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)

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)

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.

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)

One of the world's pre-eminent Max Weber scholars here presents a comprehensive analysis of Weber's ambiguous stance toward modernity considered from a normative, theoretical, and historical point of view. The book is in two parts. Part I scrutinises Weber's world view. On the basis of his thinking about the meaning and inter-relationships of science, politics, and ethics in the modern era, Weber is seen as the embodiment of a social scientist and political thinker who exposes himself to intellectual risks and (...) existential tensions while resisting final solutions. It includes a masterly analysis of Weber's two famous speeches 'Science as a Vocation' and 'Politics as a Vocation'. Part II considers Weber's unfinished project on the sociology of religion. Piecing together planned and partially completed works on Islam and Western Christianity, Schluchter locates them in the history and theory of Weber's overall work. This reconstruction of Weber's work on religion emphasises its interplay between religion, economy, politics, and law. (shrink)

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)

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)

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)

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)

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)

What type of reason will work under the present conditions? To answer this question a meaningful conception of reason (as distinct from rationality) has to be developed, and is contemporary conditions (due to change in the field of rationality) have to be specified.In part I. of the paper, the radically altered structure of rationality is analysed; it turns out to be characterized by rational disorder. Part II. offers a redefinition of reason; guided by the idea of justice reason operates in (...) transition from one rationality to another. This new kind of reason - "transversal reason " - is further elaborated in part III. It is regarded as a key-element of any type of reason. (shrink)