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)

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.

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)

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)

La menzogna è irrinunciabile per vincere in politica? Davi ci spiega quali sono i meccanismi di persuasione a cui ricorrono taluni politici per farsi eleggere e quali le responsabilità di quegli elettori che scelgono comunque di votare chi sostiene anche ciò che non può essere vero. È indubbio che la comunicazione politica si rifaccia al simbolismo e al linguaggio delle favole; non necessariamente per occultare la realtà, ma più direttamente per esprimere con maggiore efficacia il suo messaggio. Alle celebri favole (...) di 'Biancaneve', 'Cenerentola', 'Il brutto anatroccolo' sono ricorsi infatti uomini politici del calibro di Berlusconi, Prodi, Nixon, Carter, Mitterrand e partiti quali la Democrazia Cristiana; l'hanno fatto per conquistare voti ma anche per attivare ampi meccanismi di consenso che attingessero direttamente dall'inconscio collettivo. Le conseguenze - ammonisce l'autore - possono essere molto serie, come nel caso dell'attuale politica americana che ha portato la manipolazione e l'inganno a essere riconosciuti come tratti identitari della presidenza di George W. Bush. (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.

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)

I show that in his De motu animalium Aristoteles proposes a teleology of the practical on the most general zoological level, i.e. on the level common to humans and self-moving animals. A teleology of the practical is a teleological account of the highest practical goals of animal and human self-motion. I argue that Aristotle conceives of such highest practical goals as goals that are contingently related to their realizations. Animal and human self-motion is the kind of action in which certain (...) state of affairs that realize values are mechanized. (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.

This important and challenging book is the fruit of many years of engagement with Aristotle’s thinking about the soul-body relation by one of the most distingui.

This paper discusses Aristotle's notion of the practical syllogism. It is argued that the notion of ‘practical’ reasoning in the sense of reasoning which implies motion in one sense or the other is alien to Aristotle's philosophy of nature. All (at least in type) the relevant passages will be discussed. The outcome is that there are three different contexts in which it would be justified to speak of practical syllogisms: (i) human deliberation, (ii) the illustration of the triggering cause of (...) animal motion, and (iii) the teleological ex post explanationof human action. (i) is genuine, but non-deductive reasoning which does not immediately result in action/motion, whereas (ii) is not genuine reasoning, but an analogy with deductive reasoning. Finally, the relation between (i) and (ii) in Aristotle's theory of animal motion will be discussed. (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)

The aim of this chapter is to explain Aristotle’s definition of the vegetative part of the soul in the De anima from a methodological point of view. I discuss Aristotle’s conception of the soul and his conception of “parts of the soul” before I turn to his definition of the vegetative part of the soul in De anima II 4. I argue that the definition of the vegetative capacity is deliberately abstract so as to cover its various activities under one (...) common heading. I also argue that the De anima deliberately avoids a positive and determinate description of the activity of the soul that is properly responsible for the vegetative functions, and that Aristotle offers such a positive and determinate description in his works dedicated to the actions and affections “common to body and soul”. (shrink)

Proceedings of the NATO Advanced Study Institute on Proof and Computation, held in Marktoberdorf, Germany, July 20 - August 1, 1993.

How do animals make themselves move? Unlike most modern theories, Aristotle answers this question through a general theory of animal movement valid for both humans and animals. This book interprets this theory and analyses its fundamental concepts.

Images are objects of work in the laboratory. On its face, this work is achieved through talk Yet the talk attached to these images makes reference to other images, which are drawn from varcous environments. In this article, four such environments are identified: the domain of laboratory practice; the context of invisible physical reactions; the future image as it will appear in publication; and the domain of case precedents and reference scenarios from the field. The work of image analysis brings (...) the outside of the image into it and takes the inside out. Thus it can be seen that images are not just taken, they are designed and made. (shrink)

Plato's depiction of the world soul's cognitive activity in Timaeus 37 A 2‐C 5 offers a general account of intellectual cognition. He gives this account by describing the activity of an ideal cognitive agent, involving the very same comparative mechanism that governs human intellectual activity, namely, the active production of a propositional grasp of sameness and difference that things have in relation to each other in several respects. Plato depicts the world soul's intellectual activity as entirely devoid of immediate forms (...) of cognition such as perception and/or intellectual intuition: everything the world soul cognizes is the outcome of its active comparison of things with each other. In particular, there is no direct cognitive grasp of the being of things. The paper ends with a suggestion as to how to understand Plato's account of the world soul's activity as an instance of the ‘like is known by like’ principle of cognition. (shrink)

Among scholars it is common to assume that Aristotle’s practical syllogism does two jobs. It is often taken to explain both animal motion and human deliberation. I will call this the “two-jobs view of the practical syllogism”. In what follows, I will argue that the two-jobs view of the practical syllogism is not working. I will then try to give a very brief and incomplete sketch of how to conceive of a non-two-jobs view of the Aristotelian practical syllogism. Finally, I (...) will discuss two possible problems for the non-two-jobs view. (shrink)

Zusammenfassung Der Beitrag verfolgt das Ziel, Mechanismen der Inklusion und Exklusion in Sportvereinen zu identifizieren, die die Partizipation von Personen mit Migrationshintergrund am organisierten Sport erklären können. Im Lichte von theoretischen Überlegungen zur „symbolischen Grenzziehung“ und „Zugehörigkeit“ werden Ergebnisse aus Fallstudien in Nordrhein-Westfalen und Baden-Württemberg präsentiert.

Zusammenfassung Der Beitrag untersucht den Gebrauch von Moral in der Kommunikation zwischen Trainer und Ath­leten im Spitzensport. Dabei wird moralische Kommunikation aus systemtheoretischer Perspektive als soziale Tatsache konstruiert, um im Lichte dieser Konstruktion konkrete Beispiele aus den Sport­arten Handball und Hockey analysieren und im Hinblick auf ihre Funktionen und Folgen reflektie­ren zu können. Die Ergebnisse dieser Analysen münden in Empfehlungen an Trainer, die zu einem sensiblen Umgang mit Moral raten, da insbesondere dem polemogenen Charakter moralischer und moralisierender Kommunikation Rechnung zu (...) tragen ist. (shrink)

A definition of emotion common to the affective sciences is an urgent desideratum. Lack of such a definition is a constant source of numerous misunderstandings and a series of mostly fruitless debates. There is little hope that there ever will be agreement on a common definition of emotion, given the sacred traditions of the disciplines involved and the egos of the scholars working in these disciplines. Our aim here is more modest. We propose a list of elements for a working (...) definition of emotion and discuss the justification for the inclusion of elements from our respective perspectives (philosophy and psychology). This working partial definition may at least serve as a litmus test to examine theories of emotion, old and new, across disciplinary boundaries. (shrink)

Zusammenfassung Die Vereinbarkeit von Spitzensport- und Schulkarriere gestaltet sich für schulpflichtige Nachwuchsathleten sehr schwierig. Der vorliegende Beitrag konstruiert diese Unvereinbarkeit zunächst als Inklusionsproblem und beschreibt dann prinzipielle Lösungsmöglichkeiten im Rahmen einer Funktionalisierung von Schulen. Dabei wird insbesondere die sachliche Funktionalisierung in Form der strukturellen Kopplung von Spitzensport und Schule in den Blick genommen. Am Beispiel der „NRW-Sportschulen" und der „Spezialschulen Sport" in Brandenburg werden schließlich Möglichkeiten und Grenzen dieser strukturellen Kopplung diskutiert und Barrieren der sachlichen Funktionalisierung von Schulen identifiziert.

Zusammenfassung Spitzensport zu betreiben und gleichzeitig ein Hochschulstudium zu absolvieren, scheint unter den derzeitigen Umständen nahezu unmöglich. Der Artikel konstruiert dieses Phänomen der Unvereinbarkeit zweier Karrieren zunächst gesellschaftstheoretisch als Inklusionsproblem. Da eine merkliche Verbesserung der Situation der Athleten letztlich nur auf Seiten der Hochschule erwartet werden darf, werden anschließend aus organisationstheoretischer Perspektive die dortigen Möglichkeiten und Grenzen interner Strukturveränderungen reflektiert. Schließlich wird diskutiert, wie Hochschulen mit den Erwartungen des Spitzensports umgehen können und in welcher Weise sich im Rahmen von Netzwerken (...) womöglich doch Kooperationsbeziehungen zwischen den beteiligten Organisationen zugunsten studierender Spitzensportler aufbauen lassen. (shrink)