§1. The origins of recursion theory. In dedicating a book to Steve Kleene, I referred to him as the person who made recursion theory into a theory. Recursion theory was begun by Kleene's teacher at Princeton, Alonzo Church, who first defined the class of recursive functions; first maintained that this class was the class of computable functions ; and first used this fact to solve negatively some classical problems on the existence of algorithms. However, it was Kleene (...) who, in his thesis and in his subsequent attempts to convince himself of Church's Thesis, developed a general theory of the behavior of the recursive functions. He continued to develop this theory and extend it to new situations throughout his mathematical career. Indeed, all of the research which he did had a close relationship to recursive functions.Church's Thesis arose in an accidental way. In his investigations of a system of logic which he had invented, Church became interested in a class of functions which he called the λ-definable functions. Initially, Church knew that the successor function and the addition function were λ-definable, but not much else. During 1932, Kleene gradually showed1 that this class of functions was quite extensive; and these results became an important part of his thesis 1935a. (shrink)

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm (...) of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (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.

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)

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)

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)

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)

Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...) the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. (shrink)

Seit dem 2. nachchristlichen Jahrhundert werden die Schriften von Aristoteles kommentiert. Diese Ausgabe enthält griechische Kommentare zu seinem Werk vom 3. bis 8. Jahrhundert n. Chr., u. a. von Alexander von Aphrodiensias, Themistios, Joh. Philoponus, Simplicius in griechischer Sprache.

9th and 10th Nov. 2013 at Kyoto University. Organizers: Takeshi Sato and Shunsuke Sugimoto.