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)

Immanuel Kant claims that transcendental idealism yields a form of realism at the empirical level. Polite silence might best describe the reception this assertion has garnered among even sympathetic interpreters. This book challenges that prejudice, offering a controversial presentation and rehabilitation of Kant's empirical realism that places his realist credentials at the centre of the account of representation he offers in the Critique of Pure Reason. This interpretation ranges over the major themes contained in the Analytic of Principles and relevant (...) portions of the Dialectic. Kant's analysis of the conditions necessary for determinate representation is shown to involve a realist understanding of the relation of mind and world. The realist character of Kant's account of empirical truth, and his commitment to the unity of nature, are defended against competing empiricist, pragmatist, and methodological readings. This title links Kant studies to contemporary philosophical debates, and will appeal to scholars and students of Kant, as well as epistemologists, metaphysicians, and philosophers of science interested in a powerful, experience-sensitive, form of realism. (shrink)

In their highly topical paper, Grahamet alargued that Trusted Research Environments (TREs) are not actually about trust because they reduce or remove ‘…the need for trust in the use and sharing of patient health data’. We believe this is fundamentally mistaken. TREs mitigate or remove some risks, but they do not address all public concerns. In this regard, TREs provide evidence for people to decide whether the bodies holding and using their data can be trusted. TREs may make it easier (...) for people to trust but there is still a need for that trust. (shrink)

This chapter contains sections titled: Introduction Section 1: Rational Judgment and Understanding Section 2: The Structure of Systematicity Section 3: Systematicity as Methodological Maxim? Section 4: Nature and Rational Structure.

General introduction -- The concept of science in the context of Western Civilization and the debate between science and faith -- Relationship between science and religion -- The unity of reason -- General conclusion.

The ‘universal cell reaction’ (UCR), a coordinated biphasic response to external (noxious and other) stimuli observed in all living cells, was described by Nasonov and his colleagues in the mid‐20th century. This work has received no attention from cell biologists in the West, but the UCR merits serious consideration. Although it is non‐specific, it is likely to be underpinned by precise mechanisms and, if these mechanisms were characterized and their relationship to the UCR elucidated, then our understanding of the integration (...) of cellular function could be improved. As a step towards identifying such mechanisms, I review some recent advances in understanding cell mechanics and the stress response and I suggest potentially testable hypotheses. There is a particular need for time‐course studies of cellular responses to different stimulus doses or intensities. I also suggest a correspondence with hormesis; re‐investigation of the UCR using modern biophysical and molecular‐biological techniques might throw light on this much‐discussed phenomenon. BioEssays 29:324–333, 2007. © 2007 Wiley Periodicals, Inc. (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)

Objective: While behavioral recommendations regarding physical activity commonly focus on reaching demanding goals by proposing ‘thresholds’, little attention has been paid to the question of how much of a behavioral change is needed to make people feel that they have changed. The present research investigated this relation between actual and felt behavior change. Design: Using data from two longitudinal community samples, Study 1 and 2 comprised 614 (63 % women) and 398 participants (61 % women) with a mean age of (...) 40.9 years (SD = 13.6) and 42.5 years (SD = 13.4), respectively. Using a stage-approach, participants were classified into four groups by asking them at the respective second measurement to indicate whether they had become more physically active since their last participation six months ago (“Changers”), had tried but did not succeed in becoming more physically active (“Attempters”), were already physically active on a regular basis (“Regular Actives”), or had not tried to become more physically active (“Non-Attempters”). Physical activity was measured using the International Physical Activity Questionnaire (IPAQ), and fitness level was assessed as physical working capacity (PWC) via bicycle ergometry. Mixed ANOVAs including Time and Perceived Change as within and between factors were conducted, followed up by simple effect analyses. Results: Participants stating to have become more active in the past six months (Changers) showed a significant increase in vigorous physical activity but not in moderate physical activity, with an average of 6.8 (Study 1) and 10.6 (Study 2) MET-h per week in vigorous activity. Corroborating these findings, objective fitness also significantly increased in the group of Changers. No systematic change in moderate or vigorous physical activity was observed for the three other ‘non-changer’ groups (regular actives, attempters, non-attempters). Conclusion: The intensity of physical activity is the crucial variable for people’s perception of change in physical activity. Moderate physical activity seems not to be perceived as an effective means for behavior change. It thus might fail to unfold sufficient motivational impact, despite its known positive effects on health. (shrink)

This paper is part of a symposium on Paul Moser, _Philosophy After Objectivity (Oxford University Press, 1993). The paper replies to contributions by Philip Quinn and Robert Audi.

In this paper, I show that Nietzsche is a Kantian, and what being Kantian means. He accepts the idea that our perception is configured by concepts which unify and inform the world around us, and which result from a biological evolution of the human species. His Kantianism is thus biological and mainly influenced by Friedrich Albert Lange’s reading of Kant. But this Nietzschean conceptualism must be inscribed in his thought of the will to power, where the perceptive fixation of the (...) world is the result of a degeneration caused by the biological, psychological and historical recovery of the will to power. Thus, I show that Nietzsche’s Kantianism is as biological as it is axiological. (shrink)

This paper questions the idea that Wittgenstein’s account of meaning as use requires an intrinsically normative understanding of this notion, and suggests instead that Wittgenstein is better understood as promoting a naturalistic view of meaning that undertakes an explanation based on non–semantic and non–normative facts of word–usage. It discusses the relevant positions of Kripke, Brandom and McDowell, all of whom are found to be united by the attempt to attribute to Wittgenstein a normative understanding of language that is not convincing. (...) While language does exhibit normative properties that cannot be naturalized, the understanding speakers have of their own words is “a prima facie plausible candidate for naturalistic analysis.”. (shrink)

Après avoir subi au début des années cinquante une sorte de procès public en raison de ses idées et traversé en conséquence une crise existentielle d'une rare intensité, Albert Camus, se retrouvant face à lui-même, a estimé que le problème majeur auquel l'humanité est désormais confrontée consiste dans ce besoin impérieux qu'ont les hommes de s'accuser mutuellement et de faire ainsi de leur existence un procès permanent, transformant tour à tour les mêmes personnes en prévenus, en procureurs, en avocats, en (...) témoins et en juges. Le problème, qui n'est autre que celui du jugement que les hommes portent les uns sur les autres, tient donc au fait que ceux-ci, alors même qu'ils ne croient plus au jugement de Dieu, continuent de croire qu'être juste c'est être juge. Pour expliquer que la dissociation de la justice et du jugement devrait révéler un horizon de sens nouveau à une humanité privée de boussole, Paul Audi s'applique d'abord dans cet essai à mesurer la profondeur de la crise qui a conduit l'auteur de La Chute à coucher sur le papier, quelques mois seulement avant sa mort, ce terrible ultimatum : "Je me fais la guerre et je me détruirai ou je renaîtrai, c'est tout". (shrink)

Les mots parlent souvent d’eux-mêmes et au-delà de nos intentions les plus naturelles. Parler de décliner son identité, c’est un peu comme prétendre qu’elle est susceptible de descriptions diversement colorées. On ne se dit effectivement pas sur le même ton à l’officier de police et au groupe de travail nouvellement intégré et où l’on est..

Wittgenstein was apparently looking for someone else. It was because he had not been successful that he had knocked at the Leavises’ door, to bide his time there before he looked again. On entering the house, he immediately peered through the window into the street. Yet after a moment he turned and said abruptly: “You’ve got a gramophone, I see—I don’t suppose you’ve anything worth playing.” And “Then,” so Leavis continues the description,with a marked change of tone, he exclaimed “Ah!”: (...) from the repository just at hand he pulled out the album of Schubert’s Great C Major Symphony and put the first record on the machine. A moment after the music began to sound he lifted the tone-arm, altered the speed, and lowered... (shrink)

Le concept de nature est reconstruit en considérant le processus d'objectivation à l'oeuvre dans l'expérience systémique du scientifique, qui prend la forme d'une expérience d'immanence redoublée. Ce redoublement est ensuite analysé à l'intérieur des systèmes que le savant analyse par l'étude du passage d'un système physique auto-organisé du type transition de phase à un système biologique. [Electre 2015].

Philosophy and Kafka is a collection of original essays interrogating the relationship of literature and philosophy. The essays either discuss specific philosophical commentaries on Kafka’s work, consider the possible relevance of certain philosophical outlooks for examining Kafka’s writings, or examine Kafka’s writings in terms of a specific philosophical theme, such as communication and subjectivity, language and meaning, knowledge and truth, the human/animal divide, justice, and freedom.

This dissertation explores the dialectic of thought and existence implicit in the human person's task of self-constitution as both a knower and a chooser. By way of comparative interpretation and critical analysis of the thought of Soren Kierkegaard and Bernard Lonergan, it argues for the complementarity of cognitional and existential praxis and adumbrates the possibility of an intellectualist existentialism. ;The Kierkegaardian polarization of thought and existence is situated within the context of a polemic against Hegelian holism and its totalizing aspirations. (...) Not only does Hegelian speculation attempt to reduce Christianity to a mere philosophical theory, it also absentmindedly yet oppressively neglects the ethical and religious exigencies of the concretely existing individual. ;In Lonergan's account of the dynamism of conscious intentionality , there is found support for Kierkegaard's critique of speculative aestheticism. There occurs not only a clear differentiation between knowledge and decisiveness, but also an affirmation of the primacy of conscience. In the full expansion of this dynamism, the cognitional is sublated by the existential; immanent exigencies of intelligence are preserved, yet knowing is to be contextualized within a wider horizon of concern for actualizing the good. Hence Lonergan's intellectualism offers the possibility of re-integrating thought and existence; it is an alternative both to anti-intellectual existentialism and to anti-existential rationalism. ;The task of self-appropriation, which is the core of Lonergan's philosophy, is complementary to the Kierkegaardian retrieval of existential subjectivity. Full self-appropriation involves both self-knowledge and self-choice. Yet self-appropriation, unlike Kierkegaardian and later existentialism, also reveals how objectivity is the fruit of authentic subjectivity. Lonergan avoids, as Kierkegaard's pseudonym Johannes Climacus does not, a denigration of objectivity and theoretical knowing. ;On grounds of performative self-contradiction, an objection is raised concerning existentialism's tendency to view objectivity in a merely pejorative manner. Theoretical knowing is more relevant to ethico-religious existence and to the actualization of personalist values than is commonly realized. A normative notion of objectivity is a necessary condition for the possibility of an ethics of historical authenticity. (shrink)

La tension problématique du concept de Gestalt dans la première pensée de l’art de Heidegger indique une autre provenance que celle, implicitement reconnue par Heidegger, de Nietzsche. La première interprétation du schématisme kantien programme le dépassement phénoménologique de sa dissimulation comme « art caché ». Cette phénoménologie de la temporalité originaire, formulée en termes de « schèmes horizontaux », révèle l’échec de ce dépassement, lié à celui de la Seinsfrage. La collusion entre le problème de la liberté et celui du (...) schématisme se résout, au-delà du phénoménologique, dans le motif de la figure, nous conduisant à voir dans le retrait du schématisme un « impensé » de Heidegger, auquel il aura répondu par une surdétermination « onto-typologique » de la finitude du figural.The problematical tenseness of the concept of Gestalt in Heidegger’s first philosophy of art indicates another source than Nietzsche’s influence, which was implicitly recognized by Heidegger. The first interpretation of Kant’s schematism programs a phenomenological overstepping of its dissimulation as « hidden art ». Such a phenomenology of original temporality, formulated in terms of « horizontal schemas », shows the stumble of this overstepping, related to that of « the question of being ». The connexion between the problematics of freedom and of schematism finds a resolution, beyond phenomenology, in the motif of the figure, leading us to see the withdrawal of schematism as an « unthought », to which Heidegger responded by « onto-typological » overdetermination of the finitude of figurality. (shrink)

The Book in Mamluk Egypt and Syria : Scribes, Libraries and Market. By Doris Behrens-Abouseif. Islamic History and Civilization: Studies and Texts, vol. 162. Leiden: Brill, 2019. Pp. xii + 178. $120, €100.

Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice bases of the space, thereby making model-theoretic tools available to study the defined properties. In this note we are primarily interested in properties of continua related to unicoherence; i.e., properties that speak to the existence of (...) “holes” in a continuum and in certain of its subcontinua. (shrink)