Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Non-affirmative Theory of Education as a Foundation for Curriculum Studies, Didaktik and Educational Leadership

This chapter presents non-affirmative theory of education as the foundation for a new research program in education, allowing us to bridge educational leadership, curriculum studies and Didaktik. We demonstrate the strengths of this framework by analyzing literature from educational leadership and curriculum theory/didaktik. In contrast to both socialization-oriented explanations locating curriculum and leadership within existing society, and transformation-oriented models viewing education as revolutionary or super-ordinate to society, non-affirmative theory explains the relation between education and politics, economy and culture, respectively, as non-hierarchical. Here critical deliberation and discursive practices mediate between politics, culture, economy and education, driven by individual agency in historically developed cultural and societal institutions. While transformative and socialization models typically result in instrumental notions of leadership and teaching, non-affirmative education theory, previously developed within German and Nordic education, instead views leadership and teaching as relational and hermeneutic, drawing on ontological core concepts of modern education: recognition; summoning to self-activity and Bildsamkeit. Understanding educational leadership, school development and teaching then requires a comparative multi-level approach informed by discursive institutionalism and organization theory, in addition to theorizing leadership and teaching as cultural-historical and critical-hermeneutic activity. Globalisation and contemporary challenges to deliberative democracy also call for rethinking modern nation-state based theorizing of education in a cosmopolitan light. Non-affirmative education theory allows us to understand and promote recognition based democratic citizenship (political, economical and cultural) that respects cultural, ethical and epistemological variations in a globopolitan era. We hope an American-European-Asian comparative dialogue is enhanced by theorizing education with a non-affirmative approach

Mathematics, Experience, and Laboratories. Herbart's and Brentano's Role in the Raise of Scientific Psychology

In this article we present and compare two early attempts to establish psychology as an independent scientific discipline that had considerable influence in central Europe: the theories of Johann Friedrich Herbart (1776–1841) and Franz Brentano (1838–1917). While both of them emphasize that psychology ought to be conceived as an empirical science, their conceptions show revealing differences. Herbart starts with metaphysical principles and aims at mathematizing psychology, whereas Brentano rejects all metaphysics and bases his method on a conception of inner perception (as opposed to inner observation) as a secondary consciousness, by means of which one gets to be aware of all of one’s own conscious phenomena. Brentano’s focus on inner perception brings him to deny the claim that there could be unconscious mental phenomena – a view that stands in sharp contrast to Herbart’s emphasis on unconscious, ‘repressed’ presentations as a core element of his mechanics of mind. Herbart, on the other hand, denies any role for psychological experiments, while Brentano encouraged laboratory work, thus paving the road for the more experimental work of his students like Stumpf and Meinong. By briefly tracing the fate of the schools of Herbart and Brentano, respectively, we aim to illustrate their impact on the development of psychological research, mainly in central Europe