Plato: The Timaeus There is nothing easy about the Timaeus. Its length, limited dramatic discourse, and arid subject-matter make for a dense and menacing work. But make no mistake, it is a menacing work of great subtly and depth. Cosmology has traditionally received the bulk of scholarly attention. No less important, however, are the dialogue’s … Continue reading Plato: The Timaeus →.

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

In Concepts, Kinds, and Cognitive Development, Frank C. Keil provides a coherent account of how concepts and word meanings develop in children, adding to our understanding of the representational nature of concepts and word meanings at all ages. Keil argues that it is impossible to adequately understand the nature of conceptual representation without also considering the issue of learning. Weaving together issues in cognitive development, philosophy, and cognitive psychology, he reconciles numerous theories, backed by empirical evidence from nominal kinds (...) studies, natural-kinds studies, and studies of fundamental categorical distinctions. He shows that all this evidence, when put together, leads to a better understanding of semantic and conceptual development. The book opens with an analysis of the problems of modeling qualitative changes in conceptual development, investigating how concepts of natural kinds, nominal kinds, and artifacts evolve. The studies on nominal kinds document a powerful and unambiguous developmental pattern indicating a shift from a reliance on global tabulations of characteristic features to what appears to be a small set of defining ones. The studies on natural kinds document an analogous shift toward a core theory instead of simple definition. Both sets of studies are strongly supported by cross cultural data. While these patterns seem to suggest that the young child organizes concepts according to characteristic features, Keil argues that there is a framework of conceptual categories and causal beliefs that enables even very young children to understand kinds at a deeper, theoretically guided, level. This account suggests a new way of understanding qualitative change and carries strong implications for how concepts are represented at any point in development. A Bradford Book. (shrink)

This unusually accessible account of recent Anglo-American philosophy focuses on how that philosophy has challenged deeply held notions of subjectivity, mind, and language. The book is designed on a broad canvas in which recent arguments are placed in a historical context (in particular they are related to medieval philosophy and German idealism). The author then explores such topics as mental content, moral realism, realism and antirealism, and the character of subjectivity. Much of the book is devoted to an investigation of (...) Donald Davidson's philosophy, and there is also a sustained critique of the position of Richard Rorty. A final chapter defends the realist position against objections from postmodern thought. As a rigorous and historically sensitive account of recent philosophy, this book should enjoy a wide readership among philosophers of many different persuasions, literary theorists, and social scientists who have been influenced by postmodern thought. (shrink)

In the famous opening sentence of The Eighteenth Brumaire, Marx notes that somewhere Hegel had written that great world-historical phenomena occur twice, neglecting to add, however, the first time as tragedy, the second as farce. Given what we now know of the heretofore hidden side of Bruno Rizzi, still another revision seems in order: sometimes such phenomena make yet a third appearance, this time as embarrassment, rank embarrassment. Indeed, Rizzi's name surfaced in three such sequential contexts. The first was in (...) the late 1930s when non-stalinist Marxists, primarily Trotskyists, were debating whether or not a “new class” had emerged in the Soviet Union. (shrink)

The empirical and theoretical resources of different disciplines are often combined to shed light on questions that concern the deep history of humanity, such as the geographic origin of people groups, patterns of migration, and the diffusion of culture. In this article, I discuss three ways in which other disciplines, such as biology and archaeology, are integrated with historical linguistics to enhance our understanding of the past. First, other disciplines provide background knowledge that helps to constrain and assess competing historical (...) explanations of the data. I examine this issue in the context of the Principle of the Common Cause and Inference to the Best Explanation. Second, the synthesis of data from multiple disciplines provides a diverse and varied set of evidence, which is epistemically superior, other things being equal, to a homogeneous set of evidence. I consider several justifications for the confirmational value of diverse evidence. Finally, methods and procedures from other disciplines can often be fruitfully applied to forge new pathways to knowledge. Here, I survey the recent application of phylogenetic methods from biology, used for inferring evolutionary trees, within historical linguistics. (shrink)

The restructuration of municipalities which has been decided by the Belgian government, is not only a purely technical operatzon but rather, and in the first place, a social problem. The shape and duty-profile of a local authority should not, indeed, be attuned only to fast changing expectations as far as services are concerned, but to consultation and participation as well.Public administration research cannot keep aloof from this debate, but is considerably hampered by the institutional confusion and the insufficient explicitation of (...) the aims of the present reform. A starting-pointcan, however, be found in the mergers of municipalities that were realized in 1964 and in 1970/1971. In 67 of these municipalities an inquiry was held concerning the consequences of the merger, and moreover, in twotest-cases this inquiry grew to a full-scale systematic policy analysis.This research shows that, as a rule, the former municipalities are reasonably represented in the new entity's council, but it also reveals that few efforts are made to give this representation a broader impact along formal or informal participation-channels. Integration of employees has not caused insurmountable problems. However, in large sized municipalities, resulting from mergers, one could notice a drastic increase in municipal personnel, not only with regard to new duties and objectives but to traditional administrative and police duties as well. Such a phenomenon points to the far-reaching changes which a substantial scale-increase provokes in a municipality's structure and policy profile. A large municipality resulting from mergers is no langer a simple sum of component parts, but a completely new entity, wishing to catch up as fast as possible with comparable municipalities that passed through a progressive growth process. Therefore, scale-increase is not only a means of economizing or an intra-administrative matter, but rather a way of creating chances for further development or wealth and well-being. (shrink)

This paper situates and examines the project of genealogy as articulated by the philosopher, Michel Foucault, and draws out from that examination educative implications both in terms of research and school practice. Following Foucault, the genealogist's primary challenge, it would seem, is both to acknowledge and to respond to the entwinement of rationality and power. This paper also considers critiques which have clustered around Foucault's work, and, more specifically, his genealogical work, which argue that Foucault leaves us with no hope (...) for a better, more humane future and no positive agenda for change. Despite this “lack” in Foucault's work, I argue, here, that his genealogical agenda is philosophically, politically, and educatively significant. (shrink)

This article provides excerpts and highlights from the insights of twenty global leaders, business executives, and sustainability experts who gathered at the Esalen Institute in California for four days in March 2002 to discuss how to best leverage change toward an environmentally sustainable and socially equitable global economy. The conference topic was sparked by the path-breaking book Natural Capitalism, which outlines an expanded vision of capitalism suitable for the environmental era. The natural capitalism model is qualitatively different from industrial era (...) capitalism in that it counts both humanity and ecosystem services as valid sources of capital in addition to the traditionally recognized sources, financial and manufactured. One early adopter of natural capitalism, CEO of the Atlanta -based carpet tiling company, Interface, shared how increased efficiency and greater employee and customer satisfaction have resulted. Although some of the conference participants forecasted that globalization is likely to bring humanity face-to-face with a planetary-wide environmental, financial, and social crisis, the overall message of this gathering was positive. Through the imaginative implementation of evolutionary and biomimicry design models in the cultural, financial, and economic spheres, novel solutions to global problems already are being discovered, and, if such innovative and solutions-oriented design thinking can spread rapidly enough, humanity may be able to ameliorate-or even obviate-the deleterious effects of globalization. (shrink)

Desenvolvo um método de prova por refutação para a Lógica Proposicional Clássica, que resgata ideias dos tablôs semânticos de Evert Beth. Primeiro apresento o método em forma conjuntista, depois o utilizo em forma tabular simplificada.

Formulações da validade dedutiva clássica costumam recorrer explicitamente a modalidades: por exemplo, um argumento é classicamente dedutivamente válido se, e somente se, necessariamente se as premissas forem verdadeiras, a conclusão também é verdadeira. Não é possível abolir completamente esse apelo ao discurso modal, porque a lógica clássica é o domínio das possibilidades. Não obstante, pode-se, por intermédio de uma semântica informacional, evitar que o usuário da lógica clássica tenha de manipular modalidades, ainda que elas estejam, de algum modo, imbricadas nos (...) infons – unidades mínimas de informação. A partir do trabalho pioneiro de Carnap e de Bar-Hillel, apresentarei duas semânticas informacionais: uma delas diretamente relacionada a mundos possíveis, e a outra relacionada aos duais de mundos possíveis. (shrink)

In this classic work of philosophy, Thilly provides a comprehensive overview of inductive reasoning and its role in scientific inquiry. With clear examples and lucid prose, Thilly's text remains an essential resource for anyone seeking to understand the nature of knowledge and the scientific method. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of (...) America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This article addresses the extent and ways in which gender inequality in the newspaper coverage of arts and culture has changed in France, Germany, the Netherlands, and the United States, 1955-2005. Through a quantitative content analysis, we mapped all articles that appeared in two elite newspapers in each country in four sample years 1955, 1975, 1995, and 2005. First, despite increasing women’s employment in arts and culture and a quantitative feminization of journalism, elite newspaper coverage of women in arts and (...) culture has hardly changed, making up about 20-25 percent consistently over the last 50 years. Second, our results show surprisingly few cross-national differences in the amount of the newspaper coverage devoted to women in arts and culture. Third, although women are underrepresented in the coverage of all artistic genres, there is some evidence of horizontal sex segregation—particularly in architecture and modern dance and fashion —as well as vertical sex segregation—in that attention to women has increased in “highbrow” genres that have declined in status. Finally, as the status of an actor type increases from laymen to artistic directors, the proportion of women decreases in newspaper attention to arts and culture. (shrink)

In this article, I attempt to restore the philosophical significance of that nonformalizable, noniterable, “singular’ element of natural language that I call “style.” I begin by critically addressing the exclusion of such instances of natural language by both semantics‐oriented logical analysis and a restricted variation of structuralist linguistics. Despite the obvious advantages – with regard to style – of ”pragmatic“approaches to language, such pragmatism merely returns to rule‐determination in the guise of “normativity.” Although style by definition resists any kind of (...) rule‐determination – whether posed in terms of semantics or intersubjective regulations of speech‐acts – there can be no consideration of language that ignores the persistence of style in natural language. In terms of cognition, any discursive agent understands more than allowed by either semantics or speech‐act theory. I ascribe this element of excessive signification to the role of style. My principal thesis is twofold: (1) a hermeneutic approach (exemplified by Schleiermacher) to literature should reveal the heuristically decisive role played by style in philosophy; and, more radically still, (2) style, in fact, may be crucially determinative of philosophical discourse in general. I suggest that a closer scrutiny of the lesser‐known works of Ludwig Wittgenstein, conventionally regarded as having dreamt of a “philosophy without style,” may consolidate the restoration of style's philosophical import. (shrink)

: For quite some time now there has been an ongoing debate whether authoritative self-knowledge is compatible with anti-individualism.1 One influential line of argument against compatibilism is due to Paul Boghossian (1998). I argue that Boghossian misconstrues what the anti-individualist really is committed to. This defence of compatibilism is elaborated by showing how the Twin Earth thought experiment is meant to speak in favour of anti-individualism. Partly this will show that Boghossian is wrong in his denial that empirical background knowledge (...) is imported into the Twin Earth experiment. The main points argued are that Boghossian fails to realize, both, (1) that anti-individualism does not involve concept-individuation in terms of reference, and (2) that anti-individualism assumes a core of representational success. In effect, these two points constitute an entirely new way to defend compatibilism, a way that seems to have gone unnoticed in the literature. (shrink)

Artificial intelligence and the interrogation game; Scientific method and explanation; Godel's incompleteness theorem; Determinism and uncertainty; Axioms, theorems and formalisation; Creativity; Consciousness and free will; Pragmatics; A ...

Income redistribution and insurance are core functions of welfare states. What role should the EU play in this domain? I examine the purchase of normative theorizing on social justice on this question, focusing on the contrast between three models of EU involvement: the EU as Support, which implies the sharing of resources through intergovernmental transfers; the EU as Provider, which implies EU cross‐border transfers towards individual citizens; the EU as Norm‐setter, which implies that the EU formulates normative policy ideals. I (...) review different accounts of justice for the EU and how they bear on the choice between these models of EU involvement. Conceptions of “background justice” have some purchase in a debate on the EU's role, but that purchase is limited. They need to be complemented by shared conceptions of domestic justice and a degree of moral cosmopolitanism. I argue that a “European Social Union” should be a Support and Norm‐setter in the realm of insurance and redistribution. Through the establishment of interstate insurance, it would be a true “insurance union.” It would engage in interstate redistribution, but there are no compelling reasons of justice for it to become a direct Provider of insurance or redistribution towards individual citizens. (shrink)

We show that a stable groupG satisfying certain commutator conditions is nilpotent. Furthermore, a soluble stable group with generically splitting automorphism of prime order is nilpotent-by-finite. In particular, a soluble stable group with a generic element of prime order is nilpotent-by-finite.

Die Publizistik hat erfolgreich ihre Auffassung durchgesetzt, dass „die Diskussion einer wie auch immer gearteten ‚Zeitschriftentheorie‘“ „wenig ergiebig“ sei, woraus sich auch der schmale, auf die Inhaltsanalyse beschränkte Werkzeugkasten der Zeitschriftenforschung erklärt (dazu historisch fundierte Ergänzungsvorschläge unter Abschnitt 9 und 10). Nach einer Einführung in die Zeitschrift Die Kreatur (Abschnitt 1) scheint es deshalb nötig, das theoretische Objekt – Voraussetzung jeglicher Forschungspraxis – ‚Zeitschriften‘ vorab in aller gebotenen Kürze (Abschnitt 2–4) historisch-systematisch zu skizzieren. Die Kreatur kann dann als eine der (...) Zeitschriften im Rahmen zeitgenössischer Format-Optionen (Abschnitt 5–8) in Netzwerken wie dem um Walter Benjamin situiert werden (Abschnitt 11–13). (shrink)