In the ordinary way of representing relations, the order of the relata plays a structural role, but in the states themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relations, different assignments of objects to the positions can give exactly the same states. This is a puzzling situation. (...) The question is what is the internal structure of relations? Is the use of positions still justified, and if so, what is their ontological status? In this paper mathematical models for relations are developed that provide more insight into the structure of relations “out there” in the real world. (shrink)
We study the logical structure of relations, and in particular the notion of occurrences of objects in a state. We start with formulating a number of principles for occurrences and defining corresponding mathematical models. These models are analyzed to get more insight in the formal properties of occurrences. In particular, we prove uniqueness results that tell us more about the possible logical structures relations might have.
Argument-places play an important role in our dealing with relations. However, that does not mean that argument-places should be taken as primitive entities. It is possible to give an account of relations in which argument-places play no role. But if argument-places are not basic, then what can we say about their identity? Can they, for example, be reconstructed in set theory with appropriate urelements? In this article, we show that for some relations, argument-places cannot be modeled in a neutral way (...) in V[A], the cumulative hierarchy with basic ingredients of the relation as urelements. We argue that a natural way to conceive of argument-places is to identify them with abstract, structureless points of a derivative structure exemplified by positional frames. In case the relation has symmetry, these points may be indiscernible. (shrink)
How we talk about relations has a great influence on how we think about relations. By saying that Spain defeated the Netherlands we obviously say something entirely different from saying that the Netherlands defeated Spain. This makes many of us think that in the underlying relation itself one of the relata comes first and the other comes second. However, there are good reasons to view the order as a representational artifact. In this paper I present a new logic that allows (...) us to think and talk about relations in a coordinate-free manner. The logic is minimalistic in the sense that it has no predicates except equality, but its expressive power is the same as that of first-order predicate logic. (shrink)
A theory of relations is presented that provides a detailed account of the logical structure of relational complexes. The theory draws a sharp distinction between relational complexes and relational states. A salient difference is that relational complexes belong to exactly one relation, whereas relational states may be shared by different relations. Relational complexes are conceived as structured perspectives on states ‘out there’ in reality. It is argued that only relational complexes have occurrences of objects, and that different complexes of the (...) same relation may correspond to the same state. (shrink)
A human right to freedom of religion is not equivalent to a right to tolerance. Human rights and tolerance-rules serve for different purposes and are based on different justifications. Tolerance-rules serve to protect a peaceful living together with strangers who share no common values. Human rights serve to protect every individual’s personhood. Religion can only be a matter of human rights, if and so far as it is a condition of development and maintenance of personhood. Discussion about a human right (...) to freedom of religion makes sense only if we can identify a particular scope of protection which concerns only religion and if the freedom of religion is not embraced by wider-framed freedoms. The freedom of religious thoughts and the freedom of religious speech are embraced by the general human rights to freedom of thoughts and freedom of speech. Here, there is no need for a special human right to freedom of religion. The right not to be forced to act contrary to religiously founded moral rules is embraced by the general human right to freedom of conscience. And again, there is no need for a special human right. The target of religious practices in a narrower sense is to become flexible and porous and not to resist the threats of the sacral in order to avoid the destruction of personhood. Therefore, we have to recognize a human right to freedom of religious rites. It protects only the actions of accommodation to the overwhelming power of the sacral. It does not protect, however, any action with which it is intended to rule the world or to rule over others, to organize certain practical challenges, or to discover or to maintain scientific theories or technical means. (shrink)
Brouwer's papers after 1945 are characterized by a technique known as the method of the creating subject. It has been supposed that the method was radically new in his work, since Brouwer seems to introduce an idealized mathematician into his mathematical practice. A newly opened source, the unpublished text of a lecture of Brouwer from 1934, fully supports the conclusions of our analysis that: - There is no idealized mathematician involved in the method;- The method was not new at all;- (...) Brouwer uses an incomplete sequence, also known as choice sequence, in this method, which is special. The method does not take its place in the standard works on choice sequences. (shrink)
This is a comprehensive collection of readings from the work of Theodor Adorno, one of the most influential German thinkers of the twentieth century. What took place in Auschwitz revokes what Adorno termed the “Western legacy of positivity,” the innermost substance of traditional philosophy. The prime task of philosophy then remains to reflect on its own failure, its own complicity in such events. Yet in linking the question of philosophy to historical occurrence, Adorno seems not to have abandoned his paradoxical, (...) life-long hope that philosophy might not be entirely closed to the idea of redemption. He prepares for an altogether different praxis, one no longer conceived in traditionally Marxist terms but rather to be gleaned from “metaphysical experience.” In this collection, Adorno's literary executor has assembled the definitive introduction to his thinking. Its five sections anatomize the range of Adorno's concerns: “Toward a New Categorical Imperative,” “Damaged Life,” “Administered World, Reified Thought,” “Art, Memory of Suffering,” and “A Philosophy That Keeps Itself Alive.” A substantial number of Adorno’s writings included appear here in English for the first time. This collection comes with an eloquent introduction from Rolf Tiedemann, the literary executor of Adorno’s work. (shrink)
In this paper we study the termination behavior of Russell’s description elimination rewrite system. We discuss certain claims made by Kripke (2005) in his paper concerning the possible nontermination of elimination of descriptions.
Food consumption has been identified as a realm of key importance for progressing the world towards more sustainable consumption overall. Consumers have the option to choose organic food as a visible product of more ecologically integrated farming methods and, in general, more carefully produced food. This study aims to investigate the choice for organic from a cultural–historical perspective and aims to reveal the food philosophy of current organic consumers in The Netherlands. A concise history of the organic food movement is (...) provided going back to the German Lebensreform and the American Natural Foods Movement. We discuss themes such as the wish to return to a more natural lifestyle, distancing from materialistic lifestyles, and reverting to a more meaningful moral life. Based on a number of in-depth interviews, the study illustrates that these themes are still of influence among current organic consumers who additionally raised the importance of connectedness to nature, awareness, and purity. We argue that their values are shared by a much larger part of Dutch society than those currently shopping for organic food. Strengthening these cultural values in the context of more sustainable food choices may help to expand the amount of organic consumers and hereby aid a transition towards more sustainable consumption. (shrink)
Begriffsanalyse und empirische Forschung auf dem Gebiet der künstlichen Intelligenz zeigen, daß momentan derart kontroverse Ansätze entwickelt werden, daß gemeinschaftliche Momente in Perspektiven und angewandten Methodologien nur schwer auszumachen sind.
Recent challenges of the mechanistic world picture seem only to have strengthened the position of mathematics. So it continues to guarantee perfect predictability, the dream of physicalism. During recent decades, however, computer simulations have shown mathematicians that even simple sets of equations may have, not an exact, but a whole range of solutions. With some of their examples we demonstrate the unpredictable behavior of simple systems. As a result, the dream is over. On the other hand, mathematicians also discovered that (...) previously 'chaotic' phenomena could be represented by relatively simple formules. This leads to a dramatic increase in the explanatory power of mathematics. This change of the scientific scenery will have a profound methodological impact on the relationship between the natural and the other sciences. (shrink)
Negative gegenseitige Befruchtung mag als seltsamer Titel erscheinen. Gegenseitige Befruchtung scheint per definitionem etwas Positives zu sein. Aber diese Untersuchung will die Aufmerksamkeit auf die Tatsache richten, daß in einer großen Anzahl von Fällen die gegenseitige Befruchtung einige negative Effekte auslöst; einige von ihnen mögen sogar katastrophal sein. Dieser Artikel kann die Aufmerksamkeit nur auf die negativen Auswirkungen und die Notwendigkeit lenken, die Bedingungen, welche den positiven oder negativen Ausgang oder die Unwirksamkeit einer bestimmten gegenseitigen Befruchtung determinieren, ausführlicher zu untersuchen; (...) um die Randbedingungen auf beiden Seiten zu formulieren: Das Befruchtende und das Befruchtete. (shrink)
Summary A pattern can be found in the history of semiconductor electronics, which largely appears to coincide with that of scientific revolutions as described by Thomas Kuhn1. However, the history of semiconductor electronics has some characteristics which suggest that Kuhn's model requires correction in important respects.
Anhand von zwei Unterbereichen der künstlichen Intelligenz - den Expertensystemen und der wissenschaftlichen Entdeckung - wird aufzuzeigen versucht, daß die Beziehung zwischen der "formalen" und der "intuitiven" Kultur aus dem Gleichgewicht geraten ist. Dem Bereich der Intuition sollte größere Aufmerksamkeit gewidmet werden.
Kant is a pivotal thinker in Adorno's intellectual world. Although he wrote monographs on Hegel, Husserl, and Kierkegaard, the closest Adorno came to an extended discussion of Kant are two lecture courses, one concentrating on the _Critique of Pure Reason_ and the other on the _Critique of Practical Reason_. This new volume by Adorno comprises his lectures on the former. Adorno attempts to make Kant's thought comprehensible to students by focusing on what he regards as problematic aspects of Kant's philosophy. (...) Adorno examines Kant's dualism and what he calls the Kantian "block": the contradictions arising from Kant's resistance to the idealism that his successors—Fichte, Schelling, and Hegel—saw as the inevitable outcome of his ideas. These lectures also provide an accessible introduction to and rationale for Adorno's own philosophy as expounded in _Negative Dialectics_ and his other major writings. Adorno's view of Kant forms an integral part of his own philosophy, since he argues that the way out of the Kantian contradictions is to show the necessity of the dialectical thinking that Kant himself spurned. This in turn enables Adorno to criticize Anglo-Saxon scientistic or positivist thought, as well as the philosophy of existentialism. This book will be of great interest to those working in philosophy and in social and political thought, and it will be essential reading for anyone interested in the foundations of Adorno's own work. (shrink)
This volume makes available in English for the first time Adorno's lectures on metaphysics. It provides a unique introduction not only to metaphysics but also to Adorno's own intellectual standpoint, as developed in his major work _Negative Dialectics._ Metaphysics for Adorno is defined by a central tension between concepts and immediate facts. Adorno traces this dualism back to Aristotle, whom he sees as the founder of metaphysics. In Aristotle it appears as an unresolved tension between form and matter. This basic (...) split, in Adorno's interpretation, runs right through the history of metaphysics. Perhaps not surprisingly, Adorno finds this tension resolved in the Hegelian dialectic. Underlying this dualism is a further dichotomy, which Adorno sees as essential to metaphysics: while it dissolves belief in transcendental worlds by thought, at the same time it seeks to rescue belief in a reality beyond the empirical, again by thought. It is to this profound ambiguity, for Adorno, that the metaphysical tradition owes its greatness. The major part of these lectures, given by Adorno late in his life, is devoted to a critical exposition of Aristotle's thought, focusing on its central ambiguities. In the last lectures, Adorno's attention switches to the question of the relevance of metaphysics today, particularly after the Holocaust. He finds in metaphysical experiences, which transcend rational discourse without lapsing into irrationalism, a last precarious refuge of the humane truth to which his own thought always aspired. This volume will be essential reading for anyone interested in Adorno's work and will be a valuable text for students and scholars of philosophy and social theory. (shrink)