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 In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’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.

We study the decidability problem for metric and layered temporal logics. The logics we consider are suitable to model time granularity in various contexts, and they allow one to build granular temporal models by referring to the "natural scale" in any component of the model and by properly constraining the interactions between differently-grained components. A monadic second-order language combining operators such as temporal contextualization and projection, together with the usual displacement operator of metric temporal logics, is considered, and the theory (...) of finitely-layered metric temporal structures is shown to be decidable. (shrink)

The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed.

The still unsettled decision problem for the restricted purely universal formulae 0-formulae) of the first order set-theoretic language based over =, ∈ is discussed in relation with the adoption or rejection of the axiom of foundation. Assuming the axiom of foundation, the related finite set-satisfiability problem for the very significant subclass of the 0-formulae consisting of the formulae involving only nested variables of level 1 is proved to be semidecidable on the ground of a reflection property over the hereditarily finite (...) sets, and various extensions of this result are obtained. When variables are restricted to range only over sets, in universes with infinitely many urelements the set-satisfiability problem is shown to be solvable provided the axiom of foundation is assumed; if it is not, then the decidability of a related derivability problem still holds. That, in turn, suggests the alternative adoption of an antifoundation axiom under which the set-satisfiability problem is also solvable . Turning to set theory without urelements, assuming a form of Boffa's antifoundation axiom, the complement of the set-satisfiability problem for the full class of Δ0-formulae is shown to be semidecidable; a result that is known not to hold, for the set-satisfiability problem itself, even for a very restricted subclass of the Δ0-formulae. (shrink)

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)

In this paper, we generalize the set-theoretic translation method for polymodal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor (...) such a translation to work with specific cases of extended modal logics. (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)

In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor (...) such a translation to work with specific cases of extended modal logics. (shrink)

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.

Cultural evolution studies are characterized by the notion that culture evolves accordingly to broadly Darwinian principles. Yet how far the analogy between cultural and genetic evolution should be pushed is open to debate. Here, we examine a recent disagreement that concerns the extent to which cultural transmission should be considered a preservative mechanism allowing selection among different variants, or a transformative process in which individuals recreate variants each time they are transmitted. The latter is associated with the notion of “cultural (...) attraction”. This issue has generated much misunderstanding and confusion. We first clarify the respective positions, noting that there is in fact no substantive incompatibility between cultural attraction and standard cultural evolution approaches, beyond a difference in focus. Whether cultural transmission should be considered a preservative or reconstructive process is ultimately an empirical question, and we examine how both preservative and reconstructive cultural transmission has been studied in recent experimental research in cultural evolution. Finally, we discuss how the relative importance of preservative and reconstructive processes may depend on the granularity of analysis and the domain being studied. (shrink)

The first half of this article follows Mario Bunge’s early realist moves, his efforts to articulate the achievements of theoretical physics as gains in the quest for objective truth and understanding, particularly in the context of the fights against the idealist and subjectivist interpretations of quantum mechanics that, at least until the mid-1970s, prevailed in physics. Bunge’s answers to the problems of quantum mechanics provide a good angle for understanding how his realist positions grew on the “battlefield.” The second half (...) discusses Bunge’s general conception of the scientific realist stance and confronts it with some current approaches to realism in the mainstream literature. (shrink)

The aim of this chapter is to analyse the concept of love —understood in the broad and Christian-inspired sense of love as agape-charis love— in relation to the animes Dragon Ball and Dragon Ball Z. I first comment on the character of Piccolo —and how his friendship with Son Gohan— leads to him losing all his original villainous traits. I argue that the evolution of the character of Piccolo through his friendship with Son Gohan illustrates the philosophical claim that a (...) loving and giving of oneself to the other —far from being a sign of weakness— is a courageous and self-affirming exercise. The result may move the individual to an inner transformative experience that leads to the enjoyment of a renewed and authentic life that is worth living. I then argue that Son Goku’s respectful attitude towards his opponents is ultimately a loving attitude. Last, I argue that it is the inspiring and loving example of Son Goku that ultimately explains why characters such as Vegeta —who are at first presented as villains— end up losing their villainous traits after fighting against Son Goku. (shrink)

Introduction: Jai Mata Di (praise the mother goddess) -- Sutra 1: Samadhi, or yogic ecstasy -- Sutra 2: realization, or the practice of yoga -- Sutra 3: the Siddhis, or the magical powers -- Sutra 4: absolute freedom.

In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (3-modal) (...) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames. (shrink)

The aim of this chapter is to analyze the movie Fight Club, directed by David Fincher, written by Jim Uhls, and first released in the fall of 1999. The movie is based on the homonym novel by Chuck Palahniuk, published in 1996. I will argue that Fight Club is to be understood in primarily existentialist, nonethical, and nonevidential terms, showing the struggle felt by each and every one of us to find a convincing answer to the question of what (if (...) anything) counts as an authentic life that is worth living. Moreover, I will argue that the movie does not merely illustrate the struggle and the existential angst it engenders; it also advances, if not strictly speaking a theoretical answer grounded in an indisputable philosophical reasoning, then at least a practical way to face it. It is only after positively endorsing the claim that absolutely nothing (whatever it may be) externally imposed on a person can give their life ultimate meaning that a person is free to engage in a conscious, laborious, and exhausting attempt at self-affirmation, a full and positive endorsement of one’s own authenticity. (shrink)

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. (...) An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings. (shrink)

This major publication is a history of the semantic tradition in philosophy from the early nineteenth century through its incarnation in the work of the Vienna Circle, the group of logical positivists that emerged in the years 1925-1935 in Vienna who were characterised by a strong commitment to empiricism, a high regard for science, and a conviction that modern logic is the primary tool of analytic philosophy. In the first part of the book, Alberto Coffa traces the roots of (...) logical positivism in a semantic tradition that arose in opposition to Kant's theory that a priori knowledge is based on pure intuition and the constitutive powers of the mind. In Part II, Coffa chronicles the development of this tradition by members and associates of the Vienna Circle. Much of Coffa's analysis draws on the unpublished notes and correspondence of many philosophers. The book, however, is not merely a history of the semantic tradition from Kant 'to the Vienna Station'. Coffa also critically reassesses the role of semantic notions in understanding the ground of a priori knowledge and its relation to empirical knowledge and questions the turn the tradition has taken since Vienna. (shrink)

People’s awareness of tactile stimuli has been investigated in far less detail than their awareness of stimuli in other sensory modalities. In an attempt to fill this gap, we provide an overview of studies that are pertinent to the topic of tactile consciousness. We discuss the results of research that has investigated phenomena such as “change blindness”, phantom limb sensations, and numerosity judgments in tactile perception, together with the results obtained from the study of patients affected by deficits that can (...) adversely affect tactile perception such as neglect, extinction, and numbsense. The similarities as well as some of the important differences that have emerged when visual and tactile conscious information processing have been compared using similar experimental procedures are highlighted. We suggest that conscious information processing in the tactile modality cannot be separated completely from the more general processing of spatial information in the brain. Finally, the importance of considering tactile consciousness within the larger framework of multisensory information processing is also discussed. (shrink)

In just the last decade, many conference proceedings have been published on Plato’s Timaeus and its influence on the history of philosophy. The present vo­lume, which is the result of a symposium held at Seoul National University in September 2011, testifies to the enduring and widespread interest the Platonic dia­logue is able to elicit. The nine studies here collected by Euree Song center on the figure of the demiurge as maker of the world and they all deal with authors who, (...) while having di... (shrink)

Contenido: Iconoclasia: Teoría, práctica y desidia -- Censura -- El final de las academias, los estilos y las instituciones -- Abolición total del arte.

Obra estructurada en cinco ponencias: la primera acerca de aspectos básicos para el posterior desarrollo de las relaciones ciencia-trascendencia; la segunda sobre la difícil consideración acerca del tiempo; la tercera sobre el papel que desempeña la neurocienca; la cuarta sobre las relaciones de la trascendencia ética con lo científico, y la quinta sobre el sentido de la religión y del cristianismo desde el punto de vista de la ciencia.

This open access book discusses individual, collective, and institutional responsibilities with regard to vaccination from the perspective of philosophy and public health ethics. It addresses the issue of what it means for a collective to be morally responsible for the realisation of herd immunity and what the implications of collective responsibility are for individual and institutional responsibilities. The first chapter introduces some key concepts in the vaccination debate, such as ‘herd immunity’, ‘public goods’, and ‘vaccine refusal’; and explains why failure (...) to vaccinate raises certain ethical issues. The second chapter analyses, from a philosophical perspective, the relationship between individual, collective, and institutional responsibilities with regard to the realisation of herd immunity. The third chapter is about the principle of least restrictive alternative in public health ethics and its implications for vaccination policies. Finally, the fourth chapter presents an ethical argument for unqualified compulsory vaccination, i.e. for compulsory vaccination that does not allow for any conscientious objection. The book will appeal to philosophers interested in public health ethics and the general public interested in the philosophical underpinning of different arguments about our moral obligations with regard to vaccination. (shrink)

The branching-time logic called Peircean by Arthur Prior is considered and given an infinite axiomatization. The axiomatization uses only the standard deduction rules for tense logic.

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.

In the tree-like representation of Time, two histories are undivided at a moment t whenever they share a common moment in the future of t. In the present paper, it will first be proved that Ockhamist and Peircean branching-time logics are unable to express some important sentences in which the notion of undividedness is involved. Then, a new semantics for branching-time logic will be presented. The new semantics is based on trees endowed with an indistinguishability function, a generalization of the (...) notion of undividedness. It will be shown that Ockhamist and Peircean semantics can be viewed as limit cases of the semantics developed in this paper. (shrink)

Johannes Müller von Königsberg (1436-1476), better known as Regiomontanus, is widely considered as the most influential astronomer and mathematician of 15th-century Europe. He was active as an astrologer and deemed astrology to be the queen of mathematical sciences. Despite this, Regiomontanus's astrological activity has yet to be fully explored. A brief examination of Regiomontanus's manuscripts shows that his astrological interests were accompanied by interests in the arts and in methods of prognostication. This article studies an unconventional astrological-chiromantical text, whose relevance (...) is threefold: a) it sheds new light on Regiomontanus's astrological interests; b) it enriches our knowledge of Regiomontanus's efforts to learn and understand Greek-Regiomontanus transcribed it into his own manuscript during his sojourn in Italy from 1460-1467; and c) it is the sole extant text in the Greek tradition that provides a system for prognostication from the study of a person's hand, the parts of which are considered as being under the domain of planets. The article provides an English translation of Regiomontanus's transcription, alongside a brief commentary, and studies the intellectual and historical context of that production through manuscript analysis. (shrink)

A Political Life is the compelling autobiography of Norberto Bobbio, one of the foremost political thinkers in postwar Italy. In dramatic and lively prose, Bobbio guides us through some of the most significant events of the twentieth century, charting their influence on his life and work. Born in 1909, Norberto Bobbio's early life was marked by the experience of growing up in Mussolini's Italy - an experience that helped to shape his passionate commitment to the anti-fascist cause. As a result (...) of these early experiences, Bobbio has tirelessly emphasized the fundamental, unassailable importance of democratic rights in the modern state. He has been a voice of reason and moderation in a political context where democratic values have often been threatened by extremes. This masterly autobiography traces the development of Bobbio's political thought, providing a penetrating analysis of the changing political landscape of Italy. At the same time, it represents an intimate account of Bobbio's personal experiences, giving a rare insight into the life and work of this distinguished thinker.A Political Life will be of great interest to students and scholars of social and political theory and of Italian politics, as well as to a general readership interested in political biography and contemporary politics. (shrink)