We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half of a nontrivial relativized $\mathcal {K}$ -pair. This leads to a structural dichotomy in the enumeration degrees.

We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half a nontrivial relativized K-pair. This leads to a structural dichotomy in the enumeration degrees.

A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity (...) of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN. (shrink)

We prove that the degree structures of the d.c.e. and the 3-c.e. Turing degrees are not elementarily equivalent, thus refuting a conjecture of Downey. More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees f > e > d > 0 such that any degree u ≤ f is either comparable with both e and d, or incomparable with both.

Recall that B is PA relative to A if B computes a member of every nonempty $\Pi ^0_1(A)$ class. This two-place relation is invariant under Turing equivalence and so can be thought of as a binary relation on Turing degrees. Miller and Soskova [23] introduced the notion of a $\Pi ^0_1$ class relative to an enumeration oracle A, which they called a $\Pi ^0_1{\left \langle {A}\right \rangle }$ class. We study the induced extension of the relation B is PA relative (...) to A to enumeration oracles and hence enumeration degrees. We isolate several classes of enumeration degrees based on their behavior with respect to this relation: the PA bounded degrees, the degrees that have a universal class, the low for PA degrees, and the ${\left \langle {\text {self}\kern1pt}\right \rangle }$ -PA degrees. We study the relationship between these classes and other known classes of enumeration degrees. We also investigate a group of classes of enumeration degrees that were introduced by Kalimullin and Puzarenko [14] based on properties that are commonly studied in descriptive set theory. As part of this investigation, we give characterizations of three of their classes in terms of a special sub-collection of relativized $\Pi ^0_1$ classes—the separating classes. These three can then be seen to be direct analogues of three of our classes. We completely determine the relative position of all classes in question. (shrink)

We study punctual categoricity on a cone and intrinsically punctual functions and obtain complete structural characterizations in terms of model-theoretic notions. As a corollary, we answer a question of Bazhenov, Downey, Kalimullin, and Melnikov by showing that relational structures are not punctually universal. We will also apply this characterisation to derive an algebraic characterisation of relatively punctually categorical mono-unary structures.

Working toward showing the decidability of the $\forall \exists $ -theory of the ${\Sigma ^0_2}$ -enumeration degrees, we prove that no so-called Ahmad pair of ${\Sigma ^0_2}$ -enumeration degrees can join to ${\mathbf 0}_e'$.

Defining the degree of categoricity of a computable structure ${\mathcal{M}}$ to be the least degree d for which ${\mathcal{M}}$ is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0 (n) can be so realized, as can the degree 0 (ω).

For a computable structure $\mathcal {M}$, the categoricity spectrum is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable copies of $\mathcal {M}$. If the spectrum has a least degree, this degree is called the degree of categoricity of $\mathcal {M}$. In this paper we investigate spectra of categoricity for computable rigid structures. In particular, we give examples of rigid structures without degrees of categoricity.

The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.

It is proved that for every countable structure and a computable successor ordinal α there is a countable structure which is ‐least among all countable structures such that is Σ‐definable in the αth jump. We also show that this result does not hold for the limit ordinal. Moreover, we prove that there is no countable structure with the degree spectrum for.

We show that the Δ0 2 enumeration degrees are dense. We also show that for every nonzero n-c. e. e-degree a, with n≥ 3, one can always find a nonzero 3-c. e. e-degree b such that b < a on the other hand there is a nonzero ωc. e. e-degree which bounds no nonzero n-c. e. e-degree.

We extend the limitwise monotonicity notion to the case of arbitrary computable linear ordering to get a set which is limitwise monotonic precisely in the non‐computable degrees. Also we get a series of connected non‐uniformity results to obtain new examples of non‐uniformly equivalent families of computable sets with the same enumeration degree spectrum.

We introduce a hierarchy of sets which can be derived from the integers using countable collections. Such families can be coded into countable algebraic structures preserving their algorithmic properties. We prove that for different finite levels of the hierarchy the corresponding algebraic structures have different classes of possible degree spectra.

A structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent automata-presentable structures is ${\rm{\Sigma (...) }}_1^1 $-complete. We also use similar methods to show that there is no reasonable characterisation of the structures with a polynomial-time presentation in the sense of Nerode and Remmel. (shrink)

Marsilio Ficino’s fame as a translator, not least due to his contributions to theology and the development of hermeticism, has already been established by Frances Yates and debated by Wouter Hanegraaff. For each of his translations of Greek texts, Ficino wrote a preface to guide and to manipulate the reader. This paper presents an analysis of the auctoritas in the paratext of the Corpus Hermeticum, analyzing it as a rhetorical device used by Ficino to express his ideas, particularly the role (...) of Hermes Trismegistus. Ficino used his rhetorical skill not only to translate from Greek to Latin but also to support his theories in commentaries, letters, or, in this case, prefaces. (shrink)

We show that the e-degree 0'e and the map u ↦ u' are definable in the upper semilattice of all e-degrees. The class of total e-degrees ≥0'e is also definable.

It is proved that the (2p)-c. e. e-degrees are not elementarily equivalent to the (2p + 1)-c. e. e-degrees for each nonzero p ∈ ω. It follows that m-c. e. e-degrees are not elementarily equivalent to the n-c. e. e-degrees if 1 < m < n.

There is a global shortage of nurses that affects healthcare delivery, which will be exacerbated with the increasing demand for healthcare professionals by the aging population. The growing shortage requires an ethical exploration on the issue of nurse migration. In this article, we discuss how migration respects the autonomy of nurses, increases cultural diversity, and leads to improved patient satisfaction and health outcomes. We also discuss the potential for negative impacts on public health infrastructures, lack of respect for cultural diversity, (...) and ethical concerns related to autonomy and justice, including coercion and discrimination. This analysis is written from a rights-based ethics approach by referring to rights held by nurses and patient populations. Nurse migration highlights conflicts between nurses and between nurses and healthcare systems. Increased awareness of ethical challenges surrounding nurse migration must be addressed to enhance the well-being of nurses and patient populations. (shrink)

This volume gathers together for the first time are all the key texts in a crucial debate in modern philosophy, centered on Leibniz's famous 1695 essay, the "New System of the Nature of Substances and their Communication," in which he introduced his strikingly original theory of metaphysics. His "system" became increasingly famous and drew him into discussion and development of these ideas, both in public and in private, with a variety of thinkers, most notably the great French philosopher Pierre Bayle. (...) Woolhouse's and Francks's new English edition gives the only full representation of this debate, and will therefore be essential reading for anyone who wishes to gain a proper understanding of Leibniz's philosophy and its intelletual context. All the texts are newly translated and extensively annotated; many appear in English for the first time. (shrink)

ABSTRACTThere is a growing body of literature describing conceptual frameworks for working with participatory visual methods. Through a global health lens, this paper examines some key themes within these frameworks. We reflect on our experiences of working with with an array of PVM to engage community members in Vietnam, Kenya, the Philippines and South Africa in biomedical research and public health. The participants that we have engaged in these processes live in under-resourced areas with high prevalence of communicable and non-communicable (...) diseases. Our paper describes some of the challenges that we have encountered while using PVM to foster knowledge exchange, build relationships and facilitate change among individuals and families, community members, health workers, biomedical scientists and researchers. We consider multiple ethical situations that have arisen through our work and discuss the ways in which we have navigated and negotiated them. We offer our reflections and learning from facil... (shrink)

Plato's dialogues frequently criticize traditional Greek myth, yet Plato also integrates myth with his writing. Daniel S. Werner confronts this paradox through an in-depth analysis of the Phaedrus, Plato's most mythical dialogue. Werner argues that the myths of the Phaedrus serve several complex functions: they bring nonphilosophers into the philosophical life; they offer a starting point for philosophical inquiry; they unify the dialogue as a literary and dramatic whole; they draw attention to the limits of language and the limits of (...) knowledge; and they allow Plato to co-opt cultural authority as a way of defining and legitimating the practice of philosophy. Platonic myth, as a species of traditional tale, is thus both distinct from philosophical dialectic and similar to it. Ultimately, the most powerful effect of Platonic myth is the way in which it leads readers to participate in Plato's dialogues and to engage in a process of self-examination. (shrink)

t. 1. Apo ton prōto skeptomeno anthrōpo mechri ton 6. aiōna M.Ch. -- t. 2. Apo ton 7. aiōna M.Ch. mechri to sēmera.

This article is the guest editors’ introduction to the special issue in Business & Society on “SMEs and CSR in Developing Countries.” The special issue includes four original research articles by Hamann, Smith, Tashman, and Marshall; Allet; Egels-Zandén; and Puppim de Oliveira and Jabbour on various aspects of the relationship of small and medium enterprises to corporate social responsibility in developing countries.

Since the launch of applications such as DALL-E, Midjourney, and Stable Diffusion, generative artificial intelligence has been controversial as a tool for creating artwork. While some have presented longtermist worries about these technologies as harbingers of fully automated futures to come, more pressing is the impact of generative AI on creative labour in the present. Already, business leaders have begun replacing human artistic labour with AI-generated images. In response, the artistic community has launched a protest movement, which argues that AI (...) image generation is a kind of theft. This paper analyzes, substantiates, and critiques these arguments, concluding that AI image generators involve an unethical kind of labour theft. If correct, many other AI applications also rely upon theft. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

In Seeing Things as They Are (Searle 2015), Searle developed a direct realist’s theory of perception. According to direct realism, physical objects are directly and immediately perceived. Searle claims that Berkeley’s theory of perception goes against direct realism. For Searle, Berkeley’s theory suggests that only subjective experiences (ideas) are directly and immediately perceived, not physical objects. Contrary to Searle, G. S. Pappas claims that Berkeley’s theory of perception is consistent with the view that physical objects are immediately perceivable (Pappas 1982; (...) Pappas 1987). Given the conflicting interpretations of Berkeley’s theory of perception, this paper attempts to defend Searle’s position on Berkeley’s theory of perception. It refutes Pappas’ interpretation by arguing that he is inconsistent with Berkeley’s theses of ontological phenomenalism and heterogeneity thesis. (shrink)

Capital punishment—the legally authorized killing of a criminal offender by an agent of the state for the commission of a crime—stands in special need of moral justification. This is because execution is a particularly severe punishment. Execution is different in kind from monetary and custodial penalties in an obvious way: execution causes the death of an offender. While fines and incarceration set back some of one’s interests, death eliminates the possibility of setting and pursuing ends. While fines and incarceration narrow (...) one’s routes to happiness, death eliminates its possibility. Not surprisingly, there is much debate about the moral permissibility of capital punishment. This entry maps the terrain of this debate. The first section discusses justifications of the death penalty as they appear in major theories of punishment. The second section surveys moral objections to execution that apply to most justifications. The third addresses procedural criticisms, which do not target the morality of execution so much as the justice of its implementation. (shrink)

Many people are worried about the harmful effects of climate change but nevertheless enjoy some activities that contribute to the emission of greenhouse gas (driving, flying, eating meat, etc.), the main cause of climate change. How should such people make choices between engaging in and refraining from enjoyable greenhouse-gas-emitting activities? In this chapter, we look at the answer provided by decision theory. Some scholars think that the right answer is given by interactive decision theory, or game theory; and moreover think (...) that since private climate decisions are instances of the prisoner’s dilemma, one rationally should engage in these activities provided that one enjoys them. Others think that the right answer is given by expected utility theory, the best-known version of individual decision theory under risk and uncertainty. In this chapter, we review these different answers, with a special focus on the latter answer and the debate it has generated. (shrink)