Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic ...

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

It is widely asserted that we are now living in a post-truth society. What that means, this book argues, is that the contemporary global world is thoroughly infested not only with trickster figures but an entire and operational trickster logic; or, that we now live in a Trickster Land - an argument advanced by the claim that in modernity liminality has become permanent; or that modern life is patently absurd. The first part of the book presents a series of 'guides' (...) to this condition, in the form of key thinkers and writers who can help us understand and navigate our Trickster Land. Such guides include Hermann Broch, Lewis Hyde, Roberto Calasso, Michel Serres, Sándor Márai, Colin Thubron, and Albert Camus. The second part goes on to discuss five main regions of Trickster Land: art, thought, the economy, politics, and society. This last, central chapter of the book contrasts trickster logic with the basic, foundational logic of social life, presented as gift-giving by Marcel Mauss and as sociability by Georg Simmel, and which is expressed here, combining Heraclitus and Plato with the Gospel of John, by three basic terms of ancient Greek culture, as arkhé charis logos: meaningful social life originally and in its essence is animated by the power of kind benevolence. This volume will appeal to scholars of social theory, anthropology and sociology with interests in political thought and contemporary culture. (shrink)

Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that (...) co-granular or point-wise approximations defined by σ-ideals/filters (for an arbitrary relation σ) fit easily into the entire scheme. Concepts of the rationality of objects (vague or crisp) and their types are introduced and are shown to be applicable to most general rough sets by the present author. Surprising results on these are proved on these by her in this part of the research paper. The present paper is the first of a three part study on the topic. (shrink)

This paper is dedicated to the memory of Mike Dunn. His untimely death is a loss not only to logic, computer science, and philosophy, but to all of us who knew and loved him. The paper gives an argument for closure under γ in standard systems of relevance logic (first proved by Meyer and Dunn 1969). For definiteness, I chose the example of R. The proof also applies to E and to the quantified systems RQ and EQ. The argument uses (...) semantic tableaux (with one exceptional rule not satisfying the subformula property). It avoids the previous arguments’ use of cutting down inconsistent sets of formulas to consistent sets. Like all tableau arguments, it extends partial valuations to total valuations. (shrink)

In this illuminating study of Kant's theory of imagination and its role in interpretation, Rudolf A. Makkreel argues against the commonly held notion that Kant's transcendental philosophy is incompatible with hermeneutics. The charge that Kant's foundational philosophy is inadequate to the task of interpretation can be rebutted, explains Makkreel, if we fully understand the role of imagination in his work. In identifying this role, Makkreel also reevaluates the relationship among Kant's discussions of the feeling of life, common sense, and the (...) purposiveness of history. (shrink)

Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing (...) before He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor. (shrink)

Verse and prose commentaries, with text, on Nyāyāvatārasūtra, verse treatise on Jain logic, by Siddhasena Divākara.

Different questions generate different forms of practical reasoning. A contextually unrestricted ‘What shall I do?’ is too open to focus reflection. More determinately, an agent may ask, ‘Shall I do X, or Y?’ To answer that, he may need to weigh things up—as fits the derivation of ‘deliberation’ fromlibra(Latin for ‘scales’). Ubiquitous and indispensable though this is, I mention it only to salute it in passing. Or he may ask how to achieve a proposed end: if his end is to (...) do X, he may ask ‘How shall I do X?’ Or he may ask how to apply a universal rule or particular maxim. Aristotle supplies examples inDe Motu Animalium(7.701a7 ff.), whose wording I freely adapt to my own purposes:A1 reasons to a necessary means to achieving an end:I will make a cloak.To make a cloak I must do A.So, I will do A. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as (...) Kant conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

Keine ausführliche Beschreibung für "Logik" verfügbar.

In the light of two unpublished letters from Carnap to Kuhn, this essay examines the relationship between Kuhn's The Structure of Scientific Revolutions and Carnap's philosophical views. Contrary to the common wisdom that Kuhn's book refuted logical empiricism, it argues that Carnap's views of revolutionary scientific change are rather similar to those detailed by Kuhn. This serves both to explain Carnap's appreciation of The Structure of Scientific Revolutions and to suggest that logical empiricism, insofar as that program rested (...) on Carnap's shoulders, was not substantially upstaged by Kuhn's book. (shrink)