This article affirms the modern origin of sociology as a science and posits a critical posture as its fundamental component. As such, sociology is opposed to any dogmatic conception of knowledge. The critical stance has both internal and external dimension. Sociology is under the obligation to observe a constant vigilance towards the knowledge it produces. A considerable methodological privilege bestowed upon the researchers in sociology requires that they have to be capable of criticizing their conceptual tools and operational procedures. Furthermore, critical attitude consists also in questioning conditioning of results linked to the dependence arising from the subsidizing of research. These preconditions of critical posture are illustrated by consideration of the challenges of researching the so-called “school failure”. Ultimately, responsibility commands a sociologist to respect the principle of precaution. When political action is concerned, the researchers must demand that their rights of intellectual property be preserved. To criticize, in this sense, is not to denounce; nonetheless, sociology will only remain faithful to what can pass legitimately as its essence by demanding the right, against threats and seductions, to speak the truth about social reality. and Claude Javeau.
In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.
N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the <span class="tex">L<sub>1</sub></span> view of density estimation. The Cencov's work is available in Russian only and it hasn't been translated, so late Igor Vajda decided to translate the Cencov's paper and to add some remarks on the occasion of organizing the session "25 Years of the <span class="tex">L<sub>1</sub></span> Density Estimation" at the Prague Stochastics 2010 Symposium. In this paper we complete his task, i.e., we translate the Cencov's chapter and insert some remarks on the related literature focusing primarily on Igor's results. We would also like to acknowledge the excellent work of Alexandre Tsybakov who translated the Devroye and Györfi book in Russian, annotated it with valuable comments and included some related references published in Russian only.
The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that λ-additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.
Der vorliegende Beitrag ist eine teils gekürzte, teils überarbeitete und ergänzte Nachschrift des frei gehaltenen Vortrags. Der Charakter der freien Rede wurde durchgehend gewahrt. Der Leser möge also bedenken, daß der Status des einzelnen Wortes, des einzelnen Satzes und der Satzfolge in frei gesprochener Rede gänzlich verschieden ist von der in einem ausgearbeiteten Text. Die Zitate sind an den Vorlagen überprüft worden. Den Herstellern der Umschrift und Herrn Dr. Felix Wörner bin ich für die Ermöglichung der Veröffentlichung in dieser Form sehr dankbar