Our main results are:Theorem 1. Con implies Con. [In fact equiconsistency holds.]Theorem 3. Con implies Con.Theorem 5. Con ”) implies Con.We start with a discussion of the canonical functions and look at some combinatorial principles. Assuming the domination property of Theorem 1, we use the Ketonen diagram to show that ω2V is a limit of measurable cardinals in Jensen’s core model KMO for measures of order zero. Using related arguments we show that ω2V is a stationary limit of measurable cardinals (...) in KMO, if there exists a weakly normal ultrafilter on ω1. The proof yields some other results, e.g., on the consistency strength of weak*-saturated filters on ω1, which are of interest in view of the classical Ulam problem. (shrink)

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)

The focus of this book is on conceptual and philosophical issues of perception including the classic notion of unconscious inferences in perception. The book consists of contributions from a group of internationally renowned researchers who spent a year together as distinguised fellows at the German Centre for Advanced Study.

Is causal analysis an appropriate method to discover causal laws? Some prerequisites for any successful application of mathematical causal models are worked out and discussed. It can be shown that these prerequisites cannot be fulfilled by present models and there are strong reasons to assume that they cannot be satisfied by any model. Therefore causal analysis will probably be of no importance for the discovery of causal laws in sociology.

In spite of incomplete knowledge we are permanently forced to act in complex real-life situations. First, a modern concept of information, the non-trivial transition from information to knowledge, patterns of missing knowledge, and the concept of perspective notions are studied. The main sections review some guidelines for action under incomplete information. A modern view of the concepts of holism and wholeness reveals that (in contrast to some critics) general system theory does not require any metaphysical assumption or previously accepted worldview. (...) The concepts of holism and wholeness, as well as general system theory, are well-founded, even under strict criteria. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 106 Heft: 1 Seiten: 68-77.

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)

It is shown how Bohmian trajectories can be derived without the need for Bohmian assumptions such as the guidance law or equilibrium postulate. According to the standard Copenhagen interpretation, Bohmian trajectories cannot be understood as physical paths of particles but must be considered in the framework of descriptive statistics. This does not render them useless but clarifies the field of applications. Without the necessity of the non-crossing rule, the conservation of probability between two Bohmian trajectories can still be proven. The (...) concept is further extended to momentum space and is demonstrated explicitly using general Gaussian wave packets as example. (shrink)

Discussing the concept of duty in Groundwork 1, Kant refers to a ‘second proposition’ and a ‘third proposition’, the latter being a ‘Folgerung aus beiden vorigen’. However, Kant does not identify what the ‘first proposition’ is. In this paper, I will argue that the first proposition is this: An action from duty is an action from respect for the moral law. I defend this claim against a critique put forward by Allison according to which ‘respect’ is a concept that is (...) not, and could not be, introduced in paragraphs 9–13 of Groundwork 1. Further, I will argue that the first proposition as I understand it can also be reconstructed as the conclusion (‘Folgerung’) of a deductive argument proper; however, I will also discuss the option that ‘Folgerung’ could be understood as a corollary rather than a conclusion. Finally, Allison's own interpretation will be criticized. (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)

Adolf Menzel was one of the most important German artists of the 19th century, yet he is scarcely known outside his native land. In this study a leading art historian argues that Menzel deserves to be recognized not only as one of the greatest painters and draftsmen of his century but also as a master realist whose work engages profoundly with an extraordinary range of issues - artistic, scientific, philosophical and socio-political. Michael Fried explores Menzel's large and (...) fascinating oeuvre, and in so doing seeks to make the artist's achievement accessible to a wide audience. (shrink)

Dieter Henrich is one of the most respected and frequently cited philosophers in Germany today. His extensive and highly innovative studies of German Idealism and his systematic analyses of subjectivity have significantly impacted on advanced German philosophical and theological debates. Dieter Henrich and Contemporary Philosophy presents a comprehensive analysis of Henrich's work on subjectivity, evaluating it in the context of contemporary debates in both continental and analytic traditions. Familiarising the non-German reader with an important development in contemporary German (...) philosophy, this book explains the significance of subjectivity for any philosophy that attempts to offer existential orientation and contrasts competing conceptions in analytic philosophy and in the social philosophy of Juergen Habermas. Presenting Henrich's philosophy of subjectivity as a credible alternative to analytic philosophy of mind and a radical challenge to Heideggerian, Habermasian, neo-pragmatist, and postmodern positions, Freundlieb argues that a philosophy of the kind developed by Henrich can regain the cultural significance philosophical thinking once possessed. Dieter Freundlieb is Senior Lecturer in the School of Humanities, Griffith University, Australia. (shrink)

In this paper, an argument of Alvin Plantinga's for the existence of abstract possible worlds is shown to be unsound. The argument is based on a principle Plantinga calls "Quasicompactness", due to its structural similarity to the notion of compactness in first-order logic. The principle is shown to be false.

Henrich, Dieter: Theorieformen moderner Kunsttheorie. ISer, Wolfgang: Interpretationsperspektiven moderner Kunsttheorie. GAdamer, Hans G.: Zur Fragwurdigkeit des asthetischen BewuSStseins. INgarden, Roman: Prinzipien einer erkenntnistheoretischen Betrachtung der asthetischen Erfahrung.. KUhn, Helmut: Die Ontogenese der Kunst. ARnheim, Rudolf: Gestaltpsychologie und kunstlerische Form. [ubersetzt von Jurgen Schlaeger]. GOmbrich, Ernst H.: Norm und Form. KUhns, Richard: Psychoanalytische Theorie als Kunstphilosophie. [ubersetzt von Dieter Henrich]. GEhlen, Arnold: uber einige Kategorien des entlasteten, zumal des asthetischen Verhaltens. SImmel, Georg: Soziologische Asthetik. LUkács, Georg: Kunst und objektive (...) Wahrheit. ADorno, Theodor W.: ErpreSSte Versohnung. ZU Georg Lukács: "Wider den miSSverstandenen Realismus. MEad, George H.: Asthetische Erfahrung. [ubersetzt von Jens Kulenkampff]. MOrris, Charles W.: Asthetik und Zeichentheorie. [ubersetzt von Roland Posner]. RItchie, Benbow: Die formale Struktur des asthetischen Gegenstands. [ubersetzt von Jens Kulenkampff]. CReed-Hungerland, Isabel: uber die Ausdruckskraft ikonischer Zeichen. [ubersetzt von Jens Kulenkampff]. ECo, Umberto: Die asthetische Botschaft. [ubersetzt in Zusammenarbeit mit dem Autor von Jurgen Trabant]. MOles, Abraham A.: Informationelle Poetik - Strukturen der poetischen Nachricht - Empfindungsebenen. [ubersetzt von Hans Ronge]. CAvell, Stanley: Welt durch die Kamera gesehen. [ubersetzt von Lore Iser]. KAplan, Abraham: Referenz in der Kunst. [ubersetzt von Jens Kulenkampff]. ZIff, Paul: Was es heiSSt zu definieren, was ein Kunstwerk ist. [ubersetzt von Jens Kulenkampff]. URmson, James O.: Darstellung auf der Buhne. [ubersetzt von Jens Kulenkampff]. GOodman, Nelson: Kunst und Erkenntnis. [ubersetzt von Jens Schlaeger]. (shrink)

First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). The central question here is that about the actual reason for antinomic structures. It turns out to be a form (...) of negative self-conditioning (chap.3). This makes it necessary to clarify the status of negative concepts (chap.4). The generalization of these considerations (chap.5) leads to the actual analysis of the antinomic basic structure (chap.6): Decisively for the pragmatics of the concept is that it positively owns a meaning, so that positivity is always constituted by the concept qua concept. Thus a negative concept is characterized by a fundamental ambivalence: From a semantic point of view it has negative character, in its pragmatic status as a concept, however, it has positive character. If the meaning is especially that of a negative self-reference, the ambivalence leads to the antinomic constellation of a negative self-condition – that is the crux of the matter here! The concept thus possesses the property defined by it exactly when it does not possess it and vice versa. A closer analysis shows that the function of reflective structures for the occurrence of antinomies has to be judged much more differentiated than previous opinions suggest. Not only are four forms of reflectivity to be distinguished in this context – ontic, semantic, pragmatic reflectivity, and especially the form of negative self-condition; but it is also apparent that these are intertwined with each other in a way that is difficult to be understood. The astonishing variety of relationships associated with this makes the irritation that has always emanated from the antinomy problem appear more comprehensible. In the developed pragmatic perspective furtheron parallels to the structure of self-consciousness become visible (chap.7). I conclude with considerations about the significance of the antinomic structure for the problem of dialectics, especially for the synthesis formation of mutually exclusive terms (chap.8). ---------- Zunächst wird gezeigt, dass das Verbot sprachlicher Selbstreferenz als Lösung des Antinomienproblems einen pragmatischen Widerspruch enthält und damit nicht nur zu restriktiv, sondern geradezu inkonsistent ist (Kap.1). Ferner werden Möglichkeiten nicht-restriktiver Strategien zur Antinomienvermeidung diskutiert, wobei sich die explizite Einbindung der – pragmatisch präsupponierten – Konsistenzforderung als optimale Strategie erweist (Kap.2). Zentral ist hier die Frage nach dem eigentlichen Grund antinomischer Strukturen. Er erweist sich als eine Form von negativer Selbst-Bedingung (Kap.3). Dies nötigt zu einer Klärung des Status negativer Begriffe (Kap.4). Die Verallgemeinerung dieser Überlegungen (Kap.5) leitet über zur eigentlichen Analyse der antinomischen Grundstruktur (Kap.6): Entscheidend zur Pragmatik des Begriffs gehört, dass ihm eine Bedeutung positiv zukommt, sodass durch den Begriff qua Begriff stets auch Positivität konstituiert ist. Dadurch ist ein negativer Begriff durch eine prinzipielle Ambivalenz gekennzeichnet: In semantischer Hinsicht hat er negativen Charakter, in seinem pragmatischen Status als Begriff hingegen positiven Charakter. Ist die Bedeutung insbesondere die eines negativen Selbstbezugs, führt die Ambivalenz zur antinomischen Konstellation einer negativen Selbst-Bedingung – das ist hier der springende Punkt! Der Begriff besitzt so die durch ihn definierte Eigenschaft genau dann, wenn er sie nicht besitzt und umgekehrt. Die nähere Analyse zeigt, dass hierbei die Funktion reflexiver Strukturen für das Auftreten von Antinomien weitaus differenzierter zu beurteilen ist, als bisherige Auffassungen nahelegen. Nicht nur dass in diesem Kontext vier Formen von Reflexivität – ontische, semantische, pragmatische Reflexivität und insbesondere auch die Form negativer Selbstbedingung – unterschieden werden müssen; es zeigt sich auch, dass diese in schwer durchschaubarer Weise ineinander verschränkt sind. Die damit verbundene erstaunliche Beziehungsvielfalt läßt die Irritation, die seit je vom Antinomienproblem ausging, begreiflicher erscheinen. In der entwickelten pragmatischen Perspektive werden ferner Parallelen zur Struktur von Selbstbewußtsein sichtbar (Kap.7). Ich schließe mit Überlegungen zur Bedeutung der antinomischen Struktur für das Problem der Dialektik, insbesondere zur Synthesebildung einander ausschließender Bestimmungen (Kap.8). (shrink)

[[[ (Here only the chapters 3 – 8, see *** ) First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). ]]] The central question here is that about the (...) actual reason for antinomic structures. It turns out to be a form of negative self-conditioning (chap.3). This makes it necessary to clarify the status of negative concepts (chap.4). The generalization of these considerations (chap.5) leads to the actual analysis of the antinomic basic structure (chap.6): Decisively for the pragmatics of the concept is that it positively owns a meaning, so that positivity is always constituted by the concept qua concept. Thus a negative concept is characterized by a fundamental ambivalence: From a semantic point of view it has negative character, in its pragmatic status as a concept, however, it has positive character. If the meaning is especially that of a negative self-reference, the ambivalence leads to the antinomic constellation of a negative self-condition – that is the crux of the matter here! The concept thus possesses the property defined by it exactly when it does not possess it and vice versa. A closer analysis shows that the function of reflective structures for the occurrence of antinomies has to be judged much more differentiated than previous opinions suggest. Not only are four forms of reflectivity to be distinguished in this context – ontic, semantic, pragmatic reflectivity, and especially the form of negative self-condition; but it is also apparent that these are intertwined with each other in a way that is difficult to be understood. The astonishing variety of relationships associated with this makes the irritation that has always emanated from the antinomy problem appear more comprehensible. In the developed pragmatic perspective furtheron parallels to the structure of self-consciousness become visible (chap.7). I conclude with considerations about the significance of the antinomic structure for the problem of dialectics, especially for the synthesis formation of mutually exclusive terms (chap.8). (shrink)

There are many reasons for dissatisfaction with current U.S. health care. One-sixth of the population is uninsured, costs are 150-200% of those in other economically advanced nations, and the quality of care, as measured by disease specific mortality and morbidity data, is rarely better and often worse than in others nations’ less costly systems. A case for reform can mirror any or all of these concerns: cover more of the population with insurance, control costs, improve the effectiveness of prevention and (...) treatment. I argue that two of these goals — greater population coverage and more disciplined costs — gain a significant part of their justification from moral beliefs about justice and fairness. (shrink)