This work introduces two new curves that are multivariate generalizations of the “classical” Lorenz curve. All data of d-variate distributions can be visualized by drawing these curves in the plane, whereas Koshevoy’s and Mosler’s generalization by a lift zonoid in ℝd+1 can only be drawn for d = 2. The generalizations of the Lorenz curve induce partial orderings of d-variate distributions. Furthermore, two inequality or heterogeneity measures that are consistent with the induced rankings are proposed. They can be considered as (...) new generalizations of the univariate Gini coefficient. For deciding which of the two measures is more appropriate for measuring a sort of convergence concerning different countries of an union or of regions of a country, we establish systems of axioms. Although these systems are reflecting natural properties, several of the axioms are new. Moreover, by means of these axioms well- known inequality measures are tested, too. (shrink)

Though since Werner Jaeger's famous Studien zur Entstehungsgeschichte der Metaphysik des Aristoteles of 1912 remarkable observations were made, the topic "Composition of the Metaphysics" almost disappeared from the agenda. As, however, neglect of this philological task results in either selective reading or anachronistic systematization, the author has resumed it, extending it to the internal structure of the singular books.

Though since Werner Jaeger's famous Studien zur Entstehungsgeschichte der Metaphysik des Aristoteles of 1912 remarkable observations were made, the topic "Composition of the Metaphysics" almost disappeared from the agenda. As, however, neglect of this philological task results in either selective reading or anachronistic systematization, the author has resumed it, extendig it to the internal structure of the singular books.

We define classes Φnof formulae of first-order arithmetic with the following properties:(i) Everyφϵ Φnis classically equivalent to a Πn-formula (n≠ 1, Φ1:= Σ1).(ii)(iii)IΠnandiΦn(i.e., Heyting arithmetic with induction schema restricted to Φn-formulae) prove the same Π2-formulae.We further generalize a result by Visser and Wehmeier. namely that prenex induction within intuitionistic arithmetic is rather weak: After closing Φnboth under existential and universal quantification (we call these classes Θn) the corresponding theoriesiΘnstill prove the same Π2-formulae. In a second part we consideriΔ0plus collection-principles. We (...) show that both the provably recursive functions and the provably total functions ofare polynomially bounded. Furthermore we show that the contrapositive of the collection-schema gives rise to instances of the law of excluded middle and hence. (shrink)

Im ersten Teil des Buches wird das «Ich»-Verständnis der christlichen Lehre, insbesondere anhand der Position von Nikolaus von Kues und Schriften von Papst Johannes Paul II., analysiert, beziehungsweise an der Position Platons gemessen. Es wird zu zeigen versucht, daß die christliche Trinitätslehre wesentliche Impulse dafür liefert, zu einer Argumentation alleine gemäß der von Platon grundgelegten noetischen Dialektik finden zu können. Im Rahmen hiervon wird dargelegt, wo das «Ich»-Verständnis der christlichen Trinitätslehre hinter jenem Platons zurückbleibt. Im zweiten Teil des Buches wird (...) eine Skizze vom «Ich» im Sinne der noetischen Dialektik gegeben, beziehungsweise dargelegt, daß jegliches Bedenken von der Aussage «Ich bin» auszugehen hat. (shrink)

It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one step (...) of revision. The paper discusses and rejects two solutions within the confines of AGM theory. It then introduces ranking functions (as I prefer to call them now; in the paper they are still called ordinal conditional functions) as the proper (and, I find, still the best) solution of the problem, proves that conditional independence w.r.t. ranking functions satisfies the so-called graphoid axioms, and proposes general rules of belief change (in close analogy to Jeffrey's generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory. Indeed, the parallel to probability theory is amazing. Probability theory can profit from ranking theory as well since it is also plagued by the problem of iterated belief revision even if probability measures are conceived as Popper measures (see No. 11). Finally, the theory is compared with predecessors which are numerous and impressive, but somehow failed to explain the all-important conditional ranks in the appropriate way. (shrink)

Elaborating on the substantial parallels between Molina’s and Kant’s attempts to reconcile human freedom with divine foreknowledge and natural causal determinism respectively, my aim is to establish a proper historical connection as well. Leibniz is shown to be the crucial mediator in two respects: (i) Kant knew Molina’s account of divine knowledge in general in its Leibnizian version through Baumgarten’s Metaphysica. In this work, scientia media plays no role in the explication as to how God knows absolute future contingents. (ii) (...) In the Critique of Practical Reason Kant resorted to doctrines similar to Molina’s in his criticism of Leibniz’s alternative explication which drew on complete concepts of monads. (shrink)

Der Fortschritt der Aussagenlogik in jungster Zeit HiBt es sinnvoll erscheinen, einen breiteren Leserkreis mit dieser Entwicklung bekannt zu machen. Obwohl vorliegendes Buch als Lehrbuch, nicht als Monographie fUr einen engeren Spezialistenkreis konzipiert wurde, soli es in einigen Themen einen tieferen Einblick in den aktuellen Stand der Dinge vermitteln. Kap. lund ein Tei! von Kap. II befassen sich mit der zweiwertigen Aussagenlogik und sind fUr Leser gedacht, die an Logik interessiert sind, doch noch nicht niiher mit ihr befaBt waren. Die (...) etwas breitere Darstellung in diesen Teilen sollte allerdings kein falsches Bild von den wahren Proportionen entstehen lassen. Denn danach nimmt die zweiwertige Aussagenlogik nicht nur innerhalb der Logik insgesamt, sondern schon innerhalb der Aussagenlogik einen Platz ein, der vergleichbar ist mit dem der euklidischen Planimetrie im Rahmen der neueren Geometrie. Lesern mit ausreichenden Vorkennt­ nissen wird es nichts ausmachen, die anfanglichen Teile zu ubergehen und dort zu be­ ginnen, wo Aussagenlogik erst interessant zu werden beginnt, niimlich wo sie den Rahmen zweiwertiger Logik verliiBt. (shrink)

Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their (...) neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises the following six volumes : I. Classical Logic W. Rautenberg II. Non-classical Logics W. Rautenberg III. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. Proof Theory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. (shrink)

A concept for a primitive angiospermous branch system is given in order to have a starting point for the derivation of the diverse and highly differentiated branch systems observed in contemporary angiosperms. Hitherto Troll's (1964, 1969) comparative study of the synflorescences in this plant group — developed out predominantly on herbaceous plants — was the most comprehensive and sophisticated treatment dealing with branch systems. Unfortunately, the work on tropical tree architecture by Hallé et al. (1978) has no reference to the (...) classical studies of Troll and his pupils. Thus Müller-Doblies and Weberling (1984) emphasized the high degree of terminological incompatibility between the two works. Angiosperms are seen as a monophyletic plant division. Consequently, the branch system of the first primitive angiosperms must be the starting point in the evolution of the abundant diversity of branch systems and growth forms of modern angiosperms. If it is accepted that primitive angiospermous shoots were terminated by a large flower, one may assume, that the reproductive end of the shoot was enriched by paracladia early in evolution, thereby developing a terminal inflorescence instead of a single flower. Thus the primitive shoot unit was divided into a basal vegetative region — the trophotagma, branching retardively — and the reproductive terminal region, the anthotagma, branching simultaneously. It is demonstrated through a selection of different examples, that the construction of such a system possesses the options for several modifications, enabling the evolution of the abundant diversity of branch systems which characterizes contemporary angiosperms. (shrink)

The creation of new institutions and the initiation of new forms of behaviour cannot be explained only on the basis of constitutive rules – they also require a broader commitment of individuals who participate in social practices and, thus, to become members of a community. In this paper, I argue that the received conception of constitutive rules shows a problematic intellectualistic bias that becomes particularly manifest in three assumptions: (i) constitutive rules have a logical form, (ii) constitutive rules have no (...) normative force, and (iii) rules are essentially tied to a sanctioning authority. I discuss these three claims in light of real-life examples. The goal of this discussion is to show that the normative force of constitutive rules is based on the shared commitment of participants who engage in the relevant practices. The inner cohesion and the persistence in time of these practices is possible only because participants continuously calibrate their own forms of behaviour to that of the other members of the community, which underscores the social dimension of constitution. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Violence and Religion:Walter Burkert and René Girard in ComparisonWolfgang Palaver (bio)Translated by Gabriel Borrud1Since the attacks of September 11th, 2001, the relationship between violence and religion has been the center of focus of ever more discussions and examinations. Often, however, these inquiries lack a profound theory that will enable a real understanding of how the two phenomena are related. Walter Burkert and René Girard are two thinkers who grasp (...) the connection between religion and violence, and the present essay will take a closer look at how the two understand this connection. There are similarities and differences between the two thinkers, and these will be highlighted in three sections. In the first, attention will be turned to Burkert and Girard's interpretation of how religion and violence are related—and how this understanding can offer an evolutionary explanation of religion. The second section will examine Girard's thoughts on the mimetic roots of violence, which will serve as a frame of comparison between the two thinkers. A final section will contrast Burkert and Girard with regard to the biblical religions of Judaism and Christianity. [End Page 121]1. Two "Seismographs" for the Relationship Between Religion and ViolenceThe art historian and scholar Aby Warburg once called Jakob Burkhardt and Friedrich Nietzsche "sensitive seismographs," referring to their ability to register the ramifications of the past with uncanny precision.2 Warburg's characterization is appropriate for Burkert and Girard as well, as each shows a hypersensitive understanding of the role religion and violence play in the origins and stability of human culture. It is no coincidence that Burkert and Girard arrived at their respective theories almost simultaneously—both mentioned the significance of violence and religion for the foundation of civilization in works published in 1972. Just years after World War II, the atrocities in the Nazi concentration camps, and the United States's dropping of atomic bombs on Hiroshima and Nagasaki, Girard and Burkert revealed in explicit terms just how central violence and religion were in the formation of human culture.The significance of Girard and Burkert's ideas only grows in the context of contemporary critiques of religion, especially those coming from Darwinian circles. The virulent critique of the evolutionary biologist, Richard Dawkins, for instance, comes to mind. In all of Dawkins's prolific work, however, he fails to offer a convincing explanation of the evolutionary nature of religion: in a word, he doesn't adequately answer the question of why religion is a universal cultural phenomenon.3 Dawkins asserts that religion is a mere by-product of certain psychological dispositions—for instance, a by-product of the naïve readiness to place one's trust in a superior, or a by-product of an instinctive dualism. However, by implementing a mere cognitive construct in his explanation of how religious rituals have shaped human culture over thousands of years, he only broaches the subject matter. One of the main reasons why Dawkins falls short of explaining the omnipresence of religion in human civilization is his rather one-sided and rash explication of violence, which in his opinion stems solely from religion.4 Dawkins proposes that humans are peaceful, quasi-Rousseauian beings that inherit their violent streak only through religious agitation. Following Dawkins's line of thought, the abolition of religion would mean the creation of a world of peace; however, even those who support his very legitimate critique of religious fundamentalism will find these thoughts rather naïve.Burkert and Girard, meanwhile, are able to delve into the essence of religion by explaining both its ritualistic nature and its importance for human evolution. In the case of Burkert, one sees his interest in evolutionary theory from the outset, as his book Homo Necans (first published 1972)5 contains passages [End Page 122] that refer directly to the work of the behavioral scientist Konrad Lorenz. In the "Gifford Lectures" of 1989, Burkert even speaks of the "tracks of biology in early religion."6 In an article published in 2000, Burkert shows that religion is an indispensable part of the process of humanization—and fundamental to the evolution of human culture.7The concrete examples that Burkert employs to... (shrink)

The focus of this contribution lies on eighteenth-century chemistry up to Lavoisier’s anti-phlogistic chemical system. Some main features of chemistry in this period will be examined by discussing classificatory practices and the understanding of the substances these practices imply. In particular, the question will be discussed of whether these practices can be regarded as natural historical practices and, hence, whether chemistry itself was a special natural history (part I). Furthermore, discussion of the famous Methode de nomenclature chimique (1787) raises the (...) question of what modes of classification tell us about chemists’ understanding of the substances they deal with (part II). Finally, in investigating what taxonomic orders reveal about deep structures of chemists’ understanding of the world of substances, the contribution will examine the question of whether Lavoisier’s anti-phlogistic chemical system was a revolution on the level of a deep structure or a revision within the untouched frame of such a structure (part III). (shrink)

The dissertation has two parts. In Part I, I argue that the method of question and answer, that is, dialectic, had its origins not, as Plato and Aristotle might lead us to expect, with Zeno or Socrates, but with the Sophists of the fifth century. They were at the vanguard of a new rationalism that made matters which tradition had regarded as settled, subjects for debate and inquiry. They were committed to a self-consciously rationalistic conception of the arts that held (...) that expertise is a matter of rationally grounded knowledge and hence teachable. ;Of particular importance, especially in democracies, and central to their educational program was the art of rhetoric, that is, the art of rational deliberation and argumentation. It is as part of the instruction in this art that dialectic first emerges. Dialectic is a method subject to specific rules , it provides for at least two roles , and provides criteria for judging who has won a question-and-answer exchange. ;In Part II, I examine Plato's Protagoras. I focus on two sorts of passages: those where the participants seem to be engaged in such a question-and-answer exchange, and those where they comment on what they are doing. Examination of the text leads to the conclusion that both Socrates and Protagoras proceed as if this method of argumentation were antecedently familiar, and Socrates and Protagoras both ask and answer questions in accord with its rules. Thus the difference between Socrates and the Sophists cannot consist in their relying on essentially different methods of argumentation . ;I end by suggesting that if there is a difference between Socrates and the Sophists, it consists in Socrates making explicit what the Sophists had been relying on, though only imperfectly: a commitment to the avoidance of contradictions. (shrink)

Philosophy in the historical Kingdom of Bohemia has never received much attention in the Anglophone world. Yet in the early modern period, Bohemia and especially Prague were an extraordinarily fertile ground for philosophical thought. Stanislav Sousedík of Charles University in Prague is now the foremost expert on this region and period. His Philosophy in the Bohemian Lands between the Middle Ages and the Enlightenment appeared in Czech in 1997 and is now available in a nearly identical German translation.Within the Holy (...) Roman Empire, the Bohemian Lands formed a cultural unity that was also under independent rule until it came under the Habsburg crown in 1526. This study reveals the contribution of philosophy to the creation of this unity from the late Middle Ages until the end of Joseph II’s rule in 1790.The book starts with the Thomism , the Scotism , and the Lullism taught at the University of Prague after Jan Hus had imposed a strict ontological realism. Under independent Bohemian kings, political philosophy became relevant, and Renaissance Platonism was eventually received and flourished in coexistence with the inherited. (shrink)

In many of his logical writings, G. W. Leibniz makes use of two kinds of symbols : while A, B, C, . . . stand for certain determinate or definite concepts, X, Y, Z, . . . are referred to as "indefinite concepts". We investigate the various rôles played by these variables and show i) that their most important function consists in serving as quantifiers ; ii) that Leibniz's elliptic representation of the quantifiers by means of two sorts of „indefinite (...) concepts” leads to certain difficulties; iii) that despite these problems Leibniz anticipated the most fundamental logical principles for the quantifiers and may thus be viewed as a forerunner of modern predicate logic. (shrink)

Die „Wahl“ des jungen P. Cornelius Scipio zum Prokonsul in Spanien im Frühjahr 210 - mitten im Hannibalischen Krieg - stellt in der römischen Geschichte in mehrfacher Hinsicht eine Einmaligkeit dar: Nur hier wird eigens ein Promagistrat für einen außeritalischen Kriegsschauplatz vom Volk direkt gewählt, zudem ein Amtloser, der keinerlei Erfahrung in der Führung von Legionen hat. Zuerst ist die früheste Quelle für diesen Vorgang, Livius, auf ihren historischen Gehalt zu untersuchen (I). Die dortigen staatsrechtlichen Unwahrscheinlichkeiten empfehlen eine Analyse der (...) späteren Berichte des Silius Italicus, des Appian und des Cassius Dio/Zonaras (II). Deren Abweichungen von Livius deuten auf die Existenz einer Ursprungsversion von Scipios „Wahl“, deren inhaltliche Hauptlinien, Tendenz und sogar vermutlicher Autor sich durch einen Vergleich der Parallelberichte rekonstruieren lassen (III). Dabei hilfreich ist die Einbeziehung zweier anderer Fragmente aus Cassius Dio über Scipio, die ebenfalls auf denselben Autor zurückgehen könnten (IV). Die Entstehungsbedingungen und Motive dieser rekonstruierten Ursprungsversion werden insbesondere im Umfeld von Pompeius’ Imperien gegen die Piraten und Mithridates gesucht (V). Weiteren Aufschluß bietet auch die Klärung der Frage, welchen Rang M. Iunius Silanus, der Mitfeldherr des Scipio in Spanien, einnahm (VI). Schließlich verhilft Ciceros Verschweigen von Scipios „Wahl“ dazu, einen terminus post quem für die Verbreitung der rekonstruierten Ursprungsversion zu bestimmen (VII). (shrink)

Einleitung. 1. Pantragismus - Panlogismus - 2. Der Begriff der Negativitat - 3. Zum methodischen Vorgehen der Arbeit Erster Teil: Der Systemansatz der ersten Jenaer Jahre. I. Der Tod Gottes, die griechische Tragodie und das absolute Nichts. 1. Bedrohungen der Freiheit - 2. Die Tragodie im Sittlichen - 3. Das Absolute als Nacht, Nichts und Abgrund - II. Grundlagen der Kritik an der Verstandesreflexion. 1. Die kritische Funktion von Logik und Skeptizismus - 2. Ansatze zu einer Geschichtsphilosophie - III. Kritik (...) an der neuzeitlichen Subjektivitats- und Reflexionsphilosophie. 1. F.H. Jacobis Philosophie der Subjektivitat - 2. Fichtes Ausgang vom reinen Selbstbewusssein - 3. Kants Antinomienlehre - IV. Der Begriff der Negativitat als Grundlegung spekulativen Denkens. 1. Die Durchfuhrbarkeit des spekulativen Ansatzes - 2. Die Ambivalenz der Aussagen der praktischen Philosophie - 3. Auseinandersetzung mit der philosophischen Tradition Zweiter Teil: Die Ausarbeitung und Umwandlung des Systemansatzes in den Jahren 1803-1806. I. Die Negativitat der modernen, neuzeitlichen Gesellschaft. 1. Kritik an den neuzeitlichen Naturrechtstheorien auf der Grundlage einer Theorie des Kampfes um Anerkennung - 2. Das Gefuge der Stande - 3. Der Staat - II. Negativitat und Selbstbewusstsein in den Jenaer Systementwurfen. 1. Die Rekon- struktion der absoluten Sittlichkeit im System der Sittlichkeit - 2. Die Bewusstseinslehre des Systementwurfs von 1803/04 - 3. Das Erkennen und die Metaphysik der Subjektivitat in der Logik und Metaphysik von 1804/05 - 4. Die Negativitat des Selbstbewusstseins in der Realphilosophie von 1805/06 - III. Das Verhaltnis der verschiedenen Formen von Negativitat zueinander. 1. Negativitat des Seins und Selbstbewusstseins - 2. Die Negativitat der Entzweiung in der modernen Gesellschaft - 3. Vorblick auf die Phanomenologie Dritter Teil: Der Begriff der Negativitat in der Phanomenologie des Geistes. I. Die Idee einer Geschichte des Selbstbewusstseins. 1. Pragmatische Ges". (shrink)