This paper provides the first examples of rings of algebraic numbers containing the rings of algebraic integers of the infinite algebraic extensions of where Hilbert's Tenth Problem is undecidable.

This paper surveys the recent developments in the area that grew out of attempts to solve an analog of Hilbert's Tenth Problem for the field of rational numbers and the rings of integers of number fields. It is based on a plenary talk the author gave at the annual North American meeting of ASL at the University of Notre Dame in May of 2009.

We show that Diophantine equivalence of two suitably presented countable rings implies that the existential polynomial languages of the two rings have the same "expressive power" and that their Diophantine sets are in some sense the same. We also show that a Diophantine class of countable rings is contained completely within a relative enumeration class and demonstrate that one consequence of this fact is the existence of infinitely many Diophantine classes containing holomophy rings of Q.

Let F be a finitely generated field and let j : F → N be a weak presentation of F, i.e. an isomorphism from F onto a field whose universe is a subset of N and such that all the field operations are extendible to total recursive functions. Then if R1 and R2 are recursive subrings of F, for all weak presentations j of F, j is Turing reducible to j if and only if there exists a finite collection of (...) non-constant rational functions {Gi} over F such that for every x ε R1 for some i, Gi ε R2. We investigate under what circumstances such a collection of rational functions exists and conclude that in the case when R1 R2 are both holomorphy rings and F is of characteristic 0 or is an algebraic function field over a perfect field of constants, the existence of the above-described collection of rational functions is equivalent to the requirement that the non-archimedean primes which do not appear as poles of elements of R2 do not have factors of relative degree 1 in some simple extension of K. (shrink)

We investigate the issues of Diophantine definability over the non-finitely generated version of non-degenerate modules contained in the infinite algebraic extensions of the rational numbers. In particular, we show the following. Let k be a number field and let K inf be a normal algebraic, possibly infinite, extension of k such that k has a normal extension L linearly disjoint from K inf over k. Assume L is totally real and K inf is totally complex. Let M inf be a (...) non-degenerate O k -module, possibly non-finitely generated and contained in O Kinf . Then M inf contains a submodule M¯ inf such that M inf /M¯ inf is torsion and O k has a Diophantine definition over M¯ inf. (shrink)

One of the main theorems of the paper states the following. Let R-K-M be finite extensions of a rational one variable function field R over a finite field of constants. Let S be a finite set of valuations of K. Then the ring of elements of K having no poles outside S has a Diophantine definition over its integral closure in M.

We consider the problem of constructing first-order definitions in the language of rings of holomorphy rings of one-variable function fields of characteristic 0 in their integral closures in finite extensions of their fraction fields and in bigger holomorphy subrings of their fraction fields. This line of questions is motivated by similar existential definability results over global fields and related questions of Diophantine decidability.

Let K be a computable field. Let F be a collection of recursive functions over K, possibly including field operations. We investigate the following question. Given an r.e. degree a, is there an injective map j: K $\longrightarrow \mathbb{N}$ such that j(K) is of degree a and all the functions in F are translated by restrictions of total recursive functions.

We show that elliptic curves whose Mordell–Weil groups are finitely generated over some infinite extensions of ${\mathbb {Q}}$ , can be used to show the Diophantine undecidability of the rings of integers and bigger rings contained in some infinite extensions of rational numbers.

Let K be a countable field. Then a weak presentation of K is an isomorphism of K onto a field whose elements are natural numbers, such that all the field operations are extendible to total recursive functions. Given a pair of two non-finitely generated countable fields contained in some overfield, we investigate under what circumstances the overfield has a weak presentation under which the given fields have images of arbitrary Turing degrees or, in other words, we investigate Turing separability of (...) various pairs of non-finitely generated fields. (shrink)

It is shown that for any computable field K and any r.e. degree a there is an r.e. set A of degree a and a field F ≅ K with underlying set A such that the field operations of F (including subtraction and division) are extendible to (total) recursive functions. Further, it is shown that if a and b are r.e. degrees with b ≤ a, there is a 1-1 recursive function $f: \mathbb{Q} \rightarrow \omega$ such that f(Q) ∈ a, (...) f(Z) ∈ b, and the images of the field operations of Q under f can be extended to recursive functions. (shrink)

Fried and Kollár constructed a fully faithful functor from the category of graphs to the category of fields. We give a new construction of such a functor and use it to resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure${\cal S}$, there exists a countable field${\cal F}$of arbitrary characteristic with the same essential computable-model-theoretic properties as${\cal S}$. Along the way, we develop a new “computable category theory”, and prove that our functor and (...) its partially defined inverse are computable functors. (shrink)

Although self‐testing apps, a form of mobile health (mHealth) apps, are often marketed as empowering, it is not obvious how exactly they can empower their users—and in which sense of the word. In this article, I discuss two conceptualisations of empowerment as polar opposites—one in health promotion/mHealth and one in feminist theory—and demonstrate how both their applications to individually used self‐testing apps run into problems. The first, prevalent in health promotion and mHealth, focuses on internal states and understands empowerment as (...) an individual process. However, this version of empowerment has been accused of paternalism and responsibilisation. The second, feminist version considers structural conditions and foregrounds collective, political change, whose realisation is not obviously attainable for an individually used app. By pointing out the flaws of the positions that focus on either internal states or external conditions, and by engaging with theory from critical phenomenology, I argue that the interplay between them is where empowerment can take place. I propose to formulate empowerment in phenomenological terms as a shift in being‐in‐the‐world and discuss how this conceptualisation of empowerment would avoid the criticism of previous empowerment narratives while being realisable by self‐testing apps. (shrink)

It is uncontroversial that something goes wrong with the blaming practices of hypocrites. However, it is more difficult to pinpoint exactly what is objectionable about their blaming practices. I contend that, just as epistemologists have recently done with blame, we can constructively treat hypocrisy as admitting of an epistemic species. This paper has two objectives: first, to identify the epistemic fault in epistemically hypocritical blame, and second, to explain why epistemically hypocritical blamers lose their standing to epistemically blame. I tackle (...) the first problem by appealing to an epistemic norm of consistency. I address the second by arguing that the epistemically hypocritical blamer commits to an opting-out of the set of shared epistemic standards that importantly underlies our standing to epistemically blame. I argue further that being epistemically hypocritical undermines a blamer’s standing even to judge epistemically blameworthy. (shrink)

In _The Cosmic Perils of Qadi Ḥusayn Maybudī in Fifteenth-Century Iran_ Alexandra Dunietz explores the life and works of a provincial judge whose life exemplifies the intellectual, spiritual and political tensions of the Timurid, Ak Koyunlu and Safavid spheres.

Empirical studies indicate that business compliance with the UK Modern Slavery Act is disappointing, but they struggle to make sense of this phenomenon. This article offers a novel framework to understand how business organizations construct the meaning of compliance with the UK Modern Slavery Act. Our analysis builds on the endogeneity of law theory developed by Edelman. Empirically, our study is based on the analysis of the modern slavery statements of 10 FTSE 100 (Financial Times Stock Exchange 100 Index) companies (...) in the food and tobacco sector, backed by interviews with business, civil society, and public officers. We offer a dynamic model that draws attention to the role of compliance professionals in framing ambiguous rules and devising a variety of organizational responses to modern slavery law. Contrary to extant research that tends to praise organizations for going “beyond compliance”, our study underlines the risks of managerialization of modern slavery law, whereby merely symbolic structures come to be associated with legal compliance, even when they are ineffective at tackling modern slavery. (shrink)

Temporal discounting is the tendency to devalue temporally distant rewards. Past studies have examined the k-value, the indifference point, and the area under the curve as dependent measures on this task. The current study included these three measures and a fourth measure, called the interest rate total score. The interest rate total score was based on scoring only those items in which the delayed choice should be preferred given the expected return based on simple interest rates. In addition, associations with (...) several individual difference measures were examined including intelligence, executive functions (inhibition, working memory, and set-shifting), thinking dispositions (Need for Cognition and Consideration of Future Consequences) and engagement in substance use and gambling behavior. A staircase temporal discounting task was examined in a sample of 99 university students. Replicating previous studies, temporal discounting increased with longer delays to reward and decreased with higher reward magnitudes. A hyperbolic function accounted for variance in temporal discounting better than an exponential function. Reaction time at the indifference point was significantly longer than at the other choice points. The four dependent measures of temporal discounting were all significantly correlated and were also significantly associated with our individual difference measures. That is, the tendency to wait for a larger delayed reward on all of the temporal discounting measures was associated with higher intelligence, higher executive functions and more consideration of future consequences. Associations between our measures of temporal discounting and outcomes related to substance use and gambling behavior were modest in our university sample. (shrink)

The article argues that there are different ways of justifying suspension of judgement. We suspend judgement not only privatively, that is, because we lack evidence, but also positively, that is, because there is evidence that provides reasons for suspending judgement: suspension is more than the rational fallback position in cases of insufficient evidence. The article applies the distinction to recent discussions about the role of suspension for inquiry, Turri's puzzle about withholding, and formal representations of suspension.

This article explores the politics of digital protest and emergent forms of sociality in the #NoDAPL movement using Elizabeth Povinelli’s concept of geontopower. I begin by situating the concept of geontopower in relation to a range of biopolitical, decolonial, and ecocritical theory in order to show its importance in conceptualizing the interconnectedness of decolonial and environmental interests. I use this theoretical framework to analyze several instances of what I call ‘digital decoloniality’ in the #NoDAPL movement, cases where the particular affordances (...) of social media technologies and the efforts of Indigenous activists and non-Indigenous allies disrupted normative assumptions regarding the boundaries of the digital and ‘analog’ worlds and resisted the geontopolitical structuring of life and nonlife. I argue that the #NoDAPL hashtag works to enact the prerogatives of Western science-based environmentalism and Indigenous epistemological tenets in common, performatively generating new possibilities for conceptualizing social struggle and shared history. (shrink)

In this paper, I provide an account of the wrong that is done to women when everyday people fail to believe allegations of sexual assault made by women. I argue that an everyday person wrongs both the accuser and women causally distant from the accuser when they fail to believe the accuser’s allegation. First, I argue that there are responses that we, as everyday members of society, owe to victims of sexual assault. A condition enabling everyday people to respond in (...) the way owed to victims is that they have an outright belief that the accuser was assaulted. Actively suspending judgement about whether a crime occurred is in tension with the ability to respond to the victim in a way that supports and validates them. When an everyday person fails to have an outright belief in the truth of an allegation, they wrong the accuser because they risk failing to satisfy the conditions enabling them to fulfill their obligation to her. Second, I argue that everyday people wrong women who are causally distant from the accuser because in our social context, women are often treated in particular ways – especially in the sexual domain – because they are women. As a result, when women hear that an everyday person fails to believe a particular allegation, they easily project themselves into the accuser’s position and reasonably worry that if they were to be assaulted, they too would be met with doubt and disbelief by the people in their community. (shrink)

The aim of this paper is to propose a systematic classification of emotions which can also characterize their nature. The first challenge we address is the submission of clear criteria for a theory of emotions that determine which mental phenomena are emotions and which are not. We suggest that emotions as a subclass of mental states are determined by their functional roles. The second and main challenge is the presentation of a classification and theory of emotions that can account for (...) all existing varieties. We argue that we must classify emotions according to four developmental stages: 1. pre-emotions as unfocussed expressive emotion states, 2. basic emotions, 3. primary cognitive emotions, and 4. secondary cognitive emotions. We suggest four types of basic emotions (fear, anger, joy and sadness) which are systematically differentiated into a diversity of more complex emotions during emotional development. The classification distinguishes between basic and non-basic emotions and our multi-factorial account considers cognitive, experiential, physiological and behavioral parameters as relevant for constituting an emotion. However, each emotion type is constituted by a typical pattern according to which some features may be more significant than others. Emotions differ strongly where these patterns of features are concerned, while their essential functional roles are the same. We argue that emotions form a unified ontological category that is coherent and can be well defined by their characteristic functional roles. Our account of emotions is supported by data from developmental psychology, neurobiology, evolutionary biology and sociology. (shrink)

I will discuss the relationship between two different accounts of remedial duty ascriptions. According to one account, the beneficiary account, individuals who benefit innocently from injustices ought to bear remedial responsibilities towards the victims of these injustices. According to another account, the causal account, individuals who caused injustices ought to bear remedial duties towards the victim. In this paper, I examine the relation between the principles central to these accounts: the Beneficiary Pays Principle and the well-established principle of Strict Liability (...) in law. I argue that both principles display a strong yet unexplored similarity as they make certain kinds of causal connection sufficient for incurring liability. Because of this similarity, I suggest that insights into the Beneficiary Pays Principle can be gained from exploring its relation with Strict Liability. In particular, I examine two new positive arguments that could be adapted to support of the Beneficiary Pays Principle: the Minimising Injustice Argument and the Normative Connection Argument. However, I’ll show that only one of those arguments, namely the Normative Connection Argument, can truly support the Beneficiary Pays Principle. I conclude that, if you endorse the Normative Connection Argument for Strict Liability, you have at least a strong prima facie reason to endorse the parallel argument for the Beneficiary Pays Principle. (shrink)

A standard view in philosophy is that knowledge entails justification. Yet recent research suggests otherwise. We argue that this admirable and striking research suffers from an important limitation: participants were asked about knowledge but not justification. Thus it is possible that people attributed knowledge partly because they thought the belief was justified. Perhaps though, if given the opportunity, people would deny justification while still attributing knowledge. It is also possible that earlier findings were due to perspective taking. This paper reports (...) further research that directly addresses these questions. Our findings support the hypothesis that knowledge entails justification on the ordinary view. (shrink)

I will argue here a) that we have a right to have opportunities to meaningful relationships, b) that such a right is distinct from a right focusing only on protecting access to more basic social interactions, and c) that to the extent that we have rights to both kinds of social interactions, the one focused on more meaningful relationships should have priority because it secures an interest of greater importance for us.

Is there anything wrong with publishing philosophical work which one does not believe (publishing without belief, henceforth referred to as ‘PWB’)? I argue that there is not: the practice isn’t intrinsically wrong, nor is there a compelling consequentialist argument against it. Therefore, the philosophical community should neither proscribe nor sanction it. The paper proceeds as follows. First, I’ll clarify and motivate the problem, using both hypothetical examples and a recent real-world case. Next, I’ll look at arguments that there is something (...) wrong with PWB, and show that none is sound. Then, I’ll give some reasons for thinking a norm against PWB is detrimental to the profession. Do I believe these arguments? If I’m right, it shouldn’t matter. (shrink)

Les approches classiques de l'engagement se sont principalement intéressées à ses déterminants, rapportés à des variables sociodémographiques, des dispositions, des vertus ou des rétributions, comme à autant de motifs déjà constitués en amont et extrinsèques à l'expérience de l'engagement. Or, les intérêts des personnes - et leur puissance d'agir elle-même - peuvent s'analyser comme des produits de l'engagement, pour peu qu'on le saisisse dans sa dimension temporelle, itérative et située. Envisagé comme expérience, il paraît indissociable d'une enquête menée à la (...) fois sur soi et sur le monde, où les personnes interrogent autant leurs propres désirs et possibilités d'agir, que la vie commune qu'elles souhaitent cultiver ou voir advenir. Ce volume rassemble une série de contributions théoriques et empiriques qui explorent des façons d'articuler souci de soi et souci du monde. Elles documentent la façon dont les engagements circulent entre différentes sphères de la vie et entre moments biographiques, en suivant les formes d'expérimentation auxquelles ils donnent lieu. Notre compréhension du rapport au politique s'en trouve enrichie, ressaisie depuis la trame des expériences de la vie commune faites en personne"--Page 4 of cover. (shrink)

Cet article a déjà paru dans Techniques & Culture en ligne, 48-49 | 2007 Résumé : L'œuvre d'André Leroi-Gourhan est traversée par une anthropologie du rythme. Celle-ci ne part pas d'une socialité constituée, de rythmes dits « sociaux », mais inscrit au contraire l'analyse de la rythmicité dans une approche de l'homme comme être vivant, comme totalité indivise. Elle pose en des termes renouvelés le problème classique du groupement des hommes et des liens entre l'individu et son milieu. Avec la (...) question - Anthropologie. (shrink)

Eighteenth-Century Stoic Poetics: Shaftesbury, Akenside, and the Discipline of the Imagination offers a fresh perspective on the eighteenth-century poetics of Lord Shaftesbury and Mark Akenside. This book traces the two authors' debt to Roman Stoic spiritual exercises and early modern conceptions of the care of the self, which informs their view of the poetic imagination as a bundle of techniques designed to manage impressions, cultivate right images in the mind and rectify judgement. Alexandra Bacalu traces the roots of this (...) articulation in early modern writings on the imagination, as well as in Restoration and Augustan debates on wit, exploring the fruitful tension between ideas of imaginative enthusiasm and imaginative regulation that it provokes. (shrink)

It is frequently claimed that the human mind is organized in a modular fashion, a hypothesis linked historically, though not inevitably, to the claim that many aspects of the human mind are innately specified. A specific instance of this line of thought is the proposal of an innately specified geometric module for human reorientation. From a massive modularity position, the reorientation module would be one of a large number that organized the mind. From the core knowledge position, the reorientation module (...) is one of five innate and encapsulated modules that can later be supplemented by use of human language. In this paper, we marshall five lines of evidence that cast doubt on the geometric module hypothesis, unfolded in a series of reasons: (1) Language does not play a necessary role in the integration of feature and geometric cues, although it can be helpful. (2) A model of reorientation requires flexibility to explain variable phenomena. (3) Experience matters over short and long periods. (4) Features are used for true reorientation. (5) The nature of geometric information is not as yet clearly specified. In the final section, we review recent theoretical approaches to the known reorientation phenomena. (shrink)

Every language has a way of talking about seeing, hearing, smelling, tasting and touching. This can be done through lexical means, and through grammatical evidentials. The studies presented here focus on the experssions of perception and cognition in languages of Africa, Oceania, and South America.

Previous research suggested a role of gaze in preference formation, not merely as an expression of preference, but also as a causal influence. According to the gaze cascade hypothesis, the longer subjects look at an item, the more likely they are to develop a preference for it. However, to date the connection between viewing and liking has been investigated predominately with self-paced viewing conditions in which the subjects were required to select certain items from simultaneously presented stimuli on the basis (...) of perceived visual attractiveness. Such conditions might promote a default, but non-mandatory connection between viewing and liking. To explore whether the connection is separable, we examined the evaluative processing of single naturalistic food images in a 2 x 2 design, conducted completely within subjects, in which we varied both the type of exposure (self-paced versus time-controlled) and the type of evaluation (non-exclusive versus exclusive). In the self-paced exclusive evaluation, longer viewing was associated with a higher likelihood of a positive evaluation. However, in the self-paced non-exclusive evaluation, the trend reversed such that longer viewing durations were associated with lesser ratings. Furthermore, in the time-controlled tasks, both with non-exclusive and exclusive evaluation, there was no significant relationship between the viewing duration and the evaluation. The overall pattern of results was consistent for viewing times measured in terms of exposure duration (i.e., the duration of stimulus presentation on the screen) and in terms of actual gaze duration (i.e., the amount of time the subject effectively gazed at the stimulus on the screen). The data indicated that viewing does not intrinsically lead to a higher evaluation when evaluating single food images; instead, the relationship between viewing duration and evaluation depends on the type of task. We suggest that self-determination of exposure duration may be a prerequisite for any influence from viewing time on evaluative processing, regardless of whether the influence is facilitative. Moreover, the purported facilitative link between viewing and liking appears to be limited to exclusive evaluation, when only a restricted number of items can be included in a chosen set. (shrink)

ICTs, personal data, digital rights, the GDPR, data privacy, online security… these terms, and the concepts behind them, are increasingly common in our lives. Some of us may be familiar with them, but others are less aware of the growing role of ICTs and data in our lives - and the potential risks this creates. These risks are even more pronounced for vulnerable groups in society. People can be vulnerable in different, often overlapping, ways, which place them at a disadvantage (...) to the majority of citizens; Table 3 in this guide presents some of the many forms and causes of vulnerability. As a result, vulnerable people need greater support to navigate the digital world, and to ensure that they are able to exercise their rights. This guide explains where such support can be found, and also answers the following questions: - What are the main ethical and legal issues around ICTs for vulnerable citizens? - Who is vulnerable in Europe? - How do issues around ICTs affect vulnerable people in particular? This guide is a resource for members of vulnerable groups, people who work with vulnerable groups, and citizens more broadly. It is also useful for data controllers1 who collect data about vulnerable citizens. While focused on citizens in Europe, it may be of interest to people in other parts of the world. It forms part of the Citizens’ Information Pack produced by the PANELFIT project, and is available in English, French, German, Italian and Spanish. You are welcome to translate this guide into other languages. Please send us a link to online versions in other languages, so that we can add them to the project website. (shrink)

Since the early 80s, metonymy has progressively gained central stage in linguistic investigations. The advent of cognitive linguistics marked a new turn in the study of this trope conceived, not as a deviation from semantic conventions (contra classical rhetorical theories), but as a phenomenon rooted in non-language-specific mechanisms of conceptualization and structuring of the world. Focusing on the particular case of whole-for-part (WP) metonymy, the general stand of this presentation will be to argue for the need to re-inject properly semantic (...) (descriptive and formal) considerations in the study of metonymy. It will be shown that semantic typologies of meronymic relations, as well as recent results in the semantics of partial predicates and colour predicates, can be jointly exploited to attain a better understanding of the mechanism of WP-metonymy. The resulting view will in particular connect such metonymies to mechanisms of reference and property attribution to functional parts for classificatory purposes. (shrink)

Recent empirical studies have established that disgust plays a role in moral judgment. The normative significance of this discovery remains an object of philosophical contention, however; ‘disgust skeptics’ such as Martha Nussbaum have argued that disgust is a distorting influence on moral judgment and has no legitimate role to play in assessments of moral wrongness. I argue, pace Nussbaum, that disgust’s role in the moral domain parallels its role in the physical domain. Just as physical disgust tracks physical contamination and (...) pollution, so moral disgust tracks social contamination. I begin by examining the arguments for skepticism about disgust and show that these arguments threaten to overgeneralize and lead to a widespread skepticism about the justifiability of our moral judgments. I then look at the positive arguments for according disgust a role in moral judgment, and suggest that disgust tracks invisible social contagions in much the same way as it tracks invisible physical contagions, thereby serving as a defense against the threat of socio-moral contamination. (shrink)