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)

Noam Chomsky and Frances Egan argue that David Marr’s computational theory of vision is not intentional, claiming that the formal scientific theory does not include description of visual content. They also argue that the theory is internalist in the sense of not describing things physically external to the perceiver. They argue that these claims hold for computational theories of vision in general. Beyond theories of vision, they argue that representational content does not figure as a topic within formal computational theories (...) in cognitive science. I demonstrate that Chomsky’s and Egan’s claims about Marr’s theory are false. Marr’s computational theory contains a mathematical theory of visual content, based on empirical psychophysical evidence. It also contains mathematical descriptions of distal physical surfaces and objects, and of their optic projection to the perceiver. Much computational research on vision contains these types of intentional and externalist components within the formal, mathematical, theories. Chomsky’s and Egan’s claims demonstrate inadequate study and understanding of Marr’s work and other research in this area. Computational theories of vision, by containing empirically based mathematical theories of visual content, to this extent present naturalizations of semantics. (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)

This edition includes a new introduction by Peter J. Gomes that reflects on the impact of this book in the years since it was written.

Paul Thom's book presents Kilwardby's science of logic as a body of demonstrative knowledge about inferences and their validity, about the semantics of non-modal and modal propositions, and about the logic of genus and species. This science is thoroughly intensional. It grounds the logic of inference on "that in virtue of which" the inference holds. It bases the truth conditions of propositions on relations between conceptual entities. It explains the logic of genus and species through the notion of essence. (...) Thom interprets this science as a formal logic of intensions with its own proof theory and semantics. This comprehensive reconstruction of Kilwardby's logic shows the medieval master to be one of the most interesting logicians of the thirteenth century. (shrink)

In this chapter a new problem about rule-following is outlined, one that is distinct both from Kripke’s and Wright’s versions of the problem. This new problem cannot be correctly responsed to, as Kripke’s can, by invoking Wright’s Intentional Account of rule-following. The upshot might be called, following Kant, an antinomy of pure reason: we both must — and cannot — make sense of someone’s following a rule. The chapter explores various ways out of this antinomy without here endorsing any of (...) them. (shrink)

This is a collection in translation of essays by Paul Ricoeur which presents a comprehensive view of his philosophical hermeneutics, its relation to the views of his predecessors in the tradition and its consequences for the social sciences. The volume has three parts. The studies in the first part examine the history of hermeneutics, its central themes and the outstanding issues it has to confront. In Part II, Ricoeur's own current, constructive position is developed. A concept of the text (...) is formulated as the implications of the theory are pursued into the domains of sociology, psychoanalysis and history. Many of the essays appear here in English for the first time; the editor's introduction brings out their background in Ricoeur's thought and the continuity of his concerns. The volume will be of great importance for those interested in hermeneutics and Ricoeur's contribution to it, and will demonstrate how much his approach offers to a number of disciplines. (shrink)

De milieuproblematiek staat pas sinds kort op de agenda als een fenomeen dat de mensheid bedreigt. Toch blijkt het negentiende-eeuwse gedachtegoed van Karl Marx verrassende inzichten te bieden om deze actuele problemen te duiden. Marx laat zien dat het menselijk ingrijpen in de natuur leidt tot zelfvervreemding: de mens ondermijnt zijn bestaan als een wezen dat zelf deel uitmaakt van de natuur. Deze zelfvervreemding cumuleert in de kapitalistische samenleving. Marx lezend zien we dat de milieuproblematiek geen historische vergissing is, maar (...) fundamenteel samenhangt met de mens als redelijk wezen. Onze beheersingsrede heeft geleid tot de vervreemding van de natuur. Toch geeft dezelfde rede die de mens de vrijheid biedt zich boven het ecologische evenwicht te verheffen, hem de mogelijkheid zich te verzoenen met de natuur. Marx verwijst naar dit dubbele gezicht van de rede als hij stelt dat het 'rijk van de vrijheid' in de schoot van het kapitalisme wordt geboren. In dit boek onderzoekt Paul Cobben welke aanzetten de huidige samenleving biedt om vorm te geven aan de verzoening met de natuur. Paul Cobben is emeritus hoogleraar geschiedenis van de moderne filosofie aan Tilburg University. Momenteel is hij gastonderzoeker aan de Vrije Universiteit Amsterdam en redacteur van de serie 'Critical Studies in German Idealism'. Van zijn hand verscheen o.a. 'Value in Capitalist Society. Rethinking Marx's Criticism of Capitalism' (2015)."-- Publisher information. (shrink)

The Renaissance was a period of great intellectual change and innovation as philosophers rediscovered the philosophy of classical antiquity and passed it on to the modern age. Renaissance philosophy is distinct both from the medieval scholasticism, based on revelation and authority, and from philosophers of the seventeenth and eighteenth centuries who transformed it into new philosophical systems. Despite the importance of the Renaissance to the development of philosophy over time, it has remained largely understudied by historians of philosophy and professional (...) philosophers. This anthology aims to correct this by providing scholars and students of philosophy with representative translations of the most important philosophers of the Renaissance. Its purpose is to help readers appreciate philosophy in the Renaissance and its importance in the history of philosophy. The anthology includes translations from philosophers from the thirteenth to the seventeenth centuries, and it ranges from works on moral and political philosophy, to metaphysics, epistemology, and natural philosophy, thereby providing historians and students of philosophy with a sense for the nature, breadth, and complexity of philosophy in the Renaissance. Each translation is accompanied by an introduction by a historian of Renaissance philosophy, as well as select secondary sources, in order to encourage further study. (shrink)

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)

Paul Helm investigates what religious faith is and what makes it reasonable.

Logic brings elementary logic out of the academic darkness into the light of day. Paul Tomassi makes logic fully accessible for anyone trying to come to grips with the complexities of this challenging subject. This book is written in a patient and user-friendly way which makes both the nature and value of formal logic crystal clear. This textbook proceeds from a frank, informal introduction to fundamental logical notions to a system of formal logic rooted in the best of our (...) natural deductive reasoning in daily life. The book includes plenty of exercise to put the students' reading to test, summay boxes of key points, a glossary and many illustrations. This book will be useful to any student who needs a patient and comprehensible introduction to what otherwise can be a daunting subject. (shrink)

We sometimes strive to achieve difficult goals when our evidence suggests that success is unlikely – not just because it will require strength of will, but because we are targets of prejudice and discrimination or because success will require unusual ability. Optimism about one’s prospects can be useful for persevering in these cases. That said, excessive optimism can be dangerous; when our evidence is unfavourable, we should be at most agnostic about whether we will succeed. This paper explores the nature (...) and rational significance of agnostic practical commitments. Most importantly, the rationality of striving against the odds can depend on investing in a plan for failure: a plan B. I aim to make headway on an account of what backup plans are, how they are related to primary plans, and whether the standard norms of plan rationality apply to our agnostic commitments. (shrink)

The hatchet and the seed -- A tree with deep roots -- The critical tools -- A field crystallizes -- Destruction of nature -- Construction of nature -- Degradation and marginalization -- Conservation and control -- Environmental conflict -- Environmental identity and social movement -- Where to now?

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes and (...) pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (shrink)

The Oxford Handbook of Epistemology contains 19 previously unpublished chapters by today's leading figures in the field. These chapters function not only as a survey of key areas, but as original scholarship on a range of vital topics. Written accessibly for advanced undergraduates, graduate students, and professional philosophers, the Handbook explains the main ideas and problems of contemporary epistemology while avoiding overly technical detail.

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)

This paper introduces constitutivism about practical reason, which is the view that we can justify certain normative claims by showing that agents become committed to these claims simply in virtue of acting. According to this view, action has a certain structural feature – a constitutive aim, principle, or standard – that both constitutes events as actions and generates a standard of assessment for action. We can use this standard of assessment to derive normative claims. In short, the authority of certain (...) normative claims arises from the bare fact that we are agents. This essay explains the constitutivst strategy, surveys the extant attempts to generate constitutivist theories, and considers the problems and prospects for the theory. (shrink)

Le philosophe, collègue et ami de Michel Foucault, fait le portrait de ce dernier et présente les grands thèmes de sa pensée philosophique et politique.

Vorrangig als der "strengste Methodenfanatiker und Logizist" der Marburger Schule des Neukantianismus bekannt, trat Natorp jedoch genau an diesem Punkt mit der selbständigen Form seines späten Philosophierens hervor: der Überschreitung der Methode in der Idee einer allgemeinen Logik. Unter allgemeiner Logik versteht er die streng einheitliche logische Grundlegung der Gegenstandssetzung, ja aller irgendwie logisch erfaßlichen Setzung. Damit war ein Zugang geschaffen zu der von Natorp angestrebten Erkenntnis des Geistigen in seiner Ureinheit, aus der erst die Besonderungen hervorgehen.

The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.