Edward Nieznanski developed in 2007 and 2008 two different systems in formal logic which deal with the problem of evil. Particularly, his aim is to refute a version of the logical problem of evil associated with a form of religious determinism. In this paper, we revisit his first system to give a more suitable form to it, reformulating it in first-order modal logic. The new resulting system, called N1, has much of the original basic structure, and many axioms, definitions, and (...) theorems still remain; however, some new results are obtained. If the conclusions attained are correct and true, then N1 solves the problem of evil through the refutation of a version of religious determinism, showing that the attributes of God in Classical Theism, namely, those of omniscience, omnipotence, infallibility, and omnibenevolence, when adequately formalized, are consistent with the existence of evil in the world. We consider that N1 is a good example of how formal systems can be applied in solving interesting philosophical issues, particularly in Philosophy of Religion and Analytic Theology, establishing bridges between such disciplines. (shrink)

In this paper, I present a proposal for a Formal Natural Theology. The approach employed for this task is through a first-order theory, in which fundamental concepts such as divine, necessary, and supreme beings, are formally introduced, which allow obtaining the theorems of existence and uniqueness of a divine being, according to the perspective of classical theism.

Edward Nieznański developed two logical systems to deal with the problem of evil and to refute religious determinism. However, when formalized in first-order modal logic, two axioms of each system contradict one another, revealing that there is an underlying minimal set of axioms enough to settle the questions. In this article, we develop this minimal system, called N3, which is based on Nieznański’s contribution. The purpose of N3 is to solve the logical problem of evil through the defeat of a (...) version of religious determinism. On the one hand, these questions are also addressed by Nieznański’s systems, but, on the other hand, they are obtained in N3 with fewer assumptions. Our approach can be considered a case of logic of religion, that is, of logic applied to religious discourse, as proposed by Józef Maria Bocheński; in this particular case, it is a discourse in theodicy, which is situated in the context of the philosophy of religion. (shrink)

Internal misconduct is a universal problem in prisons and affects the maintenance of social order. Consequently, correctional institutions often develop rehabilitation programs to reduce the likelihood of inmates committing internal offenses and criminal recidivism after release. Therefore, it is necessary to identify the profile of each offender, both for the appropriate indication of a rehabilitation program and the level of internal security to which he must be submitted. In this context, this work aims to discover the most significant characteristics in (...) predicting inmate misconduct from ML methods and the SHAP approach. A database produced in 2004 through the Survey of Inmates in State and Federal Correctional Facilities in the United States of America was used, which provides nationally representative data on prisoners from state and federal facilities. The predictive model based on Random Forest performed the best, thus, we applied the SHAP to it. Overall, the results showed that features related to victimization, type of crime committed, age and age at first arrest, history of association with criminal groups, education, and drug and alcohol use are most relevant in predicting internal misconduct. Thus, it is expected to contribute to the prior classification of an inmate on time, to use programs and practices that aim to improve the lives of offenders, their reintegration into society, and consequently, the reduction of criminal recidivism. (shrink)

In a recent paper, Pruss proves the validity of the rule beta-2 relative to Lewis’s semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counter-examples to beta-2 formulated with the actuality operator and rigidified descriptions. We offer a novel and two-dimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can (...) be formulated. This new transfer rule is immune to the counter-examples involving the actuality operator and rigidified descriptions. However, we show that counter-examples to this new rule can also be generated, demanding that the Lewisian semantics be generalized for higher dimensions where counter-examples can always be generated. (shrink)

Focused on city-scale automation, and using self-driving cars (SDCs) as a case study, this article reflects on the role of AI—and in particular, computer vision systems used for mapping and navigation—as a catalyst for urban transformation. Urban research commonly presents AI and cities as having a one-way cause-and-effect relationship, giving undue weight to AI’s impact on cities and overlooking the role of cities in shaping AI. Working at the intersection of data science and social research, this paper aims to counter (...) this trend by exploring the reverse perspective: how do cities affect the development, and expose the present limits, of SDCs? The contribution of this paper is threefold. First, by comparing urban and nonurban environments and thoroughly examining the relationship between computer vision and city-specific sociality and form, it defines machine autonomy/automation as a function of the sociotechnical milieu in which an AI system operates. Second, and related, the paper problematizes the notion of SDCs as autonomous technologies and the role it plays in envisioning contending policy arrangements and technical solutions for achieving full driving automation. Finally, the article offers insight into a materialist and spatialized understanding of AI—namely, not as an abstract quality susceptible to replication within discrete machines, but rather as a distributed property emerging through embodied interactions among a multiplicity of agents (human, non-human, and technological) within/with their environments. (shrink)

In a recent article, P. Roger Turner and Justin Capes argue that no one is, or ever was, even partly morally responsible for certain world-indexed truths. Here we present our reasons for thinking that their argument is unsound: It depends on the premise that possible worlds are maximally consistent states of affairs, which is, under plausible assumptions concerning states of affairs, demonstrably false. Our argument to show this is based on Bertrand Russell’s original ‘paradox of propositions’. We should then opt (...) for a different approach to explain world-indexed truths whose upshot is that we may be morally responsible for some of them. The result to the effect that there are no maximally consistent states of affairs is independently interesting though, since this notion motivates an account of the nature of possible worlds in the metaphysics of modality. We also register in this article, independently of our response to Turner and Capes, and in the spirit of Russell’s aforementioned paradox and many other versions thereof, a proof of the claim that there is no set of all true propositions one can render false. (shrink)

Populism is widely thought to be in tension with liberal democracy. This article clarifies what exactly is problematic about populism from a liberal–democratic point of view and goes on to develop normative standards that allow us to distinguish between more and less legitimate forms of populism. The point of this exercise is not to dismiss populism in toto; the article strives for a more subtle result, namely, to show that liberal democracy can accommodate populism provided that the latter conforms to (...) particular discursive norms. What the article calls a ‘liberal ethics of populism’ turns out to be closely bound up with a broader ethics of peoplehood, understood as a way of articulating who ‘the people’ are in a way that is compatible with liberal–democratic principles of political justification. Such an ethics, concludes the article, inevitably has a much wider audience than populist political actors: its addressees are all those who seek legitimately to exercise power in the name of the people. (shrink)

It is a widely held principle that no one is able to do something that would require the past to have been different from how it actually is. This principle of the fixity of the past has been presented in numerous ways, playing a crucial role in arguments for logical and theological fatalism, and for the incompatibility of causal determinism and the ability to do otherwise. I will argue that, assuming bivalence, this principle is in conflict with standard views about (...) knowledge and the semantics for ‘actually’. I also consider many possible responses to the argument. (shrink)

Populist movements have become key players in European politics. These movements are readily criticized by journalists or political rivals, yet none of the common objections to populism seems to arrest their success. This article turns to normative political theory to cultivate sensitivity to problems arising from some existing arguments against populism, and to explore possible alternatives. It offers a critical reading of prototypical liberal and conservative arguments against populism, and proposes that the principles of solidarity and procedure provide good grounds (...) for a sustainable critique of populism. (shrink)

Popular sovereignty requires that citizens perceive themselves as being able to act and implement decisions, and that they are de facto causally connected to mechanisms of decision making. I argue that the two most common understandings of the exercise of popular sovereignty—which center on direct decision making by the people as a whole and the indirect exercise of democratic agency by elected representatives, respectively—are inadequate in this respect, and go on to suggest a complementary account that stresses the central role (...) of internally democratic and participatory political parties in actualising popular sovereignty, drawing on the democratic theory of Hans Kelsen. (shrink)

Populism is widely thought to be in tension with liberal democracy. This article clarifies what exactly is problematic about populism from a liberal–democratic point of view and goes on to develop...

In recent times, representation theory has become one of the most productive and interesting sub-fields in democratic theory. Arguably, the most important theoretical innovation are the so-called ‘constructivist’ approaches to political representation. These approaches play a central role in Creating Political Presence: The New Politics of Democratic Representation and The Constructivist Turn in Political Representation, two impressive volumes that take stock of the state of the art in representation theory. I discuss the two volumes by focusing on three broader and (...) interconnected themes: the problem that constructivism is meant to respond to, the tendency of representation theorists to expand the possibilities of representation as broadly as possible, and the normative aspects of political representation and how constructivists deal with them. (shrink)

Evolutionary Debunking Arguments are defined as arguments that appeal to the evolutionary genealogy of our beliefs to undermine their justification. Recently, Helen De Cruz and her co-authors supported the view that EDAs are self-defeating: if EDAs claim that human arguments are not justified, because the evolutionary origin of the beliefs which figure in such arguments undermines those beliefs, and EDAs themselves are human arguments, then EDAs are not justified, and we should not accept their conclusions about the fact that human (...) arguments are unjustified. De Cruz's objection to EDAs is similar to the objection raised by Reuben Hersh against the claim that, since by Gödel's second incompleteness theorem the purpose of mathematical logic to give a secure foundation for mathematics cannot be achieved, mathematics cannot be said to be absolutely certain. The response given by Carlo Cellucci to Hersh's objection shows that the claim that by Gödel's results mathematics cannot be said to be absolutely certain is not self-defeating, and can be adopted to show that EDAs are not self-defeating as well in a twofold sense: an argument analogous to Cellucci's one may be developed to face De Cruz's objection, and such argument may be further refined incorporating Cellucci's response itself in it, to make it stronger. This paper aims at showing that the accusation of being self-defeating moved against EDAs is inadequate by elaborating an argument which can be considered an EDA and which can also be shown not to be self-defeating. (shrink)

In recent times, representation theory has become one of the most productive and interesting sub-fields in democratic theory. Arguably, the most important theoretical innovation are the so-called ‘constructivist’ approaches to political representation. These approaches play a central role in Creating Political Presence: The New Politics of Democratic Representation and The Constructivist Turn in Political Representation, two impressive volumes that take stock of the state of the art in representation theory. I discuss the two volumes by focusing on three broader and (...) interconnected themes: the problem that constructivism is meant to respond to, the tendency of representation theorists to expand the possibilities of representation as broadly as possible, and the normative aspects of political representation and how constructivists deal with them. (shrink)

Several theists, including Linda Zagzebski, have claimed that theism is somehow committed to nonvacuism about counterpossibles. Even though Zagzebski herself has rejected vacuism, she has offered an argument in favour of it, which Edward Wierenga has defended as providing strong support for vacuism that is independent of the orthodox semantics for counterfactuals, mainly developed by David Lewis and Robert Stalnaker. In this paper I show that argument to be sound only relative to the orthodox semantics, which entails vacuism, and give (...) an example of a semantics for counterfactuals countenancing impossible worlds for which it fails. (shrink)

In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate (...) over different notions of validity such as local, general, and diagonal, besides being general enough for several two-dimensional logics proposed in the literature. We also motivate the introduction of a new operator into two-dimensional languages and explore some of the philosophical questions raised by it concerning the relations there are between actuality, necessity, and the a priori, that seem to undermine traditional intuitive interpretations of two-dimensional operators. (shrink)

Solidarity can be conceived in multiple ways. This article probes possible underlying ontological and normative assumptions of solidarity. In order to conceptually clarify the notion of solidarity, we distinguish between five types of solidarity. We suggest that solidarity is either grounded in the Enlightenment ideas of liberty, or a category of loyalty and allegiance. If the former is the case, solidarity can be justified on rational grounds. If the latter is the case, it is contingent on narratives of historical continuity (...) and a non-rational sense of belonging. Moreover, we show that different types of solidarity can be derived from Anglo-Saxon and continental thought, which hints at different conceptions of community. (shrink)

Implicações da noção de consciência histórica nas ciências humanas e sociais: um modo de projeção para o futuro e de posição em relação ao passado Resumo: O presente texto, de caráter bibliográfico, discute o problema da consciência histórica com o objetivo de pensar o sentido dessa expressão na atualidade e as variações que esse conceito adquiriu ao longo da história das Ciências Humanas e Sociais, com ênfase no século XX. A hipótese é que a discussão a respeito da consciência histórica (...) passou a se ocupar, na modernidade, com uma múltipla relatividade de pontos de vista, o que é destacado por Gadamer em sua análise sobre os preceitos implicados na definição do que significa “ter senso histórico”. É defendida a tese, portanto, de que a noção de consciência histórica não se limita ao conhecimento das experiências vivenciadas no passado, mas se apresenta como condição de possibilidade de projetar o futuro e se posicionar em relação ao passado, especialmente no que diz respeito às ciências humanas e sociais. A defesa desta ideia central é realizada por meio de dois gestos reflexivos, com apresentação, primeiramente, do marco teórico da consciência histórica e, posteriormente, de suas implicações na constituição das Ciências Humanas e Sociais. Palavras-chave: Ciências humanas e sociais. Senso histórico. Passado. Futuro. Implications of the notion of historical consciousness in human and social sciences: a mode of projection for the future and position in relation to the past: This bibliographic text discusses the problem of historical consciousness with the purpose of thinking about the meaning of this expression in the present time and the variations that this concept has acquired throughout the history of the Humanities and Social Sciences, with emphasis on the twentieth century. The hypothesis is that the discussion about historical consciousness has come to concern itself, in modernity, with a multiple relativity of points of view, which is highlighted by Gadamer in his analysis of the precepts involved in defining what “having a historical sense” means. Therefore, the thesis that the notion of historical consciousness is not limited to the knowledge of past experiences is defended, but is presented as a condition of possibility of projecting the future and positioning itself in relation to the past, especially with regard to humanities and social sciences. The defense of this central idea is made through two reflexive gestures, presenting, first, the theoretical framework of historical consciousness and, later, its implications in the constitution of the Human and Social Sciences. Keywords: Human and social sciences. Historical sense. Past. Future. Implicaciones de la noticia de conciencia histórica en las ciencias humanas y sociales: un modo de proyección para el futuro y de posición en relación al pasado Resumen: El presente texto, de carácter bibliográfico, discute el problema de la conciencia histórica con el propósito de pensar sobre el significado de esta expresión en la actualidad y las variaciones que este concepto ha adquirido a lo largo de la historia de las Humanidades y las Ciencias Sociales, con énfasis en el siglo XX. La hipótesis es que la discusión sobre la conciencia histórica ha llegado a ocuparse, en la modernidad, de una relatividad múltiple de puntos de vista, que Gadamer destaca en su análisis de los preceptos involucrados en la definición de lo que significa “tener un sentido histórico”. " Por lo tanto, se defiende la tesis de que la noción de conciencia histórica no se limita al conocimiento de experiencias pasadas, sino que se presenta como una condición de posibilidad de proyectar el futuro y posicionarse en relación con el pasado, especialmente con respecto a humanidades y ciencias sociales. La defensa de esta idea central se realiza a través de dos gestos reflexivos, presentando, primero, el marco teórico de la conciencia histórica y, luego, sus implicaciones en la constitución de las Ciencias Humanas y Sociales. Palabras clave: Ciencias Humanas y Sociales. Sentido histórico. Pasado. Futuro. Data de registro: 28/05/2019 Data de aceite: 24/10/2019. (shrink)

We present a new puzzle about logical truth, necessity, and moral responsibility. We defend one solution to the puzzle. A corollary of our preferred solution is that prominent arguments for the incompatibility of determinism and moral responsibility are invalid.

RESUMO: O objetivo deste artigo é examinar o que entendemos ser uma prova original da existência de Deus na obra de Pierre Duhem. Cremos que a originalidade dessa prova consiste especialmente nas premissas usadas pelo filósofo. Quanto à forma, a mesma assemelha-se ao conhecido argumento do desígnio, mas a sua versão se caracteriza por buscar na história das teorias físicas a matéria da qual a existência de uma Providência é derivada. É a complexa evolução das teorias e, a despeito dela, (...) a sua espantosa progressividade em direção a estágios sempre mais perfeitos que servem de premissa para a via duhemiana de acesso a Deus. Tudo se passa como se houvesse uma suposta pré-ordenação divina do curso das teorias, uma finalidade intrínseca a ele. ABSTRACT: The aim of this paper is to examine what we believe to be an original proof of the existence of God in the work of Pierre Duhem. We think that the originality of this proof consists especially in the assumptions used by the French philosopher in his argumentation. Regarding the form, it resembles the well-known design argument, but his version is characterized by seeking in the history of physical theories the matter from which the existence of a Providence is derived. It is the complex evolution of theories and, despite it, its amazing progress towards ever more perfect theories that serves as the premise for Duhem's way of access to God. Everything goes as if it had been a divine preordainment and an intrinsic goal ruling the evolution of theories. (shrink)

RESUMO: O objetivo deste artigo é examinar o que entendemos ser uma prova original da existência de Deus na obra de Pierre Duhem. Cremos que a originalidade dessa prova consiste especialmente nas premissas usadas pelo filósofo. Quanto à forma, a mesma assemelha-se ao conhecido argumento do desígnio, mas a sua versão se caracteriza por buscar na história das teorias físicas a matéria da qual a existência de uma Providência é derivada. É a complexa evolução das teorias e, a despeito dela, (...) a sua espantosa progressividade em direção a estágios sempre mais perfeitos que servem de premissa para a via duhemiana de acesso a Deus. Tudo se passa como se houvesse uma suposta pré-ordenação divina do curso das teorias, uma finalidade intrínseca a ele.ABSTRACT: The aim of this paper is to examine what we believe to be an original proof of the existence of God in the work of Pierre Duhem. We think that the originality of this proof consists especially in the assumptions used by the French philosopher in his argumentation. Regarding the form, it resembles the well-known design argument, but his version is characterized by seeking in the history of physical theories the matter from which the existence of a Providence is derived. It is the complex evolution of theories and, despite it, its amazing progress towards ever more perfect theories that serves as the premise for Duhem's way of access to God. Everything goes as if it had been a divine preordainment and an intrinsic goal ruling the evolution of theories. (shrink)

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some point (...) on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

The idea that an adequate semantics of ordinary language calls for some theory of events has sparked considerable debate among linguists and philosophers. On the one hand, so many linguistic phenomena appear to be explained if (and, according to some authors, only if) we make room for logical forms in which reference to or quantification over events is explicitly featured. Examples include nominalization, adverbial modification, tense and aspect, plurals, and singular causal statements. On the other hand, a number of deep (...) philosophical questions arise as soon as we take events into consideration. Are events entities of a kind? What are their identity and individuation criteria? How does semantic theorizing depend on such metaphysical issues? The aim of this book is to address such issues in some depth, with emphasis precisely on the interplay between linguistic applications and philosophical implications. Contributors: N. Asher, P. M. Bertinetto, J. Brandl, D. Delfitto, R. Eckardt, J. Higginbotham, A. Lenci, T. Parsons, A. ter Meulen, H. Verkuyl. A comprehensive introductory essay (pp. 3-47) is included. (shrink)

Recent developments in Hungary and Poland have made democratic backsliding a major issue of concern within the European Union. This article focuses on the secondary agents that facilitate democratic backsliding in Hungary and Poland: the European People’s Party, which has continually protected the Hungarian Fidesz government from EU sanctions, and the Hungarian ruling party Fidesz, which repeatedly promised to block any EU-level sanctions against Poland in the Council. The article analyses these agents’ behaviour as an instance of transnational complicity and (...) passes a tentative judgment as to which of the two cases is normatively more problematic. The analysis has implications for possible countervailing responses to democratic backsliding within EU member states. (shrink)

Richard Feldman’s well-known principle about disagreement and evidence – usually encapsulated in the slogan, ‘evidence of evidence is evidence’, (EEE) – invites the question, what should a rational believer do when faced by such evidence, especially when the disagreement is with an epistemic peer? The question has been the subject of much controversy. However, it has been recently suggested both that the principle is subject to counterexamples and that it is trivial. If either is the case, the question of what (...) to do in the face of evidence of evi- dence becomes less pressing. We contend that even if one or the other of these suggestions is right about (EEE) as a general principle about evidence, they leave it untouched insofar as it plays a role in the debates about the rational way to respond to disagreement and, in particular, to disagreement by an epistemic peer. This is because in such cases the evidence about which one has evidence and which is supposed to provide evidence against one's belief is the mere fact of someone’s disagreeing, rather than something that is related to the content of the proposition about which the parties disagree. We go on to argue that, so understood, the principle is false. (shrink)

Book 1 of Euclid's Elements opens with a set of unproved assumptions: definitions, postulates, and ‘common notions’. The common notions are general rules validating deductions that involve the relations of equality and congruence. The attested postulates are five in number, even if a part of the manuscript tradition adds a sixth, almost surely spurious, that in some manuscripts features as the ninth, and last, common notion. The postulates are called αἰτήματα both in the manuscripts of the Elements and in the (...) ancient exegetic tradition. It is not said, however, that this denomination is original, as it coincides with the nomen rei actae associated with the verbal form introducing the postulates themselves. Since antiquity it has been recognized that the postulates naturally split into two groups of quite different character: the first three are rules licensing basic constructions, the fourth and the fifth are assertions stating properties of particular geometric objects. I transcribe postulates 1–3 in the text established by Heiberg : ᾐτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖνκαὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖνκαὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράϕεσθαι. (shrink)

Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces 'spooky' hidden mechanisms. Whether one can produce a genuinely quantum framework in order to discover causal structure remains an open question. Here we introduce a new framework for quantum causal modelling that allows for the discovery of causal structure. We define quantum analogues for core features of classical causal modelling techniques, including (...) the causal Markov condition and faithfulness. Based on the process matrix formalism, this framework naturally extends to generalised structures with indefinite causal order. (shrink)

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli’s results and recent developments (...) on the axiomatization of non-binary preferences, and its impact on “complete” independence, are described. (shrink)

Fábio Alves dos Santos (1954-2013) cursou Pedagogia, Ciências Sociais e Teologia, era Especialista em Filosofia da Religião (PUC Minas), Advogado (PUC Minas) e Mestre em Direito Constitucional (UFMG). Lecionou na PUC Minas como professor de Cultura Religiosa e depois como professor no Curso de Direito, atuando principalmente no Serviço de Assistência Judiciária – SAJ, especialmente cuidado de causas populares como as da ASMARE (Associação dos Catadores de Papel, Papelão e Material Reaproveitável de Belo Horizonte), da Pastoral de Rua, da (...) Pastoral Carcerária, de movimentos de “Sem Casa”, de ocupações e tantos outros grupos. Fábio sofria de grave problema de visão há mais de 15 anos. Quase ficou cego depois de diversas cirurgias de miopia. Isso, porém, não o impedia de seguir seu constante compromisso com as lutas populares. Na última entrevista que concedeu, menos de um mês antes de sua morte (19 de outubro de 2013), depois de duro sofrimento de quase dois anos, no tratamento de um câncer no pâncreas, conta um pouco de sua vida, sua luta e sua percepção de várias realidades, especialmente da Igreja e da pastoral. Militante formado na Teologia da Libertação, de profunda espiritualidade, marcada por traços da religiosidade popular nordestina e comprometida com a libertação, Fábio Alves também buscou em sua vida abrir-se à teologia do pluralismo religioso, especialmente com o Santo Daime, em cuja tradição religiosa chegou a ser “fardado”, mantendo uma profunda atitude espiritual aberta ao diálogo inter-religioso. Sua primeira publicação foi “Começo de mundo novo: sofrimento, luta e vitória dos posseiros de Santana dos Frades”, Sergipe, numa versão popular em 1981 e outra pela Editora Vozes (1990). Fruto de sua dissertação de mestrado, publicou o livro “Direito Agrário: política fundiária no Brasil (1995). Em 2001 saiu seu último livro, uma coletânea de artigos publicados em diversos jornais: “Em defesa da vida”. Num artigo em Horizonte (2004), juntamente com o advogado, amigo e colega Prof. Cristiano de Melo Bastos, discutiu “A prática jurídica na missão da PUC Minas”. Palavras-chave : Teologia da Libertação. Militância. Igreja Católica. Pastoral. Lutas populares. (shrink)

ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, (...) a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context. (shrink)