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)

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.

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)

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.

Proprio perché fuori moda è bene occuparsi di Kelsen – è questa la convinzione sottesa ai contributi qui pubblicati di Bernardo Sordi, Sara Lagi e Carlos M. Herrera. E proprio per fare emergere l’eccentricità di Kelsen rispetto al mainstream giusfilosofico contemporaneo e, quindi, proprio per questo motivo, la sua perdurante attualità, gli autori hanno trattato del suo pensiero a partire da un’angolatura diversa da quella consueta – una prospettiva “al di là della purezza”.

In 1685, during the heyday of Scottish Cartesianism, regent Robert Lidderdale from Edinburgh University declared Cartesianism the best philosophy in support of the Reformed faith. It is commonplace that Descartes was ostracised by the Reformed, and his role in pre-Enlightenment Scottish philosophy is not yet fully acknowledged. This paper offers an introduction to Scottish Cartesianism, and argues that the philosophers of the Scottish universities warmed up to Cartesianism because they saw it as a newer, better version of their own traditional (...) Reformed scholasticism, chiefly in metaphysics and natural philosophy. (shrink)

Despite the radically different interests that motivate Emil Fackenheim’s and Henry Harris’s respective interpretations of Hegel, the two have significant points of commonality. They in fact come the closest precisely at points where they seem to differ most. The need and the possibility of ‘reconciliation’ is the theme that animates both interpretations, and both also agree in their assessment of Hegel’s treatment of ‘evil.’ There are nevertheless crucial differences separating the two, which the essay details. The essay concludes wondering, on (...) the one hand, how seriously Harris recognizes that, in a post-Holocaust world, ‘reconciliation’ calls for existential conditions such as Hegel could never have imagined; and on the other hand, how much Fackenheim would be willing to admit that his immersion into history will necessarily bring violent consequences in train for which there will have to be an accounting. (shrink)