In this programmatic paper we renew the well-known question “What is a proof?”. Starting from the challenge of the mathematical community by computer assisted theorem provers we discuss in the first part how the experiences from examinations of proofs can help to sharpen the question. In the second part we have a look to the new challenge given by “big proofs”.

In “The Book of the Crown (_Kitāb al-Iklīl_) of pseudo-Rhazes” Oliver Kahl and Henrietta Sharp Cockrell offer a facsimile edition, with annotated English translation and introductory study, of a unique and highly unusual medieval Arabic medical text.

Jon Sobrino and Jean-Marc Éla provide unique contributions for theological ethics in reflecting suffering as mystery of evil (mysterium iniquitatis) and suffering as the driving force for liberation (mysterium salutis). As a proponent of liberation theology, Sobrino focuses on structural problem of evil. In this regard, Éla gives his unique voice by analyzing suffering from its socio-cultural perspectives. Putting Sobrino and Éla in dialog shows the need for interdisciplinary approach in doing theological ethics. This interdisciplinary reflection on suffering on the (...) one hand will bring a more holistic view on the complexity of the problem of suffering. On the other hand, it brings a more contextual understanding on the meaning of discipleship in a violent world. Keywords: Saffering, evil, liberation, resocialization, structural & socio- cultural approach, discipleship. Abstrak: Jon Sobrino dan Jean-Marc Éla memberikan sumbangan yang khas bagi refleksi teologis etis tentang kompleksitas problem penderitaan sebagai misteri kejahatan (mysterium iniquitatis) namun sekaligus menawarkan daya dorong bagi kesetiaan menapaki jalan pembebasan (mysterium salutis). Sobrino yang menekankan analisa struktural atas kejahatan membutuhkan analisa sosio-kultural dari Éla sehingga aneka upaya “memberi nama” dan melawan problem kejahatan mendapatkan pijakannya pada praktik-praktik kultural dalam komunitas lokal. Dialog Sobrino dan Éla juga menunjukkan bahwa teologi mesti membuka diri pada kajian interdisipliner dengan ilmu lain sehingga, di satu sisi, misteri penderitaan dapat didekati secara lebih utuh dan, di sisi lain, jalan kemuridan yang muncul karena tanggapan atasnya menjadi lebih kontekstual. Kata-kata kunci: Penderitaan, kejahatan, pembebasan, resosialisasi, pendekatan struktural, pendekatan sosio-kultural, kemuridan. (shrink)

In this study, we use a mixed methods research design to investigate how national cultural forces may impede or enhance the positive impact of females’ economic and political empowerment on increasing gender diversity of corporate boards. Using both a longitudinal correlation-based methodology and a configurational approach with fuzzy-set qualitative comparative analysis, we integrate theoretical mechanisms from gender schema and institutional theories to develop a mid-range theory about how female empowerment and national culture shape gender diversity on corporate boards around the (...) world. With our configurational approach, we conceptually and empirically model the complexity that is associated with the simultaneous interdependencies, both complementary and substitutive ones, between female empowerment processes and various cultural dimensions. Our findings contribute unique insights to research focused on board gender diversity as well as provide information for firm decision makers and policymakers about possible solutions for addressing the continuing issue of the underrepresentation of women on corporate boards. (shrink)

In many countries publications in Web of Knowledge journals are dominant in the evaluation of educational research. For various purposes comparisons are made between the output of philosophers of education in these journals and the publications of their colleagues in educational research generally, sometimes also including psychologists and/or social scientists. Taking its starting-point from Hayden’s article in this journal (Stud Philos Educ 31:1–27, 2012), this paper discusses the situation of educational research in three countries: The Netherlands, South Africa and Norway. (...) In this paper an alternative for comparing research output is offered by invoking comparisons with colleagues at the international level from within the same sub-discipline. It is argued that if one would do so a different picture would emerge, even if one were to limit oneself to particular kinds of publications. The case is then made that if comparisons are regarded as a necessary part of the evaluation of an individual scholar (for appointment, promotion, tenure, and/or funding application purposes), it would be more fair to use a proxy system which is sub-discipline specific, or minimally contains some kind of correction factor in relation to the over-all quality assessment device. Debates about the relevance or irrelevance of philosophy of education in the context of educational sciences are now obscured, even poisoned by focusing almost exclusively on a particular kind of publication output. As the ‘reward’ system that is developed accordingly is possibly the most important driver of educational research, it puts the sub-discipline unduly under pressure to the extent that it possibly cannot survive. (shrink)

This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{ the exact proof-theoretic ordinals of these systems are presented.

We give recursion-theoretic characterizations of the counting class \(\textsf {\#P} \), the class of those functions which count the number of accepting computations of non-deterministic Turing machines working in polynomial time. Moreover, we characterize in a recursion-theoretic manner all the levels \(\{\textsf {\#P} _k\}_{k\in {\mathbb {N}}}\) of the counting hierarchy of functions \(\textsf {FCH} \), which result from allowing queries to functions of the previous level, and \(\textsf {FCH} \) itself as a whole. This is done in the style of (...) Bellantoni and Cook’s safe recursion, and it places \(\textsf {\#P} \) in the context of implicit computational complexity. Namely, it relates \(\textsf {\#P} \) with the implicit characterizations of \(\textsf {FPTIME} \) (Bellantoni and Cook, Comput Complex 2:97–110, 1992) and \(\textsf {FPSPACE} \) (Oitavem, Math Log Q 54(3):317–323, 2008), by exploiting the features of the tree-recursion scheme of \(\textsf {FPSPACE} \). (shrink)

With this book, respected academic and community leader, Paulus Zulu, cuts right to the heart of our current malaise. Drawing equally on Western concepts and on African traditional thought, he provides a searing indictment of the state of the nation, casting new light on corruption, incompetence and mismanagement."--Back cover.

This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{<\alpha};$ the exact proof-theoretic ordinals of these systems are presented.

In 2000, a draft note of David Hilbert was found in his Nachlass concerning a 24th problem he had consider to include in the his famous problem list of the talk at the International Congress of Mathematicians in 1900 in Paris. This problem concerns simplicity of proofs. In this paper we review the traces of this problem which one can find in the work of Hilbert and his school, as well as modern research started on it after its publication. We (...) stress, in particular, the mathematical nature of the problem.1. (shrink)

Falk Wagner was the leading Hegelian in late 20th century German Protestant theology. Wagner who had studied philosophy with Theodor W. Adorno and Wolfgang Cramer in Frankfurt am Main and Systematic Theology with Wolfhart Pannenberg at the University of Mainz taught Systematic Theology at the Universities of Munich and, since 1988, Vienna. He published several influential books. In his lectures and seminars he frequently handed out short theory papers to his students which should serve as the basis for debate. The (...) five texts presented here for the first time deal with the problems of individual in society and of the modern history of theology, with the doctrine of God, with the significance of the Bible for the systematic theology and finally with the concept of „Subjektivität“ in G. W. F. Hegel’s philosophy. These texts are an essential source for the development of Wagner’s thought when teaching at the university of Munich until 1988. (shrink)

This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's.

Jacques Derrida is doubtless one of the most controversial phi- losophers of our time. Controversies surrounding him are mainly caused by his radical ideas which have shaken the main traditions of thinking in Western Philosophy. He demonstrates the contradictions of various philophical concepts. He also uses a provocative approach by connect- ing religion with atheism. This essay will demonstrate Derrida’s concept of religion and how it is connected with atheism. Derrida does not present a theology; however his idea of atheistic (...) faith can contribute to a critical understanding of faith and its expressions within religions. Keywords: Iman (faith), agama (religion), teror (terror), ateis (atheist; athe- istic), hadiah (gift; reward), pengetahuan (knowlegde). (shrink)

Time, space, causality, communicating and acting together set limits on our freedom. Starting from the position of Wittgenstein, who advocates neither a position of pure subjectivity nor of pure objectivity, and taking into account what is implied by initiation into the symbolic order of language and culture, it is argued that the limitations on our freedom are not to be deplored. The problems of conservatism, relativism and scepticismwhich confront us often in the context of education and child rearingare inadequately dealt (...) with if attention is primarily focused on ways to resist or act differently. Following Cavell and his insistence that we should not try to escape from the existential conditions we find ourselves in and look for false certainties, the relevance of embracing a particular stance is elaborated. A commitment to giving substance to an ideal of the good life is neither an injustice towards the other nor an ignorance of her freedom. On the contrary, here responsibility is accepted, and at the same time it is acknowledged that we always have only the particular points of departure that we contingently start from. Coming to terms with this kind of dependency constitutes living out the scepticism that is implied by our being human: the logic of this is given along with our human condition. (shrink)

This paper is the sequel to Part 1, which appeared in this Journal, Vol. 46 No. 2, 2012. Following Cavell and his insistence that we should not try to escape from the existential conditions we find ourselves in and look for false certainties, the relevance of embracing a particular stance is elaborated. A commitment to giving substance to an ideal of the good life is neither an injustice towards the other nor an ignorance of her freedom. On the contrary, here (...) responsibility is accepted and at the same time it is acknowledged that we always have only the particular points of departure that we contingently start from. Coming to terms with this kind of dependency constitutes living out the scepticism that is implied by our being human: the logic of this is given along with our human condition. (shrink)

Psychology has penetrated many domains of society and its vocabulary and discourse has become part of our everyday conversations. It not only carries with it the promise that it will deliver insights into human behaviour, but it is also believed that it can address many of the problems human beings are confronted with. As a discipline it thrives in the present climate of performativity, where more attention is given to means than to ends. The article observes first that for education (...) and thus for educational research, though psychology's approach can be valuable, other theoretical stances are also necessary. It then analyses why psychology may be attractive nowadays in the educational field and identifies its prestige in academia, partly arising from its professionalization, but above all the use of a particular method and the focus on certain contents. This has historical antecedents, and so some illustrations are given of previous developments, paying attention as well to the controversies in which educational psychology has been involved in the past, as well as to the need of biographical research, which warns us to be careful with generalizations. It is argued that a more balanced approach (invoking the particularities of the situation as well as a broader concept of practical rationality) is required for the study of education and that educational researchers therefore should resist the tendency to see psychology as the default auxiliary science of education; instead they should reclaim their territory, do justice to the responsibility that is required and highlight the importance of understanding social practices to a large extent in terms of reasons and intentions. (shrink)