Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local (...) deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open. (shrink)

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.

Contra those proclaiming the end of philosophy, Badiou aims to restore philosophical thought to the complete space of the truths that condition it.

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

Explores the link between mathematics and ontology.

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, (...) Glymour and Halvorson. (shrink)

We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.

Depuis la publication des Dits et écrits, la place de la littérature dans l’oeuvre de Michel Foucault a une position bien assignée dans les recherches académiques, où l’on souligne surtout l’approche nietzschéenne de la lecture qu’a proposé le philosophe. Prenant appui sur des nouvelles publications et sur des manuscrits inédits, notre texte envisage ce thème sous un autre prisme, à partir du structuralisme de l’analyse littéraire et de l’enjeu philosophique de la revue Tel Quel dans son rapport avec le Nouveau (...) Roman. En repérant l’importance du concept de « distance » dans ses écrits sur la littérature, nous discuterons comment plusieurs des notions créées par Foucault se trouvent en dialogue avec cette constellation théorique plus large. Nous y établirons ainsi le rapport entre la structure et l’événement, la paire conceptuelle au centre des débats philosophiques des années 1960, qui nous guidera dans la compréhension des tensions et des adhésions de la méthodologie foucaldienne à l’égard de l’analyse structurale. A abordagem da « distância » nos escritos literários de Michel Foucault, ou como inscrever o acontecimento na estrutura Desde a publicação dos Ditos e Escritos, o lugar da literatura na obra de Michel Foucault possui uma posição bem definida nas pesquisas acadêmicas, nas quais se ressalta sobretudo a abordagem nietzscheana da leitura proposta pelo filósofo. Recorrendo a novas publicações e aos manuscritos inéditos do Fonds Foucault-BnF, este texto enfocará o tema da literatura sob um outro prisma, à partir do estruturalismo da análise literária e do contexto filosófico da revista Tel Quel em sua relação com o Nouveau Roman. Enfatizando a importância do conceito de “distância” em seus escritos sobre a literatura, discutir-se-á como várias das noções criadas por Foucault se encontram em diálogo com esta constelação teórica mais ampla. A relação entre a estrutura e o acontecimento, enquanto par conceitual que se encontrava no centro dos debates filosóficos nos anos 1960, nos guiará na compreensão das tensões e das adesões da metodologia foucaltiana no que tange à análise estrutural.Palavras-chave: Análise literária. Estruturalismo. Distância. Acontecimento. Tel Quel; BnF Inéditos. (shrink)

O artigo compreende o cerne da obra de Georges Canguilhem como um ponto de cruzamento entre problemáticas fundamentalmente médico biológicas e problemáticas sócio-políticas. A consideração histórica descontinuísta do desenvolvimento de conceitos científicos e a classificação da técnica enquanto prótese do organismo vivo, entre outras particularidades, situam o pensamento canguilhemeano na fronteira entre áreas do conhecimento demarcadas separadamente. O que integra e individualiza o seu trabalho filosófico é a ponderação do vital enquanto categoria de base para intelecção e reconstrução de problemas (...) interdisciplinares. Após indicar o posicionamento de Canguilhem dentro do quadro da filosofia francesa do século XX, o artigo procura demonstrar de que maneira a função de regulação é um dos pilares organizadores do pensamento do “vivo” em sua obra. (shrink)

Alexandre Grothendieck foi um dos maiores matemáticos do século 20 e um dos mais atípicos. Nascido na Alemanha a um pai anarquista de origem russa, sua infância foi marcada pela militância política dos seus pais, assim passando por revoluções, guerras e sobrevivência. Descoberto por sua precocidade matemática por Henri Cartan, Grothendieck fez seu doutorado sob orientação de Laurent Schwartz e Jean Dieudonné. As principais contribuições dele são na área da topologia e na geometria algébrica, assim como na teoria das categorias. (...) No final dos anos de 1960, ele se dedicou à militância política e ecológica, organizando a revista Survivre durante três anos. Em 1986, publicou um manuscrito autobiográfico de 1000 páginas, Récoltes et semailles, em que ele descreve sua experiência e sua prática da matemática, assim suas contribuições à comunidade matemática francesa. Pouco comentado na filosofia, as implicações dos seus descobrimentos fora mais recentemente discutidas por Alain Badiou na sua "fenômeno-lógica", em Logiques des mondes e Arkady Plonitsky, Mathgematics, Science and postclassical Theory, pesquisa trata da semelhança entre os aspectos formais da filosofia de Gilles Deleuze e da topologia de Grothendieck. (shrink)

En el presente trabajo se valora la impronta de la perspectiva deconstructiva del mal en/de/por la soberanía, en la obra de Jaques Derrida, para una crítica anti-idolátrica de la democracia. Parte del estudio crítico de dos tradiciones de fundamentación contemporánea de la democracia representativa. El examen de la propuesta de democracia deliberativa de Habermas y de la concepción de radicalización de la democracia de Ernesto Laclau, las cuales permiten evidenciar la reproducción del proceso de formalización de la democracia. Ambas critican (...) al paradigma del conflicto material de clases de origen marxista y responden con una comprensión comunicativa que parte de la centralidad del lenguaje y el discurso como práctica subjetiva consensual. A partir de la reducción del proceso subjetivo a la anterioridad preminente del discurso, la democracia deja de comprender las condiciones materiales de reproducción del sujeto corporal. Marco ante el cual valoramos el papel de la crítica al malestar de la soberanía presente en la obra de Jaques Derrida. El pensamiento derridiano en torno al Malestar de Soberanía critica la reducción de la diferencia desde una constelación categorial y metódica que implica el reconocimiento del conflicto irreductible que representa la emergencia contingencial del otro. La espectralidad como intuición comprensiva permite la afirmación de la responsabilidad ética, como base de toda posición gnoseológica, que pretenda dar condición de posibilidad a un discurso verdadero. Posición que resguarda la posibilidad transformadora del ejercicio de la soberanía a partir de develar sus procesos de represión subjetiva. Esta constelación categorial es sustantiva a una crítica de la reducción de la democracia en tanto ejercicio soberano. (shrink)

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous E = mc² . The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of (...) accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. (shrink)

Cardiovascular diseases present the leading cause of death worldwide. Over the last decade, their preventio has become not only a central medical and public health issue but also a matter of political concern as well as a major market for pharma, nutrition, and exercise. A preventive assemblage has formed that integrates diverse kinds of knowledges, technologies, and actors, from molecular biology to social work, to foster a specific healthy lifestyle. In this article, the authors analyze this preventive assemblage as a (...) heterogeneous engineer, that is, as an attempt to order complex everyday life into an architecture of modernism. This article draws on research conducted as part of the interdisciplinary research cluster ‘‘preventive self’’ bringing together analyses from social anthropology, history, linguistics, sociology of knowledge, and medicine. The authors report here primarily from ethnographic investigations into biomedical research, primary care, and educational practices in kindergartens. The authors conclude that the preventive assemblage largely fails to install any kind of singular order. Instead, it is translated into existing orderings producing heterogeneity of a different nuance. (shrink)

In 1978, Yu. F. Borisov presented an axiom system using a few basic assumptions and four explicit axioms, the fourth being a formulation of the relativity principle; and he demonstrated that this axiom system had (up to choice of units) only two models: a relativistic one in which worldview transformations are Poincaré transformations and a classical one in which they are Galilean. In this paper, we reformulate Borisov’s original four axioms within an intuitively simple, but strictly formal, first-order logic framework, (...) and convert his basic background assumptions into explicit axioms. Instead of assuming that the structure of physical quantities is the field of real numbers, we assume only that they form an ordered field. This allows us to investigate how Borisov’s theorem depends on the structure of quantities. We demonstrate (as our main contribution) how to construct Euclidean, Galilean, and Poincaré models of Borisov’s axiom system over every non-Archimedean field. We also demonstrate the existence of an infinite descending chain of models and transformation groups in each of these three cases, something that is not possible over Archimedean fields. As an application, we note that there is a model of Borisov’s axioms that satisfies the relativity principle, and in which the worldview transformations are Euclidean isometries. Over the field of reals it is easy to eliminate this model using natural axioms concerning time’s arrow and the absence of instantaneous motion. In the case of non-Archimedean fields, however, the Euclidean isometries appear intrinsically as worldview transformations in models of Borisov’s axioms and neither the assumption of time’s arrow, nor the rejection of instantaneous motion, can eliminate them. (shrink)

We present three natural but distinct formalisations of Einstein’s special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.

Introduced by Leon Henkin back in the fifties, the notion of neat reducts is an old venerable notion in algebraic logic. But it is often the case that an unexpected viewpoint yields new insights. Indeed, the repercussions of the fact that the class of neat reducts is not closed under forming subalgebras turn out to be enormous. In this paper we review and, in the process, discuss, some of these repercussions in connection with the algebraic notion of amalgamation. Some new (...) unpublished results concerning neat reducts and amalgamation are given. . Several counterexamples which convey the gist of techniques used in this area are presented two of which are new It is known that the algebraic notion of amalgamation in a class of algebras corresponds to the metalogical notion of interpolation in the corresponding logic. Answers to open question in the recent paper [31] concerning both amalgamation and interpolation are summarized in tabular form at the end of this paper. This paper appears in two parts. The first part contains results on neat reducts. The present second part contains results relating the notion of neat embeddings to various amalgamation properties.1. (shrink)

ABSTRACT The two main directions pursued in the present paper are the following. The first direction was started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova's theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than (...) 2. To extend the characterization beyond multi-modal logics, we look at arbitrary algebraizable logics. We will introduce an algebraic property equivalent with the Craig interpolation property in algebraizable logics, and prove that the superamalgamation property implies the Craig interpolation property. The problem of extending the characterization result to non-normal non-unary modal logics also will be discussed. In the second direction pursued herein: for non-normal modal logic with one unary modality Lemmon [Lem 66] gave a possible worlds semantics. Here we give a more general possible worlds semantics for not necessarily normal multi-modal logics with arbitrarily many not necessarily unary modalities. Strongly related to the above is the theorem, proved, e.g., in Jóns son-Tarski [JT 52] and Henkin-Monk-Tarski [HMT 71], that every normal Boolean algebra with operators can be represented as a subalgebra of the complex algebra of some relational structure. We extend this result to not necessarily normal BAO's as follows. We define partial relational structures and show that every not necessarily normal BAO is embeddable into the complex algebra of a partial relational structure. This gives a possible worlds semantics for not necessarily normal multi-modal logics. (shrink)

Jacques Derrida is known for his attempt at including the perspective of woman in his philosophical work. His efforts received the acclaim of women philosophers, despite the fact that his philosophy remains marked by the omission of any mention to the work of Simone de Beauvoir. The topic of this paper shall not be woman, as in Derrida’s 1972 conference Spurs, but phallogocentrism. That is, the economy, dynamic and limits of this concept as a critique of history, or rather, as (...) the history of the lie, the term by which Derrida seems to conceive of the possibility of any history whatsoever. We agree that phallogocentrism in Derrida’s hands enabled anti-philosophical forays by which to include woman as singularity in the male-dominated French philosophy of the 1970s. However, we also argue that the specter of man was maintained untouched throughout Derrida’s work, thereby suggestion that deconstruction overlooked what may very well be the primary prohibition in Western thought. (shrink)

This is the second part of the paper [Part I] which appeared in the previous issue of this journal.

O prestígio acadêmico adquirido pela bioética neste último meio século decorre, em parte, do fortalecimento dos espaços de liberdade social nas democracias representativas. No âmbito da ética, criou-se a noção de liberdade, mas sem as formas legalizadas da liberdade a ética não consegue crescer como fonte criativa das normas pelas quais formulam-se as múltiplas formas do juízo moral. Nesta época da pós-verdade e da produção estratégica de mentiras e de ódio políticos, o efeito sobre os sujeitos políticos parece indicativo de (...) carência psicológica, educacional e sobretudo econômica. Diante este cenário, faz-se importante reconsiderar o afastamento da teoria da verdade como “filtro” dos discursos e das orientações políticas produzidas pela ética. A tarefa que se coloca à filosofia é a de estender a força conceitual e discursiva da bioética para contemplar formas de subjetividade em ruptura com uma estrutura de Estado produtora de injustiça. Para tanto, analisamos criticamente a proposta de uma bioética das verdades, filtro separador no sistema de Alain Badiou pelo qual se organiza a relação entre ontologia, fenomenologia e as condições históricas de produção de verdades. (shrink)

In Being and Event, Alain Badiou disconnects the infinite from the One and the Absolute, thus recasting the basis from which to craft a new theory of generic subject, the existence of which is demonstrated through set theory. In Logics of Worlds, Badiou turns his attention to the modes by which this subject appears in a world. It does so by being incorporated as a subjectivizable body, a body of truth. As opposed to Being and Event, the demonstration of this (...) argument takes shape according to two distinct levels, that of a “calculated phenomenology” and that of a formalism in which category theory provides a general logic, the combination of which delineates an “onto-logic”. In this essay, we trace Badiou’s derivation of the notion of body of truth and evaluate the innovative phenomenological methodology applied to explain its association with a world. (shrink)

This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers (...) that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself. (shrink)

Introduced by Leon Henkin back in the fifties, the notion of neat reducts is an old venerable notion in algebraic logic. But it is often the case that an unexpected viewpoint yields new insights. Indeed, the repercussions of the fact that the class of neat reducts is not closed under forming subalgebras turn out to be enormous. In this paper we review and, in the process, discuss, some of these repercussions in connection with the algebraic notion of amalgamation. Some new (...) unpublished results concerning neat reducts and amalgamation are given. . Several counterexamples which convey the gist of techniques used in this area are presented two of which are new . It is known that the algebraic notion of amalgamation in a class of algebras corresponds to the metalogical notion of interpolation in the corresponding logic. Answers to open question in the recent paper [54] concerning both amalgamation and interpolation are summarized in tabular form at the end of this paper. This paper appears in two parts. The present first part contains results on neat reducts. The second part contains results relating the notion of neat embeddings to various amalgamation properties.1. (shrink)

para o LucaA striking sentence among so many in his work that strike. In the 1960 book Questions de meéthode, Sartre writes: "Today's Marxists care only about adults; when reading them, one would think that we are born at the age at which we earn our.first salary. Marxists have forgotten their own childhood. When reading them, it is as if human beings.first experienced their alienation and their rei.cation in their own work, whereas everyone experiences it.first, as a child, in their (...) parents' work."2 Questions de meéthode-Search for Method-included as a tentative introduction to the Critique de la raison dialectique, is in fact the real introduction to Sartre's three volume study of Flaubert-a study written through the spectrum of the author's childhood. Readers of Sartre already know his fascination with childhood and that was explicitly so in his autobiography, Les Mots, written in the early 1950s. This can only lead us to stop and question Stanley Cavell who, when regarding the initial stages of Wittgenstein's Philosophical Investigations, writes: "the.gure of the child is present in this portrait of civilization more prominently and decisively than in any other work of philosophy I can think of The child demands consent of its culture, attention from it; it may never forgive the cost of exacting it, or of failing to.". (shrink)

One of the constants in Noam Chomsky’s philosophical, linguistic and ethical positions is the existence of what he calls “human nature”. Following Marx, Darwin and last century’s revolutions in the social sciences, human nature has been one of the most contested conceptual holdovers from modern European philosophy. Chomsky’s discoveries and models on syntax and language make up one of the frameworks to most critically offset the traditional moral dimension of human nature. Contrary to most traditions prior to his work, language (...) can no longer be restricted to either mind, soul or spirit. Language, as Chomsky has continually upheld and sharply refined, is a physical and biological process. But how his notion of human nature derives from this process is complex, as he seems to disregard philosophy’s classic analytic delineation between the descriptive causal realm of human nature and the normative axiological extensions of the same concept. In this paper, we seek to examine the philosophical and ontological implications of Chomsky’s claim that human nature derives from the innate dimension of the language faculty. Not only does Chomsky maintain the category of human nature, he also indexes it to the question of freedom. We thereby argue for the coherence of his proposal and show how it operates to weld the perspective of a modal theory of biologically-rooted creativity to innate conditions specific to his theory of language generation. However, we question whether its restriction to humans alone is sustainable from a scientific perspective by putting forth the claim that Chomsky’s science is in fact a radical ontology of social subjectivation. (shrink)

Deleuze’ün Spinozacı yaşam tahayyülünde ‘ne yapmalıyız?’ sorusuna normatif, ahlaki ya da siyasi bir yanıt bulamıyoruz ama varoluşu düşünmenin içkin bir olanağını keşfediyoruz. Düşünmeye 'dışarıdan' yani dünyadan başlamak insani (kurgusal) bir dünyaya değil, içinde yaşadığımız gerçek dünyaya inanmak demektir. İçkinliğin politik anlamı düşünceyi dünyaya getirmektir.

Исследование посвящено философскому осознанию природы духовности человека. Автор рассматривает духовность внутреннего мира человека как единство высших чувств души и нравственного сознания. Для специалистов в области философии, методологии науки.

How do we refer to people in everyday conversation? No matter the language or culture, we must choose from a range of options: full name ('Robert Smith'), reduced name ('Bob'), description ('tall guy'), kin term ('my son') etc. Our choices reflect how we know that person in context, and allow us to take a particular perspective on them. This book brings together a team of leading linguists, sociologists and anthropologists to show that there is more to person reference than meets (...) the eye. Drawing on video-recorded, everyday interactions in nine languages, it examines the fascinating ways in which we exploit person reference for social and cultural purposes, and reveals the underlying principles of person reference across cultures from the Americas to Asia to the South Pacific. Combining rich ethnographic detail with cross-linguistic generalizations, it will be welcomed by researchers and graduate students interested in the relationship between language and culture. (shrink)