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)

Renewing the deontology tradition of moral obligation requires, especially in relation to catastrophe and disaster, a broader methodological perspective which would enable deontology to transcend its own limits. The demand for pluralistic research approaches brings with challenging requirements that have to be considered when shaping a hybrid moral theory that incorporates a proactive approach. The personalist approach to the individual, based on the principles of integrity, responsibility and solidarity and seeking the wellbeing of a person, may prove inspirational in shaping (...) such a proactive approach. (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.

In the United States today, the human body defines a lucrative site of reusable parts, ranging from whole organs to minuscule and even microscopic tissues. Although the medical practices that enable the transfer of parts from one body to another most certainly relieve suffering and extend lives, they have also irrevocably altered perceptions of the cultural values assigned to the body. Organ transfer is rich terrain to investigate—especially in the American context, where sophisticated technological interventions have significantly shaped understandings of (...) health and well-being, suffering, and death. In _Bodies, Commodities, and Biotechnologies_, Lesley Sharp probes the ideological assumptions underlying the transfer of body parts, the social significance of donors' deaths, and the medico-scientific desires surrounding complex forms of body repair. Sharp also considers the experimental realm, in which nonhuman species and artificial devices present further opportunities for recovery and for controversy. A compelling scientific investigation and social critique, _Bodies, Commodities, and Biotechnologies_ explores the pervasive, and at times pernicious, practices shaping American biomedicine in the twenty-first century. (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)

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.

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)

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)

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)

In the United States today, the human body defines a lucrative site of reusable parts, ranging from whole organs to minuscule and even microscopic tissues. Although the medical practices that enable the transfer of parts from one body to another most certainly relieve suffering and extend lives, they have also irrevocably altered perceptions of the cultural values assigned to the body. Organ transfer is rich terrain to investigate—especially in the American context, where sophisticated technological interventions have significantly shaped understandings of (...) health and well-being, suffering, and death. In _Bodies, Commodities, and Biotechnologies_, Lesley Sharp probes the ideological assumptions underlying the transfer of body parts, the social significance of donors' deaths, and the medico-scientific desires surrounding complex forms of body repair. Sharp also considers the experimental realm, in which nonhuman species and artificial devices present further opportunities for recovery and for controversy. A compelling scientific investigation and social critique, _Bodies, Commodities, and Biotechnologies_ explores the pervasive, and at times pernicious, practices shaping American biomedicine in the twenty-first century. (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)

Empowerment, an already central concept in public health, has gained additional relevance through the expansion of mobile health (mHealth). Especially direct-to-consumer self-testing app companies mobilise the term to advertise their products, which allow users to self-test for various medical conditions independent of healthcare professionals. This article first demonstrates the absence of empowerment conceptualisations in the context of self-testing apps by engaging with empowerment literature. It then contrasts the service these apps provide with two widely cited empowerment definitions by the WHO, (...) which describe the term as a process that, broadly, leads to knowledge and control of health decisions. We conclude that self-testing apps can only partly empower their users, as they, we argue, do not provide the type of knowledge and control the WHO definitions describe. More importantly, we observe that this shortcoming stems from the fact that in the literature on mHealth and in self-testing marketing, empowerment is understood as a goal rather than a process. This characterises a shift in the meaning of empowerment in the context of self-testing and mHealth, one that reveals a lack of awareness for relational and contextual factors that contribute to empowerment. We argue that returning to a process-understanding of empowerment helps to identify these apps’ deficits, and we conclude the article by briefly suggesting several strategies to increase self-testing apps’ empowerment function. (shrink)

The development of empathy is central to positive social adjustment. However, issues remain with integrating empathy research conducted with children, adolescents, and adults. The current article (...

Regulatory agencies vary widely in their classification of FMT, with significant impact on patient access. This article conducts a global survey of national regulations and collates existing FMT classification statuses, ultimately suggesting that the human cell and tissue product designation best fits FMT's characteristics and that definitional objectives to that classification may be overcome.

Empathy is an extensively studied construct, but operationalization of effective empathy is routinely debated in popular culture, theory, and empirical research. This article offers a process-focused approach emphasizing the relational functions of empathy in interpersonal contexts. We argue that this perspective offers advantages over more traditional conceptualizations that focus on primarily intrapsychic features. Our aim is to enrich current conceptualizations and empirical approaches to the study of empathy by drawing on psychological, philosophical, medical, linguistic, and anthropological perspectives. In doing so, (...) we highlight the various functions of empathy in social interaction, underscore some underemphasized components in empirical studies of empathy, and make recommendations for future research on this important area in the study of emotion. (shrink)

Contrary to the contemporary view that negation is a logical operation that modifies the mere content of a thought or judgment, but not the act of thinking or judging it, Kant maintains that negation is an act of logical apperception through which I exclude a thought or judgment from what ‘I think.’ In this paper, I argue against two interpretations of Kant’s account of logical negation. According to the first, negation is a subjective psychological act of excluding an erroneous judgment. (...) Against this, I will show that for Kant, negation is an operation of logical, not empirical apperception. The second interpretation views logical negation as an objective representation either of a relation of opposition or of non-being. I argue that, on the contrary, the logical function of negation is merely formal, not material, and therefore does not have semantic content. The paper’s final section develops a positive conception of logical negation as a formal function of judging. (shrink)

ABSTRACTResearch on bilingualism and emotions has shown stronger emotional responses in the native language compared to a foreign language. We investigated the potential of purposeful second language use as a means of decreasing the experience of psychological distress. Native Swedish speakers read and answered questions about negative and neutral texts in their L1 and their L2 and were asked to rate their level of distress before or after the questions. The texts and associated questions were either written in the same, (...) or different languages. We found that within-language trials when the text was written in participants’ native language resulted in an increase of distress, whilst cross-language trials resulted in a decrease of distress. This implies that purposeful second language use can diminish levels of distress experienced following a negative event encoded in one's first language. (shrink)

This paper offers a defense of ‘publishing without belief’ (PWB) – the view that authors are not required to believe what they publish. I address objections to the view ranging from outright denial and advocacy of a belief norm for publication, to a modified version that allows for some cases of PWB but not others. I reject these modifications. In doing so, I offer both an alternative story about the motivations for PWB and a diagnosis of the disagreement over its (...) permissibility. The original defense focused on consequentialist reasons for allowing PWB, offering mostly defensive arguments against potential criticisms. But I argue that once we shift our focus to the reasons why authors might be prone to PWB, we see a difference in two types of motivation: whereas I imagine PWB as arising from underconfident agents, critics point to cagey or nefarious authorial practices, or authors’ failure to clarify their own degrees of belief. Underlying the debate over norms of philosophical publishing, we find two different conceptions of philosophy itself. (shrink)

Democracy and the Divine articulates a democracy that is based on the principle of giving oneself to another. For this project, the author highlights two traditions that rarely have been read side by side or considered seminal to the philosophical idea of democracy: nineteenth-century German romanticism and French postmodernism.

_ Source: _Volume 25, Issue 2, pp 232 - 255 In Book III of _The Star of Redemption_, Franz Rosenzweig contrasts Judaism and Christianity: Judaism consists in the eternal passage of a people from creation to revelation; it suspends the divide between God’s presence and his worldly manifestation. For Rosenzweig, being Jewish means to be with God in the world. Christianity, however, defers salvation. While Judaism is with God in the world, Christianity retreats from God and the world. Christianity therefore (...) has no “immediacy.” How can both Judaism and Christianity then live in immediacy with God in the world? Seeking to overcome Rosenzweig’s dichotomy, I endeavor to think an immediate relationship with God in the world by turning to one of Rosenzweig’s “biggest names”: Hermann Cohen. Following Cohen, I take it that Judeo-Christian continuity begins before both religions. I wish to explore the passage from the origin to the prophetic that constitutes the idea of a “pure monotheism” in Cohen’s philosophy. (shrink)

This book focuses on how gender in its many guises - Linguistic, Natural, Social - is reflected in human languages, how it features in myths and metaphors, and the role it plays in human cognition. Examples are drawn from all over the world, with a special focus on Aikhenvald's extensive fieldwork in Amazonia and New Guinea.

ABSTRACT This study investigated the effect of conspiracy ideation, moral disengagement, and intolerance of uncertainty on compliance with the anti-SARS-COV-2 social distancing rules and two other facets of people’s reactions toward the coronavirus crisis. A convenience sample of 245 Romanians completed an online survey in March 2020. Results indicate that conspiracy ideation is associated with lower assessments of virus risk and lower compliance with the confinement measures. Moral disengagement had a parallel effect of undermining personal compliance to the social distancing (...) regulations, highlighting the need to define social distancing as morally relevant and prevent individual justifications for noncompliance. (shrink)

I strongly agree with the criticisms of the restrictive isomorphic matching definition of empathy made by Murphy, Lilienfeld, and Algoe, and largely agree with their conceptualization of empathy as a dynamic process best defined by its function. In this commentary, I extend this argument by emphasizing the relational, interpersonal aspects of empathy. It is my view that in order to understand the functions of empathy, we must take into account not only the internal experience of the individual empathizing, but also (...) the individual whose perspective the empathizer is attempting to take. I highlight how the emotional needs of others are dynamic and require flexible adaptation and underscore the role of context in appreciating the function of empathy. (shrink)

The philosophical debate over disgust and its role in moral discourse has focused on disgust’s epistemic status: can disgust justify judgments of moral wrongness? Or is it misplaced in the moral domain—irrelevant at best, positively distorting at worst? Correspondingly, empirical research into disgust has focused on its role as a cause or amplifier of moral judgment, seeking to establish how and when disgust either causes us to morally condemn actions, or strengthens our pre-existing tendencies to condemn certain actions. Both of (...) these approaches to disgust are based on a set of assumptions that I call, in what follows, the evidential model of disgust. This paper proposes an alternative model, which I call the response model. Instead of looking at disgust as a cause and justification of judgments of moral wrongness, I will argue that disgust is better understood as a response to wrongness. More precisely, I argue that disgust is a response to norm violations, and that it is a fitting response insofar as norm violations are potentially contagious and therefore pose a threat to the stability and maintenance of norms. (shrink)

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)

Perceptual learning involves an improvement in perceptual judgment with practice, which is often specific to stimulus or task factors. Perceptual learning has been shown on a range of visual tasks but very little research has explored chromatic perceptual learning. Here, we use two low level perceptual threshold tasks and a supra-threshold target detection task to assess chromatic perceptual learning and category effects. Experiment 1 investigates whether chromatic thresholds reduce as a result of training and at what level of analysis learning (...) effects occur. Experiment 2 explores the effect of category training on chromatic thresholds, whether training of this nature is category specific and whether it can induce categorical responding. Experiment 3 investigates the effect of category training on a higher level, lateralized target detection task, previously found to be sensitive to category effects. The findings indicate that performance on a perceptual threshold task improves following training but improvements do not transfer across retinal location or hue. Therefore, chromatic perceptual learning is category specific and can occur at relatively early stages of visual analysis. Additionally, category training does not induce category effects on a low level perceptual threshold task, as indicated by comparable discrimination thresholds at the newly learned hue boundary and adjacent test points. However, category training does induce category effects on a supra-threshold target detection task. Whilst chromatic perceptual learning is possible, learnt category effects appear to be a product of left hemisphere processing, and may require the input of higher level linguistic coding processes in order to manifest. (shrink)