This paper introduces the logic of evidence and truth \ as an extension of the Belnap–Dunn four-valued logic \. \ is a slightly modified version of the logic \, presented in Carnielli and Rodrigues. While \ is equipped only with a classicality operator \, \ is equipped with a non-classicality operator \ as well, dual to \. Both \ and \ are logics of formal inconsistency and undeterminedness in which the operator \ recovers classical logic for propositions in its scope. (...) Evidence is a notion weaker than truth in the sense that there may be evidence for a proposition \ even if \ is not true. As well as \, \ is able to express preservation of evidence and preservation of truth. The primary aim of this paper is to propose a probabilistic semantics for \ where statements \\) and \\) express, respectively, the amount of evidence available for \ and the degree to which the evidence for \ is expected to behave classically—or non-classically for \ \). A probabilistic scenario is paracomplete when \ + P 1\), and in both cases, \ < 1\). If \ = 1\), or \ = 0\), classical probability is recovered for \. The proposition \, a theorem of \, partitions what we call the information space, and thus allows us to obtain some new versions of known results of standard probability theory. (shrink)

The aim of this text is to reply to criticisms of the logics of evidence and truth and the epistemic approach to paraconsistency advanced by Barrio [2018], and Lo Guercio and Szmuc [2018]. We also clarify the notion of evidence that underlies the intended interpretation of these logics and is a central point of Barrio’s and Lo Guercio & Szmuc’s criticisms.

The main aim of this paper is to introduce first-order versions of logics of evidence and truth, together with corresponding sound and complete Kripke semantics with variable and constant domains. According to the intuitive interpretation proposed here, these logics intend to represent possibly inconsistent and incomplete information bases over time. The paper also discusses the connections between Belnap-Dunn’s and da Costa’s approaches to paraconsistency, and argues that the logics of evidence and truth combine them in a very natural way.

The aim of this paper is to present and analyze the truthmaker monism , a result according to which any truthmaker makes true any true proposition. Truthmaker monism depends on the characterization of the truthmaking relation in terms of strict implication, the principle of excluded middle and the so called disjunction thesis. I will restrict the discussion to a theory of truthmakers of empirical truths and I will argue that, in the scope of such a theory, the problem does not (...) lie in the use of strict implication neither in the excluded middle but, rather, in the disjunction thesis, that must be rejected. (shrink)

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify (...) paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence. (shrink)

The book Paraconsistent Logic: Consistency, Contradiction and Negation by Walter Carnielli and Marcelo Coniglio is the most thorough study of Logics of Formal Inconsistency...

Foreword : Consistency, Contradiction, and Consequence.

The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence, and extends it to the Logic of Evidence and Truth. The latter is a logic of (...) formal inconsistency and undeterminedness that is able to express not only preservation of evidence but also preservation of truth. LETj is anti-dialetheist in the sense that, according to the intuitive interpretation proposed here, its consequence relation is trivial in the presence of any true contradiction. Adequate semantics and a decision method are presented for both BLE and LETj, as well as some technical results that fit the intended interpretation. (shrink)

The main aim of this paper is to introduce the logics of evidence and truth $$LET_{K}^+$$ and $$LET_{F}^+$$ together with sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics $$LET_{K}$$ and $$LET_{F}^-$$ with rules of propagation of classicality, which are inferences that express how the classicality operator $${\circ }$$ is transmitted from less complex to more complex sentences, and vice-versa. The six-valued semantics here proposed extends the 4 values of Belnap-Dunn logic with 2 more values (...) that intend to represent (positive and negative) reliable information. A six-valued non-deterministic semantics for $$LET_{K}$$ is obtained by means of Nmatrices based on swap structures, and the six-valued semantics for $$LET_{K}^+$$ is then obtained by imposing restrictions on the semantics of $$LET_{K}$$. These restrictions correspond exactly to the rules of propagation of classicality that extend $$LET_{K}$$. The logic $$LET_{F}^+$$ is obtained as the implication-free fragment of $$LET_{K}^+$$. We also show that the 6 values of $$LET_{K}^+$$ and $$LET_{F}^+$$ define a lattice structure that extends the lattice L4 defined by the Belnap-Dunn four-valued logic with the 2 additional values mentioned above, intuitively interpreted as positive and negative reliable information. Finally, we also show that $$LET_{K}^+$$ is Blok-Pigozzi algebraizable and that its implication-free fragment $$LET_{F}^+$$ coincides with the degree-preserving logic of the involutive Stone algebras. (shrink)

A ficção corresponde a um estilo de escrita que sustenta a construção de narrativas capazes de arrancar o escritor de si mesmo em um sentido de, por meio do experimento da própria linguagem, constituir-se esteticamente. Quando observamos as obras de Nietzsche, percebemos que há uma pluralidade de estilos literários, compostos, frequentemente, por aforismos que demandam outro performático: a escrita hiperbólica. Por meio da escrita artística, Nietzsche cria um mundo compreendido como vontade de poder em que dá a si mesmo como (...) personagem dentre outros tipos psicológicos. Já na filosofia de Foucault o traço marcante de suas obras é o tom histórico com o qual aborda seus temas. Porém, como o próprio afirma em algumas entrevistas, não escreve outra coisa que não sejam ficções, seleciona e organiza enunciados históricos criando diversos cenários, sujeitos e objetos de seu discurso. Este estilo presente em ambos entra em contato com o exterior provocando um reposicionamento do leitor, que é afetado promovendo, como efeito de subjetivação, um reposicionamento político de insubmissão de não querer mais ser governado dessa forma. (shrink)

Utopía, la posibilidad de la imposibilidad: una lectura desde Thomas More, es un trabajo que muestra, por un lado, la vitalidad de la utopía; por otro lado se destaca su grado de necesidad en la sociedad contemporánea. La Utopía de Thomas More se presenta como un paradigma del pensamiento utópico, y del influjo que éste ejerce en las diferentes sociedades. Además, ésta se yergue como el epítome de toda posibilidad de visualizar un mejor mundo, es la máxima expresión de la (...) simbología del Renacimiento y es la obra cumbre del humanismo de aquel período histórico. La utopía no es la simple imposibilidad que sugiere su construcción semántica. Utopía es la posibilidad de construir el mejor mundo posible, de volver a ubicar en su perspectiva correcta la esperanza y toda la capacidad simbólica del género humano. (shrink)

From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation of intuitionistic logic is (...) in terms of preservation of constructive proof; of paraconsistency is in terms of preservation of evidence. In this paper, we explain and defend the epistemic approach to paraconsistency. We argue that it is more plausible than dialetheism and allows a peaceful and fruitful coexistence with classical logic. (shrink)

Proof-theoretic semantics provides meanings to the connectives of intuitionistic logic without the need for a semantics in the standard sense of an attribution of semantic values to formulas. Meanings are given by the inference rules that, in this case, do not express preservation of truth but rather preservation of availability of a constructive proof. Elsewhere we presented two paraconsistent systems of natural deduction: the Basic Logic of Evidence and the Logic of Evidence and Truth. The rules of BLE have been (...) conceived to preserve a notion weaker than truth, namely, evidence, understood as reasons for believing in or accepting a given proposition. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$LET_{J}$$\end{document}, on the other hand, is a logic of formal inconsistency and undeterminedness that extends \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BLE$$\end{document} by adding resources to recover classical logic for formulas taken as true, or false. We extend the idea of proof-theoretic semantics to these logics and argue that the meanings of the connectives in BLE are given by the fact that its rules are concerned with preservation of the availability of evidence. An analogous idea also applies to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$LET_{J}$$\end{document}. (shrink)

This papers’ goal is to present a survey of the contemporary discussions regarding truthmakers. The emphasis will be on the characterization of the truthmaking relation and on the problems involved in universal propositions and negations.

Uno de los factores fundamentales para comprender la problemática de la paz es el de la memoria. Un presupuesto de este artículo es que dicha memoria se realiza en el lenguaje, especialmente en el lenguaje articulado, que es el medio por el que se hace púbica y se despliega, no sólo la expresión de un pasado, sino también las perspectivas que orientan nuestras argumentaciones para el presente y el futuro. Cuando hablo de lenguaje, propongo que de lo que se trata, (...) no son sólo de palabras, sino de sintagmas, es decir del habla desplegada en una época, y en contextos biográficos y comunidades interpretativas de cada uno y de cada comunidad. Dos factores a considerar en esta definición de nociones, categorías y conceptos son lo imaginario y la ideología, que están relacionados con la educación y las condiciones de vida, colectivas e individuales.Otro asunto que hay que considerar son los contextos o niveles de diversa escala y poder, entre ellos, los contextos contemporáneos, es decir la escala macro-estructural ─escala preferida de quienes piensan que la paz no es posible─, que interviene decisivamente en la formulación de las posibilidades no sólo de la paz, sino de la memorialización, la que puede ser sometida a políticas públicas y privadas de diverso alcance.En este artículo se abordan los problemas asociados a las posibilidades de formulación de las políticas de paz en su nivel intermedio, es decir las que median entre las escalas macro y micro, con especial énfasis en las últimas, que es donde la memoria, la acción colectiva y la autoreflexividad pueden aportar. (shrink)

The book Paraconsistent Logic: Consistency, Contradiction and Negation by Walter Carnielli and Marcelo Coniglio is the most thorough study of Logics of Formal Inconsistency...

We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically (...) justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we argue that an intuitive reading of the bivalued semantics for the logic mbC, a logic of formal inconsistency based on classical logic, fits in well with the basic ideas of an intuitive interpretation of contradictions. On this interpretation, the acceptance of a pair of propositions A and ¬A does not mean that A is simultaneously true and false, but rather that there is conflicting evidence about the truth value of A. (shrink)

In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson’s logic N4 and the logic of first-degree entailment with a classicality operator ∘ that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these models represent a database that receives information as time passes, and such information can be positive, negative, non-reliable, or reliable, while a formula ∘A means that the information about (...) A, either positive or negative, is reliable. This proposal is in line with the interpretation of N4 and FDE as information-based logics, but adds to the four scenarios expressed by them two new scenarios: reliable information for the truth and for the falsity of a given proposition. (shrink)

Harmful but culturally cherished practices often endure in spite of the damages they cause. Meat consumption is increasingly becoming one of such cases and may provide an opportunity from which to observe these phenomena. Growing evidence indicates that current and projected production and consumption patterns are important contributors to significant environmental problems, public health degradation, and animal suffering. Our aim is to contribute to a further understanding of the psychological factors that may hinder or promote personal disposition to change food (...) habits to benefit each of these domains. Drawing from previous evidence, this study explores the proposition that some consumers are motivated to resort to moral disengagement strategies when called upon to consider the impacts of their food habits. Data were collected from six semi-structured focus groups with a sample of 40 participants. Although affirming personal duties towards preserving the environment, promoting public health, and safeguarding animal welfare, participants did not show personal disposition to change their meat consumption habits. Several patterns of response that resonate with the principles of moral disengagement theory were observed while discussing impacts and the possibility of change. Results seem to support the proposition that the process of moral disengagement may play a role in hindering openness to change food habits for the benefit of the environment, public health, and animals, and point towards the relevance of further exploring this approach. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics of formal inconsistency and by the logics of formal undeterminedness. LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the validity of (...) the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core—in the case studied here, this common core is classical positive propositional logic. The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of LFI and undeterminedness, namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion one at a time. The last sections offer an algebraic account for such logics by adapting the swap structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite nondeterministic matrices. (shrink)

The coming to office of Jair Bolsonaro in Brazil has brought to the fore the need to understand the rise of the far right and to come to terms with the conflicted legacies of more than a decade of rule under the Workers’ Party. This forum brings together six leading intellectuals from different traditions on the left and introduces their reflections on the contradictions and complexities of the Workers’ Party, the 2008 crisis, the June 2013 protests, the weakness of the (...) Brazilian left, corruption, and on how to characterise Bolsonaro’s regime. Their interventions offer crucial insights that are relevant today not just to Brazil, or even Latin America, but to the politics of the left worldwide. (shrink)

The coming to office of Jair Bolsonaro in Brazil has brought to the fore the need to understand the rise of the far right and to come to terms with the conflicted legacies of more than a decade of rule under the Workers’ Party. This forum brings together six leading intellectuals from different traditions on the left and introduces their reflections on the contradictions and complexities of the Workers’ Party, the 2008 crisis, the June 2013 protests, the weakness of the (...) Brazilian left, corruption, and on how to characterise Bolsonaro’s regime. Their interventions offer crucial insights that are relevant today not just to Brazil, or even Latin America, but to the politics of the left worldwide. (shrink)

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...) both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...) validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

Esse artigo aborda a atuação de Abílio de Nequete como liderança no movimento comunista brasileiro entre os anos de 1917 e 1924. Nequete era um imigrante libanês que trabalhava como barbeiro na cida­de de Porto Alegre, que se tornou uma figura importante no movimento operário durante a Greve Geral de 1917 e foi o fundador da União Maximalista no ano de 1918, um dos primeiros grupos operários do Brasil identificados com as ideias da Revolução Russa. Após o ano de 1920, (...) o militante se articulou com a Internacional Comunista a partir de contatos na Argentina e no Uruguai, sendo um dos responsáveis pela formação do Partido Comunista do Brasil em 1922. Sua permanência como Secretário Geral do PCB foi rápida, rompendo com o partido por conta de uma série de conflitos internos em 1924. O objetivo desse texto é analisar a trajetória de Nequete como liderança maximalista e comunista em um período formativo dessa corrente política, compreendendo especificidades e contradições de uma fase de definições do que era ser comunista no Brasil. (shrink)

In a recent work, Walter Carnielli and Abilio Rodrigues present an epistemically motivated interpretation of paraconsistent logic. In their view, when there is conflicting evidence with regard to a proposition A (i.e. when there is both evidence in favor of A and evidence in favor of ￢A) both A and ￢A should be accepted without thereby accepting any proposition B whatsoever. Hence, reasoning within their system intends to mirror, and thus, should be constrained by, the way in which we (...) reason about evidence. In this article we will thoroughly discuss their position and suggest some ways in which this project can be further developed. The aim of the paper is twofold. On the one hand, we will present some philosophical critiques to the specific epistemic interpretation of paraconsistent logic proposed by Carnielli & Rodrigues. First, we will contend that Carnielli & Rodrigues’s interpretation implies a thesis about what evidence rationally justifies to accept or believe, called Extreme Permissivism, which is controversial among epistemologists. Second, we will argue that what agents should do, from an epistemic point of view, when faced with conflicting evidence, is to suspend judgment. On the other hand, despite these criticisms we do not believe that the epistemological motivation put forward by Carnielli & Rodrigues is entirely wrong. In the last section, we offer an alternative way in which one might account for the epistemic rationality of accepting contradictions and, thus, for an epistemic understanding of paraconsistency, which leads us to discuss the notion of diachronic epistemic rationality. (shrink)

In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose a Basic Logic of Evidence whose natural deduction rules are thought of as preserving evidence instead of truth. BLE turns out to be equivalent to Nelson’s paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic, KX4, in which \ can be read as (...) asserting there is implicit evidence for X, where we understand evidence to permit contradictions. We show BLE embeds into KX4 in the same way that Intuitionistic logic embeds into S4. Then we formulate a new justification logic, JX4, in which the implicit evidence motivating KX4 is made explicit. KX4 embeds into JX4 via a realization theorem. Thus BLE has both implicit and explicit possibly contradictory evidence interpretations in a formal sense. (shrink)

Cuba es un país insular en donde los fenómenos meteorológicos han sido elementos metafóricos importantes en la configuración de los mitos fundacionales. Será útil entonces observar los fenómenos histórico-socioculturales como fenómenos meteorológicos, pues matizarían cuestiones locales y globales, en lo referente a la identidad y diversidad cultural, estudios estéticos y literarios. La insularidad de Cuba ha pasado por distintos estadios de análisis, desde el plano ontológico hasta el plano político o literario. La inte-racción entre espacio imaginado y expresado en la (...) literatura exige un acercamiento mediado entre los referentes “reales” y meta-literarios. La utilización de la metáfora de la isla ha sido perenne en la historia cultural cubana. Las generaciones de escritores en Cuba, desde hace treinta años aproximadamente, buscan superar algunas barreras ideotemáticas y estilísticas mediante la re-expresión de sus propias sub-versiones literarias. Para ellos, la insularidad o la isla se convierten en un tópico versátil que tensa las relaciones entre las estéticas y sus categorías. Tales fenómenos literarios serían perceptibles en la narrativa de Abilio Estévez, Marilyn Bobes y Antonio José Ponte, lo cual presenta un debate interdisciplinario centrado particularmente en el posicionamiento global de la narrativa cubana y las contemporáneas subversiones literarias. (shrink)