Let T be a complete o-minimal extension of the theory of real closed fields. We characterize the convex hulls of elementary substructures of models of T and show that the residue field of such a convex hull has a natural expansion to a model of T. We give a quantifier elimination relative to T for the theory of pairs (R, V) where $\mathscr{R} \models T$ and V ≠ R is the convex hull of an elementary substructure of R. We deduce (...) that the theory of such pairs is complete and weakly o-minimal. We also give a quantifier elimination relative to T for the theory of pairs (R, N) with R a model of T and N a proper elementary substructure that is Dedekind complete in R. We deduce that the theory of such "tame" pairs is complete. (shrink)

I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular,Twill denote a completeo-minimal theory extending RCF, the theory of real closed fields. Let (,V) ⊨Tconvex, let=V/m(V)be the residue field, with residue class mapx↦:V↦, and let υ:→ Γ be the associated valuation. “Definable” will mean “definable with parameters”.The main goal of this article is to determine the structure induced by(,V)on its residue fieldand on its (...) value group Γ. In [9] we expanded the ordered fieldto a model ofTas follows. Take a tame elementary substructure′ ofsuch thatR′ ⊆VandR′maps bijectively ontounder the residue class map, and make this bijection into an isomorphism′ ≌ofT-models. (We showed such′ exists, and that this gives an expansion ofto aT-model that is independent of the choice of′.). (shrink)

I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular,Twill denote a completeo-minimal theory extending RCF, the theory of real closed fields. Let (,V) ⊨Tconvex, let=V/m(V)be the residue field, with residue class mapx↦:V↦, and let υ:→ Γ be the associated valuation. “Definable” will mean “definable with parameters”.The main goal of this article is to determine the structure induced by(,V)on its residue fieldand on its (...) value group Γ. In [9] we expanded the ordered fieldto a model ofTas follows. Take a tame elementary substructure′ ofsuch thatR′ ⊆VandR′maps bijectively ontounder the residue class map, and make this bijection into an isomorphism′ ≌ofT-models. (We showed such′ exists, and that this gives an expansion ofto aT-model that is independent of the choice of′.). (shrink)

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of “logarithmic-exponential series” , which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert operators to show that each LE-series has a formal integral. We give evidence for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields. We define (...) composition of LE-series and establish its basic properties, including the existence of compositional inverses. Various interesting subfields of the field of LE-series are also considered. (shrink)

The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

Van den Dries, L. and J. Holly, Quantifier elimination for modules with scalar variables, Annals of Pure and Applied Logic 57 161–179. We consider modules as two-sorted structures with scalar variables ranging over the ring. We show that each formula in which all scalar variables are free is equivalent to a formula of a very simple form, uniformly and effectively for all torsion-free modules over gcd domains . For the case of Presburger arithmetic with scalar variables the result takes (...) a still simpler form, and we derive in this way the polynomial-time decidability of the sets defined by such formulas. (shrink)

Related Works: Original Paper: Lou Van Den Dries. $T$-Convexity and Tame Extensions II. J. Symbolic Logic, Volume 62, Issue 1 , 14--34. Project Euclid: euclid.jsl/1183745182.

For any group satisfying a suitable chain condition, we construct a finitely additive measure on it that is invariant under certain actions.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

In lieu of an abstract, here is a brief excerpt of the content:BreathingLuk Van den Dries (bio)This text, "Breathing," was conceived for the book From Act to Acting: Fabre's Guidelines for the Performer of the 21st Century (2021). The book was conceived and designed by Jan Fabre, author, theatre artist, and visual artist, active since the 1970s. The book was written by Luk Van den Dries, dramaturg and theatre researcher of the University of Antwerp, in tight collaboration with (...) Jan Fabre and the three most important performers/teachers of the Belgian theatre company, Troubleyn (Annabelle Chambon, Cédric Charron, and Ivana Jozic). The book sheds new light on the physical, mental, and vocal training of the performer and furthermore gives insight into Fabre's revolutionary thoughts on contemporary theatre.1Breathing is the first of the ten performative principles that together create the basic grammar in which the language of the performers is grounded.Three-phased breathing (one part in, one part out, one part nothing) is a basic condition in the series of exercises Jan Fabre developed throughout his career. This respiration technique returns in all exercises. Also, it is the first principle that the performers are taught: by dividing breathing into three equal parts, energy is built up and stress or fatigue is canalized. It is a way to rebalance, to find a place of rest after a strenuous effort, or it can also be used as a springboard to a heightened performance. Very regularly during individual exercises, Fabre will refer to this respiration technique, especially in specific situations of high adrenaline, but of course the performers should learn to use this respiration technique autonomously. They should become so familiar with the rhythm of this breathing that they automatically fall back on it when necessary. Because this respiration technique is so crucial to Fabre's acting pedagogy, it is described in detail as the very first exercise in his book. Its basic principles are explained below as well, as the first performative principle.Breathing is a sign of life, and on this primal and essential level it needs to be understood that, through breathing, the performer gives life. He breathes life into the performance. Fabre himself has described this basic condition for the birth of theatre through breathing very precisely: [End Page 30]The most important weapon of the warrior of beauty is his respiration. When the performance starts, life stops. Life itself dies. The warrior of beauty is alive, but life itself is dead. The warrior of beauty remains with just his own breath. When he enters the stage, he needs to breathe life into deceased life. Like a god gives his breath to create life. In the same way he will create life with his breath. How will he achieve this? By breathing correctly: one-third inhaling through the nostrils, one-third exhaling through pursed lips, one-third without breathing. And then the miracle happens. The breath becomes imagination and the imagination breathes. The warrior of beauty is the master of breath and life.2Fabre's abdominal breathing differs from regular forms of breathing, such as techniques derived from Asian yoga techniques, Chi-kung or Tai-chi, as it stresses different parts. At the same time, it is closely related to it, because these practices also adopt the notion that breathing in the first place rouses vitality and spirit and that the right kind of breathing thus aims at controlling life currents and bringing about a clear mind. In yoga it is called pranayama: prana meaning spirit or force of life, ayama meaning 'control' or 'grasp.' Yoga knows many variants in directing the breath, depending on the asanas (yoga postures) in which they are bedded. Sometimes focusing mainly on the diaphragm and the flanks, sometimes on abdominal breathing. Also, suspending your breath (kumbhaka) is a yoga technique, applied at the end of inhalation as well as after exhalation and during taking breath.In Fabre's case, abdominal breathing is stressed: first, air is inhaled through the nose, subsequently sent in the direction of the peritoneal cavity and the flanks, and then again exhaled via a very precise blowing technique (a dosed flow of air through an imaginary straw). During the cycle the diaphragm remains... (shrink)

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

The literature on the epistemology of ignorance already discusses how certain forms of discrimination, such as racism and sexism, are perpetuated by the ignorance of individuals and groups. However, little attention has been given to how speciesism—a form of discrimination on the basis of species membership—is sustained through ignorance_._ Of the few animal ethicists who explicitly discuss ignorance, none have related this concept to speciesism as a form of discrimination. However, it is crucial to explore this connection, I argue, as (...) ignorance is both an integral part of the injustice done to animals as well as an obstacle to improving their treatment. In order to adequately criticize sustained structural speciesism and injustices towards animals, I develop an epistemological account of ‘speciesist ignorance’. I begin by defining and distinguishing between individual and group-based accounts of speciesist ignorance. I argue that humans, taken as a group, enjoy a position of privilege, which allows them to comfortably remain ignorant of their participation in collective wrongdoings towards animals. Additionally, I point out that speciesist ignorance is structurally encouraged and thereby maintains the dominant view that the human-animal-relationship, as it stands, is just. In sum, this article lays the groundwork for a social epistemology of speciesist ignorance. In particular, it informs further debate about individual and institutional epistemic duties to inquire into speciesism and to inform the public, about the moral culpability of ignorant actions, and about effective animal advocacy and policy which actively rejects speciesist ignorance. (shrink)

In the present paper I investigate the role that analogy plays in eighteenth-century biology and in Kant’s philosophy of biology. I will argue that according to Kant, biology, as it was practiced in the eighteenth century, is fundamentally based on analogical reflection. However, precisely because biology is based on analogical reflection, biology cannot be a proper science. I provide two arguments for this interpretation. First, I argue that although analogical reflection is, according to Kant, necessary to comprehend the nature of (...) organisms, it is also necessarily insufficient to fully comprehend the nature of organisms. The upshot of this argument is that for Kant our understanding of organisms is necessarily limited. Second, I argue that Kant did not take biology to be a proper science because biology was based on analogical arguments. I show that Kant stemmed from a philosophical tradition that did not assign analogical arguments an important justificatory role in natural science. Analogy, according to this conception, does not provide us with apodictically certain cognition. Hence, sciences based on analogical arguments cannot constitute proper sciences. (shrink)

Are psychiatric disorders natural kinds? This question has received a lot of attention within present-day philosophy of psychiatry, where many authors debate the ontology and nature of mental disorders. Similarly, historians of psychiatry, dating back to Foucault, have debated whether psychiatric researchers conceived of mental disorders as natural kinds or not. However, historians of psychiatry have paid little to no attention to the influence of (a) theories within logic, and (b) theories within metaphysics on psychiatric accounts of proper method, and (...) on accounts of the nature and classification of mental disorders. Historically, however, logic and metaphysics have extensively shaped methods and interpretations of classifications in the natural sciences. This paper corrects this lacuna in the history of psychiatry, and demonstrates that theories within logic and metaphysics, articulated by Christian Wolff (1679-1754), have significantly shaped the conception of medical method and (psychiatric) nosology of the influential nosologist Boissier De Sauvages (1706-1767). After treating Sauvages, I discuss the method of the influential nosologist William Cullen (1710-1790), and demonstrate the continuity between the classificatory methods of Sauvages and Cullen. I show that both Sauvages and Cullen were essentialists concerning medical diseases in general and psychiatric disorders in particular, contributing to the history of conceptions of the ontology and nature of mental disorders. (shrink)

Women often embody the central values and practices of their religious tradition. When they leave their community, women find a part of the “religious tapestry” remaining with them long after their disengagement. In this article, we draw from research in the UK and Finland to explore women’s efforts to unlearn parts of their former religious belonging. We draw on in total thirty-five interviews with women who disengaged from the Mormon Church, Jehovah’s Witnesses and Conservative Laestadianism. We conceptualize un/learning as a (...) multi-layered process consisting of both un-learning and re-learning. We explore women’s narratives about negotiating bodily limits, conduct and belonging, and understand these as suggesting experiences of a threefold un/learning: gendered, spatial-social and epistemic. We argue that examining gendered and embodied un/learning helps to understand women’s disengagement processes from minority Christian traditions in Western and Northern European secularized contexts such as the UK and Finland. (shrink)

Vladimir Solov'ev (1853-1900- is regarded as the most original and systematic of the Russian philosophers in the 19th century. He has once again become the subject of international scholarly attention both in Slavic countries and the West. This volume contains selected papers presented at the international conference on Vladimir Solov'ev held at Nijmegen University, the Netherlands, in September 1998. The scope of this conference was wide-ranging, dealing with theological, metaphysical, philosophical and historical themes. Though Solov'ev's broad intellectual activity defies any (...) strict attempt at categorisation, the editors have classified its major themes under the dual characteristic of reconciliation and polemics. Solov'ev was passionately committed to the reconciliation of all beings under the idea of all-unity, which he attemted to achieve by engaging in uncompromising polemics with his contemporaries, The thirty contributors to this volume are specialists from Russia, Ukraine, Bulgaria, Western Europe and the United States. The volume makes a significant contribution to the intellectual reassesment of Vladimir Solov'ev since the rediscovery of his philosophical heritage in his own homeland in the 1980s. (shrink)

Even in the Netherlands, where the practice of physician-assisted death (PAD) has been legalized for over 20 years, there is no such thing as a ‘right to die’. Especially patients with extraordinary requests, such as a wish for PAD based on psychiatric suffering, advanced dementia, or (a limited number of) multiple geriatric syndromes, encounter barriers in access to PAD. In this paper, we discuss whether these barriers can be justified in the context of the Dutch situation where PAD is legally (...) permitted for those who suffer unbearably and hopelessly as a result of medical conditions. Furthermore, we explore whether there are options to address some of the barriers or their consequences, both within the Dutch legal framework or by adjusting the legal framework, and whether these options are feasible. We conclude that although there are insufficient arguments to overrule the doctor’s freedom of conscience in the Netherlands, there are ways to address some of the barriers, mainly by offering support to doctors that would be willing to support a request. Moreover, we believe it is morally required to reduce or mitigate where possible the negative consequences of the barriers for patients, such as the long waiting time for those who suffer from psychiatric disorders, because it is unlikely the adjustments suggested to the system will ensure reasonable access for these patient groups. (shrink)

People often say that humans are omnivores in order to justify eating meat as normal and veganism as abnormal. The is one of the arguments that vegetarians and vegans encounter when meat-eaters try to defend the moral acceptability of body parts on their plate. When responding to this argument, the position of the vegan is similar to the atheist who time and again is confronted with the same fallacious arguments in support of the existence of god(s). Veganism and atheism are (...) both ethical default positions. Similarly, not killing other people is also a default position. (shrink)

New means of transport and communication allowed unprecedented mobility of people, goods and ideas in the late nineteenth and early twentieth century, which contributed to far-reaching economic, social and political changes in a first wave of globalisation. In its genuine transnationality, the European historical avant-garde can be seen as a product of this development. Cosmpolitanism, internationality and internationalism became emblems of the avant-garde in its pursuit of a 'new', modern international culture trangressing 'old' borders and limitations dictated by conceptions of (...) nationhood, linguistic restrictions, and state boundaries. Simultaneously, national and nationalist reflexes can be traced in the avant-garde as well - in a European context marked by a plethora of competing nationalisms. This collection of essays focuses on the transnationality and inter-nationalisms in the European avant-garde as well as on conflicts, paradoxes and debates in the avant-garde as genuinely transnational configuration of artistic movements, which possessed nevertheless many nationalist edges. The book presents a panorama of the historical avant-garde oscillating and operating between transnationality, internationalism and nationalisms of different kinds, both in national cultural fields and a transnational European arena - from Iceland to Greece and from the Pale of Settlement to the Atlantic. (shrink)

This paper analyzes debates on animal language in eighteenth-century German philosophy and science. Adopting a history of ideas approach, I explain how the study of animal language became tied to the investigation into the origin and development of language towards the end of the eighteenth century. I argue that for large parts of the eighteenth century, the question of the existence of animal languages was studied within the context of the philosophical question of whether animals possess reason. In Germany, the (...) debate concerning animal reason was influenced by Christian Wolff and was taken up by diverse thinkers such as Winkler, Meier, and Reimarus. I argue that in the second half of the eighteenth century the study of animal language became more loosely related to the question of whether animals possess reason: animal language was studied not only in light of the debate on animal reason but also because it sheds light on the nature of animals, on the differences and similarities between animals and humans, and on the origin and development of language. This systematic study of animal language coincided with the rise of linguistics, anthropology, and biology as independent sciences. (shrink)