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)

Theodor Adorno's famous aesthetic theory was not merely a theory of the aesthetic; it also made a wider claim about the aesthetic implications of all theory. At the same time we have to deal with aesthetic objects and events in which an aesthetic theory is inherent, which show themselves as art. From both sides--theory and aesthetics--a link can be made to the etymological meaning of theōria, which understands the theoretical as a seeing or perspective. Featuring lucid essays by major thinkers, (...) the book examines this link, focusing equally on the aesthetic implications of theory and the theoretical implications of aesthetic events. (shrink)

Wer kennt GOTTLOB FREGE (1848-1925)? Nur wenige verbinden mit seinem Namen einen der groaten Logiker aller Zeiten, ohne dessen "Logik von Funktion und Argument" die heutige Computertechnik kaum denkbar ist. Frege fuhlte sich zeitlebens zu seiner Heimat im Norden Deutschlands hingezogen. In Wismar verbrachte er seine Kindheit und in Bad Kleinen, in unmittelbarer Nahe, seinen Lebensabend. Das im Jahre 2000 gegrundete Gottlob-Frege-Zentrum der Hochschule Wismar organisierte ihm zu Ehren im Mai 2013 in seiner Geburtsstadt eine internationale Konferenz, an der Forscher (...) aus der mathematischen Grundlagenforschung und der Analytischen Philosophie teilnahmen. Im Konferenzband erfahren Sie von bekannten Wissenschaftlern u.a., begin{itemize} item was Frege zur Entwicklung der Mathematik, Logik und Philosophie leistete, item welche wissenschaftlichen Auffassungen Frege vertrat und welche er scharf kritisierte, item mit welchen bekannten Wissenschaftlern Frege korrespondierte und wer sein Werk fortsetzte oder in Frage stellte, item was wir heute noch aus Freges Arbeiten lernen konnen. (shrink)

--Über Schellings Konstruktion des Christentums, von W. Becker.--Zur systematischen Differenz von Apriorität und Reinheit in Kants Lehre von den synthetischen Urteilen a priori, von K. Cramer.--Endlichkeit des Bewusstseins und absolulte Gewissheit bei Descartes, von H. Fahrenbach.--Objektivation und Designation, von W. Flach.--Über den spekulativen Anfang, von H.F. Fulda.--Vorgestalten der Reflexion, von H.-G. Gadamer.--Formalisierung und Formalismus von J. Glöckl.--Naturzweck und Wesenbegriff, von E. Heintel.--Fichtes ursprüngliche Einsicht, von D. Heinrich.--Zur Präsenz der transzendentalen Differenz in der dialektischen Vernunft, von W. Marx.--Zum Verhältnis von Faktizität (...) und Reflexion in der Transzendent alphilosophie, von H. Radermacher.--Beziehung und Beziehungsloses (Absolutes) von J.J. Schaaf.--Ist Metaphysik des Transzendenten möglich? von H. Wagner.--Vernunft als Kanon, Organon und Kathartikon des allgemeinen Verstandes, von R. Wiehl.--Gestaltwelt, von G. Wolandt. (shrink)

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two (...) worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws. (shrink)

Zu den Grenzfragen des Lebens. Bioethik als Feld intensiver Auseinandersetzung im fachwissenschaftlichen Diskurs und kontroverser Diskussionen in der breiten Öffentlichkeit. Das Handbuch erläutert die Grundlagen und gibt einen Überblick über Bereiche, in denen bioethische Fragen relevant sind, wie Menschenwürde, Leben, Tod und Krankheit. Daneben widmet es sich den speziellen bioethischen Problemen wie etwa Zulässigkeit von Sterbehilfe, Präimplantationsdiagnostik oder embryonaler Stammzellenforschung und zeigt die Schnittstellen der Bioethik zu anderen Disziplinen und gesellschaftlichen Bereichen auf (Bioethik in der Lehre, Biopolitik, Biorecht und Ethikkommissionen).

Für die 3. Auflage wurde der Band durchgesehen und die Literaturliste aktualisiert. Der Band gibt einen Überblick über die Probleme der Moralphilosophie und die Antworten der Ethik auf die Frage nach dem Wesen, den Funktionen und den Inhalten der Moral. Ein besonderer Akzent liegt auf der Unterscheidung der Ebenen, auf denen moralische und ethische Diskurse geführt werden. Geeignet ist die Einführung auch für Leser ohne besondere Vorkenntnisse.

Our starting point is the question ‘What is mass’, what in particular enables mass to constitute duration: so that mass can be regarded as moving as well as at rest (the kinematic principle of relativity). In a thought experiment, this question is attacked here not from the perspective of mass itself, but from that of a standing light wave. In this model, mass-analogous structures can be re- constructed that can be in relative motion to each other. The (empirically known) constancy (...) of the speed of light in every reference system is not as- sumed here. However, it can be shown that the speed of light is identical in all systems constituted by mass-analogous structures that move uniformly relative to each other and that the speed of light moreover is the limiting speed of mo- tions. This indepence of the motion of light from the system of reference, this character of absoluteness, and the relativity of mass motions thus prove to be contrary but inextricably linked moments of the kinematic principle of relativi- ty: an interesting perspective concerning a philosophy of relativity theory. - The mathematical relationships are explained in more detail in the appendix. (shrink)

Einer der auffälligsten gesellschaftlichen Trends der letzten zwanzig Jahre ist die zunehmende Moralisierung von Bereichen des individuellen und gesellschaftlichen Lebens, die in früheren Zeiten eher der Logik der effektiven Interessenverfolgung vorbehalten waren. Die Forderung nach der Übernahme und Wahrnehmung moralischer Verantwortung hat Lebensbereiche erfasst, die lange Zeit weitgehend außerhalb der Moral standen: Wirtschaft, Umwelt, Ressourcennutzung.

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)

Ausgangspunkt ist die Frage, was Masse ist, wodurch sie insbesondere befähigt ist, Dauer zu konstituieren und deshalb - im Sinn des kinematischen Relativitätdprinzips - ebenso als bewegt wie als ruhend betrachtet werden kann. In einem Gedankenexperiment wird diese Frage, in Umkehrung der Perspektive, hier nicht von der Masse selbst, sondern von einer stehenden Lichtwelle her angegangen. In diesem Modell lassen sich masse-analoge Strukturen rekonstruieren, die in relativer Bewegung sein können. Die (empirisch bekannte) Unabhängigkeit der Lichtgeschwindigkeit vom Bezugssystem ist dabei nicht (...) vorausgesetzt. Doch kann gezeigt werden, dass die Lichtgeschwindigkeit Grenzgeschwindigkeit solcher relativer Bewegungen ist, dass dies für alle durch masse-analoge Strukturen konstituierte, relativ zueinander gleichförmig bewegten Bezugssysteme gilt und dass die Lichtgeschwindigkeit selbst in allen diesen Systemen gleich ist. Die Absolutheit der Lichtgeschwindigkeit und die Relativität der Massebewegungen erweisen sich so als zwar differente, aber intrinsisch zusammengehörende Momente des kinematischen Relativitätsprinzips: ein Beitrag zu einer Philosophie der Relativitätstheorie. - Die mathematischen Zusammenhänge werden im Anhang ausführlicher dargelegt. (shrink)

Die Geschichte des Diskurses um Mills Moralphilosophie verläuft in einer Kurve wechselnder Konjunkturen. Phasen des Interesses und der überwiegend positiven Würdigung wechseln sich ab mit Phasen des Desinteresses und überwiegender Ablehnung. Im viktorianischen England war Mill der bekannteste Intellektuelle seiner Epoche – ungeachtet der Tatsache, dass er zu vielen Themen alles andere als zu seiner Zeit populäre Auffassungen vertrat. Allerdings galt das Interesse seiner Zeitgenossen weniger seiner Moralphilosophie als vielmehr seiner ökonomischen Theorie und der in seinem System of Logic enthaltenen (...) Methodologie der induktiven Wissenschaften. Dagegen erregte der Kern seiner Moralphilosophie, die in seinem Essay Utilitarianism dargelegte Version eines nicht-Bentham’schenBentham, Jeremy Utilitarismus, weniger Aufsehen, als sich Mill erhofft hatte. (shrink)

Dieter Flader explores how current social and cultural concerns are connected to the unconscious, and how this affects our responses to them. Flader focuses on the role of the ego, assessing how our feelings about these issues in adulthood grow from childhood fears and desires, and integrating the existing psychoanalytic theories of Winnicott, Lacan, Kohut and others with sociological and political theory. The interdisciplinary approach not only analyses current social issues but also generates new perspectives and solutions, and examines (...) examples including climate change, bullying and vegetarianism. (shrink)

Dieter Flader explores how current social and cultural concerns are connected to the unconscious, and how this affects our responses to them. Flader focuses on the role of the ego, assessing how our feelings about these issues in adulthood grow from childhood fears and desires, and integrating the existing psychoanalytic theories of Winnicott, Lacan, Kohut and others with sociological and political theory. The interdisciplinary approach not only analyses current social issues but also generates new perspectives and solutions, and examines (...) examples including climate change, bullying and vegetarianism. (shrink)

Die meisten Sozial- und Geisteswissenschaften kennzeichnen sich durch das Bemühen darum, die Welt mit klaren Kategorien zu erkennen. Diesem unterliegt die Vorstellung der linearen Grenze. Unter Rückgriff auf Befunde aus dem nordafrikanischen und europäischen Mittelmeerraum kontextualisiert der vorliegende Artikel mit ethnologischem Blick das Gedankenmodell der Linearität historisch, politisch und kulturell, indem er dieses mit Grenzen als Zonen des Überganges kontrastiert und nach dem epistemologischen Gewinn fragt, der sich daraus für die Disziplinen entfaltet.