A Note on the Minimum Number of Edges in Hypergraphs with Property O

An oriented $k$-uniform hypergraph is said to have Property O if for every linear order of the vertex set, there is some edge oriented consistently with the linear order. Recently Duffus, Kay and R\"{o}dl investigated the minimum number $f(k)$ of edges in a $k$-uniform hypergaph with Property O. They proved that $k! \leq f(k) \leq (k^2 \ln k) k!$, where the upper bound holds for $k$ sufficiently large. In this short note we improve their upper bound by a factor of $k \ln k$, showing that $f(k) \le \left(\lfloor \frac{k}{2} \rfloor +1 \right) k! - \lfloor \frac{k}{2} \rfloor (k-1)!$ for every $k\geq 3$. We also show that their lower bound is not tight. Furthermore, Duffus, Kay and R\"{o}dl also studied the minimum number $n(k)$ of vertices in a $k$-uniform hypergaph with Property O. For $k=3$ they showed $n(3) \in \{6,7,8,9\}$, and asked for the precise value of $n(3)$. Here we show $n(3)=6$.Comment: 6 pages, 1 figur

Relativism in the Context of National Socialism

The aim of this chapter is to clarify the use and meaning of the concept of relativism in the context of National Socialism (NS). Section 1 examines the critical reproach that NS is a form of relativism. I analyze and criticize the common core of this widespread argument which has dominated discussions about the topic up to the present. Section 2 sketches the general debates on relativism before and during NS. I show that fascist thought could be associated with both relativism and anti-relativism. In contrast to the received view, I argue that Nazi intellectuals regarded relativism as problem, and presented NS as the overcoming of relativism. Subsequently I turn to two major philosophers who connected their philosophy with NS. Section 3 investigates Bruno Bauch’s (1887–1942) nationalist philosophy. I show that he linked his concept of the nation with an objectivist value theory intended to oppose all kinds of relativism. Section 4 turns to Erich Rothacker’s (1888–1965) cultural anthropology. I argue that the revision of his philosophical views in the 1930s was accompanied by a political turn towards NS and a withdrawal from relativism. The brief conclusion (Section 5) summarizes the findings of the chapter. I conclude that, in the context of NS, relativism is mostly used in a pejorative sense

Consolidation Coal v. William Kusch

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Die Ahnenreihe des Aspelta

Im Fokus der Untersuchung steht eine linear über sieben Generationen von weiblichen Vorfahren laufende Genealogie, die auf der Inthronisationsstele des Königs Aspelta, der im frühen 6. Jh. v. Chr. in Nubien herrschte, erhalten ist. Es wird vorgeschlagen, dieses in seiner Art einmalige Zeugnis als einen von mehreren Versuchen der Legitimation des Aspelta zu sehen. Die Identifikation der im Giebelfeld dargestellten und zugleich an erster Stelle in der Genealogie genannten Frau mit Nasalsa wird hinterfragt und abgelehnt

Resonancia y proyección del pensamiento de Rodolfo Kusch. A propósito de una obra reciente de Carlos M. Pagano

La tesis doctoral de Carlos M. Pagano Fernández "Un modelo de filosofía intercultural: Rodolfo Kusch (1922-1976). Aproximación a la obra del pensador argentino", defendida en la Rheinisch-Westfalische Technische Hochschule de Aachen, Alemania, en 1998 y publicada durante el presente año en la serie de Monografías de la Revista Internacional de Filosofía Concordia, que dirige Raúl Fomet-Betancourt en la misma ciudad, reviste entre otros aspectos el valor y audacia de poner a consideración en un ámbito académico prestigioso, extranjero, un pensamiento que, como bien afirma su autor, aún no ha sido suficientemente apreciado entre nosotros, en su ejemplar fuerza pionera de saber abrirse camino desde la propia experiencia histórico cultural, ni aprovechado en todas sus potencialidades

Form, Funktion, Geographie

Die so genannte Völkertafel von Genesis 10 ist ein fiktionaler Text, der die Kategorien Abstammung und Verwandtschaft als Darstellungsmittel verwendet, um in narrativer Weise eine räumliche Ordnung der vorfindlichen Welt vorzunehmen. Die Völker kommen in Genesis 10 als autonome Größen eigenen Rechts in den Blick und werden unter drei Ausgangsgrößen (entsprechend den drei Großmachtsphären) systematisiert. Die Darstellung der Völkerschaften als verwandt macht deutlich, dass alle Menschen trotz ihrer kulturellen Eigenheiten zueinander in Beziehung stehen. In der Erzähllinie des Buches Genesis ist die Völkertafel eine Ätiologie für die Ausbreitung der Menschheit im Raum und eine Erfüllung des Schöpfungssegens: Alle existierenden Völker gehören zu der von Gott geschaffenen Menschheit. Die Völkertafel hat außerdem die Funktion, die bekannten Völker geographisch zu verorten und sie über genealogische Beziehungen auch zueinander ins Verhältnis zu setzen. Genesis 10 zeigt die Weltdeutung und die politische Sichtweise ihrer Verfasser zu deren Zeit

Measure for Measure: Wittgenstein's Critique of the Augustinian Picture of Music

This article concerns the distinction between memory-time and information-time, which appeared in Wittgenstein’s middle-period lectures and writings, and its relation to Wittgenstein’s career-long reflection about musical understanding. While the idea of “information-time” entails a public frame of reference typically pertaining to objects which persist in physical time, the idea of pure “memory-time” involves the totality of one’s present memories and expectations that do now provide any way of measuring time-spans. I argue that Wittgenstein’s critique of Augustine notion of pure memory-time entails ipso facto a critique of an influential idea of musical motion, which has been recurring in the work of some major philosophers of music up until the present day. The article connects Wittgenstein’s critical remarks on the confused foundations of such “Augustinian Picture of Music” with his emphasis on the notion of phrasing or characterization in language and music. Wittgenstein’s reversal of Augustinian priorities regarding musical time brings to surface the particularity of expression and the aesthetically “right” in music, evoked by Wittgenstein’s remarks on simultaneity and tempo in music and language. Wittgenstein renders musical simultaneity as enabled by a “protocol” which inheres in musizieren, in the aptly collaborative quest for drawing in significance by means of the phrasing and re-phrasing of a passage in order to characterize it, enabling by means of such comparative investigation meaningful distinctions between right and wrong