limits. These notions are used to formalize levels of modal operators.

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.

The Aristotelian view of universals, according to which each universal generically depends for its existence on its instantiations, has recently come under attack by a series of ground-theoretic arguments. The last such arguments, presented by Raven, promises to offer several significant improvements over its predecessors, such as avoiding commitment to the transitivity of ground and offering new reasons for the metaphysical priority of universals over their instantiations. In this paper, we argue that Raven's argument does not effectively avoid said commitment (...) and that Raven's new reasons fail. Moreover, we present a novel ground-theoretic interpretation of the Aristotelian view, referred to as strong immanence, and introduce a new argument against the Aristotelian view, intended to sidestep any commitment to the transitivity of ground. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

O Programa de Filosofia para Crianças de Matthew Lipman e Ann Margaret Sharp tem pouco mais de 40 anos e à sua criação de imediato se sucederam a difusão e a adaptação em diversos contextos geográficos e culturais. Quer isto dizer que a história da Filosofia para Crianças, sobretudo nas últimas décadas, tem consistido numa marcha, mais ou menos vertiginosa, de inovação e renovação. E nem sempre este ritmo de rápida disseminação se tem mostrado compatível com a sedimentação de reflexões (...) apuradas sobre as diferentes dimensões e problemáticas que a prática coloca. A formação dos facilitadores de sessões de Filosofia para Crianças, de acordo com o modelo da comunidade de investigação filosófica de Lipman e Sharp, é uma das dimensões deste projeto pioneiro que aguardam um debate de maior desenvolvimento. A presente reflexão pretende contribuir para essa discussão, apresentando de forma concisa algumas posições que consideramos relevantes para a compreensão do que está em causa. Não temos a pretensão de assumir a forma acabada de um cânone, mas de justificar opções que nos parecem decisivas no presente contexto de implementação da Filosofia para Crianças em Portugal. Esperamos, assim, contribuir para que se possa gerar uma comunidade alargada de diálogo sobre este tópico. (shrink)

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...) does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies. (shrink)

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; (...) and (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules. (shrink)

After almost a decade of study, research, and dissemination in the field of philosophy for children (p4c), the University of the Azores has created a Master’s degree in Philosophy for Children. While it may appear to be just another university course of study in the academic field of philosophy, we believe that this Master’s is a case study in its own right, as it has allowed us to think about what p4c is capable of when it takes over the university. (...) Not only has the Master’s degree helped shape p4c, but p4c has itself driven the development of the Master’s. Through this process, a different way of existing “within the university” emerges, revealing points worthy of attention that conventional academia does not always value. This article reflects on some of the ideas relating to this process and, without any pretension of establishing rules or claiming to be a finished product, offers some considerations that in our view constitute a turning point for the way people exist within the university. After experiencing a Master’s based upon p4c, neither the university nor philosophy itself can be understood in the same way as before. What is it about p4c, then, that makes it capable of transforming whatever it touches? (shrink)

Esta nota mostra como reduzir o quadrado bidimensional de oposições ao segmento de oposições (uma dimensão) e ao ponto de oposições (objeto sem dimensão).

The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics _S__T_ and _T__S_. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...) these systems derivability can be characterized in terms of a notion we call absolute global validity. However, arriving at these results doesn’t lead us to disregard local validity. First, because we discuss the conditions under which local, and also global validity, can be expected to coincide with derivability. Secondly, because we show how taking into account certain families of valuations can be useful to describe derivability for different calculi used to present _S__T_ and _T__S_. (shrink)

The aim of this article is to discuss the extent to which certain substructural logics are related through the phenomenon of duality. Roughly speaking, metainferences are inferences between collect...

Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collapsible schemes, (...) in which the middle value acts like one of the classical values). For $st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible. (shrink)

De modo geral, este texto é uma incursão em lógica filosófica e filosofia da lógica. Ele contém reflexões originais acerca dos conceitos de paraconsistência, modalidades e cognoscibilidade e suas possíveis relações. De modo específico, o texto avança em quatro direções principais: inicialmente, uma definição genérica de lógicas não clássicas utilizando a ideia de lógica abstrata é sugerida. Em seguida, é mostrado como técnicas manuais de paraconsistentização de lógicas são usadas para gerar sistemas particulares de lógicas paraconsistentes. Depois, uma definição de (...) possibilidade lógica é proposta por meio da ideia de limites de sequências de fórmulas. Por fim, muitas abordagens distintas ao paradoxo de Fitch e, consequentemente, aos limites do conhecimento são apresentadas considerando as reflexões anteriores. (shrink)