This article discusses the history of the concepts of potential infinity and actual infinity in the context of Christian theology, mathematical thinking and metaphysical reasoning. It shows that the structure of Ancient Greek rationality could not go beyond the concept of potential infinity, which is highlighted in Aristotle's metaphysics. The limitations of the metaphysical mind of ancient Greece were overcome through Christian theology and its concept of the infinite God, as formulated in Gregory of Nyssa's theology. That is how the (...) concept of actual infinity emerged. However, Gregory of Nyssa's understanding of human rationality went still further. He said that access to the infinity of God was to be found only in an asymptotic ascension, as expressed in apophatic theology, and this view endangered the rationality of theology. Deeply influenced by the apophatic tradition, Nicholas of Cusa avoided this danger by showing that infinity could be accessed by symbolic representation and asymptotic mathematical reasoning. Thus, he made an immense contribution in making infinity rationally accessible. This endeavor was finally realized by Georg Cantor. This rational accessibility revealed discernible structures of infinity, such as the continuum hypothesis, and the cardinal numbers. However, the probable logical inconsistency of Georg Cantor's all-encompassing Absolute Infinity points to an intuitive understanding of infinity that goes beyond its rational structures – as in apophatic theology. (shrink)

ZusammenfassungDie Mystik gilt im interreligiösen Dialog als diejenige Dimension von Religion, die gemäß dem Essentialismus den gemeinsamen Kern der Religionen darstellt. In Unterschied dazu vertritt der Kontextualismus die These, dass Mystik nur in spezifischen religiösen Kontexten entsteht und so seine unverwechselbare Eigenheit erhält. Saeed Zarrabi-Zadeh vergleicht in seiner Arbeit Meister Eckhart und Rumi methodisch so miteinander, dass er die jeweiligen Stärken des Essentialismus und des Kontextualismus nutzt und ihre Schwächen vermeidet. Auf der Grundlage dieses methodischen Neuansatzes und eines weitgefassten Mystikbegriffs, (...) der Ethik, Praxis, Spekulation und Dogmatik umfasst, kommt er zu neuen Differenzierungen im religionsphänomenologischen Vergleich und legt zugleich erhebliche Differenzen im theologischen Deutehorizont der jeweiligen Mystiker offen. Darüberhinaus arbeitet er mit seiner Interpretation der. (shrink)

Hermann Grassmann is known to be the founder of modern vector and tensor calculus. Having as a theologian no formal education in mathematics at a university he got his basic ideas for this mathematical innovation at least to some extent from listening to Schleiermacher’s lectures on Dialectics and, together with his brother Robert, reading its publication in 1839. The paper shows how the idea of unity and various levels of reality first formulated in Schleiermacher’s talks about religion in 1799 were (...) transformed by him into a philosophical system in his dialectics and then were picked up by Grassmann and operationalized in his philosophical-mathematical treatise on the extension theory in 1844. (shrink)

ZUSAMMENFASSUNGEs werden aus der Theologiegeschichte vier Typen von Willensfreiheit erhoben: der Typus liberum arbitrium , der Typus des nominalistischen Willensbegriffs , der Typus des mystischen Willensbegriffs und der Typus der Rechtfertigungslehre. Die ersten drei Typen werden psychologisch interpretiert im Sinne der Ichentwicklung als präautonom, autonom und transautonom. Nach der Darstellung und Diskussion der gegenwärtigen neurowissenschaftlichen Debatte um die Willensfreiheit wird ein systemisch verstandener Personbegriff als Brückenkonzept vorgeschlagen.SUMMARYFour types of free will are identified from the history of theology: The type of (...) the liberum arbitrium, the type of nominalism, the type of mysticism and the type of justification. For the first three types a psychological interpretation in terms of pre-autonomy, autonomy, and trans-autonomy is offered, based on self-transcendence as a religious feature. Two basically opposing interpretations of the same empirical data favoring free will and favoring a non-free will are discussed and compared with the theological tradition. A new notion of the person, based on the system theory, is suggested as a bridging concept to link the theological and neuro-scientific ideas of free will. (shrink)

Theories of the nature of time offered by anthropology, science, and religion are not only numerous but also very different. This groundbreaking book cuts through the confusion by introducing a provocative new tripolar model of time that integrates the human, natural, and religious dimensions of time into a single, harmonious whole. Wolfgang Achtner, Stefan Kunz, and Thomas Walter begin by exploring the structures of time in anthropological terms. They discuss time phenomenologically, showing how it can be experienced in (...) three distinct ways -- the mythic-cyclic, the rational-linear, and the mystic-holistic -- and they root these experiences in the findings of modern neuroscience and trace these three forms of the perception of time within various cultures of antiquity. The second part of the book looks at time as it has been described by some of sciences most profound theories, including classical mechanics, the special and general theories of relativity, quantum mechanics, thermodynamics, and chaos theory. The authors then bring religion into the equation by surveying how time is conceived in both the Hebrew Bible and the Christian New Testament. They distinguish time concepts in wisdom and apocalyptic literature from time concepts in prophetic literature, and they demonstrate the basic eschatological orientation of the Christian view of time. "Dimensions of Time culminates by tying together the various strands of the authors' multidisciplinary, tripolar model of time. Offering a fascinating application of their unique theory, Achtner, Kunz, and Walter show how the unhealthy acceleration of life in contemporary society needs to be balanced by a rediscovery ofthe mystical experience of time, leading to a greater, deeper sense of human fulfillment. (shrink)

This paper addresses three issues. In the first part the relation between consciousness and time is being discussed as it developed in the history of philosophy and theology. This covers Plato, Plotinus and St. Augustine. It continues in the second part to describe that time is being perceived in the mystical consciousness as eternity which means in this context timelessness. Examples from world religions are offered. The question is asked if this eternity in mystical experience can be understood as relating (...) to the eternity of God or as a mere self-experience. In order to settle this question mystical experiences are being interpreted from the angle of modern neuroscience as the result of self-organizing processes of meditation that can be described as attractors. In the final third part it is suggested to discern the eternity of mystical states of mind as timelessness from eternity as an attribute of the triune God. (shrink)

'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (1862-1943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen (...) world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"--Provided by publisher. (shrink)

Rational agents are supposed to maximize expected utility. But what are the options from which they choose? I outline some constraints on an adequate representation of an agent’s options. The options should, for example, contain no information of which the agent is unsure. But they should be sufficiently rich to distinguish all available acts from one another. These demands often come into conflict, so that there seems to be no adequate representation of the options at all. After reviewing existing proposals (...) for how to construe decision-theoretic options and finding them all wanting, I suggest that our model of rational agents should include a special domain of ‘virtual’ option propositions to serve as formal objects of deliberation and choice. (shrink)

Dieses Buch geht davon aus, dass eine moderne Hermeneutik als Theorie des Verstehens im begrifflichen Rahmen der gegenwärtigen Theorie des Geistes und der Semantik rekonstruiert werden sollte. Vor diesem theoretischen Hintergrund, der in einem eigenen Kapitel näher umrissen wird, soll die Geschichte der Hermeneutik neu gelesen werden. Dabei wird deutlich, dass diese Lesart vielfach neue historische Interpretationen zu entwickeln und die wichtigsten Stationen der Geschichte der Hermeneutik theoretisch auf neue Weise zu integrieren vermag. Über die hermeneutischen Positionen hinaus, die in (...) den bisherigen Gesamtdarstellungen auftauchen, werden auch Entwürfe diskutiert, die besonders unter geist-theoretischen Aspekten interessant sind, zum Beispiel die antike Hermeneutik, die Hermeneutik Max Webers, die Hermeneutik der logischen Empiristen und die naturalistische Hermeneutik. Vor allem aber wird belegt, dass die Geschichte der Hermeneutik teilweise zu großen Einsichten gelangt ist, an die eine moderne Hermeneutik anknüpfen kann. Das Buch wendet sich nicht nur an Spezialisten der Hermeneutik-Geschichte, sondern an alle Interessierten, denen das Schicksal der verstehenden Wissenschaften am Herzen liegt, und möchte ihnen eine Perspektive empfehlen, unter der sich der Status und die Autonomie der Geisteswissenschaften sowie ihr Bezug auf das Humane unter Heranziehung substantieller Theorien auf neue Weise würdigen lassen. (shrink)

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other (...) academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui tivity and concreteness. (shrink)

Einflussreiche Denkerin des 20. Jahrhunderts. Das Handbuch erklärt die philosophischen, politischen und literarischen Kontexte, die Hannah Arendts Denken geprägt haben. Es präsentiert neben Informationen zur Biografie und den zeitgenössischen Bezügen alle wichtigen Werke und gibt Hinweise zu deren internationaler Rezeption in vielen Disziplinen. Zentrale Begriffe und Konzepte im Gesamtwerk Hannah Arendts werden ausführlich erklärt darunter: Antisemitismus, Das Böse, Macht, Revolution, Republik/Nation, Totalitarismus u. v. a.

Adorno, an important selection by Horkheimer and Adorno (from Dialectic of Enlightenment), as well as works by Walter Benjamin, Leo Lowenthal, Herbert Marcuse, Norbert Elias, and Jurgen Habermas."--BOOK JACKET.

Gottlob Frege has exerted an enormous influence on the evolution of twentieth-century philosophy, yet the real significance of that influence is still very much a matter of debate. This book provides a completely new and systematic account of Frege's philosophy by focusing on its cornerstone: the theory of sense and reference. Two features distinguish this study from other books on Frege. First, sense and reference are placed absolutely at the core of Frege's work; the author shows that no adequate account (...) of the theory can avoid analysing the notion of thought that underpins it, or explaining how it has clarified our concept of judgement. Second, the theory is situated within the development of Frege's thought; the author reveals how the theory caused Frege to alter many of his fundamental views. In doing so the author presents a clearer picture of the problems the theory was intended to solve, and delineates more sharply the characteristic features of Frege's philosophy. (shrink)

Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that it is (...) much more concise than most others, and the material is treated in a streamlined fashion which allows the professor to cover many important topics in a one semester course. Although the book is intended for use as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. This material is of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and other subjects. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. The author has provided exercises for each chapter, as well as hints to selected exercises. About the German edition: …The book can be useful to the student and lecturer who prepares a mathematical logic course at the university. What a pity that the book is not written in a universal scientific language which mankind has not yet created. - A.Nabebin, Zentralblatt. (shrink)

The paper argues that Gareth Evans’ argument for transparent self-knowledge is based on a conflation of doxastic transparency with ascriptive transparency. Doxastic transparency means that belief about one’s own doxastic state, e.g., the belief that one thinks that it will rain, can be warranted by ordinary empirical observation, e.g., of the weather. In contrast, ascriptive transparency says that self-ascriptions of belief, e.g., “I believe it will rain”, can be warranted by such observation. We first show that the thesis of doxastic (...) transparency is ill-motivated and then offer a non-epistemic interpretation of ascriptive transparency by reference to the theory of explicit expressive acts: “I think it will rain” requires attendance to the weather because the utterance expresses a belief about the weather, not about ourselves. This will allow us to avoid what is often called “the puzzle of transparent self-knowledge” while remaining faithful to Evans’ linguistic observations. (shrink)

This paper starts out from the idea that semantics is a “special science” whose aim, like that of chemistry or ecology, is to identify systematic, high-level patterns in a fundamentally physical world. I defend an approach to this task on which sentences are associated with with sets of possible worlds (of some kind). These sets of worlds, however, are not postulated for the compositional treatment of intensional contexts; they are not meant to capture what is intuitively asserted or communicated by (...) an utterance; nor are they supposed to shed light on the cognitive processes that underlie out linguistic competence. Instead, their job description is to capture certain regularities in the interactions between subjects using the relevant language. I also raise some questions about how the relevant worlds might be construed. (shrink)

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

While Kant’s position concerning human freedom and divine foreknowledge is perhaps the least Molinist element of his multifaceted take on free will, Kant’s Molinism (minimally defined) is undeniable when it comes to the threat ensuing from the idea of creation. In line with incompatibilism and with careful qualifications in place, he ultimately suggests regarding free agents as uncreated. Given the limitations of our rational insight, this assumption is indispensable for granting that finite free agents can acquire their intelligible characters by (...) themselves. Nonetheless, Kant concedes that creation may, as a matter of fact, be compatible with what for Molina is the pre-volitionality of the counterfactuals of freedom. (shrink)

English summary: A commentary on Spinoza's final work, Tractatus Politicus has until recently remained a desideratum. In contrast to his metaphysics and his philosophy of religion, Spinoza's theories on politics, the state and law have received little attention in the German-speaking countries. It's only recently that Spinoza's political philosophy again become widely discussed in Germany. Having established the role of political philosophy and working always within the context of Spinoza's complete work, this volume comments firstly on Spinoza's theory on the (...) natural genesis of law and the state, including the foundations of political philosophy, the relationship between natural and national law and the theory of sovereignty and international relations. Continuing on this basis it moves on to his concept for the optimization of the system of political and legal institutions in all three forms of government. Finally, there is an analysis of the current relevance of Spinoza's thought and its impact on current debate. The work includes contributions by Tilman Altwicker, Wolfgang Bartuschat, Tobias Herbst, Gunnar Hindrichs, Rainer Keil, Stephan Kirste, Martin Leiner, Oliver W. Lembcke, Tilman Reitz and Manfred Walther. German description: Ein Kommentar zu Spinozas letztem Werk Tractatus politicus war bislang ein Desiderat. Spinozas Theorie der Politik, des Staates und des Rechts ist anders als seine Metaphysik und seine Religionsphilosophie im deutschsprachigen Bereich lange wenig beachtet worden. Erst in jungerer Zeit ist die Beschaftigung mit Spinozas politischer Philosophie auch in Deutschland wieder intensiver geworden. Nach einer Bestimmung des Ortes der Politischen Philosophie und stets im Kontext von Spinozas Gesamtwerk kommentiert der Band zunachst Spinozas Theorie der naturlichen Genese von Recht und Staat, so die Grundlagen der politischen Philosophie, das Verhaltnis von naturlichem und staatlichem Recht, die Theorie der Souveranitat und der internationalen Beziehungen. Auf dieser Grundlage folgt dann seine Konzeption einer Optimierung des Systems politisch-rechtlicher Institutionen fur alle drei Regierungsformen. Abschliessend werden die Aktualitat des Denkens Spinozas und sein Einfluss auf gegenwartige Debatten analysiert. Mit Beitragen von: Tilman Altwicker, Wolfgang Bartuschat, Tobias Herbst, G unnar Hindrichs, Rainer Keil, Stephan Kirste, Martin Leiner, Oliver W. Lembcke, Tilman Reitz, Manfred Walther. (shrink)

Magnetism in meta-semantics is the view that the meaning of our words is determined in part by their use and in part by the objective naturalness of candidate meanings. This hypothesis is commonly attributed to David Lewis, and has been put to philosophical work by Brian Weatherson, Ted Sider and others. I argue that there is no evidence that Lewis ever endorsed the view, and that his actual account of language reveals good reasons against it.