Albert Lewis's article analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of n-dimensional outer algebra.Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that:i. Grassmann, although a self-taught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary (...) mathematical education and culminating in the modern mathematics of the late 19th Century, it was reflected in the contributions of Grassmann, Riemann, Jacobi and Eisenstein.ii. Hermann Grassmann, his father Justus, and his brother Robert were all demonstrably influenced by Schleiermacher's dialectic; however the two brothers responded to it in very different ways.iii. Whilst the more philosophical parts of Hermann's 1844 Extension Theory are characterised by the influence of Schleiermacher and also by the mathematical knowledge of his father, the entire development of this work is the unfolding of a single idea based on the father's interpretation of combinatorial multiplication as a ‘chemical conjunction‘, which was developed largely dialectically by Hermann. (shrink)

English summary: 'Metamorphoses of the holy' denotes the changing aesthetic presentation of the sacred which is connected to the creation and institutionalization of religion as art. The focus of the essays in this volume is the structure and dynamic of this process, something which affects all art genres. The sacralization of aesthetic subjectivity is prerequisite to religion as art as evidenced by the belief in the partaking of the sacred through aesthetic experience. On the basis of aesthetic subjectivity's sacralization, it (...) becomes possible to interpret its various forms of expression as witnesses to the holy and award them a fitting reception. These contributions dedicate themselves to an interdisciplinary scrutiny of religion as art and its cross-points of reference with political and civil religion. German description: 'Metamorphosen des Heiligen' bezeichnen hier den Gestaltwandel asthetischer Vergegenwartigung des Heiligen, der sich mit der Entstehung und Institutionalisierung von Kunstreligion verbindet. Im Zentrum der Beitrage des Bandes stehen Struktur und Dynamik dieses Gestaltwandels, der alle Kunstgattungen betrifft. Kunstreligion hat die Sakralisierung der asthetischen Subjektivitat zur Voraussetzung, erkennbar an der Uberzeugung, der Mensch konne durch das Vermogen asthetischer Erfahrung Anteil am Heiligen haben. Auf der Grundlage der Sakralisierung asthetischer Subjektivitat wird es moglich, auch deren verschiedene Ausdrucksformen als Zeugnisse des Heiligen zu deuten und eine entsprechende Rezeption dieser Zeugnisse anzusinnen. Die Beitrage widmen sich der Kunstreligion sowie ihren Interferenzen mit der politischen Religion und der Zivilreligion in interdisziplinarer Perspektive. Mit Beitragen von: Stefan Alkier, Bernd Auerochs, Manuel Bauer, Wolfgang Braungart, Reinhard Brandt, Heinrich Detering, Hermann Deuser, Carola Groppe, Gunter Hantzschel, Joachim Jacob, Markus Kleinert, Dietrich Korsch, Volkhard Krech, Johann Kreuzer, Dorit Messlin, Jurgen Oelkers, Bernhard Schafers, Magnus Schlette, Peter Steinacker. (shrink)

Music, art, and poetry were profound forces in Hermann Cohen’s thought. If we attempt to comprehend this philosopher, whose name is synonymous with the School of Marburg, that small charming town in Hesse from which Kant’s works and influence spread abroad like the magic of an irresistible melody, then we are forced to appreciate those lovers of music and art that brought him the friendship of the violinist Joseph Joachim, the admiration of painters such as Max Liebermann, Lenid (...) Pasternak, the father of Boris, and others whose names are now distant from us. European culture is alive in philosophy, not merely as illustrative references, but as the achievements of the mind devoted to reason and the power of imagination. This culture was not simply created by a mind that ignored the senses. The body was appreciated as the source of subtle and artistic movement, its power to build and form depended upon the grace and delicacy of the hands, sound awakened in us the inexhaustible dimension and possibilities of communication and relationship, sight the sensitivity to colors, to a variety of architectural forms that evoke a sense of beauty and sublimity by their effect and receptivity, taste and touch cultivate form and allow us to receive and be receptive with a heightened sense of delicacy and appreciation allowing form to be given to us in indescribable and unexpected ways. Through the senses we develop that intimacy with others that the mind can only define and analyze but never feel. Cohen has come forth from his detractors and even from his admirers as the distant and unapproachable “professor” of a forgotten philosophical “system.” He did his service in Kant’s army of interpreters adding volumes of interpretation and appreciation to the old master. Here he paid his dues to his profession and university. Cohen was a cultured man, a deeply sensitive individual, a fine product of artistic sensitivity and generosity. When he turned to the arts, when he moved to music, to religion, to social activity, the humaneness of his personality overcame the professor in him; it showed that tenderness for human relationship, that deep respect for love that Cohen found in his beloved Wolfgang Amadeus Mozart, whose operas he believed reflected a sensitivity to moral and aesthetic values. (shrink)

Music, art, and poetry were profound forces in Hermann Cohen’s thought. If we attempt to comprehend this philosopher, whose name is synonymous with the School of Marburg, that small charming town in Hesse from which Kant’s works and influence spread abroad like the magic of an irresistible melody, then we are forced to appreciate those lovers of music and art that brought him the friendship of the violinist Joseph Joachim, the admiration of painters such as Max Liebermann, Lenid (...) Pasternak, the father of Boris, and others whose names are now distant from us. European culture is alive in philosophy, not merely as illustrative references, but as the achievements of the mind devoted to reason and the power of imagination. This culture was not simply created by a mind that ignored the senses. The body was appreciated as the source of subtle and artistic movement, its power to build and form depended upon the grace and delicacy of the hands, sound awakened in us the inexhaustible dimension and possibilities of communication and relationship, sight the sensitivity to colors, to a variety of architectural forms that evoke a sense of beauty and sublimity by their effect and receptivity, taste and touch cultivate form and allow us to receive and be receptive with a heightened sense of delicacy and appreciation allowing form to be given to us in indescribable and unexpected ways. Through the senses we develop that intimacy with others that the mind can only define and analyze but never feel. Cohen has come forth from his detractors and even from his admirers as the distant and unapproachable “professor” of a forgotten philosophical “system.” He did his service in Kant’s army of interpreters adding volumes of interpretation and appreciation to the old master. Here he paid his dues to his profession and university. Cohen was a cultured man, a deeply sensitive individual, a fine product of artistic sensitivity and generosity. When he turned to the arts, when he moved to music, to religion, to social activity, the humaneness of his personality overcame the professor in him; it showed that tenderness for human relationship, that deep respect for love that Cohen found in his beloved Wolfgang Amadeus Mozart, whose operas he believed reflected a sensitivity to moral and aesthetic values. (shrink)

Ludwig Wittgenstein’s remarks on contradictions and paradoxes have been met with incomprehension and have fueled the widespread and long-standing prejudice that his later thoughts on the foundations of logic and mathematics are the “surprisingly insignificant product of a sparkling mind” (Kreisel, British Journal for the Philosophy of Science 9:135–158, 1959, p. 158). This paper disagrees; it argues that Wittgenstein’s remarks on semantic paradoxes suggest an account of the Liar and its kin that is not only of historical interest but also (...) represents a hitherto unnoticed paraconsistent alternative to established approaches to the Liar. In what follows, a reading of Wittgenstein’s remarks will be offered according to which Wittgenstein subscribes to a form of dialetheism (that is, the view that there are sentences that are both true and false). In contrast to modern dialetheist approaches to the Liar, however, some of Wittgenstein’s remarks suggest combining a dialetheist position with what is called ‘logical nihilism’ (that is, the view that there are no universally valid inference rules). (shrink)

Hermann Cohen's Religion of Reason, Out of the Sources of Judaism is widely taken to be the greatest work in Jewish philosophy and religious thought since Maimonides' Guide to the Perplexed. It is at once a Jewish book and a philosophical one: Jewish because it takes its material from the literary tradition that extends from the bible to the rabbis to the great medieval philosophers; philosophical because it studies that material in order to construct a worldview that is rational (...) in the broadest sense of the term. This edition reprints a 1972 introduction by Leo Strauss and includes an essay on the work by Steven Schwarzchild. A new introduction by Kenneth R. Seeskin situates Cohen's masterwork in the history of modern philosophical and religious thought. (shrink)

Title: Föderalismus und Europäische Gemeinschaften Unter Besonderer Berücksichtigung von Umwelt und Gesundheit, Kultur und BildungPublisher: Duncker & HumblotISBN: 3428078934Author: Detlef Merton Title: Die Deutschen Länder im Prozess der Europäischen Einigung: Eine Analyse der Europapolitik Unter Intergrationspolitischen GesichtpunktenPublisher: Duncker & HumblotISBN: 3428072790Author: Doris Fuhrmann-MittlmeierTitle: Föderalismus und Integrationsgewalt: Die Bundesrepublik Deutschland, Spanien, Italien, und Belgien als Dezentralisierte Saaten in der EG, Schriften zun Europäischen Recht, vol. 7Publisher: Duncker & HumblotISBN: 3428071131Author: Hermann-Josef BlankeTitle: Europa der Regionen: Aktuelle Dokumente zur Rolle und Zukunft (...) der Deutschen Länder im Europäischen IntegrationsprozessPublisher: Duncker & HumblotISBN: 3428074777Author: Joachim Bauer. (shrink)

In the last 20 years, a stream of research emerged under the label of „complex problem solving“ (CPS). This research was intended to describe the way people deal with complex, dynamic, and intransparent situations. Complex computer-simulated scenarios were as stimulus material in psychological experiments. This line of research lead to subtle insights into the way how people deal with complexity and uncertainty. Besides these knowledge-rich, realistic, intransparent, complex, dynamic scenarios with many variables, a second line of research used more simple, (...) knowledge-lean scenarios with a low number of variables („minimal complex systems“, MCS) that have been proposed recently in problem-solving research for the purpose of educational assessment. In both cases, the idea behind the use of microworlds is to increase validity of problem solving tasks by presenting interactive environments that can be explored and controlled by participants while pursuing certain action goals. The main argument presented here is: both types of systems - CPS and MCS – can only be dealt with successfully if causal dependencies between input and output variables are identified and used for system control. System knowledge is necessary for control and intervention. But CPS and MCS differ in their way of how causal dependencies are identified and how the mental model is constructed; therefore, they cannot be compared directly to each other with respect to the cognitive processes that are necessary for solving the tasks. Knowledge-poor MCS tasks address only a small fraction of the cognitive processes and structures needed for knowledge-rich CPS situations. (shrink)

English summary: Friedrich Schleiermacher's work as a theologian and Plato scholar marked the start of a new epoch: as a system-forming philosopher, he claimed independent validity, and as church politician, educational policy-maker, and academic theorist, he was one of the most important figures during the Prussian reforms, whose contributions to pedagogy remain influential to this day. This volume provides a clear-sighted overview of the various stages in Schleiermacher's life (1768-1834), with each contribution portraying his fields of work and their contexts, (...) placing his literary work and conceptions in the framework of the respective contemporary debates. Important stages in Schleiermacher reception and impact history are likewise considered. The authors' diverse approaches to interpreting and understanding his output mean that the Guide to Schleiermacher offers concentrated insight into the consensus on and controversies in current Schleiermacher research. German description: Friedrich Schleiermacher (1768-1834) hat als Theologe, aber auch als Plato-Forscher Epoche gemacht; als systembildender Philosoph erhob er selbstandigen Geltungsanspruch, als Kirchen- und Bildungspolitiker sowie als Theoretiker der Universitat gehorte er zu den wichtigsten Akteuren der preussischen Reformen, und seine Beitrage zur Padagogik wirken bis heute nach. Die Gliederung des Handbuchs folgt grob Schleiermachers Lebensstationen. Die einzelnen Beitrage schildern seine Arbeitsfelder und -kontexte und stellen seine literarischen Arbeiten und Entwurfe in den jeweiligen zeitgeschichtlichen Debattenlagen dar. Auch wichtige Stationen seiner Wirkungs- und Rezeptionsgeschichte werden thematisiert.Die Autorinnen und Autoren der Beitrage verfolgen ganz unterschiedliche Interpretations- und Deutungsansatze. Deshalb bietet das Handbuch auch einen konzentrierten Einblick in den gegenwartigen Stand der Schleiermacher-Forschung mit ihren Konsensen und ihren Kontroversen. Mit Beitragen von: Christian Albrecht, Andreas Arndt, Bernd Auerochs, Ulrich Barth, Albrecht Beutel, Georg Eckert, Hermann Fischer+, Ursula Frost, Albrecht Geck, Simon Gerber, Wilhelm Grab, Peter Grove, Matthias Heesch, Eilert Herms, Kirsten Huxel, Walter Jaeschke, Lutz Kappel, Hans-Martin Kirn, Dietz Lange, Inken Madler, Helmut Merkel, Martin Ohst, Claus-Dieter Osthovener, Hermann Patsch, Reiner Preul, Andreas Reich, Joachim Ringleben, Jan Rohls, Martin Rossler, Dirk Schmid, Friedemann Voigt, Folkart Wittekind, Matthias Wolfes. (shrink)

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language (...) of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines. (shrink)

Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist (...) view of mathematics and allows one to gain insight into why a theorem is true by answering what-if-things-had-been-different questions. (shrink)

What are consequential world problems? As “grand societal challenges”, one might define them as problems that affect a large number of people, perhaps even the entire planet, including problems such as climate change, distributive justice, world peace, world nutrition, clean air and clean water, access to education, and many more. The “Sustainable Development Goals”, compiled by the United Nations, represent a collection of such global problems. From my point of view, these problems can be seen as complex. Such complex problems (...) are characterized by the complexity, connectivity, dynamics, intransparency, and polytely of their underlying systems. These attributes require special competencies for dealing with the uncertainties of the given domains, e.g., critical thinking. My position is that it is not IQ, but complex problem-solving competencies for dealing with complex and dynamic situations, that is important for handling consequential global problems. These problems require system competencies, i.e., competencies that go beyond analytical intelligence, and comprise systems understanding as well as systems control. Complex problem-solving is more than analytic intelligence. (shrink)

Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians often believe that this type of argumentation leaves no room for errors and unclarity. Philosophers of mathematics have differentiated between absolutist and fallibilist views on mathematical knowledge, and argued that these views are related to whether one looks at mathematics-in-the-making or finished mathematics. In this paper we take a closer look at mathematical practice, more (...) precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature, given the special status of mathematics, is highly reliable is too naive. We will discuss several problems in the publication process that threaten this view, and give several suggestions on how this could be countered.Las matemáticas parecen tener un estatuto especial cuando se las compara con otras áreas del conocimiento humano. Este estatuto especial está conectado con el papel de la demostración. Los matemáticos creen con frecuencia que este tipo de argumentos no deja margen para el error o la falta de claridad. Los filósofos de la matemática han distinguido entre una concepción absolutista y una falibilista del conocimiento matemático, argumentando que estas concepciones están relacionadas con una consideración de las matemáticas-en-proceso o en tanto que matemáticas ya hechas. En este artículo examinamos más de cerca la práctica matemática, más en concreto el proceso de publicación en matemáticas. Argumentaremos que la idea preconcebida de que la literatura matemática, dado el estatuto especial de las matemáticas, es altamente fiable, es demasiado ingenua. Discutiremos algunos problemas del proceso de edición que amenazan esta visión y haremos algunas sugerencias sobre cómo enfrentarlos. (shrink)

Dieses Buch stellt sich die Aufgabe, Wege und Umwege nachzuzeichnen, die die philosophia practica universalis - Ethik, Politik, Okonomik - seit ihren Anfangen bis in unsere Tage zuruckgelegt hat. Dieses Programm setzt eine Kontinuitat voraus, die schon allein durch die Massgabe der praktischen Philosophie, namlich tugendhaft und gut zu leben, hinreichend gesichert ist. Gleichwohl sind Spannungen und Bruche zwischen Theorie und Lebenspraxis unumganglich, sofern praktische Philosophie, wenn sie glaubhaft sein will, ihre Argumente stets anlassbezogen im Blick auf sich andernde aussere (...) Umstande vortragen muss. So verkurzten die Stoiker in Abkehr von Platon und Aristoteles die praktische Philosophie notgedrungen auf die Ethik, weil ihr Spielraum aufgrund der Machtverhaltnisse eingeschrankt war. Dagegen war die unverkurzte Wiederkehr der praktischen Philosophie mitsamt ihrem methodischen Rustzeug geradezu ein Gebot der Stunde, als in den Tagen der Franzosischen Revolution sowie in den Jahren nach dem Zweiten Weltkrieg die Herstellung der Rechtsstaatlichkeit zum essentiellen Thema wurde. Tragende Saulen der philosophischen Begleitung dieses weltgeschichtlichen Geschehens wurden Ethik und Politik und ganz besonders die Okonomik als Ethik mit anderen Mitteln. Neben Sokrates, Platon und Aristoteles bezieht sich Armin Muller vor allem auf die antiken Denker Zenon, Chrysipp und Cicero sowie auf Hobbes, Kant, Hegel, Joachim Ritter, Gunther Bien, Hermann Lubbe und Odo Marquard. (shrink)

Complex problem solving (CPS) emerged in the last 30 years in Europe as a new part of the psychology of thinking and problem solving. This paper introduces into the field and provides a personal view. Also, related concepts like macrocognition or operative intelligence will be explained in this context. Two examples for the assessment of CPS, Tailorshop and MicroDYN, are presented to illustrate the concept by means of their measurement devices. Also, the relation of complex cognition and emotion in the (...) CPS context is discussed. The question if CPS requires complex cognition is answered with a tentative “yes.”. (shrink)

Hermann Cohen. Hermann Cohen Band 113. Kommentar' zu Immanuel Kants Kritik der reinen Vernunft. Kommentar Zu Immanuel Kants Kritik Der Reinen Vernunft (Job an, Kommentar z. Kants Kritik d. rein. Vernunft. 1. Front Cover.

One of the central aims of the philosophical analysis of mathematical explanation is to determine how one can distinguish explanatory proofs from non-explanatory proofs. In this paper, I take a closer look at the current status of the debate, and what the challenges for the philosophical analysis of explanatory proofs are. In order to provide an answer to these challenges, I suggest we start from analysing the concept understanding. More precisely, I will defend four claims: understanding is a condition for (...) explanation, unificatory understanding is a type of explanatory understanding, unificatory understanding is valuable in mathematics, and mathematical proofs can contribute to unificatory understanding. As a result, in a context where the epistemic aim is to unify mathematical results, I argue it is fruitful to make a distinction between proofs based on their explanatory value. (shrink)

This article focusses on women and the organisational leadership structures of the Apostolic Faith Mission in Zimbabwe. The aim is to identify the roles, practices and contributions of women to the developmental agenda in the church. The AFM in Zimbabwe identifies leadership positions in their various assemblies as pastor, elder, deacon and lay worker. From these ranks, the provincial and national leadership is chosen. The access to and participation of women in these offices and leadership positions will be investigated to (...) ascertain their input to the development of the church and perception of women in the society. The article discusses the mechanisms for the election of leadership in the AFM in Zimbabwe. It analyses leadership succession and leadership roles within the AFM in Zimbabwe from the perspective of gender equity and the involvement of women in policy-making, decision-making and the management of the church. Four aspects of the Exploratory Descriptive Normative Action research model were utilised from a practical theology perspective. The article shows that women do not have access to top leadership positions in the AFM in Zimbabwe even though there are no explicit policies that regulate their exclusion. It highlights their contribution to the development of the church despite this exclusion and engages critically with the unspoken assumption that women are not fit to take up the presidium offices and develop the AFM. The article finds that unquestioned patriarchal discourse contributes to women’s invisibility, which results in their not being taken into consideration when choices are made to elect people for higher leadership positions in the church. (shrink)

Hermann Lotze, der zu den bedeutendsten deutschen Philosophen des 19. Jahrhunderts zählt (und bis in die Zwanzigerjahre zu den meistdiskutierten gehörte), hat nicht nur den Neukantianismus und die Lebensphilosophie, sondern auch Husserls Phänomenologie und die frühe analytische Philosophie maßgeblich beeinflusst. Aufgrund seiner Doppelprofession als Philosoph und Mediziner steht Lotze im Zentrum der großen Transformationsbewegung im wissenschaftlichen Diskurs des 19. Jahrhunderts, die die Abtrennung der Wissenschaften von der idealistischen Philosophie und die Bemühung einer kritisch reflektierten Philosophie um Annäherung an die (...) Erfahrungswissenschaften mit sich brachte. Lotzes Einsicht, dass der Mensch nicht mehr im Mittelpunkt der Natur steht, sondern "dislociert" ist, weist in das Zentrum seines großen Werkes Mikrokosmos. Ideen zur Naturgeschichte und Geschichte der Menschheit (1856). Von ihm selbst in eine Linie mit Herders Ideen und A. v. Humboldts Kosmos-Schrift gestellt, liefert Mikrokosmos schon vor dem Erscheinen von Darwins Origin of Species (1859) eine hellsichtige Kritik des neuen Materialismus und der anthropologischen Grundproblematik unserer Epoche. Gegen den analytischen Geist in den Wissenschaften und gegen die Rastlosigkeit ihres Fortschritts hält er an der Vorstellung fest, dass jede Weltbeschreibung der Selbstdeutung des Menschen angemessen sein muss. Mit dem Begriff der "Dislocirung" wird auf den Punkt gebracht, was noch knapp hundert Jahre später die philosophische Anthropologie beschäftigen wird: Die Stellung des Menschen in der Natur ist fragwürdig geworden, innerhalb des Gesamtprozesses vom Leben gibt es keine eindeutige Position mehr für den Menschen. (shrink)