This is a book that every enthusiast for Gödel’s proofs of his incompleteness theorems will want to own. It gives an up-to-date account of connections between systems of modal logic and results on provability in formal systems for arithmetic, analysis, and set theory.

This paper obtains lower and upper bounds for the number of alternations of bounded quantifiers needed to express all formulas in certain ordered Abelian groups admitting elimination of unbounded quantifiers. The paper also establishes model-theoretic tests for equivalence to a formula with a given number of alternations of bounded quantifiers.

The study of existentially closed closure algebras begins with Lipparini’s 1982 paper. After presenting new nonelementary axioms for algebraically closed and existentially closed closure algebras and showing that these nonelementary classes are different, this paper shows that the classes of finitely generic and infinitely generic closure algebras are closed under finite products and bounded Boolean powers, extends part of Hausdorff’s theory of reducible sets to existentially closed closure algebras, and shows that finitely generic and infinitely generic closure algebras are elementarily (...) inequivalent. Special properties of algebraically closed, existentially closed, finitely generic, and infinitely generic closure algebras are established along the way. (shrink)

If are structures for a first-order language , is said to be algebraically closed in just in case every positive existential -sentence true in is true in . In 1976 Elliott showed that unital AF algebras are classified up to isomorphism by corresponding dimension groups with order unit. This paper shows that one dimension group with order unit is algebraically closed in another just in case the corresponding AF algebras, viewed as metric structures, fall in the same relation.

In the context of continuous logic, this paper axiomatizes both the class \ of lattice-ordered groups isomorphic to C for X compact and the subclass \ of structures existentially closed in \; shows that the theory of \ is \-categorical and admits elimination of quantifiers; establishes a Nullstellensatz for \ and \; shows that \\in \mathcal {C}\) has a prime-model extension in \ just in case X is Boolean; and proves that in a sense relevant to continuous logic, positive formulas (...) admit in \ elimination of quantifiers to positive formulas. (shrink)

In a dimension group, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The dimension groups obeying a stronger version of this result, true in dense Archimedean ordered groups, are characterized algebraically and provided with a simple set of axioms.

A nontrivial ring with unit eliminates imaginaries just in case its complete theory has the following property: every definable m-ary equivalence relation E may be defined by a formula f = f, where f is an m-ary definable function. We show that for certain natural expansions of the field of p-adic numbers, elimination of imaginaries fails or is independent of ZPC. Similar results hold for certain fields of formal power series.

If one builds a topological model, analogous to that of Moschovakis , over the product of uncountably many copies of the Cantor set, one obtains a structure elementarily equivalent to Krol's model . In an intuitionistic metatheory Moschovakis's original model satisfies all the axioms of intuitionistic analysis, including the unrestricted version of weak continuity for numbers.

There is a model, for a system of intuitionistic analysis including Brouwer's principle for numbers and Kripke's schema, in which math formula ø-definable discrete sets of choice sequences are subcountable.

This paper extends theorems of Belegradek about poly-regular groups of finite rank to certain poly-regular groups of infinite rank. A model-theoretic property aiding these investigations is the elimination of unbounded quantifiers, and the paper establishes both a general model-theoretic test for this property and results about bounded quantifiers in the special context of ordered Abelian groups.

In the ordered Abelian group of reals with the integers as a distinguished subgroup, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The result is uniform in the integer coefficients and moduli of the initial generalized halfspaces.

While finitely generic dimension groups are known to admit no proper self-embeddings, these groups also have no automorphisms other than scalar multiplications, and every countable infinitely generic dimension group admits proper self-embeddings and has automorphisms other than scalar multiplications. The finite-forcing companion of the theory of dimension groups is recursively isomorphic to first-order arithmetic, the infinite-forcing companion of the theory of dimension groups is recursively isomorphic to second-order arithmetic, and the first-order theory of existentially closed dimension groups is a complete (...) $\Pi_{1}^{1}$-set. While many special properties of f.g. dimension groups may be realized in recursive e.c. dimension groups, and many special properties of i.g. dimension groups may be realized in hyperarithmetic e.c. dimension groups, no f.g. dimension group is arithmetic and no i.g. dimension group is analytical. Yet there is an f.g. dimension group recursive in first-order arithmetic, and there is an i.g. dimension group recursive in second-order arithmetic. (shrink)

The ninth edition of Media Ethics: Issues and Cases has been updated to reflect the most pressing ethical issues in media. Featuring 25 new cases on hot topic issues from fake news to drones and a new chapter on social justice, this authoritative case book gives students the tools to make ethical decisions in an increasingly complex environment.

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

In this chapter, we consider ethical and philosophical aspects of trust in the practice of medicine. We focus on trust within the patient-physician relationship, trust and professionalism, and trust in Western (allopathic) institutions of medicine and medical research. Philosophical approaches to trust contain important insights into medicine as an ethical and social practice. In what follows we explain several philosophical approaches and discuss their strengths and weaknesses in this context. We also highlight some relevant empirical work in the section on (...) trust in the institutions of medicine. It is hoped that the approaches discussed here can be extended to nursing and other topics in the philosophy of medicine. (shrink)

The proposition that digital innovations can put people in charge of their health has been accompanied by prolific talk of empowerment. In this paper we consider ethical challenges and opportunities of trying to achieve justice and empowerment using digital health initiatives. The language of empowerment can misleadingly suggest that by using technology, people can control their health and take responsibility for health outcomes to a greater degree than is realistic or fair. Also, digital health empowerment often primarily reaches people who (...) already have high technological and health literacy, leaving others behind. We critically investigate whether the concept of health empowerment could be re-engineered to mean something different, namely the process of improving the health literacy and access of those who least possess it, in line with recent proposals for conceptual engineering in the service of justice. We settle on the weaker conclusion that underlying ethical values including justice should be used to interpret the existing concept of empowerment. To conclude, we take a high-level view of various strategies for achieving the ethical value associated with digital health empowerment. (shrink)

Instead of conceiving ethical commands as divine revelations or as the discoveries of brilliant thinkers, we should see our ethical practices as evolving over tens of thousands of years, as members of our species have worked out how to live together and prosper. Here, Kitcher elaborates his radical vision of this millennia-long ethical project.

Academic misconduct is a threat to the validity and reliability of online examinations, and media reports suggest that misconduct spiked dramatically in higher education during the emergency shift to online exams caused by the COVID-19 pandemic. This study reviewed survey research to determine how common it is for university students to admit cheating in online exams, and how and why they do it. We also assessed whether these self-reports of cheating increased during the COVID-19 pandemic, along with an evaluation of (...) the quality of the research evidence which addressed these questions. 25 samples were identified from 19 Studies, including 4672 participants, going back to 2012. Online exam cheating was self-reported by a substantial minority (44.7%) of students in total. Pre-COVID this was 29.9%, but during COVID cheating jumped to 54.7%, although these samples were more heterogenous. Individual cheating was more common than group cheating, and the most common reason students reported for cheating was simply that there was an opportunity to do so. Remote proctoring appeared to reduce the occurrence of cheating, although data were limited. However there were a number of methodological features which reduce confidence in the accuracy of all these findings. Most samples were collected using designs which makes it likely that online exam cheating is under-reported, for example using convenience sampling, a modest sample size and insufficient information to calculate response rate. No studies considered whether samples were representative of their population. Future approaches to online exams should consider how the basic validity of examinations can be maintained, considering the substantial numbers of students who appear to be willing to admit engaging in misconduct. Future research on academic misconduct would benefit from using large representative samples, guaranteeing participants anonymity. (shrink)

A concise and accessible introduction to the evolution of the concept of moral self-cultivation in the Chinese Confucian tradition, this volume begins with an explanation of the pre-philosophical development of ideas central to this concept, followed by an examination of the specific treatment of self cultivation in the philosophy of Kongzi ("Confucius"), Mengzi ("Mencius"), Xunzi, Zhu Xi, Wang Yangming, Yan Yuan and Dai Zhen. In addition to providing a survey of the views of some of the most influential Confucian thinkers (...) on an issue of fundamental importance to the tradition, Ivanhoe also relates their concern with moral self-cultivation to a number of topics in the Western ethical tradition. Bibliography and index are included. (shrink)

This volume introduces readers to emergence theory, outlines the major arguments in its defence, and summarizes the most powerful objections against it. It provides the clearest explication yet of this exciting new theory of science, which challenges the reductionist approach by proposing the continuous emergence of novel phenomena.

Introductory Chapter to the _Cambridge Handbook of Situated Cognition_ (CUP, 2009).

An esteemed philosopher discusses his theory of universal freedom, describing how even those who are members of free societies may find their liberties curtailed and includes tests of freedom including the eyeball test and the tough-luck test.

We can gain empirical knowledge of elementary arithmetic and elementary geometry because the primitive core of these subjects consists of truths about manipulations of reality. Full arithmetic and geometry idealize these operations. Later mathematics attributes much more extensive powers to the ideal agent who performs mathematical operations.

Drawing on the latest work in cognitive neuroscience, a philosopher proposes that delusions are narrative models that accommodate anomalous experiences.

_Idealist Alternatives to Materialist Philosophies of Science_ (ed. Philip MacEwen) presents some of the major challenges to materialist interpretations of science while also giving materialism a full hearing.

In “Scientific Knowledge,” Philip Kitcher challenges arguments that deny the truth of the theoretical claims of science, and he attempts to discover reasons for endorsing the truth of such claims. He suggests that the discovery of such reasons might succeed if we ask why anyone thinks that the theoretical claims we accept are true and then look for answers that reconstruct actual belief‐generating processes. To this end, Kitcher presents the “homely argument” for scientific truth, which claims that when a (...) field of science is continually applied to yield precise predictions, then it is at least approximately true. He defends this approach and offers a supplementary account that gives more attention to detail. This account includes a historical aspect that must answer to skeptical challenges and a social aspect. (shrink)

A person presented with adequate but not conclusive evidence for a proposition is in a position voluntarily to acquire a belief in that proposition, or to suspend judgment about it. The availability of doxastic options in such cases grounds a moderate form of doxastic voluntarism not based on practical motives, and therefore distinct from pragmatism. In such cases, belief-acquisition or suspension of judgment meets standard conditions on willing: it can express stable character traits of the agent, it can be responsive (...) to reasons, and it is compatible with a subjective awareness of the available options. (shrink)

Research on personality psychology is making important contributions to psychological science and applied psychology. This second edition of The Cambridge Handbook of Personality Psychology offers a one-stop resource for scientific personality psychology. It summarizes cutting-edge personality research in all its forms, including genetics, psychometrics, social-cognitive psychology, and real-world expressions, with informative and lively chapters that also highlight some areas of controversy. The team of renowned international authors, led by two esteemed editors, ensures a wide range of theoretical perspectives. Each research (...) area is discussed in terms of scientific foundations, main theories and findings, and future directions for research. The handbook also features advances in technology, such as molecular genetics and functional neuroimaging, as well as contemporary statistical approaches. An invaluable aid to understanding the central role played by personality in psychology, it will appeal to students, researchers, and practitioners in psychology, behavioral neuroscience, and the social sciences. (shrink)