The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.

As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for (...) the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper. (shrink)

Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987. The main achievement of this paper is the proof that the 'kernel' set theory whose postulates are extensionality. (E), and single-element adjunction and removal. (W) and (L), cannot be axiomatized by means of three-variable sentences. This (...) highlights a sharp edge to be crossed in order to attain an 'algebraization' of Set Theory. Indeed, one easily shows that the theory which results from the said kernel by addition of the null set axiom, (N), is in its entirety expressible in three variables. (shrink)

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. (...) The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic. (shrink)

As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.

One 1120 pages volume, with 4000 entries covering - Western philosophy: authors, schools, concepts and terminology; - religions, cultural anthropology, eastern philosophies; - Psychology and psychoanalysis; - linguistics and semiotics; - sociology and political theory.

L'A. analizza un tema fondamentale nella «querelle» sui futuri contingenti del sec. XIV, cioè il concetto di potentia absoluta di Dio. Il tema fu interpretato secondo due opposte visioni: l'interpetazione «operativa» intendeva la potentia absoluta come un potere straordinario ed «eccezionale», mentre l'interpretazione «logica», sostenuta ad esempio da Bradwardine, riteneva la potentia absoluta una mera descrizione di possibilità teoriche. L'analisi di questo problema è condotta in base alle teorie di Giovanni Buckingham e di Giovanni di Mirecourt, con riferimenti (...) alla posizione di Bradwardine, Duns Scoto, Guglielmo di Ockham e Adam Wodeham. (shrink)

1-2. Carteggio Gentile-Jaja -- 3-7. Lettere a Benedetto Croce -- 8. Carteggio Gentile-D'Ancona -- 9. Carteggio Gentile-Omodeo -- 11. Carteggio Gentile-Chiavacci -- 12. Carteggio Gentile-Pintor -- 13. Carteggio Gentile-Calogero (1926-1942) -- 14. Carteggio Gentile-Donati.

1. Le fe por la palabra -- 2. Topía y Utopía -- 3. Luz en la caverna.

Publicado por primera vez en 1982 y merecedor del Premio Nacional de Ensayo en 1983, Lo bello y lo siniestro es un texto imprescindible para comprender la historia de las ideas estéticas y de la teoría del arte. Mediante el análisis de obras diversas -desde las pinturas renacentistas de Sandro Botticelli hasta la célebre película Vertigo de Alfred Hitchcock- el genial filósofo valora la evolución histórica de dos categorías estéticas opuestas, lo bello y lo siniestro, para descubrir lo que ambas (...) tienen de sublime. Eugenio Trías persigue y consigue incansablemente para ofrecer al lector uno de los ensayos más descollantes de nuestro tiempo. (shrink)

Definition of the problem Medical ethics is increasingly faced with issues that result from power asymmetries and epistemic injustice. However, medical ethics lacks the epistemic lenses for analyzing these social context factors of clinical practice. A theoretical and conceptual reconfiguration is necessary in order to be able to address these issues. Arguments This paper discusses the foundations of critical medical ethics, which takes perspectives and epistemic categories from critical theories. This includes the Critical Theory of the Frankfurt School as well (...) as those approaches from social sciences and cultural studies that reflect on power asymmetries. By drawing on these theories, the epistemic spectrum of medical ethics could be broadened in order to better include real power relations into normative analyses. The paper starts by outlining the contribution of social sciences to empirical medical ethics. This shows that an empirical approach as such cannot bridge the epistemic gap. In a further step, epistemic lenses and concepts from critical theories are discussed, such as Critical Theory of the Frankfurt School, feminist approaches, postcolonial approaches, queer theory, gender studies, and science and technology studies (STS). The conclusion sums up the foundations of critical medical ethics and discusses its limitations. Conclusion Critical medical ethics possesses the epistemic categories and broader social perspective needed to address issues in medicine that result from power asymmetries and epistemic injustice in society. (shrink)

Conventional quantitative methods for the measurement of organizational legitimacy consider mainly three sources that make judgments about organizations visible: news media, accreditation bodies, and surveys. Over the last decade, however, social media have enabled ordinary citizens to bypass the gatekeeping function of these institutional evaluators and autonomously make individual judgments public. This inclusion of voices beyond functional and formally organized stakeholder groups potentially pluralizes the ongoing discussions about organizations. The individual judgments in blogs, tweets, and Facebook posts give indication about (...) the broader fit between an organization’s perceived behavior and heterogeneous social norms and therefore constitute an indicator of organizational legitimacy that can be accessed and measured. We propose the use of social media data and sentiment analysis to study the affect-based responses to organizational actions by citizens. We critically discuss and compare the method with existing quantitative methods for legitimacy measurement and apply them to a recent case in the banking industry. We discuss the value of the method for studying the process of legitimacy construction as the expression and negotiation of normative judgments about organizations by various evaluators. (shrink)

In this work I argue that Descartes was not a trialist by showing that the main tenets of trialist interpretations of Descartes's theory of substance are either not supported by the text or are not sufficient for establishing the trialist interpretation.

Some important ideas in Kelsen's Pure Theory of Law can be traced back to Kantian tradition, which has been very influential in Kelsen's thought, particularly in his early period. Among them we find the distinction between two radically different worlds (the world of facts and the world of norms), the normativity of legal science and the idea of validity as a binding force, based on the famous doctrine of the basic norm. These tenets and, especially, the use of a normative (...) concept of validity prove to be incompatible with Kelsen's positivistic programme of a value‐free legal science. The science of law cannot state that legal norms are obligatory or binding without trespassing the limits of Kelsen's ideal of a legal science; on the other hand, it is possible to define the concept of a legal system without resorting to the basic norm. So, if Kelsen is to be regarded as a consequent positivist, the Kantian ingredients of his theory must be rejected and the descriptive concept of validity as membership must be substituted for the normative notion of validity as a binding force. (shrink)

This paper criticizes Alexy's argument on the necessary connection between law and morality. First of all, the author discusses some aspects of the notion of the claim to correctness. Basically, it is highly doubtful that all legal authorities share the same idea of moral correctness. Secondly, the author argues that the claim to correctness is not a defining characteristic of the concepts of “legal norm” and “legal system”. Hence, the thesis of a necessary connection between law and morality based on (...) such claim cannot be accepted. (shrink)

In 1911 the Wilson cloud chamber opened new possibilities for physics pedagogy. The instrument, which visualized particles’ tracks as trails of condensed vapour, was adopted by physicists to pursue frontier research on the Compton effect, the positron and the transmutation of atomic nuclei. But as the present paper will show, Wilson's instrument did not just open up new research opportunities, but the possibility of developing a different kind of teaching. Equipped with a powerful visualization tool, some physicists–teachers employed Wilson's instrument (...) to introduce their students to a wide range of phenomena and concepts, ranging from the behaviour of clouds to Einstein's photon, the wave–particle duality and the understanding of the nucleus. This paper uses the notes, books and prototypes of these pioneering physicists–teachers to compose a pedagogical history of the Wilson cloud chamber, documenting an episode of immense ingenuity, creativity and scientific imagination. (shrink)

This volume considers contingency as a historical category resulting from the combination of various intellectual elements – epistemological, philosophical, material, as well as theological and, broadly speaking, intellectual. With contributions ranging from fields as diverse as the histories of physics, astronomy, astrology, medicine, mechanics, physiology, and natural philosophy, it explores the transformation of the notion of contingency across the late-medieval, Renaissance, and the early modern period. Underpinned by a necessitated vision of nature, seventeenth century mechanism widely identified apparent natural irregularities (...) with the epistemological limits of a certain explanatory framework. However, this picture was preceded by, and in fact emerged from, a widespread characterization of contingency as an ontological trait of nature, typical of late-Scholastic and Renaissance science. On these bases, this volume shows how epistemological categories, which are preconditions of knowledge as “historically-situated a priori” and, seemingly, self-evident, are ultimately rooted in time. Contingency is intrinsic to scientific practice. Whether observing the behaviour of a photon, diagnosing a patient, or calculating the orbit of a distant planet, scientists face the unavoidable challenge of dealing with data that differ from their models and expectations. However, epistemological categories are not fixed in time. Indeed, there is something fundamentally different in the way an Aristotelian natural philosopher defined a wonder or a “monstrous” birth as “contingent”, a modern scientist defines the unexpected result of an experiment, and a quantum physicist the behavior of a photon. Although to each inquirer these instances appeared self-evidently contingent, each also employs the concept differently. (shrink)