In 1952, Heinrich Scholz published a question in The Journal of Symbolic Logic asking for a characterization of spectra, i.e., sets of natural numbers that are the cardinalities of finite models of first order sentences. Günter Asser in turn asked whether the complement of a spectrum is always a spectrum. These innocent questions turned out to be seminal for the development of finite model theory and descriptive complexity. In this paper we survey developments over the last 50-odd years pertaining (...) to the spectrum problem. Our presentation follows conceptual developments rather than the chronological order. Originally a number theoretic problem, it has been approached by means of recursion theory, resource bounded complexity theory, classification by complexity of the defining sentences, and finally by means of structural graph theory. Although Scholz' question was answered in various ways, Asser's question remains open. (shrink)

Simone de Beauvoir offers one of the most interesting philosophical accounts of childhood, and, as numerous scholars have argued, it is one of the most important contributions that she made to existentialism. Beauvoir stressed the importance of childhood on one's ability to assume one's freedom. This radically changed how freedom was construed for existentialism. Rather than positing an adult subjectivity that tries to flee freedom through bad faith, Beauvoir's account forces a recognition of a situated freedom that itself is also (...) developmentally achieved. In this article, I explore the influence of Jean-Jacques Rousseau on Beauvoir's discussion of childhood. By reading Beauvoir through Rousseau — who was one of her favorite authors — we see not just one but two accounts of childhood in Beauvoir's philosophical work. On the one hand is the idealistic childhood wherein the child is an apprentice to freedom. On the other is the constrained childhood whose product is apprenticed to the serious. I begin with a brief summary of Rousseau's Emile. Next, I offer some justification for reading Beauvoir alongside Rousseau before offering an account of Beauvoir's discussion of childhood. I end by exploring some of the implications of my reading for freedom. (shrink)

Hermann Weyl was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben in the general relativistic framework for the Dirac equation. He preserved the central idea (...) of gauge as a “purely infinitesimal” aspect of symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations. (shrink)

1. Jugendschriften 1835-1841. Mit einem Essay "Zum Verständnis der Texte," Erläuterungen und Bibliographie hrsg. von G. Hillmann. DM 3.80 (GDB 66-A49-92)--2. Pariser Manuskripte 1844.--3. Der Mensch in Arbeit und Kooperation (Aus den Grundrissen der Kritik der politischen Ökonomie, 1857/58).

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in (...) the context of the later development of gauge theories. (shrink)

A lengthy debate in the philosophy of the cognitive sciences has turned on whether the phenomenon known as ‘systematicity’ of language and thought shows that connectionist explanatory aspirations are misguided. We investigate the issue of just which phenomenon ‘systematicity’ is supposed to be. The much-rehearsed examples always suggest that being systematic has something to do with ways in which some parts of expressions in natural languages (and, more conjecturally, some parts of thoughts) can be substituted for others without altering well-formedness. (...) We show that under one construal this yields a grossly weak claim that is not just compatible with a narrow version of associationist psychology but essentially coincides with a formalization of its descriptive power. Under another construal we get a claim (apparently unintended) that requires natural languages to fall within the context-free class, a claim that most linguists regard as too strong. Looking more closely at this proposed reconstruction of systematicity leads us to endorse, with further illustrations, the suggestion of Johnson (2004) that systematicity as a matter of substitutability of co-categorial constituents for one another does not appearto hold of natural languages at all. The appeal of the ill-delineated notion of systematicity may lie in the fact that within certain subclasses of lexical items mutual intersubstitutability does seem to hold, and theexplanation for that lies in a limitation on human memory: we simply cannot learn separate privileges of syntactic distribution for all of the huge number of words and phrases that we know. (shrink)

Bücher zählen bis heute zu den wichtigsten kulturellen Errungenschaften der Menschheit. Ihre Erfindung war mit der Einführung des Buchdrucks ähnlich bedeutsam wie des Internets: Erstmals wurde eine massenweise Weitergabe von Informationen möglich. Bildung, Wissenschaft, Forschung, aber auch die Unterhaltung wurde auf neuartige, technisch wie inhaltlich revolutionäre Basis gestellt. Bücher verändern die Gesellschaft bei heute. Die technischen Möglichkeiten des Massen-Buchdrucks führten zu einem radikalen Zuwachs an Titeln im 18. Und 19 Jahrhundert. Dennoch waren die Rahmenbedingungen immer noch ganz andere als heute: (...) Wer damals ein Buch schrieb, verfasste oftmals ein Lebenswerk. Dies spiegelt sich in der hohen Qualität alter Bücher wider. Leider altern Bücher. Papier ist nicht für die Ewigkeit gemacht. Daher haben wir es uns zur Aufgabe gemacht, das zu Buch gebrachte Wissen der Menschheit zu konservieren und alte Bücher in möglichst hoher Qualität zu niedrigen Preisen verfügbar zu machen. (shrink)

In this essay, the enlightenment is not considered as a bygone age, but as a systematic epistemological, moral and political program that can, in principle, be pursued at any time. Since Kant has done most to clarify this program, his philosophy may serve as a starting point for discussion of the questions: How do the leading ideas of the enlightenment hang together? How are they justified?

Recent decades have witnessed rape and sexual violence used on such a massive scale and often in a widespread and systematic program that the international community has had to recognize that rape and sexual violence are not just war crimes but might be crimes against humanity or even genocide. I suggest that just war theory, while limited in its applicability to mass rape, might nevertheless offer some framework for making the determination of when sexual violence and rape constitute war crimes, (...) crimes against humanity, or genocide. In addition, just war theory can provide the normative justification individual soldiers need to resist orders and actions that demonstrate egregious moral breakdown as found in instances of mass rape and systematic use of sexual violence, and just war criteria demonstrate that the use of rape and sexual violence in war time can never be legitimated, especially in the case of prisoner interrogation. (shrink)

Although blame for systemic sexual abuse in the Catholic church primarily rests with the perpetrators and institutional actors who engaged in cover-up, regular people also failed in their duties, both their secular or civil duties and their moral and religious duties. Using the language of social sin, this article examines responsibility for social sin and the structures of sin that contributed to the abuse of children within the church community. Using the tools of Catholic social teaching—especially the framework of “conversion, (...) communion, and solidarity”—the article articulates some tenets of social morality in the wake of sexual abuse and cover-up. A conversion experience is needed to see how ordinary actions unintentionally contribute to injustice and social sin, and how structures of sin lead to intentional decisions that would not otherwise be pursued. Catholic social teaching helps to provide a framework for thinking through some of the obligations of ordinary folks in the aftermath of the collective failure to protect children from abuse and the structural injustices that encouraged it to continue. (shrink)

Clonal studies of adult chimaeric mouse epithelium have demonstrated the monoclonal composition of crypts of Lieberkühn(1). In neonatal life, however, polyclonal crypts have been found, indicating that crypts are of polyclonal origin(2). We here relate these findings to studies of mosaic tissues which have addressed the question whether solid tumours are of monoclonal or polyclonal origin (ref. 3 for review, 4). The issues has so far remained unresolved because the expected frequencies of polyclonal tumours, given polyclonal origins, have not previously (...) been estimated. A general approach for the calculation of such expected values is suggested. The consistent reports of tumours with polyclonal components suggest that autocrine or paracrine mechanisms play an important role during tumorigenesis. (shrink)