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 In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’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

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)

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)

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.

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)

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)

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)

El objetivo de este artículo es clarificar la noción de «vida auténtica» tal y como es descrita por Joan Roura-Parella en su última obra Tema y variaciones de la personalidad (1950). Por «vida auténtica» se entiende una vida autogobernada, que permite al individuo realizar su propia singularidad y, por tanto, preservar su autonomía y dignidad como persona. Una vida dominada por factores ajenos al propio individuo, sean cuales sean éstos, es una vida alienada, que no permite el desarrollo del individuo (...) en tanto la persona que es. Se señala la relevancia filosófica de la propuesta de Roura-Parella, que es la de ofrecer una justificación no-evidencial para una forma de vida cristiana, agapística. De acuerdo con Roura-Parella, una forma de vida basada en la entrega amorosa para con el prójimo está justificada en tanto que ésta es el resultado último de nuestra propia condición natural, constituyendo así un acto de afirmación personal y siendo, por tanto, condición necesaria para gozar de una vida auténtica — «la vida alcanza su hondo sentido al salirse de sí misma para darse a los demás» (Roura-Parella, Tema y variaciones de la personalidad, 1950, p. 229). Se señalan las diferencias y semejanzas de la propuesta de Roura-Parella con respecto a las de Miguel de Unamuno y Joaquim Xirau, autores que fueron cercanos a Roura-Parella y quienes, aunque partiendo de razonamientos distintos a los de Roura-Parella, también concibieron la entrega amorosa para con el prójimo como un acto de afirmación personal. (shrink)

In this paper I argue for a syncretistic theory of depiction, which combines the merits of the main paradigms which have hitherto faced themselves on this issue, namely the perceptualist and semioticist approaches. The syncretistic theory indeed takes from the former its stress on experiential factors and from the latter its stress on conventional factors. But the theory is even more syncretistic than this, for the way it accounts for the experiential factor vindicates several claims defended by different perceptualist theories. (...) In a nutshell, according to the syncretistic theory a picture depicts its subject iff i) it is transformed into an entity-cum-meaning and ii) one has the twofold experience of seeing that subject in the picture qua noninterpreted entity, the image, just in case one consciously misrecognizes it in consciously seeing that image, for that subject resembles the image in some grouping properties (originally labelled Gestalt-qualities in psychology). By appealing to objective resemblance in grouping properties, the theory can vindicate what are nowadays taken to be the most neglected doctrines in the perceptualist camp: objective resemblance theories. By appealing, moreover, to conscious misrecognition, the theory not only squares with both the seeing-in and the recognition theories of depiction, but it also shows the grain of truth in illusion theories of depiction, since conscious misrecognition is a kind of perceptual illusion. (shrink)

El objetivo de este artículo es explorar la manera en que Joaquim Xirau y Miguel de Unamuno concibieron el amor. A pesar de que no hay motivos suficientes para concluir una influencia directa y filosóficamente relevante de Unamuno en la obra de Xirau, sí podemos concluir que la forma en que ambos autores concibieron el amor guarda ciertas similitudes. Así, ambos coinciden en concebir la entrega amorosa como un ejercicio de afirmación individual que trae consigo un incremento de la propia (...) singularidad. También, tanto Unamuno como Xirau conciben la entrega amorosa como un acto que, aun surgiendo del propio individuo y no de como es de hecho el mundo, personifica aquello amado, dejando de ser así visto como un mero objeto y mostrándose bajo una forma personal. Y ambos, aunque de un modo distinto, hacen del relato bíblico acerca de la vida y Resurrección de Cristo un aspecto central de sus maneras de entender el amor. (shrink)

This chapter contains sections titled: Introduction Argentina Mexico Brazil Chile and Puerto Rico Peru Other Centers Concluding Remarks References Further Reading.

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)

En este artículo expongo y analizo la propuesta berkeleyana del conocimiento nocional, que representa entre otras cosas el intento del irlandés por conocer a la mente o espíritu, esto es, a aquella cosa pensante y activa que por su propia actividad resulta irrepresentable como idea. Como el conocimiento nocional ya se menciona en los Comentarios Filosófi cos me remitiré a ellos para conocer los orígenes del mismo; sin embargo, como tal conocimiento aparece con mayor detalle en obras posteriores me serviré (...) sobre todo del Tratado para abordar la compleja doctrina nocional. // In this paper I expose and analyze the berkeleian proposal of notional knowledge. Among other things, this proposal represents Berkeley ́s attempt to know the mind or spirit, that is, the thinking and active thing that by its own activity results unrepresentable as idea. As such knowledge is already mentioned in the Philosophical Commentaries, I will refer to them in order to know the origins of that proposal. However, as notional knowledge appears in more detail in later works, I will make use especially of the Treatise to address the complex notional doctrine. (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)

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)

In der Reihe werden herausragende monographische Untersuchungen und Sammelbände zu allen Aspekten der Philosophie Kants veröffentlicht, ebenso zum systematischen Verhältnis seiner Philosophie zu anderen philosophischen Ansätzen in Geschichte und Gegenwart. Veröffentlicht werden Studien, die einen innovativen Charakter haben und ausdrückliche Desiderate der Forschung erfüllen. Die Publikationen repräsentieren den aktuellsten Stand der Forschung.

Unamuno saw in his defense of religious faith a response to Nietzsche’s criticisms of the Christian, agapeic way of life. To Nietzsche’s claim that engaging in this way of life is something antinatural and life‐denying, insofar as it goes against the (alleged) natural tendency to increase one’s own power, Unamuno responded that an agapeic way of life is precisely a direct expression of this natural tendency. Far from being something that goes against our natural inclinations, Unamuno says, an agapeic way (...) of life is a life‐affirming exercise, something we are led to given our own natural condition. Hence, the aim of this essay is to comment on Unamuno’s criticism of Nietzsche and to point out the philosophical relevance of Unamuno’s attempt to provide a natural foundation for religious faith when assessing Nietzsche’s criticisms of the possibility of carrying out a Christian, agapeic way of life. (shrink)

Character plays a central role in our everyday understanding and evaluation of ourselves and one another. It informs the expectations that ground our plans and projects, our moral responses to other people's behaviour and to opportunities we ourselves face, and our political decisions concerning formal education, criminal punishment, and other aspects of social organisation. These philosophical essays clarify this idea of character, analyse its relation with the findings of experimental psychology, and draw out the implications of this for education and (...) for criminal punishment. They emphasise that character is inherently dynamic, challenging the tendency among personality psychologists and virtue ethicists alike to focus on static snapshots of traits, and they emphasise the close integration of character with the individual's social context. The volume is intended to demonstrate the deep conceptual affinity of moral philosophy and social psychology and the consequent potential for each to benefit from the other. (shrink)

Introduzione.--La filosofia dei fisici.--I condannati a morte e le esperienze sull'uomo.--La psicologia e le sue applicazioni.--L'economia e le uniformità storiche.--Scienze della natura e scienze dell'uomo.--Conclusione.

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 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)

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)

Both landscape and aesthetics are all too often considered disengaged categories associated with leisure and contemplation. This book establishes landscape as a key concept in contemporary thought and rethinks aesthetics in political and activist terms. In order to do so, it challenges the dualism of "the environment" as the space inhabited by humans and the province of the natural sciences about which philosophy has little to say. (This separation is evident even in the name of the recent field of environmental (...) humanities.) In a holistic view, landscapes are at the intersection of environment and human, place and people, and nature and culture, and aesthetics provide an immersive and engaged approach to them. Landscapes are ways of being in the world and aesthetics practical means of inhabiting them. Utilizing a pragmatist, antiessentialist lens, Alberto L. Siani characterizes landscapes (as opposed to environments and territories) as concrete, experienced habitats, performative ways of making sense of the world, while aesthetics (following Dewey) identify values and ordering criteria that permeate them. He addresses issues such as temporality, environmentalism, justice, education, and interdisciplinarity within this framework and in conversation with scientific positions. A coda gives three phenomenological accounts of intensely experienced and inhabited landscapes. (shrink)

Examines how Leo Strauss sought to recover "nature," which he saw as inseparable from genuine philosphy since its inception in ancient Greece.