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)

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)

Au tournant des années 1820-1830, Schelling découvre au sein de la philosophie deux grandes tendances à l'oeuvre : une tendance "négative" à rendre intelligible le réel en fonction de la nécessité des lois de la pensée, une tendance "positive" à y voir au contraire le fait d'un acte libre. Scrutant cette différence, il finit par montrer qu'elle implique de scinder la philosophie même en une philosophie qui fait intervenir uniquement la raison et une philosophie où la raison se laisse instruire (...) par l'expérience. Le présent livre propose une interprétation nouvelle de ce moment crucial mais méconnu de la pensée moderne où Schelling accomplit, tout en le dépassant, l'idéalisme allemand. On y montre qu'il suspend l'avenir de la raison à un dédoublement de la philosophie qui implique de confier la réalisation des deux philosophies à un rationalisme et à un empirisme totalement inédits. Dans le rationalisme, la raison opère seule jusqu'à produire l'idée d'un principe absolu libre de poser le monde ; dans l'empirisme, elle prouve l'existence du principe par ses oeuvres effectives que sont successivement les faits de la nature et ceux de la conscience comme conscience religieuse. Ainsi, loin de produire le désespoir de la raison, Schelling montre au contraire que la raison se donne à elle-même un avenir en se différenciant. (shrink)

In metaethics, empirical approaches are not just complementary to, but continuous with, traditional approaches to the subject. This chapter addresses traditional and empirical approaches to metaethics. It discusses how empirical approaches have been brought to bear on some central metaethical questions. The chapter illustrates not just the diversity of topics within metaethics itself but also the diversity of empirical methods and approaches that philosophers and psychologists working on these topics are using. The debate between internalists and externalists is a debate (...) concerning the psychology of moral judgment, but also a debate about our concept of moral judgment. As such, it has implications for other metaethical debates. Antirealists such as relativists and noncognitivists often defend internalism, and argue that their views are best equipped to explain the link between moral judgment and motivation. (shrink)

Arts-Based Thought Experiments is a highly visual offering that engages visual arts, photography, poetry, creative non-fiction, memoir and speculative fiction. In this novel book, the authors lean deeply into concepts of the imaginary, and through artful experiments with thought, trouble the tensions between the human, the posthuman and the more than human. In the Anthropocene, with its intractable challenges and cataclysms, engaging posthuman positions when thinking of learning in socioecological terms is paramount to human survival. In this sense, the arts (...) offer creative and critical thought for the possibilities of a post-Anthropocene earth. Contributors are: Raoul Adam, Marilyn Ahearn, William Boyd, Euan Boyd, Adrienne Brown, Shae L. Brown, Teresa Carapeto, Philemon Chigeza, Amy Cutter-Mackenzie-Knowles, David Ellis, Katie Hotko, Marianne Logan, Ferdousi Khatun, Alexandra Lasczik, Yaw Ofosu-Asare, Maia Osborn, Marie-Laurence Paquette, Jemma Peisker, Ziah Peisker, Adrienne Piscopo, David Rousell, Benjamin Ryan, Billy Ryan, Lisa Siegal, Helen Widdop Quinton, Thilinika Wijesinghe and Tracy Young. (shrink)

In April 2017, scientists took to the streets in a historically unprecedented Global March for Science. The event was seen as symbolic of a crisis in the relationship of science and society. This book considers the Global March for Science from a postcolonial perspective to inquire into the toolkit that the academic field of Science & Technology Studies (STS) has to offer. It argues that new concepts and analytical approaches are necessary to investigate current global dynamics in science, technology and (...) society, so as to deliver insights that the recent expansion of STS scholars beyond Western Europe and North America alone is unlikely to provide. The book presents a Programme in Science Studies Elsewhere (SSE) to demonstrate the urgent need to carry postcolonial issues right into the centre of STS's intellectual programme. (shrink)

This book examines the conceptual and temporal frames through which modern Western historiography has linked itself to classical antiquity. In doing so, it articulates a genealogical problematic of what history is and a more strictly focused reappraisal of Greek and Roman historical thought. Ancient ideas of history have played a key role in modern debates about history writing, from Kant through Hegel to Nietzsche and Heidegger, and from Friedrich Creuzer through George Grote and Theodor Mommsen to Momigliano and Moses Finley; (...) yet scholarship has paid little attention to the theoretical implications of the reception of these ideas. The essays in this collection cover a wide range of relevant topics and approaches and boast distinguished authors from across Europe in the fields of classics, ancient and modern history and the theory of historiography. (shrink)

On range généralement la pensée de Malebranche parmi celles qui incarnent ce moment de l'histoire de la philosophie qu'on nomme "rationalisme". En prenant son départ dans l'interprétation que Schelling a produite de la "Vision en Dieu", cet ouvrage se propose de l'aborder plutôt comme un idéalisme issu du dogmatisme et enclin à suspendre l'existence des corps : pour avoir élargi le cercle de la pensée humaine aux dimensions du cercle de l'idée divine, Malebranche ferait dépendre la perception sensible de l'action (...) de Dieu seul, anticipant par-là la pensée de Berkeley. Sans doute une telle lecture dépend-elle de la manière dont Schelling a lui-même renouvelé l'idéalisme ; sans doute est-elle aussi tributaire d'une certaine réception de Malebranche. Pour autant, du point de vue qui fut celui de Malebranche, elle mérite qu'on la mette à l'épreuve de ses textes et de ses intentions. Aussi, après avoir montré comment Schelling se place devant Malebranche, on le fait comparaître devant ce que Malebranche pourrait lui opposer. Il apparaît alors que ce dernier s'attache à desserrer l'étreinte que le cercle de l'idée exerce sur son système : en faisant le pari de prouver l'existence d'un monde résolument distinct du monde intelligible, Malebranche oeuvre en effet pour un idéalisme ouvert au réalisme sans jamais renoncer à la "Vision en Dieu"."--Page 4 of cover. (shrink)

"L'idée de cet ouvrage prend sa source dans un texte du tout dernier Schelling, extrait de l'Exposé de la philosophie rationnelle pure, professé à Berlin dans les années 1847-1852 et publié ensuite par le fils de Schelling dans un ensemble plus vaste, l'Introduction à la Philosophie de la mythologie."--Prologue, p. [7].

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.

A professora Pórcia Guimarães Alves teve formação educacional diferenciada e, concluindo o ensino superior, continuou sua formação com cursos e encontros científicos no Brasil e em outros países. Durante as viagens, trocava missivas com seus familiares, que foram mantidas em arquivo pessoal em plástico denominado “Cartas enviadas ao meu pai”. Procurou-se analisar: qual a escrita de si de Pórcia contida nas cartas trocadas com seus familiares entre 1946 e 1958? Listaram-se os objetivos específicos: mapear os familiares mencionados nas cartas; analisar (...) a materialidade do suporte epistolar procurando aspectos subjetivos em seus registros autobiográficos; e identificar temas narrados nessa escrita. (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)

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)

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)

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)

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)

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)

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)

Self-transcendence has been characterized as a decrease in self-saliency (ego disillusionment) and increased connection, and has been growing in research interest in the past decade. Several measures have been developed and published with some degree of psychometric validity and reliability. However, to date, there has been no review systematically describing, contrasting, and evaluating the different methodological approaches toward measuring self-transcendence including questionnaires, neurological and physiological measures, and qualitative methods. To address this gap, we conducted a review to describe existing methods (...) of measuring self-transcendence, evaluate the strengths and weaknesses of these methods, and discuss research avenues to advance assessment of self-transcendence, including recommendations for suitability of methods given research contexts. (shrink)

Tales of saints, whether told by their adherents or detractors, frequently featured the holy persons dealings with members of other religions or cultures, or the stories themselves were appropriated by different religious or cultural groups. As such narratives moved from one social, cultural, religious or chronological milieu to another, the representation and meaning of the given holy person and the manner of his/her dealing with the religious other also often changed. As basic storylines remained recognizable, the transformations of specific details (...) often provide important clues about shifts in attitudes over time and between communities. This volume provides a varied array of case studies of this process, ranging from early China to various Christian, Muslim and Jewish cultural contexts in the late antique, medieval and early modern periods. (shrink)