Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. The answer to this question for the language of arithmetic expressions using a constant for the number one and the operations of product and exponentiation is affirmative, and the complete equational theory also characterises isomorphism in the typed lambda calculus, where the constant for one and the operations of product and exponentiation respectively correspond to the unit type and (...) the product and arrow type constructors. This paper studies isomorphisms in typed lambda calculi with empty and sum types from this viewpoint. Our main contribution is to show that a family of so-called Wilkie–Gurevič identities, that plays a pivotal role in the study of Tarski’s high school algebra problem, arises from type-theoretic isomorphisms. We thus close an open problem by establishing that the theory of type isomorphisms in the presence of product, arrow, and sum types is not finitely axiomatisable. Further, we observe that for type theories with arrow, empty and sum types the correspondence between isomorphism and arithmetic equality generally breaks down, but that it still holds in some particular cases including that of type isomorphism with the empty type and equality with zero. (shrink)

This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional temporal languages with varying expressivity and varying (...) degrees of transfer of logical properties. The temporalization method and the independent combination method are shown to transfer all three basic logical properties. The method of full join of logic systems generates a considerably more expressive language but fails to transfer completeness and decidability in several cases. So a weaker method of restricted join is proposed and shown to transfer all three basic logical properties. (shrink)

Nesta entrevista, conduzida por Gonçalo Marcelo e Maria Luísa Portocarrero, Daniel Frey, professor de filosofia da religião na Universidade de Estrasburgo e Presidente do Conselho Científico do Fonds Ricoeur, apresenta alguns aspetos centrais da sua investigação filosófica, do seu desenvolvimento intelectual e das atividades desenvolvidas no Fonds Ricoeur. Daniel Frey expõe a sua teoria hermenêutica da leitura, influenciada por Gadamer e Ricoeur, mostrando a especificidade da abordagem hermenêutica da leitura. Na entrevista, o autor também explora a importância da filosofia (...) do jovem Ricoeur dos anos 1950‑1960, e a evolução da relação entre filosofia e religião em Ricoeur. Fazendo uma breve descrição do estatuto das obras que se tornam “clássicas” e dos projetos recentes do Fonds Ricoeur, como a digitalização dos arquivos de Ricoeur, esta entrevista de Daniel Frey mostra‑nos até que ponto o trabalho de Ricoeur se encontra hoje aberto a novas leituras e interpretações. (shrink)

Robert Brandom propõe um modelo de interação social no qual defende que as atitudes práticas dos usuários da linguagem instituem os conteúdos semânticos e as normas inferenciais que determinam seus usos. Assim, o que ele descreve é uma prática linguística, caracterizado por asserções, que mostra como as atitudes dos agentes, diante das asserções sendo produzidas e consumidas, devem ser entendidas para que instituam conteúdos inferencialmente articulados. Ademais, Brandom relaciona a prática assertiva e o entendimento inferencial do conteúdo semântico a um (...) paradigma racionalista, sugerindo que os conteúdos que aparecem em asserções são aquilo que podem ser oferecidos ou exigidos, dentro da prática de uso da linguagem, como razões. Considerando estas ideias, o objetivo deste trabalho é desenvolver e relacionar os conceitos de "asserção", "inferência" e "razão", tais como Brandom os compreende. (shrink)

La presente nota crítica tiene como finalidad exponer y comentar las ideas fundamentales de la edición española del primer escrito de Jacques Derrida, El problema de la génesis en la filosofía de Husserl. Asimismo, hacemos algunas aclaraciones sobre el origen y significado de este escrito. Al concluir, añadimos algunas observaciones sobre la traducción y sobre el estudio final del editor y traductor Javier Bassas Vila sobre la filosofía del joven Derrida.

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and (...) offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. (shrink)

Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...) ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)

After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.

This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent (...) logics, supplying a sound and complete semantical interpretation for such logics. However, certain subtleties involving term substitution and replacement, that are hidden in classical structures, have to be taken into account when one ventures into the realm of nonclassical reasoning. This paper shows how such difficulties can be overcome, and offers detailed proofs showing that a smooth treatment of semantical characterization can be given to all such logics. Although the paper is well-endowed in technical details and results, it has a significant philosophical aside: it shows how slight extensions of classical methods can be used to construct the basic model theory of logics that are weaker than traditional logic due to the absence of certain rules present in classical logic. Several such logics, however, as in the case of the LFIs treated here, are notorious for their wealth of models precisely because they do not make indiscriminate use of certain rules; these models thus require new methods. In the case of this paper, by just appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus, some new constructions and crafty solutions to certain non-obvious subtleties are proposed. The result is that a richer extension of model theory can be inaugurated, with interest not only for paraconsistency, but hopefully to other enlargements of traditional logic. (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)

We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.

Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) as well as methods for decomposing logics, showing their interesting properties (...) and applications. (shrink)

In this paper, we argue that the Epicurean genealogy of justice and laws presuppose an analysis of the just as a modality of the useful, an approach that denies the conventional character of justice. This genealogical pattern differentiates the origin of justice from that of the law and refers to friendship as a relevant explanatory factor of the origin of justice. We maintain that the interpretations that underline the incoherence of this reference to friendship, in the framework of a hedonistic (...) theory, presuppose a non-Epicurean sharp distinction between altruism and selfishness. (shrink)

In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...) semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)

In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. (...) A detailed discussion about this phenomenon, as well as some elucidation for it, is given. (shrink)

The field of Philosophy of Sport has been developing in Anglo-Saxon scholarship since the 1960s and since then has achieved considerable consolidation. However, this is a progressing field in Latin American countries like Brazil. This paper aims to analyse the trajectory of the Philosophy of Sport in Brazil, presenting an overview of its development since the 1980s and some prospects that have been generated since the turn of the century. In conclusion, the article points out that the field of Philosophy (...) of Sport in Brazil is in the process of disciplinary consolidation, presenting a plurality of agents, institutions and theoretical approaches in its structure. (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)

This volume corresponds to the Proceedings of the XIII Brazilian Logic Conference held at the CLE - Centre for Logic, Epistemology and the History of Science in Campinas, SP, Brazil from May 26-30, 2003 under the auspices of the SBL - Brazilian Logic Society and the ASL - Association for Symbolic Logic.

This paper defends that the both the Buddhist tradition and the Aristotelian allow us to think of the distinction between to reason with contradictions and to accept them, understanding ' accept a contradiction ' by taking it as consistent. From this viewpoint, none of two would disagree with most contemporary paraconsistent views. The conclusions are, thus, that, firstly, there is no compelling reason to endorse any kind of metaphysical dialetheism, and, second, that a coherent form of reasoning with contradictory statements (...) is neither opposed to the Aristotelian conception of logic, nor to certain texts in the Buddhist tradition, as the Madhyamikas. (shrink)

Resumen Este artículo explora las figuras del flâneur y del "mestizo". Reúno con el sustantivo "mestizo" una serie de operaciones estilísticas y retóricas que emplea Echeverría para describir el mestizaje como fenómeno histórico de las sociedades urbanas en las colonias españolas en los siglos XVI y XVII. Partiré de la lectura de Echeverría a Benjamin de principios de los años noventa. Luego analizaré la figura del flâneur y la del mestizo para mostrar algunas líneas de conexión, desde la estrategia alegórica (...) a la relación entre el barroco y la sociedad moderna. Por último, consideraré ambas figuras como paradigmas de sujetidad barroca, es decir, como principios de inteligibilidad de formas sociales que resisten las contradicciones de la modernidad capitalista.This article explores two figures: the flâneur and the "mestizo". Under the word "mestizo" I gather a group of stylistic and rhetorical operations that Echeverría uses to describe mestizaje as a historical phenomenon occurred in the urban societies of spanish Colonies during the 16th and 17th centuries. I start with a historical approach to Echeverría's readings of Benjamin from the beginning of the 1990s. Then I show some possible connections between both figures, from the allegorical strategy to the relationship between baroque and modern society. Finally, I conceive them as paradigms of baroque sujetity; that is, principles of intelligibility of social forms that resist the contradictions of Western modern capitalism. (shrink)

El artículo presenta la “inmanencia práctica” como clave de la ética que G. Deleuze elabora a partir de B. Spinoza y F. Nietzsche. La noción involucra tres tesis que manifiestan la reivindicación incondicional de la inmanencia y la crítica a toda trascendencia: valorización del cuerpo en detrimento de la conciencia; apelación a lo bueno y lo malo, en lugar del bien y el mal; y apología de la alegría e inocencia del devenir. Se sostiene que esta ética naturalista y pluralista (...) se apoya en criterios de valoración ligados a la vida como punto fundamental de apreciación, y se propone la creación de nuevas maneras de ser como medio de enfrentar al sistema del juicio moral sobre el que descansa el nihilismo. (shrink)

RESUMEN El artículo presenta la “inmanencia práctica” como clave de la ética que G. Deleuze elabora a partir de B. Spinoza y F. Nietzsche. La noción involucra tres tesis que manifiestan la reivindicación incondicional de la inmanencia y la crítica a toda trascendencia: valorización del cuerpo en detrimento de la conciencia; apelación a lo bueno y lo malo, en lugar del bien y el mal; y apología de la alegría e inocencia del devenir. Se sostiene que esta ética naturalista y (...) pluralista se apoya en criterios de valoración ligados a la vida como punto fundamental de apreciación, y se propone la creación de nuevas maneras de ser como medio de enfrentar al sistema del juicio moral sobre el que descansa el nihilismo. ABSTRACT The article presents ‘practical immanence’ as the key to the ethics developed by G. Deleuze on the basis of B. Spinoza and F. Nietzsche. This notion involves three theses that show the unconditional vindication of immanence and the critique of all transcendence: affirmation of the body over consciousness; appealing to the good things and the bad things rather than to good and evil; and the defense of the joy and innocence of becoming. The article argues that this naturalistic and pluralistic ethics is grounded in assessment criteria linked to life as the focal point of appreciation, and suggests the creation of new ways of being as a means to tackle the system of moral judgment on which nihilism is based. (shrink)

El artículo revisa los contenidos generales del Tratado Acerca de los elementos de Manuel Antonio Talavera, que es parte de los capítulos que estudian la Física especial en su obra Instituciones de Física. En ésta, se combinan las doctrinas de filosofía natural según las enseñanzas de los filósofos modernos, los nuevos datos empíricos generados a partir de los experimentos científicos y la autoridad de las Escrituras. Se intenta mostrar cómo en la enseñanza de la disciplina durante la última época colonial (...) convivieron conocimientos propios de la modernidad matizados con elementos característicos de la escolástica. Presentamos una breve nota biográfica del autor y revisamos desde una perspectiva general los principales aspectos del tratado. La intención es visibilizar el quehacer educativo de Talavera y rescatar parte del legado filosófico latinoamericano. (shrink)

Portuguese introduction to volume 2, issue 2.

Es para nosotros un gusto presentar el tercer número de la revista Études Ricoeuriennes/Ricoeur Studies (ERRS) dedicado a la reflexión ética de Paul Ricœur. .

El trabajo propone revisar una posible articulación entre memoria, archivo y tecnología. Considera estas nociones a la luz de algunos referentes teóricos canónicos y otros contemporáneos, más cercanos a los desafíos actuales. Reflexiona acerca del valor de uso que las denominadas TIC tienen para la construcción y circulación de archivos culturales, públicos o privados, en tanto artefactos visibles de políticas de memoria. Considera los límites de lo archivable, la condición de posibilidad del desarrollo de archivos en la Era Digitaly las (...) supuestas ventajas con respecto a los archivos analógicos. Esta confrontación ubica en el centro de la discusión la relación paradojal que promete la tecnología actual y futura: al tiempo que abre horizontes deslumbrantes, marca límites entre lo deseable y lo posible, e impone la necesidad de que cada comunidad se apropie de esa tecnología de manera activa y sustentable. (shrink)

Ivan Domingues é professor do Departamento de Filosofia da Universi­dade Federal de Minas Gerais. Seu livro, “Filosofia no Brasil: legados e perspectivas” foi publicado pela Editora UNESP, ele traz em sua obra um forte e pertinente problema que muitos estudiosos se debruçam afim de entender e esclarecer pontos sobre a filosofia no Brasil, e todo contexto histórico envolto dela.

Using positron emission tomography (PET) and regional cerebral blood flow (rCBF) measurements, we investigated the cerebral correlates of consciousness in a sequence learning task through a novel application of the Process Dissociation Procedure, a behavioral paradigm that makes it possible to separately assess conscious and unconscious contributions to performance. Results show that the metabolic response in the anterior cingulate / mesial prefrontal cortex (ACC / MPFC) is exclusively and specifically correlated with the explicit component of performance during recollection of a (...) learned sequence. This suggests a significant role for the ACC / MPFC in the explicit processing of sequential material.  2003 Elsevier Science B.V. All rights reserved. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality ℵ0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are $\mu^{++}$ graphs on μ+ that taken jointly are universal for the graphs on μ+, while $2^{\mu^+} \gg \mu^{++}$ . The paper also addresses the general problem of obtaining a framework for consistency results at the (...) successor of a singular strong limit starting from the assumption that a supercompact cardinal κ exists. The result on the existence of universal graphs is obtained as a specific application of a more general method. (shrink)

The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle—which allows the inference from “snow is white” to “the sentence ‘snow is white’ is true”—and an elimination principle—which allows the inference from “the sentence ‘snow is white’ is true” to “snow is white”. It is commonly assumed that a theory of truth needs to (...) satisfy a transparency principle to fulfil the infinitary function. Picollo and Schindler (Erkenntnis 83:899–928, 2017) argue against this idea. They prove that, given certain assumptions, an elimination principle is sufficient for the purpose. Then, they pose a challenge: to show why we should incorporate introduction principles to our theory of truth. In this essay I take on the challenge. I show that, given the authors’ assumptions, an introduction principle is also sufficient to perform the infinitary function. (shrink)