Let X be any infinite, coinfinite r.e. set. We show that the index set $\{e: W_e \equiv_1 X\}$ is Σ 0 3 -complete, answering a question posed by Odifreddi in [2].

Traducción del alemán de Irene Borges-Duarte.

It will be shown that in the lattice of recursively enumerable sets all lattices $\underline{L}(X)$ are elementarily definable with parameters, where X is Σ 0 3 and $\underline{L}^3(X)$ consists of all Σ 0 3 sets containing X.

We show that every infinite computable partial ordering has either an infinite Δ 0 2 chain or an infinite Π 0 2 antichain. Our main result is that this cannot be improved: We construct an infinite computable partial ordering that has neither an infinite Δ 0 2 chain nor an infinite Δ 0 2 antichain.

It will be shown that in the lattice of recursively enumerable sets one can define elementarily with parameters a structure isomorphic to (∑ 0 4 , ∑ 0 3 ), i.e. isomorphic to the lattice of ∑ 0 4 sets together with a unary predicate selecting out exactly the ∑ 0 3 sets.

It will be shown that for all numbers n and m with n > m 1 the Boolean pairs have undecidable elementary theories.

In this article we establish the existence of a number of new orbits in the automorphism group of the computably enumerable sets. The degree theoretical aspects of these orbits also are examined.

The structure of the l-degrees included in an m-degree with a maximal set together with the l-reducibility relation is characterized. For this a special sublattice of the lattice of recursively enumerable sets under the set-inclusion is used.

Historical analysis and policy making often require counterfactual thought experiments that isolate hypothesized causes from a vast array of historical possibilities. However, a core precept of Jervis's ?systems thinking? is that causes are so interconnected that the historian can only with great difficulty imagine causation by subtracting all variables but one. Prediction, according to Jervis, is even more problematic: The more sensitive an event is to initial conditions (e.g., butterfly effects), the harder it is to derive accurate forecasts. Nevertheless, if (...) awareness of system effects can help forecasters better calibrate their probability estimates of whether or not certain events will come to pass, systems thinkers who are pessimistic about prediction are diluting their confidence too much. The challenge is a meta-cognitive one: thinking systematically about when to engage in systems thinking; and weighing the costs and benefits of using simple or complex heuristics in policy environments that can shift suddenly from quiescence to turbulence. (shrink)

Menschen können missachtet werden. Woher aber rührt diese symbolische Verletz-barkeit? Und welche Folgen hat sie für unser soziales Zusammenleben? Im Ausgangvon den Theorien der Anerkennung und den Theorien der Alterität geht Steffen Herrmann diesen beiden Fragen nach. Er argumentiert im Anschluss an G.W.F. Hegel dafür, dass eine asymmetrische Abhängigkeit von der Anerkennung von Anderendie Ursache von symbolischer Verletzbarkeit bildet. Sodann zeigt er im Anschluss an E. Levinas, dass die Folge dieser Verletzungsoffenheit eine asymmetrische Ausge-setztheit an die Verantwortung für Andere (...) ist. Aus den Arbeiten von Hegel und Levinas wird so die Grundthese der vorliegenden Untersuchung gewonnen: Die Begegnung zwischen Ich und Anderem ist strukturiert durch die doppelte Asymmetrie des Sozialen. (shrink)

Jakob Friedrich Fries (1773–1843) zählt sicherlich zu den bedeutendsten Denkern der auf Kant folgenden Phase der deutschen Philosophie. Das wird in eindrucksvoller Weise durch die Beiträge dieses Bandes belegt, die aus Vorträgen auf dem Fries-Symposion hervorgingen, das im Oktober 1997 an der Friedrich-Schiller-Universität Jena stattfand. Die Autoren beleuchten die Lebensumstände von Fries, ordnen sein Werk philosophiegeschichtlich ein und setzen sich systematisch mit erkenntnistheoretischen, naturphilosophischen, wissenschaftstheoretischen und politischen Aspekten seiner Philosophie auseinander. Auch die Rezeption des Fries’schen Werkes bei Naturwissenschaftlern wie M. (...) J. Schleiden und Philosophen wie E. F. Fries und L. Nelson kommt zur Sprache. (shrink)

Jakob Friedrich Fries is one of the most important representatives of the Critical Philosophy, someone who built immediately on the original Kantian philosophy. -/- Fries was born in 1773 in Barby (on the Elbe). In 1805 he was extraordinary professor for philosophy in Jena and in the same year was ordinary professor for philosophy in Heidelberg. Returning to Jena in 1816, one year later he was compulsorily retired because of his participation at the nationalistic and republican Wartburg Festival. In 1924 (...) he obtained a professorship for physics and mathematics, and in 1838 he was given back a professorship for philosophy. He died in 1843 in Jena. -/- The book summarizes the research results of the DFG-Project "Jakob Friedrich Fries' Influence on the Sciences of the 19th Century". The research project was carried out by Dr. Kay Herrmann (Institute of Philosophy, Jena University) and Prof. Dr. Wolfram Hogrebe (Institute of Philosophy, Bonn University). Such a study has special importance. There is available a large amount of literature about the "speculative contemporaries" of Fries, like Fichte, Schelling, and Hegel. In contrast to the "speculative philosophy", there has been published only a few studies about the Friesian natural philosophy. Fries was, in his natural-philosophical studies, looking for a link between philosophy and modern sciences, wheras his "speculative philosophical" contemporaries felt obligated to stick primarily to a descriptive, phenomenal view of nature. So far the question "How was mathematical natural philosophy regarded by scientists and mathematicians of the 19th century?" has hardly been investigated. Archival studies showed that this gap in Fries-research can be filled. The Friesian correspondence turned out to be a rich gold mine. -/- The present publication is more than a research report. The monographic first part is intended to introduce the foundations of the Friesian theory of cognition, the Friesian methodology, and the Friesian natural philosophy. This should facilitate entry into Friesian philosophy. -/- The Friesian theory is analyzed from two points of view: •How did Fries suceed in continuing and improving the Kantian approach? Is Fries able to remove the weak points of Kantian philosophy? -/- •What is the current significance of the Friesian approach? There are some interesting similarities between the Friesian approach and modern philosophical theories (such like Chomsky's theory of "universal grammer"). The lasting core of the Friesian theory of cognition is: To use empirical studies for working on philosophical problems. -/- Chapters 3 and 4 are scientific-historically oriented. These chapters analyze the Friesian position in scientific and mathematical debates (debates about the a priori foundations of physics, the problem of the identification of physics as an independent discipline, the problem of the boundary between chemistry and physics, the problem of mathematization of the sciences, the theory of the imponderabilia, the systematics and structure of sciences and mathematics, problems of infinity, the differential calculus, the theory of parallel lines) and the relation between Fries and the scientists of the 19th century. The book contains the latest findings gained by evaluation of the Friesian unpublished work (for example the correspondence with W. Weber, C. F. Gauß, E. F. Apelt, O. Schlömilch, Ch. Reichel, B. A. v. Lindenau, L. Gmelin, E. G. Fischer, A. N. Scherer, J. S. C. Schweigger) -/- One result of the research project is that some important scientists took a favourable view of the Friesian theory, but the influence of the Friesian philosophy on the sciences of the 19th century was very limited. The causes are very complex: An anti-natural-philosophical spirit of age, the limits of the Kantian inspired philosophy and some unfavourable aspects in the biography of Fries. -/- For the first time the voluminous Fries-Reichel-correspondence was evaluated. The Fries-Reichel-correspondence contains the Friesian approach to prove the 11th Euclidean axiom, and the whole transcript of the Friesian attempt at proof is given. // Der erste Teil des Buches will in die Grundprobleme Fries’scher Erkenntnis­theorie, Methodenlehre und Naturphilosophie einführen, wobei das Hauptaugenmerk auf die Fortführung der kantischen Ansätze durch Fries sowie auf die aktuelle Interpretation der Fries’schen Lehre gerichtet ist. Der wissenschaftshistorisch ausgerichtete zweite Teil analysiert Fries’ Stellung zu naturwissenschaftlichen und mathematischen Diskussionsrichtungen (Probleme der Identifizierung der Physik als eigenständige Disziplin, der Grenzziehung zwischen Physik und Chemie, der Mathematisierung der Naturwissenschaften, der Imponderabilientheorie, der Systematik von Naturwissenschaft und Mathematik, des Unendlichen, der Parallelentheorie usw.) sowie sein Verhältnis zu Naturwissenschaftlern und Mathematikern seiner Zeit. Das Buch enthält neue Erkenntnisse, die aus der Auswertung zahlreicher Nachlassmaterialien gewonnen wurden. Erstmalig wird unter dem Blickwinkel „Fries als Naturwissenschaftler und Mathematiker“ auch der sehr umfangreiche Reichel-Briefwechsel ausgewertet. Dem Reichel-Briefwechsel entstammt auch Fries’ Versuch eines Beweises des Parallelenaxioms, der in diesem Buch erstmalig in transkribierter Form vollständig vorliegt. -/- . (shrink)

Werner Heisenberg und die Natur – das wäre eine psychologische Studie wert. Der große Physiker liebte die freie Natur; seit seinen frühen Jahren, zuerst mit Eltern und Großeltern, dann mit den Freunden der Jugendbewegung und später mit Kollegen und seiner Familie erwanderte er sich Landschaften in der engeren Heimat und auswärts, in Deutschland, Österreich, Finnland, Dänemark und den USA. Gelegentlich finden sich kurze Schilderungen von Naturerlebnissen in seinen Schriften, etwa vom Gebirgsgang im Herbst 1924 durch das Karwendelgebiet am Aachensee im (...) Der Teil und das Ganze – das Landschaftsbild setzte er als Parabel für den bald erzielten Durchbruch in der Quantentheorie. (shrink)

Jakob Friedrich Fries (1773-1843): A Philosophy of the Exact Sciences -/- Shortened version of the article of the same name in: Tabula Rasa. Jenenser magazine for critical thinking. 6th of November 1994 edition -/- 1. Biography -/- Jakob Friedrich Fries was born on the 23rd of August, 1773 in Barby on the Elbe. Because Fries' father had little time, on account of his journeying, he gave up both his sons, of whom Jakob Friedrich was the elder, to the Herrnhut Teaching (...) Institution in Niesky in 1778. Fries attended the theological seminar in Niesky in autumn 1792, which lasted for three years. There he (secretly) began to study Kant. The reading of Kant's works led Fries, for the first time, to a deep philosophical satisfaction. His enthusiasm for Kant is to be understood against the background that a considerable measure of Kant's philosophy is based on a firm foundation of what happens in an analogous and similar manner in mathematics. -/- During this period he also read Heinrich Jacobi's novels, as well as works of the awakening classic German literature; in particular Friedrich Schiller's works. In 1795, Fries arrived at Leipzig University to study law. During his time in Leipzig he became acquainted with Fichte's philosophy. In autumn of the same year he moved to Jena to hear Fichte at first hand, but was soon disappointed. -/- During his first sojourn in Jenaer (1796), Fries got to know the chemist A. N. Scherer who was very influenced by the work of the chemist A. L. Lavoisier. Fries discovered, at Scherer's suggestion, the law of stoichiometric composition. Because he felt that his work still need some time before completion, he withdrew as a private tutor to Zofingen (in Switzerland). There Fries worked on his main critical work, and studied Newton's "Philosophiae naturalis principia mathematica". He remained a lifelong admirer of Newton, whom he praised as a perfectionist of astronomy. Fries saw the final aim of his mathematical natural philosophy in the union of Newton's Principia with Kant's philosophy. -/- With the aim of qualifying as a lecturer, he returned to Jena in 1800. Now Fries was known from his independent writings, such as "Reinhold, Fichte and Schelling" (1st edition in 1803), and "Systems of Philosophy as an Evident Science" (1804). The relationship between G. W. F. Hegel and Fries did not develop favourably. Hegel speaks of "the leader of the superficial army", and at other places he expresses: "he is an extremely narrow-minded bragger". On the other hand, Fries also has an unfavourable take on Hegel. He writes of the "Redundancy of the Hegelistic dialectic" (1828). In his History of Philosophy (1837/40) he writes of Hegel, amongst other things: "Your way of philosophising seems just to give expression to nonsense in the shortest possible way". In this work, Fries appears to argue with Hegel in an objective manner, and expresses a positive attitude to his work. -/- In 1805, Fries was appointed professor for philosophy in Heidelberg. In his time spent in Heidelberg, he married Caroline Erdmann. He also sealed his friendships with W. M. L. de Wette and F. H. Jacobi. Jacobi was amongst the contemporaries who most impressed Fries during this period. In Heidelberg, Fries wrote, amongst other things, his three-volume main work New Critique of Reason (1807). -/- In 1816 Fries returned to Jena. When in 1817 the Wartburg festival took place, Fries was among the guests, and made a small speech. 1819 was the so-called "Great Year" for Fries: His wife Caroline died, and Karl Sand, a member of a student fraternity, and one of Fries' former students stabbed the author August von Kotzebue to death. Fries was punished with a philosophy teaching ban but still received a professorship for physics and mathematics. Only after a period of years, and under restrictions, he was again allowed to read philosophy. From now on, Fries was excluded from political influence. The rest of his life he devoted himself once again to philosophical and natural studies. During this period, he wrote "Mathematical Natural Philosophy" (1822) and the "History of Philosophy" (1837/40). -/- Fries suffered from a stroke on New Year's Day 1843, and a second stroke, on the 10th of August 1843 ended his life. -/- 2. Fries' Work Fries left an extensive body of work. A look at the subject areas he worked on makes us aware of the universality of his thinking. Amongst these subjects are: Psychic anthropology, psychology, pure philosophy, logic, metaphysics, ethics, politics, religious philosophy, aesthetics, natural philosophy, mathematics, physics and medical subjects, to which, e.g., the text "Regarding the optical centre in the eye together with general remarks about the theory of seeing" (1839) bear witness. With popular philosophical writings like the novel "Julius and Evagoras" (1822), or the arabesque "Longing, and a Trip to the Middle of Nowhere" (1820), he tried to make his philosophy accessible to a broader public. Anthropological considerations are shown in the methodical basis of his philosophy, and to this end, he provides the following didactic instruction for the study of his work: "If somebody wishes to study philosophy on the basis of this guide, I would recommend that after studying natural philosophy, a strict study of logic should follow in order to peruse metaphysics and its applied teachings more rapidly, followed by a strict study of criticism, followed once again by a return to an even closer study of metaphysics and its applied teachings." -/- 3. Continuation of Fries' work through the Friesian School -/- Fries' ideas found general acceptance amongst scientists and mathematicians. A large part of the followers of the "Fries School of Thought" had a scientific or mathematical background. Amongst them were biologist Matthias Jakob Schleiden, mathematics and science specialist philosopher Ernst Friedrich Apelt, the zoologist Oscar Schmidt, and the mathematician Oscar Xavier Schlömilch. Between the years 1847 and 1849, the treatises of the "Fries School of Thought", with which the publishers aimed to pursue philosophy according to the model of the natural sciences appeared. In the Kant-Fries philosophy, they saw the realisation of this ideal. The history of the "New Fries School of Thought" began in 1903. It was in this year that the philosopher Leonard Nelson gathered together a small discussion circle in Goettingen. Amongst the founding members of this circle were: A. Rüstow, C. Brinkmann and H. Goesch. In 1904 L. Nelson, A. Rüstow, H. Goesch and the student W. Mecklenburg travelled to Thuringia to find the missing Fries writings. In the same year, G. Hessenberg, K. Kaiser and Nelson published the first pamphlet from their first volume of the "Treatises of the Fries School of Thought, New Edition". -/- The school set out with the aim of searching for the missing Fries' texts, and re-publishing them with a view to re-opening discussion of Fries' brand of philosophy. The members of the circle met regularly for discussions. Additionally, larger conferences took place, mostly during the holidays. Featuring as speakers were: Otto Apelt, Otto Berg, Paul Bernays, G. Fraenkel, K. Grelling, G. Hessenberg, A. Kronfeld, O. Meyerhof, L. Nelson and R. Otto. On the 1st of March 1913, the Jakob-Friedrich-Fries society was founded. Whilst the Fries' school of thought dealt in continuum with the advancement of the Kant-Fries philosophy, the members of the Jakob-Friedrich-Fries society's main task was the dissemination of the Fries' school publications. In May/June, 1914, the organisations took part in their last common conference before the gulf created by the outbreak of the First World War. Several members died during the war. Others returned disabled. The next conference took place in 1919. A second conference followed in 1921. Nevertheless, such intensive work as had been undertaken between 1903 and 1914 was no longer possible. -/- Leonard Nelson died in October 1927. In the 1930's, the 6th and final volume of "Treatises of the Fries School of Thought, New Edition" was published. Franz Oppenheimer, Otto Meyerhof, Minna Specht and Grete Hermann were involved in their publication. -/- 4. About Mathematical Natural Philosophy -/- In 1822, Fries' "Mathematical Natural Philosophy" appeared. Fries rejects the speculative natural philosophy of his time - above all Schelling's natural philosophy. A natural study, founded on speculative philosophy, ceases with its collection, arrangement and order of well-known facts. Only a mathematical natural philosophy can deliver the necessary explanatory reasoning. The basic dictum of his mathematical natural philosophy is: "All natural theories must be definable using purely mathematically determinable reasons of explanation." Fries is of the opinion that science can attain completeness only by the subordination of the empirical facts to the metaphysical categories and mathematical laws. -/- The crux of Fries' natural philosophy is the thought that mathematics must be made fertile for use by the natural sciences. However, pure mathematics displays solely empty abstraction. To be able to apply them to the sensory world, an intermediatory connection is required. Mathematics must be connected to metaphysics. The pure mechanics, consisting of three parts are these: a) A study of geometrical movement, which considers solely the direction of the movement, b) A study of kinematics, which considers velocity in Addition, c) A study of dynamic movement, which also incorporates mass and power, as well as direction and velocity. -/- Of great interest is Fries' natural philosophy in view of its methodology, particularly with regard to the doctrine "leading maxims". Fries calls these "leading maxims" "heuristic", "because they are principal rules for scientific invention". -/- Fries' philosophy found great recognition with Carl Friedrich Gauss, amongst others. Fries asked for Gauss's opinion on his work "An Attempt at a Criticism based on the Principles of the Probability Calculus" (1842). Gauss also provided his opinions on "Mathematical Natural Philosophy" (1822) and on Fries' "History of Philosophy". Gauss acknowledged Fries' philosophy and wrote in a letter to Fries: "I have always had a great predilection for philosophical speculation, and now I am all the more happy to have a reliable teacher in you in the study of the destinies of science, from the most ancient up to the latest times, as I have not always found the desired satisfaction in my own reading of the writings of some of the philosophers. In particular, the writings of several famous (maybe better, so-called famous) philosophers who have appeared since Kant have reminded me of the sieve of a goat-milker, or to use a modern image instead of an old-fashioned one, of Münchhausen's plait, with which he pulled himself from out of the water. These amateurs would not dare make such a confession before their Masters; it would not happen were they were to consider the case upon its merits. I have often regretted not living in your locality, so as to be able to glean much pleasurable entertainment from philosophical verbal discourse." -/- The starting point of the new adoption of Fries was Nelson's article "The critical method and the relation of psychology to philosophy" (1904). Nelson dedicates special attention to Fries' re-interpretation of Kant's deduction concept. Fries awards Kant's criticism the rationale of anthropological idiom, in that he is guided by the idea that one can examine in a psychological way which knowledge we have "a priori", and how this is created, so that we can therefore recognise our own knowledge "a priori" in an empirical way. Fries understands deduction to mean an "awareness residing darkly in us is, and only open to basic metaphysical principles through conscious reflection.". -/- Nelson has pointed to an analogy between Fries' deduction and modern metamathematics. In the same manner, as with the anthropological deduction of the content of the critical investigation into the metaphysical object show, the content of mathematics become, in David Hilbert's view, the object of metamathematics. -/-. (shrink)

ZusammenfassungDie wichtigsten Werke Edmund Schlinks zur ökumenischen Theologie erscheinen in einer Neuedition. Die im ersten Band enthaltenen Vorträge stellen heraus, dass Ökumene von Gott her empfangen wird. Der Mensch trägt in der Gestalt der Buße, durch die Überwindung theologischer Reduktionismen zur Ökumene bei.SummaryThe most important works of Edmund Schlink concerning the ecumenical theology will be published in a new edition. The lectures contained in the first volume of this edition emphasize: ecumene can be received by God. Man contributes to ecumene (...) by penance, by overcoming of theological reductionisms. (shrink)

Nelson's Proof of the Impossibility of the Theory of Knowledge -/- In addressing the possibility of a theory of knowledge, Leonard Nelson noted the contradiction of an epistemological criterion that one would require in order to differentiate between valid and invalid knowledge. Nelson concluded that the inconsistency of such a criterion proves the impossibility of the theory of knowledge. -/- Had the epistemological criterion had a perception, then it would presume to adjudicate on its own truth (thus epistemological circular argument). (...) However, if one were to assume that the criterion is not knowledge, one would then have to justify how this is a criterion for truth - yet this would only be possible when it may be considered as an object of knowledge. One would equally have had to predetermine the criterion in order to determine the truth of this knowledge, thereby providing another circular argument. Ostensibly, every criterion of truth fails at its very own test since it cannot guarantee its own truth, just as Munchausen, contrary to his assertion, could not draw himself out of the swamp by tugging on a tuft of his own hair. -/- Nelson proposed a solution of the epistemological problem (the question of the differentiation between valid and invalid knowledge), that based on Jakob Friedrich Fries' differentiation between proof and deduction. Proof, according to Nelson (in reference to Fries), can be defined as derivation of truth from one statement from another statement. Thus, from the truth in the statement that "all men are mortal", one is then able to say that "Socrates is a man" and thence extrapolate from the truth of the statement that "Socrates is mortal." If knowledge were to be considered somewhat judgmental (in a statement), then an attempt at proof (i.e. recourse to previous judgments) would inevitably lead to an infinite regression in justification, since each judgment would necessitate a further justification from another judgment. Every attempt to prove an epistemological criterion is thus also confronted by this regression in justification. -/- Nelson's attempt at a solution rests on the assumption of the existence of an immediate knowledge as a justification of the truth (mediate) of knowledge. Nelson considers immediate knowledge to be non-judgmental knowledge. These include intuitions (e. g. seeing-the-red-roof) and also philosophical knowledge that pre-exists in his opinion before a judgmental reflexion (immediate) in our reason (e. g. the principle of causality). -/- Proof of the truth of mediate knowledge can be effected by showing its compliance with attendant immediate knowledge (rational truth = correspondence of mediate knowledge with their immediate knowledge). Nelson considered this as a resolution of the circular epistemological argument. In regard to philosophical knowledge, Nelson sees these as subject to deduction and not proof. The following example illustrates the goal of deduction: -/- An approach for deducing the principle of causality: A) Every change has a cause. (The principle of causality) A´) A is a reiteration of an immediate knowledge. (Meta-assertion following A) -/- "A" may not be provable, but A´ may justified, and thus Nelson identified it as a deduction following from A. // reference: http://www.friesian.com/nelproof.htm. (shrink)

In the 19th century, a transition took place from the classical to the modern ideal of science: Science would no longer be regarded as a categorical-deductive system of absolute truths, but instead as a hypothetical-deductive system of problematically conditional propositions. In this process, the synthetic a priori also took on more and more of the status of something problematically conditional, which could be found out and corrected empirically, and was itself even ultimately contingent upon empiricism. Along the way, it lost (...) its original purpose, namely to formulate the conditions for the possibility of objective knowledge. To the extent that one continues to attribute objectivity to scientific knowledge, however, the question of the synthetic a priori remains current. The present volume aims to trace the historical roots and varied interpretations of the synthetic a priori while also seeking new approaches toward a contemporary reinterpretation of this fundamental concept. // -/- Im 19. Jahrhundert vollzieht sich der Übergang vom klassischen zum modernen Wissenschaftsideal: Die Wissenschaft wird nicht mehr als kategorisch-deduktives System absoluter Wahrheiten, sondern als ein hypothetisch-deduktives System problematisch-konditionaler Sätze angesehen. Damit erlangt auch das synthetische Apriori mehr und mehr den Status von etwas Problematisch-Konditionalem, das vermöge der Empirie aufgefunden und nachkorrigiert wird, schlussendlich sogar selbst von der Empirie abhängt. Es büßt dabei seinen ursprünglichen Zweck ein, nämlich die Bedingungen der Möglichkeit objektiver Erkenntnis zu formulieren. Sofern man wissenschaftlicher Erkenntnis Objektivität zugesteht, bleibt jedoch die Frage nach dem synthetischen Apriori aktuell. Das vorliegende Buch will einerseits den historischen Wurzeln sowie verschiedenen Interpretationen des synthetischen Apriori nachspüren und andererseits nach Ansätzen für eine zeitgemäße Reinterpretation dieses fundamentalen Begriffes fragen. (shrink)

Naturwissenschaften, Mathematik und Logik waren für Nelson von zentraler Bedeutung. Er pflegte bereits als Jugendlicher intensive Kontakte zu Naturwissenschaftlern und Mathematikern. Dadurch erhielt er Anregungen, die von Anfang an seine philosophischen Ansätze beeinflussten. Inspiriert von der Kant-Fries’schen Philosophie und der Axiomatik der Mathematik, konzipierte Nelson seine Philosophie als exakte Wissenschaft. Wie Kant und Fries betrachtete Nelson die Suche nach den allgemeinen Prinzipien der Naturwissenschaften als Hauptaufgabe der Naturphilosophie. Ergebnis dieser kritischen Analyse ist ein System von metaphysischen Grundsätzen der Naturwissenschaft. Nelson (...) übernimmt Kants Lehre von den Grundsätzen des reinen Verstandes. Keine empirisch gefundene Gesetzmäßigkeit könne diesen Grundsätzen widersprechen. Für die Gesetze der Newton’schen Mechanik hätten, so meint Nelson, Kant und Fries diesen Nachweis erbracht. Deshalb formulierte Nelson das sogenannte Postulat der Mechanistik, gemäß dem alle Naturerscheinungen auf mechanische Vorgänge zurückgeführt werden können. Das starre Festhalten an diesem Postulat veranlasste ihn zur Ablehnung bedeutsamer physikalischer Konzeptionen (z. B. des auf der Elektrodynamik basierenden Relativitätsprinzips, des Nahwirkungskonzepts und des Atommodells). Das „Relativitätsprinzip der Elektrodynamik“ lehnte er mit dem Argument ab, es verhindere die Anwendung der dritten Analogie der Erfahrung, da es den Verzicht auf den Begriff der Gleichzeitigkeit von Naturerscheinungen erzwinge. Eine kritische Nelson-Rezeption muss der Historizität etlicher Thesen Nelsons Rechnung tragen, aber zugleich die Bedeutsamkeit von Kernaussagen Nelson’scher Naturphilosophie im Hinblick auf die modernen Naturwissenschaften untersuchen. Das ist auch die Zielrichtung des vorliegenden Beitrages. Der erste Teil beleuchtet Nelsons wissenschaftliches Umfeld. Einerseits wird untersucht, welche Wissenschaftler Nelson beeinflussten, andererseits soll dargestellt werden, welcher Personenkreis an der Fortentwicklung der Nelson’schen Naturphilosophie beteiligt war. Beispielhaft sollen daran anschließend zwei Themenbereiche aus seinem reichhaltigen Werk disktiert werden, denen besonders im Hinblick auf aktuelle philosophische Diskussionsschwerpunkte Bedeutsamkeit zukommt. Im zweiten Teil werden nämlich Nelsons Betrachtungen zum Verhältnis von Freiheit und Naturnotwendigkeit sowie seine Unterscheidung zwischen wissenschaftlicher und ästhetischer Naturbetrachtung besprochen. Der Beitrag beansprucht nicht, die Rezeptionssgeschichte und den Inhalt von Nelsons Naturphilosophie sowie die aktuelle Bedeutsamkeit seiner Thesen im Detail darzustellen aufzuarbeiten. Vielmehr geht es darum, Ansätze für eine zeitgemäße Interpretation Rezeption aufzuzeigen und anhand von Beispielen zu erörtern. (shrink)

Das Problem einer einheitlichen Grundlage alles Bestehenden hat seit jeher eine große Rolle in der Philosophie gespielt und stets auch eine große Ausstrahlung auf die Naturwissenschaft gehabt. Exemplarisch werden verschiedene Entwürfe für eine höherdimensionale einheitliche Feldtheorie diskutiert. -/- Es wird der Frage nachgegangen, was überhaupt unter der „Einheit von Theorien“ zu verstehen ist. Dabei zeigt sich, dass sich zwischen unterschiedlichen Ebenen der „Einheit von Theorien“ unterscheiden lässt. Die „Einheit von Theorien“ kann sich beziehen auf übergreifende Begriffe (z. B. Feldbegriff), auf (...) eine formal mathematische Zusammenfassung unterschied­licher Phänomene (z. B. im Rahmen der Projektiven Einheitlichen Feldtheorie), auf einen genetischen Zusammenhang von Theorien (z. B. zwischen newtonscher und relativistischer Mechanik), auf ein einheitliches Gesetz zur Erklärung unterschiedlicher Phänomene (z. B. die Maxwelltheorie als Erklärungsgrundlage elektromagnetischer Erscheinungen), aber auch auf einen gemeinsamen Referenzbereich verschiedener Theorien (z. B. phänomenologische und statistische Thermodynamik). -/- Die Verwendung höherdimensionaler Geometrien wirft die Frage nach dem ontologischen Status höherdimensionaler Raum-Zeiten auf. Handelt es sich lediglich um mathematische Formalismen, oder kommt ihnen eine eigene Realität zu? Es zeigt sich, dass beide Interpretationskonzepte ihre Berechtigung besitzen. Spielt etwa bei der Klasse der Projektiven Einheitlichen Feldtheorien (kurz: PUFT) der höherdimensionale Raum die Rolle eines Instruments zur mathematisch eleganten Darstellung, so lassen sich bei der Klasse der Kaluza-Klein-Theorien Eigenschaften ableiten, die als Hinweis auf einen ontologisch eigenständigen Realitätsstatus gedeutet werden können. Folgt man Poppers Realitätskriterium, wonach als real zu betrachten ist, was sich durch physikalische Wirkungen nachweisen lässt, so kann etwa der Einfluss der Extradimensionen auf die Dynamik des physikalischen Geschehens in der vierdimensionalen Raum-Zeit als Hinweis auf deren Realität gedeutet werden. -/- Interessant sind die höherdimensionalen einheitlichen Feldtheorien auch unter dem Blickwinkel der Wissenschaftstheorie. Da sie recht gut dem Modell des Forschungsprogramms im Sinne von Lakatos entsprechen, stellen sie gute Musterbeispiele für theoriedynamische Betrachtungen dar. (shrink)

Sofern man die Existenz objektiver Erkenntnisse anerkennt, ist man mit der Frage nach den Bedingungen der Möglichkeit für diese Erkenntnisse konfrontiert. Der Grund muss in Voraussetzungen liegen, die selbst wiederum empirisch nicht zu rechtfertigen sind. Zwar verwerfen Popper und Carnap den Begriff des "synthetischen Urteils a priori", doch die Voraussetzung, dass es "in der Natur gesetzlich zugeht", räumen beide ein. Diese empirisch nicht zu rechtfertigende Prämisse ist ein synthetisches Urteil a priori. Gemäß Kant ist innerhalb der Klasse der Erkenntnisse a (...) priori zwischen reinen und nicht-reinen Erkenntnissen a priori zu unterscheiden. Es in vorliegender Arbeit argumentativ dafür plädiert, Naturgesetze als apriorische Erkenntnisse zu betrachten, die der Klasse der nicht-reinen synthetischen Urteile a priori zuzurechnen sind. Vor diesem Hintergrund kommt die Arbeit zu der Schlussthese: Ein empirischer (d. h. empirische Begriffe enthaltender) Satz (etwa ein Naturgesetz) kann über den (empirisch nicht einlösbaren, aber als Postulat durchaus sinnvollen) Anspruch auf allgemeine und notwendige Geltung verfügen und somit Bedingungen der Möglichkeit für objektive Erkenntnis formulieren. Doch sind für die Entdeckung empirischer Sätze mit Anspruch auf allgemeine und notwendige Geltung empirische Studien (etwa das physikalische Experiment) erforderlich. (shrink)

Dieser Aufsatz will zeigen, dass die Beiträge von Jakob Friedrich Fries (1773–1843) zur Psychiatrie leider (zu Unrecht) vergessen, aber überaus aktuell sind. Seine Überlegungen sowie die der Wissenschaftler, die ihm gefolgt sind, haben in den Darstellungen der Geschichte der Psychiatrie mehr Beachtung verdient.

According to Regulatory Focus Theory, two systems determine our strategies to pursue goals – the promotion and the prevention system. Individuals with a dominant promotion system focus on achieving gains, i.e., promoters, and individuals with a dominant prevention system focus on avoiding losses, i.e., preventers. Regulatory Fit Theory suggests that a fit between this focus and the situation causes superior performance and makes individuals feel right. We transfer the fit idea to the interaction of dominant regulatory focus with motivational direction. (...) We investigated these interaction effects on individuals’ performance and their experience within creativity workshops. In Study 1, using multi-level analyses, we found that a promotion focus was associated with fluency and a prevention focus with elaborated ideas. This effect was stronger, when preventers also scored high on avoidance motivation. Further, preventers experienced more autonomy support and were more satisfied when they scored high on avoidance. Promoters high on approach motivation reported more autonomy support and more satisfaction than preventers high on approach motivation. For Study 2, we used an experimental design: After measuring regulatory focus, we manipulated approach vs. avoidance motivation in creativity workshops. Using multi-level analyses, we did not find main or interaction effects on fluency or elaboration but we found interaction effects on participants’ experience of the creativity workshop. Preventers were more satisfied when they received the avoidance condition. Promoters reported less autonomy support, lower satisfaction, and more perceived conflicts within their teams in the avoidance condition. (shrink)

F.-W. von Herrmann was a close associate of Heidegger during the final four years of the philosopher’s life. During that time, he not only had many conversations with him, but was also granted access to many writings just now appearing in the Gesamtausgabe. As a result of his proximity to Heidegger, as well as to his writings, von Herrmann seems in a unique position to provide an authoritative account of Heidegger’s work.

We show that the partial order of Σ0 3-sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi.

Introduction: Kantian concepts, liberal theology, and post-Kantian idealism -- Subjectivity in question: Immanuel Kant, Johann G. Fichte, and critical idealism -- Making sense of religion: Friedrich Schleiermacher, John Locke, Samuel Taylor Coleridge, and liberal theology -- Dialectics of spirit: F.W.J. Schelling, G.W.F. Hegel, and absolute idealism -- Hegelian spirit in question: David Friedrich Strauss, Søren Kierkegaard, and mediating theology -- Neo-Kantian historicism: Albrecht Ritschl, Adolf von Harnack, Wilhelm Herrmann, Ernst Troeltsch, and the Ritschlian school -- Idealistic ordering: Lux Mundi, (...) Andrew Seth Pringle-Pattison, Hastings Rashdall, Alfred E. Garvie, Alfred North Whitehead, William Temple, and British idealism -- The Barthian revolt: Karl Barth, Paul Tillich, and the legacy of liberal theology -- Idealistic ironies: from Kant and Hegel to Tillich and Barth. (shrink)

Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal (...) D}$-maximal sets, we use them to show that several classes of${\cal D}$-maximal sets break into infinitely many orbits. (shrink)

Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal (...) D}$-maximal sets, we use them to show that several classes of${\cal D}$-maximal sets break into infinitely many orbits. (shrink)

The British Armed Nation, 1793?1815. By J. E. Cookson (Oxford: Oxford University Press, 1997) vi + 286 pp. £45.00/ $87.00 cloth. The Arming of Europe and the Making of the First World War. By David G. Herrmann (Princeton: Princeton University Press, 1997) 307 pp. $16.95 paper. State, Society and Mobilization in Europe during the First World War. John Horne, ed. (Cambridge U.K.: Cambridge University Press, 1997) xv + 292 pp. £35.00/ $59.95 cloth.