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 In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’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

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.

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)

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)

We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is ε X ", and (2) "If X is a well-ordering, then so is φ(α, X)", where α is a fixed computable ordinal and φ represents the two-placed Veblen function. For the former statement, we show that ω iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ${\mathrm{A}\mathrm{C}\mathrm{A}}_{0}^{+}$ over RCA₀. To prove the (...) latter statement we need to use ω α iterations of the Turing jump, and we show that the statement is equivalent to ${\mathrm{\Pi }}_{{\mathrm{\omega }}^{\mathrm{\alpha }}}^{0}{-\mathrm{C}\mathrm{A}}_{0}$ . Our proofs are purely computability-theoretic. We also give a new proof of a result of Friedman: the statement "if x is a well-ordering, then so is φ(x, 0)" is equivalent to ATR₀ over RCA₀. (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)

Abortion is largely accepted even for reasons that do not have anything to do with the fetus' health. By showing that (1) both fetuses and newborns do not have the same moral status as actual persons, (2) the fact that both are potential persons is morally irrelevant and (3) adoption is not always in the best interest of actual people, the authors argue that what we call ‘after-birth abortion’ (killing a newborn) should be permissible in all the cases where abortion (...) is, including cases where the newborn is not disabled. (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 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)

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)

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)

I argue that there are significant moral reasons in addition to harm prevention for making vaccination against certain common infectious diseases compulsory. My argument is based on an analogy between vaccine refusal and tax evasion. First, I discuss some of the arguments for compulsory vaccination that are based on considerations of the risk of harm that the non‐vaccinated would pose on others; I will suggest that the strength of such arguments is contingent upon circumstances and that in order to provide (...) the strongest defence possible of compulsory vaccination, such arguments need to be supplemented by additional arguments. I will then offer my additional argument for compulsory vaccination: I will argue that in both cases of vaccine refusal and of tax evasion individuals fail to make their fair contribution to important social and public goods, regardless of whether each individual contribution ‘makes a difference’. While fairness considerations have sometimes been used to support a moral duty to vaccinate, they have not been appealed to in order to argue for a legal duty to vaccinate. I will suggest that this is due, among other things, to a misapplication of the principle of the least restrictive alternative in public health. Finally, I will address nine possible objections to my argument. (shrink)

We describe a form of moral artificial intelligence that could be used to improve human moral decision-making. We call it the “artificial moral advisor”. The AMA would implement a quasi-relativistic version of the “ideal observer” famously described by Roderick Firth. We describe similarities and differences between the AMA and Firth’s ideal observer. Like Firth’s ideal observer, the AMA is disinterested, dispassionate, and consistent in its judgments. Unlike Firth’s observer, the AMA is non-absolutist, because it would take into account the human (...) agent’s own principles and values. We argue that the AMA would respect and indeed enhance individuals’ moral autonomy, help individuals achieve wide and a narrow reflective equilibrium, make up for the limitations of human moral psychology in a way that takes conservatives’ objections to human bioenhancement seriously, and implement the positive functions of intuitions and emotions in human morality without their downsides, such as biases and prejudices. (shrink)

We argue that individuals who have access to vaccines and for whom vaccination is not medically contraindicated have a moral obligation to contribute to the realisation of herd immunity by being vaccinated. Contrary to what some have claimed, we argue that this individual moral obligation exists in spite of the fact that each individual vaccination does not significantly affect vaccination coverage rates and therefore does not significantly contribute to herd immunity. Establishing the existence of a moral obligation to be vaccinated (...) despite the negligible contribution each vaccination can make to the realisation of herd immunity is important because such moral obligation would strengthen the justification for coercive vaccination policies. We show that two types of arguments—namely a utilitarian argument based on Parfit’s Principle of Group Beneficence and a contractualist argument—can ground an individual moral obligation to be vaccinated, in spite of the imperceptible contribution that any single vaccination makes to vaccine coverage rates. We add a further argument for a moral obligation to be vaccinated that does not require embracing problematic comprehensive moral theories such as utilitarianism or contractualism. The argument is based on a “duty of easy rescue” applied to collectives, which grounds a collective moral obligation to realise herd immunity, and on a principle of fairness in the distribution of the burdens that must be borne to realise herd immunity. (shrink)

The association of resilience-related factors with frailty is a recent research topic. Dispositional optimism and context sensitivity are two psychological factors that differently contribute to individual resilience. This study aimed at investigating whether dispositional optimism and context sensitivity might contribute to a multifactorial model of frailty, together with established relevant factors such as cognitive and physical factors. This cross-sectional study involved 141 elderly outpatients aged ≥65 years, who were referred to the Geriatrics and Multidimensional Evaluation Clinic of the University Hospital (...) of Messina. We used the following measures: the Mini-Mental State Examination to screen for global cognitive functioning; 4-m gait speed and handgrip strength to measure physical performance; a 35-item Frailty Index to evaluate patients’ frailty status; the revised Life Orientation Test to gauge dispositional optimism; and the Context Sensitivity Index to measure context sensitivity. We found that LOT-R, CSI, and MMSE were all significantly associated with FI. Gait speed was only marginally associated with FI. The present study showed a novel association of dispositional optimism and context sensitivity with frailty among elderly outpatients. These preliminary findings support a multidimensional approach to frailty in which even peculiar psychological features might provide a significant contribution. (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)

Conscientious objection in health care is a form of compromise whereby health care practitioners can refuse to take part in safe, legal, and beneficial medical procedures to which they have a moral opposition (for instance abortion). Arguments in defense of conscientious objection in medicine are usually based on the value of respect for the moral integrity of practitioners. I will show that philosophical arguments in defense of conscientious objection based on respect for such moral integrity are extremely weak and, if (...) taken seriously, lead to consequences that we would not (and should not) accept. I then propose that the best philosophical argument that defenders of conscientious objection in medicine can consistently deploy is one that appeals to (some form of) either moral relativism or subjectivism. I suggest that, unless either moral relativism or subjectivism is a valid theory—which is exactly what many defenders of conscientious objection (as well as many others) do not think—the role of moral integrity and conscientious objection in health care should be significantly downplayed and left out of the range of ethically relevant considerations. (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.

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)

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.

Cameron et al ’s1 ethical considerations about the ‘Dualism of Values’ in pandemic response emphasise the need to strike a fair balance between the interests of the less vulnerable to COVID-19 and the interests of the more vulnerable. Those considerations are at the basis of ethical defences of focused protection strategies.2 One example is the proposal put forward in the Great Barrington Declaration. It presented focused protection strategies as more ethical alternatives to lockdowns which would prevent lockdowns’ ‘irreparable damage, with (...) the underprivileged disproportionately harmed’.3 Here we want to suggest that a version of Cameron et al ’s analysis can be applied to the case of vaccines to support a focused protection vaccination strategy. At this stage, we should limit vaccination to the vulnerable and not target children in COVID-19 vaccination strategies. We argue that, given the current state of knowledge about COVID-19, immunity and vaccines, it would be wrong to pose the costs and risks of vaccines on children for three reasons. First, they are unlikely to benefit from COVID-19 vaccination …. (shrink)

The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of (...) a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

The basic notions in Prior's Ockhamist and Peircean logics of branching-time are the notion of moment and that of history. In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set (...) of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

In his essay against Eberhard, Kant denies that there are innate concepts. Several scholars take Kant’s statement at face value. They claim that Kant did not endorse concept innatism, that the categories are not innate concepts, and that Kant’s views on innateness are significantly different from Leibniz’s. This paper takes issue with those claims. It argues that Kant’s views on the origin of the intellectual concepts are remarkably similar to Leibniz’s. Given two widespread notions of innateness, the dispositional notion and (...) the input/output notion, intellectual concepts are innate for Kant no less than for Leibniz. (shrink)

Ambientato nel Regno di Napoli del tardo Seicento, il saggio esplora la cultura dell'epoca attraverso la vicenda biografica dei membri dell'Accademia degli Investiganti, Tommaso Cornelio, Lucantonio Porzio, Francesco d'Andrea e Giuseppe Valletta. Attraverso l'analisi delle opere degli Investiganti, il testo mostra un quadro della loro riflessione filosofico-scientifica dovuta alla diffusione delle teorie atomistiche dei maggiori pensatori europei (Boyle, Descartes, Galilei, etc.) nei circoli partenopei--Back cover.

Últimamente se viene hablando mucho de “guerra cultural” si bien pocas veces se concreta su significado. Tiene que ver con la batalla por el relato, pero no se limita a este campo. En todo caso, conviene diferenciar este concepto del legítimo debate e intercambio de ideas en pos de la mejora social. Nos encontraríamos por el contrario más cerca de la guerra híbrida, psicológica, cognitiva y el arte de la propaganda llevados a cabo por unos Estados contra otros, pero también (...) por determinados agentes con poder suficiente para imponer la cultura que les interesa y acabar con la del contrario. (shrink)

We address the issue of whether, why and under what conditions, quarantine and isolation are morally justified, with a particular focus on measures implemented in the developing world. We argue that the benefits of quarantine and isolation justify some level of coercion or compulsion by the state, but that the state should be able to provide the strongest justification possible for implementing such measures. While a constrained form of consequentialism might provide a justification for such public health interventions, we argue (...) that a stronger justification is provided by a principle of State Enforced Easy Rescue: a state may permissibly compel individuals to engage in activities that entail a small cost to them but a large benefit to others, because individuals have a moral duty of easy rescue to engage in those activities. The principle of State Enforced Easy Rescue gives rise to an Obligation Enforcement Requirement: the state should create the conditions such that submitting to coercive or compulsive measures becomes a fundamental moral duty of individuals, i.e. a duty of easy rescue. When the state can create such conditions, it has the strongest justification possible for implementing coercive or compulsive measures, because individuals have a moral duty to temporarily relinquish the rights that such measures would infringe. Our argument has significant implications for how public health emergencies in the developing world should be tackled. Where isolation and quarantine measures are necessary, states or the international community have a moral obligation to provide certain benefits to those quarantined or isolated. (shrink)