Starting with D. Scott's work on the mathematical foundations of programming language semantics, interest in topology has grown up in theoretical computer science, under the slogan `open sets are semidecidable properties'. But whereas on effectively given Scott domains all such properties are also open, this is no longer true in general. In this paper a characterization of effectively given topological spaces is presented that says which semidecidable sets are open. This result has important consequences. Not only follows the classical Rice-Shapiro (...) Theorem and its generalization to effectively given Scott domains, but also a recursion theoretic characterization of the canonical topology of effectively given metric spaces. Moreover, it implies some well known theorems on the effective continuity of effective operators such as P. Young and the author's general result which in its turn entails the theorems by Myhill-Shepherdson, Kreisel-Lacombe-Shoenfield and Ceĭtin-Moschovakis, and a result by Eršov and Berger which says that the hereditarily effective operations coincide with the hereditarily effective total continuous functionals on the natural numbers. (shrink)

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...) intersects the topological closure of an effectively enumerable subset of Y. As a consequence of a more general parametric inseparability result a theorem of Rice-Shapiro type is obtained. Moreover, under some additional requirements it follows that nonopen subsets have productive index sets. This implies a generalized Rice theorem: Connected spaces have only trivial completely recursive subsets. As application some decision problems in computable analysis and domain theory are studied. It follows that the complement of the halting problem can be reduced to the problem to decide of a number whether it is a computable irrational. The same is true for the problems to decide whether two numbers are equal, whether one is not greater than the other, and whether a number is equal to a given number. In the case of an effectively given continuous complete partial order the complexity of the last problem depends on whether the given element is the smallest element, in which case the complement of the halting problem is reducible to it, whether it is a base element and maximal, then the decision problem is recursively isomorphic to the halting problem, or whether it is none of these. In this case, both the halting problem and its complement are reducible to the problem. The same is true in nontrivial cases for the problems whether an element belongs to the basis, whether two elements of the partial order are equal, or whether one approximates the other. In general, for any nonempty proper subset of the partial order either the halting problem or its complement can be reduced to the membership problem of the subset. (shrink)

In examples like the total recursive functions or the computable real numbers the canonical indexings are only partial maps. It is even impossible in these cases to find an equivalent total numbering. We consider effectively given topological T 0 -spaces and study the problem in which cases the canonical numberings of such spaces can be totalized, i.e., have an equivalent total indexing. Moreover, we show under very natural assumptions that such spaces can effectively and effectively homeomorphically be embedded into a (...) totally indexed algebraic partial order that is closed under the operation of taking least upper bounds of enumerable directed subsets. (shrink)

If one wants to compute with infinite objects like real numbers or data streams, continuity is a necessary requirement: better and better (finite) approximations of the input are transformed into better and better (finite) approximations of the output. In case the objects are constructively generated, they can be represented by a finite description of the generating procedure. By effectively transforming such descriptions for the generation of the input (respectively, their codes) into (the code of) a description for the generation of (...) the output another type of computable operation is obtained. Such operations are also called effective. The relationship of both classes of operations has always been a question of great interest. In this paper the setting is extended to the case of multifunctions. Various ways of coding (indexing) sets are discussed and their relationship is investigated. Moreover, effective versions of several continuity notions for multifunctions are introduced. For each of these notions an indexing system for sets is exhibited so that the multifunctions that are effective with respect to this indexing system are exactly the multifunction which are effectively continuous with respect to the continuity notion under consideration. Mostly, in addition to being effective the multifunctions need also possess certain witnessing functions. Important special cases are discussed where such witnessing functions always exist. (shrink)

Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.

A strong reducibility relation between partial numberings is introduced which is such that the reduction function transfers exactly the numbers which are indices under the numbering to be reduced into corresponding indices of the other numbering. The degrees of partial numberings of a given set with respect to this relation form an upper semilattice.In addition, Ershov’s completion construction for total numberings is extended to the partial case: every partially numbered set can be embedded in a set which results from the (...) given set by adding one point and which is enumerated by a total and complete numbering. As is shown, the degrees of complete numberings of the extended set also form an upper semilattice. Moreover, both semilattices are isomorphic.This is not so in the case of the usual, weaker reducibility relation for partial numberings which allows the reduction function to transfer arbitrary numbers into indices. (shrink)

The different behaviour of total and partial numberings with respect to the reducibility preorder is investigated. Partial numberings appear quite naturally in computability studies for topological spaces. The degrees of partial numberings form a distributive lattice which in the case of an infinite numbered set is neither complete nor contains a least element. Friedberg numberings are no longer minimal in this situation. Indeed, there is an infinite descending chain of non-equivalent Friedberg numberings below every given numbering, as well as an (...) uncountable antichain. (shrink)

There is a consensus that satire cannot be defined, but is best characterized by a cluster account. However, I argue that a cluster account does not acknowledge the artistically and politically significant distinction between real satire and some forms of frivolous topical comedy which are casually labeled ‘satire’ in international media contexts. To uphold this distinction, I introduce a weak proposal that satire is a genre which necessarily sets out to critique and entertain (with the qualification that these purposes necessarily (...) interact, although neither is wholly instrumental to the other). I further argue that this proposal also provides necessary and sufficient conditions for a definition of satire. (shrink)

This chapter establishes the concept of a “symbolic system of representation“ to make clear how it is possible that humans use not only the language-based system of representation for cognitive contents but also a many layered non-linguistic system, a system which we probably share with other species. A symbolic system of representation denotes a general concept of a performance of which our language is only one single case, but which nevertheless is most easily explained through the case of language. A (...) system of representation should enable us to form and manipulate an idea of a state of affairs or of an event without having the appropriate intuition of it. We usually think that we do this only using linguistic expressions, but this is not the whole truth. Language is one system of representation, but we can in principle conceive of other systems of representation with the same performance. Husserl’s theory of meaning already reveals this possibility. A phenomenological analysis reveals that a non-linguistic system of representation is in fact still functioning in our own consciousness. We simultaneously use different means of representation, the most prominent of which are language, gestures, feelings and scenic images. It is especially fruitful to investigate the scenic mode of daydreaming as a central form of non-linguistic thinking. Through a close comparison of alternative systems of representation, the systematic difference of usual semantics in normal language systems based on convention and the more natural similarity semantics of some non-linguistic systems of representation is revealed. (shrink)

Irony has a suspicious moral reputation, especially in popular media and internet culture. Jonathan Lear (2011) introduces a proposal which challenges this suspicion and identifies irony as a means to achieve human excellence. For Lear, irony is a disruptive uncanniness which arises from a gap between aspiration and actualisation in our practical identity. According to Lear, such a disruptive experience of ironic uncanniness reorients us toward excellence, because it passionately propels us to really live up to that practical identity. However, (...) Lear’s understanding of irony is idiosyncratic and his proposal overlooks that disruption often results from value incompatibility between different practical identities. The disruption which follows from value incompatibility does not inherently reorient us toward excellence. The point is exactly that achieving excellence in one practical identity is sometimes incompatible with excellence in the other. Pace Lear, I do not identify this disruptive experience as a central example of irony. Instead, I consider irony a virtuous coping strategy for such disruption, because it introduces the necessary distance from our moral imperfection to sustain practical deliberation and maintain good mental health. Such virtuous irony negotiates a golden mean between too little disruption (complete insensitivity toward one’s imperfection) and too much disruption (a complete breakdown of practical deliberation and mental health). I argue that ironic media in popular culture provide a rich source of such virtuous irony, which I demonstrate through analysis of satirical examples. (shrink)

Den an den gewaltigen Umwälzungen unserer Zeit Interessierten bewegen heute in erster Linie die Probleme des sozialen Wandels - oder besser des dringend not wendigen Umbaus unserer Welt. Erst dahinter tritt seit einiger Zeit die Forderung nach dem Umbau des Menschen auf 1. Sie ist von der öffentlichkeit noch relativ wenig beachtet und offenbar als unangenehm fast tabuiert. Von den die Frage initiierenden Biologen ist diese Forderung aber durchaus ernst gemeint. Ihre Ten denz ist radikal. Außerhalb dieser Tendenz laufen aber (...) bereits unentwegt Prozesse, die zuerst Eingriff in die Physis und Psyche des Menschen, dann eben doch schon Veränderung bedeuten oder bedeuten können. Der Massenausstoß von Chemikalien bis ins Trinkwasser und in die Zahnpasta hinein und die permanente massenhafte Massenbeeinflussung teilgeplanter Art, zum Beispiel durch Werbung, deren Wirkung (besonders insgesamt!) völlig unbekannt ist, ist damit gemeint. Hier setzt unser Interesse ein. Die Idee einer Veränderung des Menschen ist einmal überhaupt bewegend. Zum anderen gilt ihr deshalb unser Fachinteresse, weil eine an der Kulturanthropologie und der sogenannten Philosophischen Anthropologie orientierte Soziologie durch die Behauptung und Verbreitung des Konzeptes von der »Offenheit« und »Plasti zität«, der unbegrenzten Beeinflußbarkeit und Lernfähigkeit des Menschen, zu sammen mit einer untheoretischen Evolutionstheorie erst den Hintergrund für die Idee der Möglichkeit eines »Umbaus« des Menschen geliefert hat. Ist der Mensch total offen, nicht festgelegt, dann kann er auch beliebig angepaßt werden. (shrink)

Theodor W. Adorno’s writings are often categorized as either political, aesthetic or critical. While all of these characteristics are legitimate, it is problematic to view Adorno from only one of these angles. In fact, many literary critics consider his thoughts about literature to be simple cultural criticism, i.e., something that leaves the realm of pure scholarship by defiling the argumentation with philosophy or politics. Political theorists and philosophers, on the other hand, often view his literary concerns as superfluous. It is (...) my thesis that Adorno’s way of thinking can only be adequately understood when these categories are not seen as mutually exclusive. In order to demonstrate this point, I will concentrate on his use of the term realism which can be seen as paradigmatic for this question. (shrink)

In der 1970 gegründeten Reihe erscheinen Arbeiten, die philosophiehistorische Studien mit einem systematischen Ansatz oder systematische Studien mit philosophiehistorischen Rekonstruktionen verbinden. Neben deutschsprachigen werden auch englischsprachige Monographien veröffentlicht. Gründungsherausgeber sind: Erhard Scheibe (Herausgeber bis 1991), Günther Patzig (bis 1999) und Wolfgang Wieland (bis 2003). Von 1990 bis 2007 wurde die Reihe von Jürgen Mittelstraß mitherausgegeben.

Constitutionalism: Past, Present, and Future will offer a definitive collection of Professor Dieter Grimm's most important scholarly writings on constitutional thought and interpretation. The essays included in this volume explore the conditions under which the modern constitution could emerge; they treat the characteristics that must be given if the constitution may be called an achievement, the appropriate way to understand and interpret constitutional law under current conditions, the function of judicial review, the remaining role of national constitutions in a (...) changing world, as well as the possibility of supra-national constitutionalism.Many of these essays have influenced the German and European discussion on constitutionalism and for the first time, much of the work of one of German's leading scholars of public law will be available in the English language. (shrink)

The following pages contain a partial edition of Husserl’s manuscript A I 35, pages 1a-28b. The first few pages are dated on May 1927 and are included mostly for completeness’ sake. The bulk of the manuscript convolute, however, is from 1912. Four pages of the convolute, 31a-34b, have been published as Beilage XII (210, 2–216, 2) in Hua XXXII. The manuscript was excluded from the text selection of Husserliana XXI3 based on its much later date of composition. A I 35/24a (...) is mentioned in Husserliana XXII (p. xxi, n. 4) as confirmation for Zermelo’s 1902 “oral report” to Husserl of his own independent discovery of the paradox. The text presented here for the first time has already been the target of at least three extensive commentaries, while still unpublished, by Claire Ortiz Hill and Guillermo Rosado Haddock. These present a good survey in english of the central issues on the text and contain many translated quotations. (shrink)

In diesem Aufsatz wird zunächst der Begriff ›Fragment‹ im Kontext einer Theorie des ›Werks‹, also des abgeschlossenen Artefakts, geklärt. Es wird gezeigt, dass Fragmente im Gegensatz zu Werken in mindestens einer Hinsicht defiziente Artefakte sind. Im folgenden Schritt wird herausgearbeitet, wo das Fragment an seine Grenzen kommt. Gemeint ist dabei einerseits die materielle Abgrenzung des Fragments von seiner Umgebung durch Schnitte, Brüche und Konturen, andererseits die begriffliche Abgrenzung des Fragments von benachbarten literarischen Formen der Prosa und der Lyrik wie Aphorismus, (...) Skizze, Entwurf, Montage und Monostichon. Ferner wird ein Blick auf ›totale Fragmente‹ (George Steiner), also Extremformen der Fragmentierung, geworfen, vor allem auf solche Fälle, in denen Artefakte ganz oder nahezu ganz gescheitert, verloren oder zerstört sind, also ein Maximum an Defizienz aufweisen. Der Schwerpunkt der Überlegungen liegt im Bereich der Literatur; andere Künste und Medien werden jedoch durchgehend vergleichend herangezogen. (shrink)

In Spescha and Strahm [15], a system of explicit mathematics in the style of Feferman [6] and [7] is introduced, and in Spescha and Strahm [16] the addition of the join principle to is studied. Changing to intuitionistic logic, it could be shown that the provably terminating operations of are the polytime functions on binary words. However, although strongly conjectured, it remained open whether the same holds true for the corresponding theory with classical logic. This note supplements a proof of (...) this conjecture. (shrink)

Review text: "... ist diese Einführung als solche uneingeschränkt zu empfehlen, da sie ihrem "analytischen? Charakter im besten Sinne des Wortes gerecht wird."Werner Wolbert in: Salzburger Theologische Zeitschrift 2/2008.

The readymades conceived and selected by Marcel Duchamp be- tween the years 1914–1917 have, with very few exceptions, not survived until the present day as ‘original.’ A variety of forms, in- cluding documentary photos, objects chosen and approved later by Duchamp as well as remakes of the historical objects comprise the readymades’ legacy. Duchamp’s remakes of his readymades as a limited edition of multiples from 1964, commemorating the 50-year anniversary of his selection of the Bottle Dryer in 1914, mark the (...) beginning of the second half of the “Readymade Century.” In contrast to their widespread visibility, the paradoxical ‘construct- edness’ of these objects is rarely discussed. The representational impact and the conceptual specificity of these multiples goes far beyond the oeuvre of Marcel Duchamp, and can be seen as a pre- monition of artistical appropriation strategies from the 1980s to the present day. (shrink)

There are many treatises concerning the soul. Plato was not the first to write on the subject. From Greek philosophy and religion the soul wandered over to Christianity. According to this religion, the soul accompanies the body, which it inhabits for a short while in order to then return to its primary homeland embodied in areas of primary existence and truth. There are many treatises concerning the soul. Plato was not the first to write on the subject. Wisława Szymborska, in (...) her collection of poems published in 2002 and titled A Moment, poses the most essential questions: Why does man exist? Why isn’t there nothingness? She also asks: What is the soul? Does man really possess a soul? What is the relationship between man and soul – to whom does the soul really belong? This is a treatise in the form of a poem which appears to be plain and modest, yet the questions it asks are fundamental. This interpretation aims to develop and translate from the language of poetry the religious and philosophical questions embraced by Szymborska’s poem. (shrink)