We study computability of the abstract linear Cauchy problem equation image)where A is a linear operator, possibly unbounded, on a Banach space X. We give necessary and sufficient conditions for A such that the solution operator K: x ↦ u of the problem is computable. For studying computability we use the representation approach to computable analysis developed by Weihrauch and others. This approach is consistent with the model used by Pour-El/Richards.

A real number x is computable iff it is the limit of an effectively converging computable sequence of rational numbers, and x is left computable iff it is the supremum of a computable sequence of rational numbers. By applying the operations “sup” and “inf” alternately n times to computable sequences of rational numbers we introduce a non-collapsing hierarchy {Σn, Πn, Δn : n ∈ ℕ} of real numbers. We characterize the classes Σ2, Π2 and Δ2 in various ways and give (...) several interesting examples. (shrink)

Every second-countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space can be considered computationally as a subspace of some computable metric space [15]. While Schröder's construction is “pointless”, i. e., only sets of a countable base but no concrete points are known, for a computable metric space a concrete dense set of computable points (...) is needed. But there may be no computable points in X. By converging sequences of basis sets instead of Cauchy sequences of points we construct a metric completion of a space together with a canonical representation equation image, equation image. We show that there is a computable embedding of in with computable inverse. Finally, we construct a notation of a dense set of points in with computable mutual distances and prove that the Cauchy representation of the resulting computable metric space is equivalent to equation image. Therefore, every computably regular space has a computable homeomorphic embedding in a computable metric space, which topologically is its completion. By the way we prove a computable Urysohn lemma. (shrink)

For semi-continuous real functions we study different computability concepts defined via computability of epigraphs and hypographs. We call a real function f lower semi-computable of type one, if its open hypograph hypo is recursively enumerably open in dom × ℝ; we call f lower semi-computable of type two, if its closed epigraph Epi is recursively enumerably closed in dom × ℝ; we call f lower semi-computable of type three, if Epi is recursively closed in dom × ℝ. We show that (...) type one and type two semi-computability are independent and that type three semi-computability plus effectively uniform continuity implies computability, which is false for type one and type two instead of type three. We show also that the integral of a type three semi-computable real function on a computable interval is not necessarily computable. (shrink)

By the Riesz representation theorem for the dual of C [0; 1], if F: C [0; 1] → ℝ is a continuous linear operator, then there is a function g: [0;1] → ℝ of bounded variation such that F = ∫ f dg . The function g can be normalized such that V = ‖F ‖. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows (...) to define natural computability for a variety of operators. We show that there are a computable operator S mapping g and an upper bound of its variation to F and a computable operator S ′ mapping F and its norm to some appropriate g. (shrink)

This paper initiates the study of sets in Euclidean spaces ℝn that are defined in terms of the dimensions of their elements. Specifically, given an interval I ⊆ [0, n ], we are interested in the connectivity properties of the set DIMI, consisting of all points in ℝn whose dimensions lie in I, and of its dual DIMIstr, consisting of all points whose strong dimensions lie in I. If I is [0, 1) or.

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees (...) can be embedded. The importance of Weihrauch degrees is based on the fact that multi-valued functions on represented spaces can be considered as realizers of mathematical theorems in a very natural way and studying the Weihrauch reductions between theorems in this sense means to ask which theorems can be transformed continuously or computably into each other. As crucial corner points of this classification scheme the limited principle of omniscience LPO, the lesser limited principle of omniscience LLPO and their parallelizations are studied. It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn—Banach Theorem in this new and very strong sense. We call a multi-valued function weakly computable if it is reducible to the Weihrauch degree of parallelized LLPO and we present a new proof, based on a computational version of Kleene's ternary logic, that the class of weakly computable operations is closed under composition. Moreover, weakly computable operations on computable metric spaces are characterized as operations that admit upper semi-computable compact-valued selectors and it is proved that any single-valued weakly computable operation is already computable in the ordinary sense. (shrink)

Der Fokus auf die Sprache bestimmte die Philosophie des 20. Jahrhunderts, die sowohl die Dekonstruktion der Metaphysik als auch den Tod des Subjekts verkündete. Der Psychoanalytiker Jacques Lacan führte das Subjekt des Begehrens wieder in den philosophischen Diskurs ein und entwickelte aus der Struktur der Sprache eine neue, symbolische Logik des Unbewussten. Die Logik des Signifikanten, deren Geschichte diese Arbeit nachzeichnet, um sie zu transzendieren, stellt die Frage nach der Dialektik von Signifikant und Begriff, Sprache und Logik, Bewusstem und Unbewusstem, (...) Ich und Subjekt, Gesetz und Begehren, Denken und Sein. Durch die Funktionen der Metonymie, der Metapher und des Stepppunktes sowie über das Schema der vier Diskurse werden die Tropen der traditionellen philosophischen Logik - Begriff, Urteil und Schluss - neu interpretiert. Das Peirce'sche Konzept der Abduktion ermöglicht es, sowohl den Borromäischen Knoten Lacans - Imaginäres, Symbolisches und Reales - wie auch die transzendentale Dialektik und Ontologie der Moderne, die auf Kants und Hegels Revolutionen der Denkungsart zurückgehen, schlusslogisch zu begründen. (shrink)

Diese komparatistische Monographie stellt zentrale Kategorien und Theorien der Literaturwissenschaft dar. Sie synthetisiert und bewertet den Stand der Forschung und unterwirft viele Dogmen der neueren Forschung einer kritischen Analyse. Resultat ist eine Reformulierung des theoretischen Kernbestandes der Literaturwissenschaft für die zentralen Kategorien Interpretation, Fiktion, Performativität, Intertextualität, Gattung, Epoche. Der Band richtet sich an alle Wissenschaften, die mit Texten als Erkenntnisobjekten umgehen; neben der Literaturwissenschaft sind also auch die Theaterwissenschaft, die Sprachwissenschaft, die Sprachphilosophie, die Kunstwissenschaft, die Geschichtswissenschaft sowie Theologie und Jurisprudenz (...) angesprochen. (shrink)

The placebo drug reactions from controlled trials were studied for the first time systematically for efficacy and the safety in drug data pooled from randomized, placebo-controlled, multicentre studies. Results: The efficacy of placebo on clinical symptoms and outcome varied between the therapeutic indications. However, no placebo effects on laboratory values, as e.g. blood glucose or Hb1c in diabetics, were noted. The frequency and type of placebo-induced adverse reactions also varied between indication groups. The placebo side effect profile was largely similar (...) to the side effect profile of the active treatment. The mechanisms of placebo effects are manyfold and varied (e.g. endorphin release, conditioning), much lacks explanation. Conclusion: Since the prescription of non-evidence based medicines (= pseudoplacebos) may clearly also result in serious adverse effects, such practice may not only be non-beneficial but may even be harmful. In clinical research, the judicious use of placebo remains essential to establish the efficacy and safety, safeguarding that patients receiving placebo will not be subject to harm and are fully informed. (shrink)

The placebo drug reactions from controlled trials were studied for the first time systematically for efficacy and the safety in drug data pooled from randomized, placebo-controlled, multicentre studies. Results: The efficacy of placebo on clinical symptoms and outcome varied between the therapeutic indications. However, no placebo effects on laboratory values, as e.g. blood glucose or Hb1c in diabetics, were noted. The frequency and type of placebo-induced adverse reactions also varied between indication groups. The placebo side effect profile was largely similar (...) to the side effect profile of the active treatment. The mechanisms of placebo effects are manyfold and varied (e.g. endorphin release, conditioning), much lacks explanation. Conclusion: Since the prescription of non-evidence based medicines (= pseudoplacebos) may clearly also result in serious adverse effects, such practice may not only be non-beneficial but may even be harmful. In clinical research, the judicious use of placebo remains essential to establish the efficacy and safety, safeguarding that patients receiving placebo will not be subject to harm and are fully informed. (shrink)

Attention is automatically allocated to stimuli that are opposite in valence to the current motivational focus (Rothermund, 2003; Rothermund, Voss, & Wentura, 2008). We tested whether this incongruency effect is due to affective–motivational counter-regulation or to an increased salience of stimuli that mismatch with cognitively activated information. Affective processing biases were assessed with a search task in which participants had to detect the spatial position at which a positive or negative stimulus was presented. In the motivational condition, positive or negative (...) affective–motivational states were induced by performance feedback after each trial. In the cognitive activation condition, participants memorised the word “good” or “bad” during the search task. The affective incongruency effect was replicated in the motivational condition, whereas an affective congruency effect obtained in the cognitive activation condition. These findings support an explanation of affective incongruency effects in terms of automatic counter-regulation that is motivational in nature. (shrink)

The achievement of unity and perfection in human action begins with a struggle for these ideals in human thought. Dr. Klaus Vondung in his collection of essays that span four decades explores examples of this in different fields of human inquiry: striving for harmonious existential unity of talents and morals, intellect and emotion; seeking to make natural sciences consonant with the humanities and thereby moving toward a more universal, "perfect" science; and establishing unity in political structures and cultivating in (...) this unity a homogenous society. Vondung has given special devotion to National Socialism as a context wherein he revisits its perverted motivation and the consequences of this despite noble ideals. Particular focus in following the thread of unity and perfection in human intellectual and practical ambitions ultimately hones in on the combination of religion and politics. Vondung in these essays unpacks the ways in which this continues to fascinate and disturb us, and in his expertise he uses National Socialism to connect this pursuit of unity and perfection to what he calls one of the signature marks of modernity--namely, secular apocalypticism. This claim stands in opposition to Eric Voegelin's remark that Gnosticism, rather, is "the nature of modernity." Vondung, who studied and wrote his dissertation under Voegelin, grapples with the contrast of these positions. Vondung is willing to challenge Voegelin, but ultimately his treatment of the latter bears the quality of tribute to this great scholar. Vondung also explores the points of contact between apocalypticism and Hermetic speculation. Despite the independence of the religious and philosophical doctrines of Hermeticism, there are parallels to be found. Apocalypticism and Hermeticism originated in antiquity and yet each represents a tradition that still holds footing today. Vondung furthermore leads the reader to see the project of salvation found in both even as each operates with a different scope. This collection of essays centers itself on a perspective of the human pursuit of unity and perfection, directly or indirectly, as objectives of intellectual endeavors, existential ideals, as social or political outcomes, and in the case of National Socialism even as perverse aberrations. Vondung's particular treatment of Voegelin's work likewise establishes what the former identifies as a stand-out question of this study: Does the search of order in history show us the unity of the history of humankind? (shrink)

In this book, linguists and philosophers combine to offer a unique insight not only into Grice's contribution to philosophy of language, but on his theories of natural and non-natural meaning, implicatures and the semantic-pragmatic distinction.

This chapter describes the phenomenology of the political world. Phenomenology must get underway with an analysis of the political world. The chapter evaluates more precisely the relation between the concept of world or worldliness and the openness of the political. Using the term ‘political world’ is preferred to utilising the traditional terms because it is less burdened by prejudice. The guiding impulse towards the clarification of the Sache of political philosophy as political world stems from Hannah Arendt, who does not (...) make use of the phenomenological conception of ‘horizon’. Science's confidence that it can attain a knowledge free of all horizonal plurality is among the most fundamental prejudices that phenomenology endeavours to overcome. Phenomenology is the decided present renewal of the most ancient idea of epistêmê. (shrink)

In the age of digitization, the world seems to be reducible to a digital computer. However, mathematically, modern quantum field theories do not only depend on discrete, but also continuous concepts. Ancient debates in natural philosophy on atomism versus the continuum are deeply involved in modern research on digital and computational physics. This example underlines that modern physics, in the tradition of Newton’s Principia Mathematica Philosophiae Naturalis, is a further development of natural philosophy with the rigorous methods of mathematics, measuring, (...) and computing. We consider fundamental concepts of natural philosophy with mathematical and computational methods and ask for their ontological and epistemic status. The following article refers to the author’s book, “The Digital and the Real World. Computational Foundations of Mathematics, Science, Technology, and Philosophy.”. (shrink)

Historical Justice and Memory highlights the global movement for historical justice—acknowledging and redressing historic wrongs—as one of the most significant moral and social developments of our times. Such historic wrongs include acts of genocide, slavery, systems of apartheid, the systematic persecution of presumed enemies of the state, colonialism, and the oppression of or discrimination against ethnic or religious minorities. The historical justice movement has inspired the spread of truth and reconciliation processes around the world and has pushed governments to make (...) reparations and apologies for past wrongs. It has changed the public understanding of justice and the role of memory. In this book, leading scholars in philosophy, history, political science, and semiotics offer new essays that discuss and assess these momentous global developments. They evaluate the strength and weaknesses of the movement, its accomplishments and failings, its philosophical assumptions and social preconditions, and its prospects for the future. (shrink)

Die Wissenschaft hat - von der Wissenschaftstheorie des 20. Jahrhunderts gründlich untersucht - bestimmte Strukturen ihres Wissens, ihrer Methodik der Wissensgewinnung und Wissensabsicherung entwickelt, die sie von anderen Arten des Umgangs mit Wissen - z.B. der Alltagserfahrung - signifikant unterscheidet. Für die Technikwissenschaften haben solche wissenschaftstheoretischen Untersuchungen jedoch bisher kaum stattgefunden. Was etwa die analytische Wissenschaftstheorie für die Naturwissenschaften geleistet hat, steht daher für die Technikwissenschaften noch aus. Denn das technische Wissen unterscheidet sich vom wissenschaftlichen Wissen in seiner inneren Struktur. (...) Diese Struktur aufzuklären ist eine lohnende Aufgabe, weil deren Kenntnis hilft, besser mit Technik umzugehen. Die in diesem Band vorgelegten analytischen Studien zur Wissenschaftstheorie der Technikwissenschaften behandeln - ausgehend vom Problem der Formalisierung und der Wahrheitsfrage in der Philosophie - die Grundeinheit des technischen Wissens, die technologische Regel, und den Aufbau und Zusammenhang technologischer Theorien. Daraus ergeben sich Hinweise auf die innere, d.h. auch logische Struktur des technischen Wissens. (shrink)

The goal of this paper is to propose a unified approach to the split scope readings of negative indefinites, comparative quantifiers, and numerals. There are two main observations that justify this approach. First, split scope shows the same kinds of restrictions across these different quantifiers. Second, split scope always involves low existential force. In our approach, following Sauerland, natural language determiner quantifiers are quantifiers over choice functions, of type <<,t>,t>. In split readings, the quantifier over choice functions scopes above other (...) operators (such as intensional verbs like must or can). Determiner quantifiers leave a choice-function trace when they move and this trace combines with the noun restriction, which is interpreted low. That split scope always involves low existential force is derived, without stipulation, from Kratzer’s idea that low existential force can be achieved via binding (into the noun restriction). (shrink)

Technischer Wandel in hoher Geschwindigkeit kennzeichnet unsere Zeit. Dieser Wandel wirft grundsätzliche Fragen auf: Können wir begreifen, was wir tun? Können wir abschätzen, was wir tun? Können wir wollen, was wir tun? Können wir sagen, was wir tun? Können wir leben, was wir tun? Mit Fragen wie diesen hat sich der Philosoph Klaus Kornwachs immer wieder auseinandergesetzt. Ihm zu Ehren widmen sich die Autorinnen und Autoren in ihren Essays der Philosophie der Technik, der Technikfolgenabschätzung sowie der Ethik, Sprache und (...) Kultur der Technik. Neben Philosophen kommen auch Vertreter der Soziologie, Medizin, Technik- und Wirtschaftsgeschichte, Psychologie, Physik, Theologie, Ingenieurswissenschaft, Ökonomie, Politologie und Rhetorik zu Wort. So entsteht - ganz im Sinne Klaus Kornwachsˈ - ein breites Spektrum von Ein- und Ansichten. (shrink)

Zusammenfassung Der Beitrag analysiert auf der Basis theoretischer Überlegungen sowie empirischer Ergebnisse Möglichkeiten und Grenzen einer „interkulturellen Öffnung“ von Sportvereinen, worunter Strukturanpassungen verstanden werden, die auf die Inklusion und Integration von Personen mit Migrationshintergrund zielen. Es wird gezeigt, inwiefern eine nachhaltige interkulturelle Öffnung der Vereine von der programmatischen Anbindung an den Vereinszweck, von der kontinuierlichen Behandlung in den Kommunikationswegen, von spezifischen Personalentscheidungen und der Kompatibilität mit der Organisationskultur abhängig ist.

Im vorliegenden Buch stellt Klaus Oehler die Lehre vom noetischen und dianoetischen Denken bei Platon und Aristoteles dar und begründet damit erstmals die These, dass das für die neuzeitliche Philosophie zentrale Problem der Reflexion und des Selbstbewusstseins schon, wenn auch nicht in gleicher Weise, in der antiken Philosophie eine Rolle gespielt hat.

Describes the classicall law theory basics. Translaltion from German.

Die Untersuchung entwickelt hermeneutisch-phänomenologisch eine Antwort auf die Frage, wie die Lebenswelt als Natur erfahren wird. Sie zeigt, wie der Naturbegriff bei Kant, insbesondere in den mathematischen Grundsätzen der «Kritik der reinen Vernunft», verarmt und wie er sich schon bei Aristoteles verengt. Bei beiden eröffnet sich aber zugleich die Möglichkeit des Rückgangs zu einem ursprünglicheren Naturverständnis im frühgriechischen Denken von Anaximander und Heraklit. Diesen Rückgang realisiert eine Neuinterpretation der Kosmologie und Psychologie des Aristoteles im weiteren Verlauf der Arbeit. Das führt (...) zu einer Phänomenologie der Erfahrung des «Elementaren», das wissenschaftsgeschichtlich in Gestalt der alten Elemente Feuer, Wasser, Erde, Luft in Erscheinung trat, aber eigentlich eine viel weitere Bedeutung hat, die in den sogenannten subjektlosen Sätzen zur Sprache kommt. (shrink)

Der Mathematiker Erhard Weigel (1625-1699) gilt bisher als einer der bedeutendsten deutschen Vertreter der sog. "Fruehaufklärung". Dieser Band hinterfragt nun diesen traditionellen und deshalb allzu bequemen philosophiegeschichtlichen Begriff nach seiner Erklärungsfunktion innerhalb der modernen Wissenschaftsgeschichte. In komparatistischer Sicht auf die deutsche Universitätslandschaft nehmen die Beiträger den institutionellen Rahmen und seine konkreten Auswirkungen auf den Lehrbetrieb in den Blick, um die Bedingungen des damaligen Wissenschaftsverständnisses und seiner Entwicklungsrichtungen zu untersuchen. Im Fokus stehen die Verwandlungen der aristotelischen Basis des Wissenschaftsverständnisses und was (...) sich damalige Universitätslehrer als Autoren explizit (z.B. in Form wissenschaftstheoretischer Schriften und Lehrbuecher) oder implizit (z.B. in Form der von ihnen praktizierten Wissenschaft) unter Wissenschaft vorgestellt und ihrem gelehrten Publikum vermittelt haben. (shrink)