We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of $B\Sigma_{1}$, that is, the theory of $\Sigma_{1}$ collection.

In June 2012, the conference Trends in Logic XI, whose main theme was Advances in Philosophical Logic, took place at the Ruhr University in Bochum. Eight of the invited papers were published in a special issue of the journal Studia Logica. The present volume contains fourteen papers, which the editors selected out of the contributed papers presented at the conference, in order to offer a panorama of the themes developed in philosophical logic in the last two decades or so, as (...) well as to indicate some promising directions for further research. In what follows, we give a brief description of each contribution, following the order in the list of contents.In the first paper, B. Armour-Garb and J.A. Woodbridge discuss a manner in which one can treat semantic pathologies, such as the Liar Paradox. According to their approach, semantically pathological sentences are s-defective, i.e. they can be understood in a sense, but they bear no content, which we can accept or reject. The a .. (shrink)

On the basis of recent work concerning the meaning of the term stoicheion in Aristotle’s Analytics, we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements.

The volume under review contains work dedicated to the memory of Leo Esakia, who died in 2010, after having worked for over 40 years towards developing duality theory for modal and intuitionistic logics. The collection comprises ten technical contributions that follow the first chapter, in which the reader can find information on Esakia’s studies and career, as well as a complete list of his research publications. In the sequel, we will refer briefly to each of these ten chapters, following the (...) order in the list of contents.B. Jónsson and A. Tarski, in two papers they published in the early 1950s in the American Journal of Mathematics, initiated the study of duality for Boolean algebras with additional operations, via the theory of canonical extensions. Esakia was among the first researchers who studied duality for lattices with additional operations [Topological Kripke models. Soviet Math.Dokl. 15 , 147–151], in particular for Heyting algebras and S4 modal algebras. M. Gehrke, a .. (shrink)

Erudite and timely, this book is a key contribution to the renewal of radical theory and politics.

We present a comprehensive study of the axiom schemas IΣ - n , BΣ - n (induction and collection schemas for parameter free Σ n formulas) and some closely related schemas.

This chapter examines the normative question of whether the cultivation of patriotic and nationalist ideals and attachments should have a central place in programs of civic education. It argues that the most useful way to draw the distinction between patriotism and nationalism focuses on their respective objects of loyalty; patriotism is loyalty to a country while nationalism is loyalty to a people. This way of distinguishing between patriotism and nationalism forms the background for the discussion of a variety of instrumental (...) and non-instrumental arguments for cultivating patriotic and nationalist political attachments in schools. It also examines an assumption common to these programs of civic education: that a shared identity is crucial for citizens to have a sense of belonging that supports social stability and desirable forms of political change. The final part of the chapter introduces a number of alternative educational proposals that aim to avoid some of the difficulties faced by patriotic and nationalist strategies. These alternative proposals aim to encourage good citizenship while taking into account new challenges generated by the political, social, and economic conditions of an increasingly globalized world. (shrink)

The concept of fitness, central to population genetics and to the synthetic theory of evolution, is discussed. After a historical introduction on the origin of this concept, the current meaning of it in population genetics is examined: a cause of the selective process and its quantification. Several difficulties arise for its exact definition. Three adequacy criteria for such a definition are formulated. It is shown that it is impossible to formulate an adequate definition of fitness respecting these criteria. The propensity (...) definition of fitness is presented and rejected. Finally it is argued that fitness is a conceptual device, a useful tool, only for descriptive purposes of selective processes, changing from case to case, and thus devoid of any substantial physical counterpart. Any attempt to its reification is an apport to the metaphysical load evolutionary theory has inherited from Natural Theology. (shrink)

The current crisis is one outcome of the financialisation of contemporary capitalism. It arose in the USA because of the enormous expansion of mortgage-lending, including to the poorest layers of the working class. It became general because of the trading of debt by financial institutions. These phenomena are integral to financialisation. During the last three decades, large enterprises have turned to open markets to obtain finance, forcing banks to seek alternative sources of profit. One avenue has been provision of financial (...) services to individual workers. This trend has been facilitated by the retreat of public provision from housing, pensions, education, and so on. A further avenue has been to adopt investment-banking practices in open financial markets. The extraction of financial profits directly out of personal income constitutes financial expropriation. Combined with investment-banking, it has catalysed the current gigantic crisis. More broadly, financialisation has sustained the emergence of new layers of rentiers, defined primarily through their relation to the financial system rather than ownership of loanable capital. Finally, financialisation has posed important questions regarding finance-capital and imperialism. (shrink)

entry for the Entry for the Stanford Encyclopedia of Philosophy, 2007.

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Journal of Philosophical Logic 34, 97-119, 2005.

The 20th Century was a rich period for Thomism. Many commentaries to the First Way were written. One of the many points of disagreement between Thomists was the actual meaning of “motion.” In this paper, I try to argue that one should take for “motion” the broad meaning of “motus” (as equivalent to “mutatio”). I do so by reviewing the position of various prominent Thomists of the last century, many of which have disagreed with this position. I make the case (...) that Aristotle is not the best interpreter of the First Way, and similarly that other works by Aquinas should only be used when the Summa Theologiae itself is not clear enough—which is not the case. (shrink)

An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.

We investigate the higher-order modal logic , which is a variant of the system presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have (...) no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory. (shrink)

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like (...) FOL + K)in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics [40].We conclude by introducing general first order neighborhood frames with constant domains and we offer a general completeness result for the entire family of classical first order modal systems in terms of them, circumventing some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of either neighborhood or relational frames). We argue that the semantical program that thus arises offers the first complete semantic unification of the family of classical first order modal logics. (shrink)

Human rights have become an important ideal in current times, yet our age has witnessed more violations of human rights than any previous less enlightened one. This book explores the historical and theoretical dimensions of this paradox. Divided into two parts, the first section offers an alternative history of natural law, in which natural rights are represented as the eternal human struggle to resist opression and to fight for a society in which people are no longer degraded or despised. At (...) the time of their birth in the 18th Century and again in the popular uprisings of the last decade, human rights became the dominant critique of law and society. The radical rhetoric of rights and its apparently endless expansive potential has led to its adoption by governments and individuals alike seeking to justify their actions on moral grounds and has undermined its radical edge. Part Two examines the philosophical logic of rights. The classical critiques of Kant, Burke, Hegel and Marx illuminate traditional aproaches to the concept of human rights. The work of Heidegger, Sartre and psychoanalysis is used to deconstruct the metaphisical essentialism of bothe universalists and cultural relativists. Finally, through a consideration of the ethics of otherness, and with reference to recent human rights violations, it is argued that the end of human rights is to judge law and politics from a moral stand point which both transcends the present and is historically relevant. (shrink)

It is now well known that, on pain of triviality, the probability of a conditional cannot be identified with the corresponding conditional probability [25]. This surprising impossibility result has a qualitative counterpart. In fact, Peter Gärdenfors showed in [13] that believing ‘If A then B’ cannot be equated with the act of believing B on the supposition that A — as long as supposing obeys minimal Bayesian constraints. Recent work has shown that in spite of these negative results, the question (...) ‘how to accept a conditional?’ has a clear answer. Even if conditionals are not truth-carriers, they do have precise acceptability conditions. Nevertheless most epistemic models of conditionals do not provide acceptance conditions for iterated conditionals. One of the main goals of this essay is to provide a comprehensive account of the notion of epistemic conditionality covering all forms of iteration. First we propose an account of the basic idea of epistemic conditionality, by studying the conditionals validated by epistemic models where iteration is permitted but not constrained by special axioms. Our modeling does not presuppose that epistemic states should be represented by belief sets (we only assume that to each epistemic state corresponds an associated belief state). A full encoding of the basic epistemic conditionals (encompassing all forms of iteration) is presented and a representation result is proved. In the second part of the essay we argue that the notion of change involved in the evaluation of conditionals is suppositional, and that such notion should be distinguished from the notion of updating (modelled by AGM and other methods). We conclude by considering how some of the recent modellings of iterated change fare as methods for iterated supposing. (shrink)

The issue of what consequences to draw from the existence of non-classical logical systems has been the subject of an interesting debate across a diversity of fields. In this paper the matter of alternative logics is considered with reference to a specific belief system and its propositions :the Azande are said to maintain beliefs about witchcraft which, when expressed propositionally, appear to be inconsistent. When the Azande have been presented with such inconsistencies, they either fail to see them as such (...) or else accept them as non-problematical. Is our knowledge of logical truths a relative and culturally determined phenomenon, or is there some (transcendent) criterion that allows us to adjudicate between alternative logical systems? The authors propose an approach for resolving disputes about the status of Azande reasoning which assumes a paraconsistent framework, thus providing a new perspective on this debate. (shrink)

Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...) as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions. (shrink)

In this paper, we prove results concerning the existence of proper end extensions of arbitrary models of fragments of Peano arithmetic. In particular, we give alternative proofs that concern a result of Clote :163–170, 1986); :301–302, 1998), on the end extendability of arbitrary models of \-induction, for \, and the fact that every model of \-induction has a proper end extension satisfying \-induction; although this fact was not explicitly stated before, it follows by earlier results of Enayat and Wong and (...) Wong. (shrink)

We study the strength (over bounded induction) of axioms expressing particular cases of the Chinese Remainder Theorem with respect to the axiom ∀ x, y∃ z (z = xy).

O presente trabalho objetiva fazer uma análise sobre algumas das principais temáticas elaboradas pelo pensador argentino Luis Alberto Warat, quais sejam: o antropofagismo waratiano, o reencontro com a subjetividade perdida e a carnavalização. Para isso, analisou- se uma das obras mais caras do pensamento waratiano: A ciência jurídica e seus dois maridos. Buscou-se através da análise empreendida, elaborar uma crítica sobre paradigmas tradicionais de ciência, incluindo aqui, a própria Ciência do Direito. Sobreleva-se o caráter de indisciplina das atividades artístico-literárias para (...) insinuar as falhas históricas das disciplinas bem instituídas, do pensamento e da cultura dominantes. Visa-se, portanto, maior interação entre aquilo que se entende como ciência e a subjetividade humana como um todo. (shrink)

It is becoming clear that many of today’s management theories are inadequate theoretically and practically to move understanding, scholarship, and practice to where it needs to be for scholars, business leaders, and policy makers to cope with an increasing fraught world. This Special Issue’s focus is on sustainability. Sustainability challenges need to incorporate multidisciplinary interventions and the trans- and interdisciplinary nature of solutions. To actively seek transformation toward sustainability, fundamental and innovative short-term as well as long-term efforts are required in (...) society, economy, technology, and education, including our understanding of human behavior and attitudes toward the management of the environment. This introductory piece presents natural science theories as a promising approach for achieving progress toward transformation for sustainability. (shrink)

This paper is a critic analysis of a doctorate thesis and a master dissertation, which subjects are the samba and the afro religions in the city of São Paulo. Both consider the samba and the religion as manifestations and cultural expressions through which the black population in afro-diaspora rebuilded and reupdated memories via religiosity, rythm, dance and performan.