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 In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’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

The aim of this paper is to argue against the received view among Unamuno scholars that Miguel de Unamuno was defending a sort of pragmatic argument for religious faith and that his notion of religious faith as “querer creer” (“wanting to believe”) is to be identified with William James’s “the will to believe”. As I will show in this paper, one of the aspects that makes Unamuno’s reasoning philosophically relevant is his ability to formulate a non-pragmatist defense of religious faith (...) without a prior commitment to the truth of any religious or theological statement and grounded in our longing for an endless existence through God’s Salvation. (shrink)

We argue that, in certain circumstances, doctors might beprofessionallyjustified to provide abortions even in those jurisdictions where abortion is illegal. That it is at least professionally permissible does not mean that they have an all-things-considered ethical justification or obligation to provide illegal abortions or that professional obligations or professional permissibility trump legal obligations. It rather means that professional organisations should respect and indeed protect doctors’ positive claims of conscience to provide abortions if they plausibly track what is in the best (...) medical interests of their patients. It is the responsibility of state authorities to enforce the law, but it is the responsibility of professional organisations to uphold the highest standards of medical ethics, even when they conflict with the law. Whatever the legal sanctions in place, healthcare professionals should not be sanctioned by the professional bodies for providing abortions according to professional standards, even if illegally. Indeed, professional organisation should lobby to offer protection to such professionals. Our arguments have practical implications for what healthcare professionals and healthcare professional organisations may or should do in those jurisdictions that legally prohibit abortion, such as some US States after the reversal ofRoe v Wade. (shrink)

This book develops a novel theory of intentionality. It argues that intentionality is an internal essential relation of constitution between an intentional state and an object or between such a state and a possible state of affairs as subsisting. The author's main claim is that intentionality is a fundamentally modal property, hence a non (scientifically) natural property in that it does not supervene, either locally or globally, on its nonmodal physical basis. This is the property, primarily for an intentional mental (...) state, to be constituted by the entities it is about. In the case of intentionality of reference, such constituents are objects, in the sense of individuals; in the case of intentionality of content, such constituents are possible states of affairs as subsisting. Constitution is meant in a mereologically literal sense: those constituents are essential parts of the relevant states. As a result, the theory claims not only that intentionality is relational, but also that is an internal, essential relation holding between an intentional state and its object or proposition-like content. Intentionality as Constitution will be of interest to scholars and advanced students working in philosophy of mind, philosophy of language, metaphysics, and cognitive science. (shrink)

Most of the existing studies on Bourdieu and the digital regards the social and class distinctions in the use of digital technologies, thus presupposing a certain transparency of technologies themselves. Our proposal is to refer to this attitude as “Bourdieu outside the digital.” Yet in this paper, another perspective called “Bourdieu inside the digital” is developed, which moves the focus on the effects of some emerging technologies on social distinctions and discrimination. The main hypothesis is that algorithms of machine learning (...) are producers and reproducers of habitus. Although their results present a greater granularity with respect to the standard techniques of the past, these algorithms still reduce individuals to categories, general trends, classes, and behaviors. Such a reduction has flattening effects on the individuals’ self-understanding, especially in terms of identity and interaction with the social world. This is the phenomenon described in the article as the “personalization without personality,” whose consequences are both existential and social-political. This idea will be illustrated through qualitative and comparative analysis between the correspondence analysis and the multiple correspondence analysis used by Bourdieu in his works and some of those techniques that are performed today in big data analytics. (shrink)

This book provides a detailed account of Julián Marías’s metaphysical anthropology with the ultimate aim of offering a coherent and systematic analysis of Marías’s argumentation for claiming that the conscious hope for Christian salvation through resurrection — and with it the hope that Jesus Christ did actually resurrect, and more generally the hope that Christian revelation is true — is justified not because the certainty or the likelihood that this salvation will, as a matter of fact, actually occur, but because (...) this hope amounts to a self-affirming exercise, a conscious endorsement of human reality, and as such a sign of authenticity. -/- . (shrink)

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)

El objetivo de este artículo es ofrecer una exposición sistemática de la propuesta filosófica de Joaquim Xirau (Figueras, 1895 – Ciudad de México, 1946), señalando así su interés filosófico al tiempo que se vinculan sus dos grandes obras ensayísticas de madurez, Amor y mundo (1940) y Lo fugaz y lo eterno (1942).

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 this paper I will argue that Unamuno was conceiving of God (and ordinary, non-religious fictional characters more generally) in realist, though non-evidentially grounded, terms. I will point out that this way of conceiving of God allowed Unamuno to claim the actual existence of God (though as a fictional, purely humanly created character) and, with this, the possibility of there being an actual relationship between the concrete religious person and God without having to dispense with his own core claim that (...) religious faith is just a subjective, though natural and thus inevitable, human reaction. (shrink)

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)

In _Plotinus on Love_, Alberto Bertozzi argues that love is the origin, culmination, and regulative force of the double movement that characterizes Plotinus' metaphysics: the derivation of all reality from the One and the return of the soul to it.

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)