We study connections between classical asymptotic density, computability and computable enumerability. In an earlier paper, the second two authors proved that there is a computably enumerable set A of density 1 with no computable subset of density 1. In the current paper, we extend this result in three different ways: The degrees of such sets A are precisely the nonlow c.e. degrees. There is a c.e. set A of density 1 with no computable subset of nonzero density. There is a (...) c.e. set A of density 1 such that every subset of A of density 1 is of high degree. We also study the extent to which c.e. sets A can be approximated by their computable subsets B in the sense that A\B has small density. There is a very close connection between the computational complexity of a set and the arithmetical complexity of its density and we characterize the lower densities, upper densities and densities of both computable and computably enumerable sets. We also study the notion of "computable at density r" where r is a real in the unit interval. Finally, we study connections between density and classical smallness notions such as immunity, hyperimmunity, and cohesiveness. (shrink)

We classify the asymptotic densities of the sets according to their level in the Ershov hierarchy. In particular, it is shown that for, a real is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any.

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse similarity classes (...) under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

The options in a decision problem generally have outcomes with common features. Putting aside the common features simplifies deliberations, but the simplification requires a philosophical justification that this book provides.

The study of alternatives to conventional industrial agricultural production has intensified in recent years. While many types of alternative production systems, and the motivations of individuals to participate in them, have been studied, there are significant gaps in the literature. One such dearth is research on those participating in self-provisioning activities. This study begins to fill the gap by looking at the self-provisioning activity of home gardening using data from the 2008 Ohio Survey of Food, Agriculture, and Environmental Issues. Discerning (...) who household gardeners are is important given the recent economic, cultural, and political climate of the United States. The results show that home gardening occurs throughout the state of Ohio at surprisingly high levels. Bivariate and multivariate analyses reveal several noteworthy associations between gardening and household characteristics, including spatial location, pro-environmental and economic hardship behaviors, and level of participation in localized food systems. (shrink)

Myślą Ludwika Gumplowicza polscy uczeni zainteresowali się stosunkowo późno. Jej pierwsze opracowania autorstwa Jana Karola Kochanowskiego, Stanisława Posnera, Mieczysława Szerera, Jana Stanisława Bystronia, Aleksandra Kraushara przypadają na lata 1910–1917, a więc na okres zwany Młodą Polską, który wpisuje się w ogólnoeuropejski modernizm. Nowa generacja uczonych, pisarzy i artystów, działająca w okresie młodopolskim znacząco różniła się w przyjmowanych założeniach filozoficzno-ideowych od pokolenia pozytywistów i realistów krytycznych. Niemniej ukształtowane w pozytywizmie nawyki myślenia nie zanikły po roku 1890 całkowicie – pozostały one indywidualnym (...) a zarazem wspólnym dorobkiem intelektualnym generacji szkół i uczonych wykształconych w dobie pozytywizmu. Postawy światopoglądowe pozytywizmu i modernizmu przenikały się, zaś zasadniczym łączącym je elementem, pomimo programowego buntu modernizmu wobec haseł pozytywistycznych, było zadłużenie wobec naturalizmu. Jednak że schyłkowe lata XIX wieku przynoszą antyscjentystyczne niepokoje, w tym krytykę pozytywistycznego modelu nauki, teorii ewolucjonizmu i jemu właściwego rozumienia postępu, protest przeciwko utylitaryzmowi i odrodzenie metafizyki. […] W polskich pracach z lat 1910–30 poświeconych socjologii L. Gumplowicza interesujące są trzy wątki, wskazujące na kierunek i postać, jaki przybrała recepcja dzieła socjologa z Grazu: zespół wspólne podzielanych przekonań odnośnie genezy systemu Gumplowicza oraz dwie warstwy wartościowania jego dorobku: pozytywna i negatywna. Zatem nasze ujęcie opinii, sądów i ocen sformułowanych przez St. Posnera, M. Szerera, J. St. Bystronia, A. Kraushara oraz F. Mirka pod adresem teorii Gumplowicza będzie miało charakter syntetyzującego przeglądu, uwzględniającego specyfikę stanowisk w kwestiach, które znacząco się od siebie różnią. Ta uwaga odnosi się przede wszystkim do bardzo zindywidualizowanej krytyki spuścizny Gumplowicza. Jako odrębne w tym przeglądzie wyróżnione zostanie stanowisko J. K. Kochanowskiego z uwagi na jego odmienność: oryginalne i twórcze nawiązanie polskiego historyka i socjologa do myśliciela z Grazu. (shrink)

Schelling und Hegel benutzen in ihren philosophischen Texten mathematische und naturwissenschaftliche Modelle wie Unendlichkeit oder Gleichgewicht. Die Strukturen dieser Begriffe liefern einen Massstab fur den Vergleich der Positionen Schellings und Hegels, der fur Schellings Identitatsphilosophie und Hegels erste Jenaer Schriften durchgefuhrt wird. Als wichtigstes Resultat kann eine grundlegende Differenz zwischen beiden Positionen bereits um 1801 nachgewiesen und gezeigt werden, dass diese auf einer unterschiedlichen Auffassung der Rolle des Absoluten beruht.

The first book-length study of a leading tenth-century Ismaili theoretician Abu Ya'qub al-Sijistani.

Zusammenfassungen der Referate in französischer Sprache.

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of (...) an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement. (shrink)

Die MISCELLANEA MEDIAEVALIA präsentieren seit ihrer Gründung durch Paul Wilpert im Jahre 1962 Arbeiten des Thomas-Instituts der Universität zu Köln. Das Kernstück der Publikationsreihe bilden die Akten der im zweijährigen Rhythmus stattfindenden Kölner Mediaevistentagungen, die vor über 50 Jahren von Josef Koch, dem Gründungsdirektor des Instituts, ins Leben gerufen wurden. Der interdisziplinäre Charakter dieser Kongresse prägt auch die Tagungsakten: Die MISCELLANEA MEDIAEVALIA versammeln Beiträge aus allen mediävistischen Disziplinen - die mittelalterliche Geschichte, die Philosophie, die Theologie sowie die Kunst- und (...) Literaturwissenschaften sind Teile einer Gesamtbetrachtung des Mittelalters. (shrink)

The centrality of death rituals has in anthropologically informed studies of Buddhism been little documented. The current volume brings together a range of perspectives on Buddhist death rituals including ethnographic, textual, historical and theoretically informed accounts, and presents the diversity of the Buddhist funeral cultures of mainland Southeast Asia and China. It arises out of the University of Bristol's Centre for Buddhist Studies research project Buddhist Death Rituals in Southeast Asia and China, funded by the United Kingdom's Arts and Humanities (...) Research Council. This project involved extensive new research in Thailand, Laos and China. Other items from that project included several public exhibitions, extensive stills photographs, and several video films. The project-team produced two 30 minutes films on the ghost festival in Laos and China, one on urban funerals in Chiang Mai (Thailand) and several shorter clips dealing with funeral cultures in Laos, Thailand and China. Most of this material (and an extensive bibliography on the topic) is available free of charge from the project website located at the webpage of the Department of Theology and Religious Studies (Centre for Buddhist Studies) at the University of Bristol. (shrink)

This article contends that the evolution toward interdisciplinary collaboration that we are witnessing in the sciences must also occur in the humanities to ensure their very survival. That is, humanists must be open to working with scientists and social scientists interested in similar research questions and vice versa. Digital humanities is a positive first step. Complexity science should be the next step. Even though much of the ground-breaking work in complexity science has been done in the natural sciences and mathematics, (...) it can, if critically adapted, provide the needed metaphor for a broad integration of disciplines, humanistic and otherwise. Given its almost a-disciplinary nature, a complexity approach to the research problems in the humanities necessarily breaks down silos. Moreover, it can restore and reframe the seamless intellectual fabric sought by researchers before the atomization of the various disciplines in the nineteenthcentury academy. (shrink)

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

Die Generales Inquisitiones von 1686 stellen die wichtigste geschlossene Arbeit Leibniz' zu Fragen der Logik dar. Wie in dem ebenfalls 1686 verfaßten Discours de Métaphysique (PhB 260) wird hier Leibniz' Auffassung deutlich, in seinem Denken eine gewisse systematische Geschlossenheit gefunden zu haben.

Participation in the local food movement has grown dramatically in the United States, with the farmers’ market being one of its most widespread and heavily promoted forums. Proponents argue that the interactions and transactions that occur at farmers’ markets benefit market participants, but, more importantly, have broader benefits for the neighborhoods they are located in and for society itself. The promise of these benefits raises several important questions, notably: where are farmers’ markets located and who has access to them? While (...) many works have examined the characteristics of individuals who frequent markets, few have examined the areas and inhabitants hosting these markets. Using data from the USDA and US Census, I explore the location of farmers’ markets areas across several geographic measurements, including at the national, census division, and census tract levels. Results reveal the following: Perhaps not being as white of a movement as critics have suggested, farmers’ markets are almost exclusively a middle to middle-upper class phenomenon; and Farmers’ markets are very unlikely to be found in neighborhoods with lower than average socio-economic statuses indicators, in specific divisions of the US, and in rural areas. Results from this research further illuminate our understanding of where farmers’ markets are located throughout United States while presenting some interesting questions for the local food movement as it continues to moves forward. (shrink)