Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.

Hildegard of Bingen was one of the most remarkable women of her day. From early childhood she experienced religious visions, and at the age of eight she entered a cloistered religious life in the Benedictine monastery of Disibondenberg. Eventually she not only became abbess of the community, but presided over the establishment of an important new convent near Bingen. All but forgotten for hundreds of years, Hildegard was rediscovered in the 1980s and since then her visionary writings have (...) been widely read and studied. Even more surprisingly, music that she composed has been performed and recorded to great acclaim. She has come to be seen by some as a proto-feminist icon -- a woman of great accomplishments who made her own way in a man's world and exerted extraordinary influence over some of the most powerful figures of her time. Much of Hildegard's correspondence has been preserved. It reveals that for more than 30 years this cloistered nun was an unflinching adviser and correspondent to all levels of church and society, from popes and kings to ordinary lay persons, from Jerusalem to England. With the 2004 OUP publication of Volume III of Joseph Baird and Radd Ehrman's translation, the complete correspondence became available for the first time in English. For this new abridgement, Baird has selected 75 of the most interesting and revealing of the letters from Volumes I, II, and III. Freed from the organizational restraints of the Latin edition of the letters, he has arranged them in roughly chronological order and provided greatly expanded, accessibly written introductory notes that contextualize the letters and explain their significance. As a result, this fascinating collection serves as a kind of life in letters that makes an ideal introduction ot this exceptional woman, her world, and her work. This book is the first to give a thorough and definitive illlumination of the personal life of Hildegard of Bingen as viewed through the defining lens of her personal correspondence: her early, hesitant bid for recognition of her spiritual gifts; her courageous, and ultimately futile, fight to retain the companionship of her close personal friend and the poignant outcome of that struggle; her vehement defiance of the male hierarchy in her bid to establish her own communities under her personal governance; her impudent challenge to contemporary conservatives views by the dress and customs she established in her community; her paean of praise for the power of music; and her adamant refusal, even at the advanced age of eighty, to give in to the demands of the male authorities even in the face of excommunication. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hildegard: Medieval Holism and ‘Presentism’—Or, Did Sigewiza Have Health Insurance?Jerome L. Kroll (bio)Keywordsholistic healing, presentism, Hildegard of Bingen, medieval medicineSuzanne Phillips and Monique Boivin have published an article examining Hildegard of Bingen’s (1098–179) treatment and cure of Sigewiza, a possessed woman. The purpose of their article is to demonstrate Hildegard’s holistic, or biopsychosocial, approach to healing as a model that we in the twenty-first century (...) have lost but would do well to recover. Several questions come to mind:What is Hildegard’s model?Have we lost it?Is it something we wish to emulate?The basics of the case history is that a noblewoman, Sigewiza, is ill or possessed of an evil spirit. Attempts by her local abbot and community to send her on pilgrimages or otherwise to cure or exorcise her, even with Hildegard’s recommendation, have only short-lived success, after which Sigewiza’s illness or demon returns. Finally, the abbot asks Hildegard to take the noblewoman into her Benedictine monastery, and after a suitable time and various interventions, Sigewiza is permanently (presumably) cured. The arduous process of effecting this cure has left Hildegard weak and ill herself, a pattern of poor physical health from which Hildegard suffered all her life.Phillips and Boivin claim that this is an early example of conceptualizing and utilizing a bio-psychosocial model to treat a complex illness. Hildegard, well known for her medical and pharmaceutical knowledge, applies the proper dietary changes to correct Sigewiza’s humoral (biological) imbalance. She treats the psyche and its partner, the soul, by long hours of discussion with Sigewiza and verbal duels with her demon, as well as by exorcising the demon, and she includes the social aspects of treatment by bringing Sigewiza into the Benedictine community of sisters as a participating member. Which of these three modalities may be sufficient for a cure depends upon the medieval literary genre in which the case appears. If in a medical text, then the proper dietary treatment and application of compounds to neutralize and correct the offending humoral imbalances would be the therapeutic agents. In medieval hagiography, [End Page 369] the biological modality is never sufficient and often ridiculed, because the entire thrust of the text is to demonstrate the futility of medical (secular) ministrations and the effectiveness of saintly intervention in producing a cure, whether or not exorcism is technically part of the process. In Sigewiza’s case, perhaps because of the stubbornness of the possessing demon or because of other factors attached to Sigewiza’s condition, the three (biopsychosocial) modalities are utilized. It seems that Sigewiza has a treatment-resistant illness.The narrative follows a familiar topos in saint’s lives (Kroll and Bachrach 2005). Attempts to cure a demoniac by prayers, pilgrimages, intercessions of other local saints or reputedly holy persons, and sometimes by physicians (when available) are to no avail. The sufferer is brought, amidst great fanfare and public attention (a media event), to the holy woman who is the central figure of the particular Vita, and the sufferer is promptly, or protractedly, cured. In such an account, the holiness of the holy woman is further demonstrated and her reputation, shrine, and influence are duly extended and enhanced. The holy person, with humility, attributes the intercession and cure to the power of God, or Jesus or Mary or a particular patron saint, but the crowd of onlookers and the audience of the Vita understand that God (or Jesus or Mary) has in fact granted the miracle cure as a way of demonstrating the holiness of this holy person in contrast to those who previously tried to cure the ill person. The abbot who ‘referred’ Sigewiza to Hildegard, and the previous saints’ shrine to whom Sigewiza was brought, although generally acknowledged as being of fine character or respectability, had to suffer the ignominy of their petitions being rejected to dramatize the special regard in which Hildegard is held.Although we can say that the “purposes” for which Hildegard’s hagiographer includes such anecdotes is to demonstrate her holiness and her importance in God’s eyes, this does not stop us, nine centuries later, from using such... (shrink)

References to mirrors were frequent in medieval texts both theological and literary, and their meanings have been abundantly studied, especially recently. Medieval writers were primarily inspired by St. Paul's famous metaphor in his First Letter to the Corinthians 13.12–13: “Now we see only puzzling reflections in a mirror, but then we shall see face to face. My knowledge now is partial; then it will be whole, like God's knowledge of me. In a word, there are three things that last forever: (...) faith, hope, and love; but the greatest of them all is love.” Mirrors were also likened to art in many texts; and so they have functioned mightily in investigations of visuality. To cite just one medieval text among many, on Mallorca in 1276, Inghetto Contardo defended pictures against a Jew's alleged attack by asserting that “the holy mother Church sets images out as a kind of mirror, so that seeing them with corporal eyes they see them with the eyes of the mind.” The claim here was that physical images, made possible by Christ's incarnation, were available to human senses and could be formed into a complete picture when they were assimilated with a memory of God's true nature. Hildegard of Bingen had already summed up the idea succinctly: “That [faith] Adam had when he saw with bodily eyes the invisible light of God … but after his disobedience, neither Adam nor any other man could have this vision; for that reason, the faithful can gaze at God only with the interior vision of the soul, in the mirror of faith, and trust to be able to be saved with him who can do all things.” Inghetto was also assimilating the ancient trope to new theories of vision being promulgated at the time by Roger Bacon, Robert Grosseteste, and Witelo and in such popular works as Peter of Limoges's Tractatus moralis de oculo, a preacher's manual composed exactly at the time of the Mallorca debate and very widely circulated afterward. In these, the site of seeing was literally a mirror, namely, the “crystalline humor” where God's light, located in the anterior part of the brain, is unified with rays from the eyes into a double vision. (shrink)

We encounter autonomy in virtually every area of philosophy: in its relation with rationality, personality, self-identity, authenticity, freedom, moral values and motivations, and forms of government, legal, and social institutions. At the same time, the notion of autonomy has been the subject of significant criticism. Some argue that autonomy outweighs or even endangers interpersonal or collective values, while others believe it alienates subjects who don't possess a strong form of autonomy. These marginalized subjects and communities include persons with physical or (...) psychological disabilities, those in dire economic conditions, LGBTI persons, ethnic and religious minorities, and women in traditional communities or households. This volume illuminates possible patterns in these criticisms of autonomy by bringing to light and critically assessing the contribution of women throughout the history of philosophy on this important subject. The essays in this collection cover a wide range of historical periods and influential female philosophers and thinkers, from medieval philosophy through to contemporary debates. Important authors whose work is considered, among many others, include Hildegard of Bingen, Margaret Cavendish, Anne Conway, Mary Wollstonecraft, Susan Moller Okin, Hélène Cixous, Iris Marion Young, and Judith Jarvis Thomson. Women Philosophers on Autonomy will enlighten and inform contemporary debates on autonomy by bringing into the conversation previously neglected female perspectives from throughout history. (shrink)

Un petit nombre de femmes-auteurs du Moyen Age se sont montrées particulièrement intéressées par l'Histoire, notamment locale, et, dans l'aire germanique, trois d'entre elles se distinguent par l'originalité de leur apport en ce domaine : Hrotsvita de Gandersheim au Xe siècle, et Hildegarde de Bingen et Herrade de Hohenbourg au XIIe. Toutes trois religieuses, elles ont livré à la postérité le récit de la fondation de leur monastère, l'une par le biais de la poésie métrique, la seconde via l'hagiographie et (...) la dernière au moyen de l'image. (shrink)

Un petit nombre de femmes-auteurs du Moyen Age se sont montrées particulièrement intéressées par l'Histoire, notamment locale, et, dans l'aire germanique, trois d'entre elles se distinguent par l'originalité de leur apport en ce domaine : Hrotsvita de Gandersheim au Xe siècle, et Hildegarde de Bingen et Herrade de Hohenbourg au XIIe. Toutes trois religieuses, elles ont livré à la postérité le récit de la fondation de leur monastère, l'une par le biais de la poésie métrique, la seconde via l'hagiographie et (...) la dernière au moyen de l'image. (shrink)

Since the 1980s scholars have been increasingly confronted with expectations to orient themselves toward societal and economic priorities. This normative demand for societal responsiveness is inscribed in discourses aimed at increasing the usefulness, competitiveness, and control of academia. New performance criteria, funding conditions, and organizational forms are central drivers of this debate – thereby, they change the conditions in which scholars conduct research and advance their careers. However, little is known so far about the impact these institutional changes have on (...) the habitus of academics. This article analyzes how stable and consistent habitus formations among academics turn out to be in the course of institutional changes. We compare the habitus formations of two generations of German scholars before and after institutional changes gained pace in Germany. Three distinct habitus formations can be identified, which we refer to as “self-fulfilling,” “self-surpassing,” and “self-asserting.” These habitus formations hold across the two generations, but the lines between them become blurry in the new generation. (shrink)

O objetivo do presente artigo consiste em apresentar uma reflexão sobre os paradigmas existentes e emergentes frente a um contexto teórico-científico e a necessidade de mudança devido aos desafios enfrentados em determinados momentos. Assim, o texto, de abordagem qualitativa e caracterizado como uma revisão bibliográfica, contextualiza acerca deste braço da filosofia que trata da natureza da pesquisa científica, do conhecimento no campo educacional, não somente do âmbito da epistemologia, mas também da fundamentação dos paradigmas das ciências e da educação, e (...) do conhecimento científico. As questões metodológicas estão diretamente relacionadas com essa reflexão sobre os resultados significativos e o que precisa ser modificado a partir de uma análise sobre o contexto social em que se está inserido. Para fundamentar este artigo, se apresentam as contextualizações que dialogam em torno de autores como Alda Judith Alves-Mazzotti, Pierre Bourdieu, Boaventura de Sousa Santos, Bernard Charlot, Edgar Morin, Thomas Kuhn e Mario Osório Marques. Portanto, o artigo expõe no seu panorama científico uma resposta às imposições das ciências na contemporaneidade, sem o rompimento com o passado e suas tradições, mas apresentando um olhar voltado para o futuro. A partir dessa perspectiva, precisamos ter clareza do campo científico em que estamos inseridos, conhecendo de fato suas peculiaridades para optarmos por um método que contemple as necessidades apresentadas, tendo segurança do que estamos fazendo. Enfim, pode-se concluir que os profissionais da educação precisam de uma base de pesquisa científica sólida para terem subsídios necessários ao experimentarem novas metodologias em suas práticas pedagógicas que sejam significativas para os estudantes. (shrink)

Starting with D. Scott's work on the mathematical foundations of programming language semantics, interest in topology has grown up in theoretical computer science, under the slogan `open sets are semidecidable properties'. But whereas on effectively given Scott domains all such properties are also open, this is no longer true in general. In this paper a characterization of effectively given topological spaces is presented that says which semidecidable sets are open. This result has important consequences. Not only follows the classical Rice-Shapiro (...) Theorem and its generalization to effectively given Scott domains, but also a recursion theoretic characterization of the canonical topology of effectively given metric spaces. Moreover, it implies some well known theorems on the effective continuity of effective operators such as P. Young and the author's general result which in its turn entails the theorems by Myhill-Shepherdson, Kreisel-Lacombe-Shoenfield and Ceĭtin-Moschovakis, and a result by Eršov and Berger which says that the hereditarily effective operations coincide with the hereditarily effective total continuous functionals on the natural numbers. (shrink)

The different behaviour of total and partial numberings with respect to the reducibility preorder is investigated. Partial numberings appear quite naturally in computability studies for topological spaces. The degrees of partial numberings form a distributive lattice which in the case of an infinite numbered set is neither complete nor contains a least element. Friedberg numberings are no longer minimal in this situation. Indeed, there is an infinite descending chain of non-equivalent Friedberg numberings below every given numbering, as well as an (...) uncountable antichain. (shrink)

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...) intersects the topological closure of an effectively enumerable subset of Y. As a consequence of a more general parametric inseparability result a theorem of Rice-Shapiro type is obtained. Moreover, under some additional requirements it follows that nonopen subsets have productive index sets. This implies a generalized Rice theorem: Connected spaces have only trivial completely recursive subsets. As application some decision problems in computable analysis and domain theory are studied. It follows that the complement of the halting problem can be reduced to the problem to decide of a number whether it is a computable irrational. The same is true for the problems to decide whether two numbers are equal, whether one is not greater than the other, and whether a number is equal to a given number. In the case of an effectively given continuous complete partial order the complexity of the last problem depends on whether the given element is the smallest element, in which case the complement of the halting problem is reducible to it, whether it is a base element and maximal, then the decision problem is recursively isomorphic to the halting problem, or whether it is none of these. In this case, both the halting problem and its complement are reducible to the problem. The same is true in nontrivial cases for the problems whether an element belongs to the basis, whether two elements of the partial order are equal, or whether one approximates the other. In general, for any nonempty proper subset of the partial order either the halting problem or its complement can be reduced to the membership problem of the subset. (shrink)

In examples like the total recursive functions or the computable real numbers the canonical indexings are only partial maps. It is even impossible in these cases to find an equivalent total numbering. We consider effectively given topological T 0 -spaces and study the problem in which cases the canonical numberings of such spaces can be totalized, i.e., have an equivalent total indexing. Moreover, we show under very natural assumptions that such spaces can effectively and effectively homeomorphically be embedded into a (...) totally indexed algebraic partial order that is closed under the operation of taking least upper bounds of enumerable directed subsets. (shrink)

If one wants to compute with infinite objects like real numbers or data streams, continuity is a necessary requirement: better and better (finite) approximations of the input are transformed into better and better (finite) approximations of the output. In case the objects are constructively generated, they can be represented by a finite description of the generating procedure. By effectively transforming such descriptions for the generation of the input (respectively, their codes) into (the code of) a description for the generation of (...) the output another type of computable operation is obtained. Such operations are also called effective. The relationship of both classes of operations has always been a question of great interest. In this paper the setting is extended to the case of multifunctions. Various ways of coding (indexing) sets are discussed and their relationship is investigated. Moreover, effective versions of several continuity notions for multifunctions are introduced. For each of these notions an indexing system for sets is exhibited so that the multifunctions that are effective with respect to this indexing system are exactly the multifunction which are effectively continuous with respect to the continuity notion under consideration. Mostly, in addition to being effective the multifunctions need also possess certain witnessing functions. Important special cases are discussed where such witnessing functions always exist. (shrink)