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)

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.

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)

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)

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.

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)

Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

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.

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.

This paper investigates conceptions of explanation, teleology, and analogy in the works of Immanuel Kant (1724-1804) and Georges Cuvier (1769-1832). Richards (2000, 2002) and Zammito (2006, 2012, 2018) have argued that Kant’s philosophy provided an obstacle for the project of establishing biology as a proper science around 1800. By contrast, Russell (1916), Outram (1986), and Huneman (2006, 2008) have argued, similar to suggestions from Lenoir (1989), that Kant’s philosophy influenced the influential naturalist Georges Cuvier. In this article, I wish to (...) expand on and further the work of Russell, Outram, and Huneman by adopting a novel perspective on Cuvier and considering (a) the similar conceptions of proper science and explanation of Kant and Cuvier, and (b) the similar conceptions of the role of teleology and analogy in the works of Kant and Cuvier. The similarities between Kant and Cuvier show, contrary to the interpretation of Richards and Zammito, that some of Kant’s philosophical ideas, whether they derived from him or not, were fruitfully applied by some life scientists who wished to transform life sciences into proper sciences around 1800. However, I also show that Cuvier, in contrast to Kant, had a workable strategy for transforming the life sciences into proper sciences, and that he departed from Kant’s philosophy of science in crucial respects. (shrink)

Dans l'oeuvre d'Edith Stein, l'alterite apparait comme constitutive de la personne humaine. D'un point de vue proprement subjectif, l'alterite renvoie... l'alter ego,... la dimension communautaire et, dans une perspective croyante, au Tout-Autre. D'un point de vue objectif, elle designe les valeurs, qui faconnent la personnalite, et la foi, qui vient au secours de la raison humaine. Un parcours des oeuvres principales de l'auteur permet de prendre la mesure... la fois de la continuite et de l'evolution de sa pensee. A partir (...) de l..., l'etude entreprend de mettre en evidence, d'une part, l'originalite de la pensee d'Edith Stein par rapport... celle de Husserl et, d'autre part, comment Edith Stein se situe par rapport... la pensee de Thomas d'Aquin. L'influence de l'oeuvre de Jean de la Croix est egalement abordee. Enfin, en dialogue avec des auteurs comme Ricoeur, Levinas ou Ladriere, la troisieme partie du livre aborde de maniere critique la question de l'alterite comme fondement de la personne et cela selon trois parcours, l'un lie... la phenomenologie d'Edith Stein, l'autre... sa philosophie chretienne, et le dernier... son attrait pour la mystique. (shrink)

Although Minsky’s interpretation of Keynes’s macroeconomics and essential message clashes with authoritative alternative interpretations, it has become increasingly influential during the years following the Global Financial Crisis, even in mainstream circles. This paper offers a critical evaluation of Minsky’s Financial Instability Hypothesis from the perspective of the alternative Austro-Wicksellian paradigm. Although some of the similarities and/or analogies between Minsky’s approach and that of the Austrian School suggest a more than merely superficial affinity between the two theoretical frameworks and although some (...) scope for cross-fertilization between both approaches can be found, both theoretically and empirically, at a fundamental conceptual level both theories remain incompatible and difficult if not impossible to reconcile, in particular in terms of fundamental causality and in terms of policy conclusions and prescriptions. Despite the fact that Minsky’s policy conclusions are multifaceted and somewhat eclectic, they manifest a lack of familiarity with the conclusions of the Austrian analysis of the problems of central planning by Big Players such as Big Bank and Big Government. Both approaches also offer contrasting interpretations of the historical experience of the Global Financial Crisis. (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)

In computer ethics, as in other branches of applied ethics, the problem of the justification of moral judgment is still unresolved. I argue that the method which is referred to as “The Method of Wide Reflective Equilibrium” (WRE) offers the best solution to it. It does not fall victim to the false dilemma of having to choose either case‐based particularist or principle‐based universalist approaches to the problem of moral justification. I claim that WRE also provides the best model of practical (...) moral reasoning available for computer ethics. It does not pretend to provide quasi‐algorithmic procedures for moral decision‐making, but neither does it abandon the regulative ideal of communicative transparency in discursive public justification. (shrink)

This study addresses two questions: (1) what visions of nature do lay people subscribe to? (2) to what extent do these visions reflect those of professional philosophers? Four philosophical images of the human-nature relationship were discussed with respondents; Master, Steward, Partner and Participant. Respondents recognise these images, but prefer to construct their own. Elements of their images are (1) that humans are part of nature, but (2) that they are responsible for nature as well. This study indicates that empirical philosophy (...) can contribute to the further development of environmental philosophy. Through an empirical turn we can discover people's own voice. (shrink)

Introduction to collection of papers by group of scholars and ACO missionaries brought together to discuss the developments within the ACO over the past hundred years during a conference that was organised by Dr Wilbert van Saane of Haigazian University in January 2021. I will briefly summarise what strikes me as characteristic of the ACO on the basis of these articles, and conclude with a discussion of how this may contribute to further reflection in Mission Studies and World Christianity.

There is widespread understanding of the close connection between religion and the ecological crisis, and that in order to amend this crisis, theological resources are needed. This monograph seeks to contribute to this endeavor by engaging the theology of Dietrich Bonhoeffer. His theology is particularly suitable in this context, due to its open-ended nature, and to the prophetic and radical nature of the questions he was prepared to ask--that is why there are many other attempts to contextualize Bonhoeffer's theology in (...) areas that he himself has not directly written about. In this monograph, Steven van den Heuvel first of all addresses the question of how to translate Bonhoeffer's theology in a methodologically sound way. He settles on a modified form of the general method of correlation. Then, secondly, van den Heuvel sets out to describe five major concepts in Bonhoeffer's work, bringing these into critical interplay with discussions in environmental ethics and eco-theology. In making the correlations he thoroughly describes each concept, situating it in the historic and intellectual background of Bonhoeffer's time. He then transposes these concepts to contemporary environmental ethics, describing what contribution Bonhoeffer's theology can make. - back of book. (shrink)

This is a fully revised and updated version of Hans van der Doel"s Democracy and Welfare Economics.

The technological advances in medicine, including prolongation of life, have constituted several dilemmas at the end of life. In the context of the Belgian debates on end-of-life care, the views of Muslim women remain understudied. The aim of this article is fourfold. First, we seek to describe the beliefs and attitudes of middle-aged and elderly Moroccan Muslim women toward withholding and withdrawing life-sustaining treatments. Second, we aim to identify whether differences are observable among middle-aged and elderly women’s attitudes toward withholding (...) and withdrawing life-sustaining treatments. Third, we aim to explore the role of religion in their attitudes. Fourth, we seek to document how our results are related to normative Islamic literature. Qualitative empirical research was conducted with a sample of middle-aged and elderly Moroccan Muslim women living in Antwerp and with experts in the field. We found an unconditional belief in God’s sovereign power over the domain of life and death and in God’s almightiness. However, we also found a tolerant attitude, mainly among our middle-aged participants, toward withholding and withdrawing based on theological, eschatological, financial and quality of life arguments. Our study reveals that religious beliefs and worldviews have a great impact on the ethical attitudes toward end-of-life issues. We found divergent positions toward withholding and withdrawing life-sustaining treatments, reflecting the lines of reasoning found in normative Islamic literature. In our interviews, theological and eschatological notions emerged as well as financial and quality of life arguments. (shrink)

In 'Signs of the Invisible', art philosopher Antoon Van den Braembussche penetrates deeper into the mystical dimension of art. In essays on Rumi, Paul Klee, Anish Kapoor and Paul Celan, he offers multifaceted reflections on the ineffable in art. More than ever, he breaks through the established boundaries between art and mysticism, tradition and innovation, religion and atheism, between Western and Eastern philosophy. In an age where the secular has taken over, art appears more than ever to respond to the (...) inner need for a deeper, existential and spiritual exploration. That makes 'Signs of the Invisible' an extremely topical book. It also embodies a new paradigm in art philosophy, in which the systematic connection between art and mysticism is central. (shrink)