This paper addresses the strength of Ramsey's theorem for pairs ($RT^2_2$) over a weak base theory from the perspective of 'proof mining'. Let $RT^{2-}_2$ denote Ramsey's theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König's Lemma and a substantial amount of $\Sigma^0_1$-induction (enough to prove the totality of all primitive recursive functions but not of all primitive recursive functionals). In the (...) resulting theory we show the extractability of primitive recursive programs and uniform bounds from proofs of $\forall\exists$-theorems. There are two components of this work. The first component is a general proof-theoretic result, due to the second author, that establishes conservation results for restricted principles of choice and comprehension over primitive recursive arithmetic PRA as well as a method for the extraction of primitive recursive bounds from proofs based on such principles. The second component is the main novelty of the paper: it is shown that a proof of Ramsey's theorem due to Erdős and Rado can be formalized using these restricted principles. So from the perspective of proof unwinding the computational content of concrete proofs based on $RT^2_2$ the computational complexity will, in most practical cases, not go beyond primitive recursive complexity. This even is the case when the theorem to be proved has function parameters f and the proof uses instances of $RT^2_2$ that are primitive recursive in f. (shrink)

In this paper we study with proof-theoretic methods the function(al) s provably recursive relative to Ramsey's theorem for pairs and the cohesive principle (COH). Our main result on COH is that the type 2 functional provably recursive from $RCA_0 + COH + \Pi _1^0 - CP$ are primitive recursive. This also provides a uniform method to extract bounds from proofs that use these principles. As a consequence we obtain a new proof of the fact that $WKL_0 + \Pi _1^0 - (...) CP + COH$ is $\Pi _1^0 $ -conservative over PRA. Recent work of the first author showed that $\Pi _1^0 + CP + COH$ is equivalent to a weak variant of the Bolzano-Weierstraß principle. This makes it possible to use our results to analyze not only combinatorial but also analytical proofs. For Ramsey's theorem for pairs and two colors $\left( {RT_2^2 } \right)$ we obtain the upper bounded that the type 2 functionals provable recursive relative to $RCA_0 + \sum\nolimits_2^0 {IA + RT_2^2 } $ are in T₁. This is the fragment of Gödel's system T containing only type 1 recursion—roughly speaking it consists of functions of Ackermann type. With this we also obtain a uniform method for the extraction of T₁-bounds from proofs that use RT2..... Moreover, this yields a new proof of the fact that $WKL_0 + \sum\nolimits_2^0 {IA} + RT_2^2 $ is $\Pi _1^0 $ -conservative over $RCA_0 + \sum\nolimits_2^0 { - IA} $ . The results are obtained in two steps: in the first step a term including Skolem functions for the above principles is extracted from a given proof. This is done using Gödel's functional interpretation. After this the term is normalized, such that only specific instances of the Skolem functions are used. In the second step this term is interpreted using $\Pi _1^0 $ -comprehension. The comprehension is then eliminated in favor of induction using either elimination of monotone Skolem functions (for COH) or Howard's ordinal analysis of bar recursion (for $RT_2^2 $. (shrink)

Review of "The Timeless Way of Building." Book by Christopher Alexander.

Die vorliegende Untersuchung entstand im Bereich Philosophische Fragen del' Wissenschaftsentwicklung des Zentralinstituts flir Philosophie del' AdW del' DDR. Sie ist Bestandteil del' Bemiihungen dieses Bereichs, die bisher erreichten Ergebnisse bei del' Erforschung philo­ sophischer Fragen del' Wissenschaftsentwicklung auf dialektisch-materialistischer Grundlage zusamrnenzu­ fassen, die vorliegende Konzeption zum Verhaltnis del' marxistisch-leninistischen Philosophie zu den anderen Wissenschaften zu prazisieren und davon ausgehend eigene Forschungsbeitrage zu leisten. Dem Autor ist es ein Bedlirfnis, Prof. Dr. sc. H. HORZ flir die stete F6rderung del' Arbeit und (...) zahlreiche hilf­ reiche Diskussionen an diesel' Stelle besonders zu danken. Er schuldet weiterhin den Professoren ALEXANDER, CIRIKOV, KASCHLUHN, KORCH, LEY, SCHMUTZER, SCHOPF, TREDER und VOGEL (t) Dank flir vielfaltige Anregungen. Die Arbeit ware ohne die hilfreiche Unterstlitzung zahlreicher Kooperationspartner des Bereichs in del' DDR und im Ausland nicht moglich gewesen. Besonders danke ich del' von Prof. Dr. M. E. OMELJANOWSKI gelei­ teten Abteilung Philosophische Fragen del' Naturwissen­ schaften des Instituts fiir Philosophie del' AdW del' UdSSR. (shrink)

Alexander von Humboldt’s depictions of mountain vegetation are among the most iconic nineteenth century illustrations in the biological sciences. Here we analyse the contemporary context and empirical data for all these depictions, namely the _Tableau physique des Andes_ (1803, 1807), the _Geographiae plantarum lineamenta_ (1815), the _Tableau physique des Îles Canaries_ (1817), and the _Esquisse de la Géographie des plantes dans les Andes de Quito_ (1824/1825). We show that the Tableau physique des Andes does not reflect Humboldt and Bonpland’s (...) field data and presents a flawed depiction of plant occurrences and vertical succession of vegetation belts, arising from Humboldt’s misreading of La Condamine’s description (1751). Humboldt's 1815 depiction, by contrast, shows a distribution of high-vegetation belts that is consistent with La Condamine’s description, while the 1824 depiction drops innovations made in 1815 and returns to simply showing numerous species’ names, thus not applying Humboldt’s own earlier zonation framework. Our analysis of contemporary reactions to Humboldt’s TPA includes Francis Hall’s posthumously published 1834 illustration of Andean plant zonation near Quito and Humboldt’s reaction to Hall’s critique. Throughout his work on plant geography, Humboldt disregarded some of his own observations, or confused them. At stake was his reputation as an innovator in the field of plant geography and a discoverer of the sequence of high-elevation vegetation belts on the world’s mountains. (shrink)

Name der Zeitschrift: Das Mittelalter Jahrgang: 18 Heft: 2 Seiten: 113-128.

This paper calls attention to some basic problems and inner contradictions in the German sociologist Ulrich Beck’s theory of the ‘(world) risk society’ or reflexive (second) modernity. A main thread in the critique is that of addressing the theoretical ambiguities that seem to characterize Beck’s at the same time ‘social constructivist’ and ‘realist’ notion of risk – ambiguities that seem to be repeated on the one hand in Beck’s view on the relation between knowledge and unawareness in reflexive modernity (...) and on the other hand in his view on the role of the mass media in the ‘(world) risk society’. Moreover, Beck’s notions of second modernity, reflexivity, rationality and critique are critically examined. With the alternative positions discussed in the paper – represented by Jeffrey C. Alexander, Niklas Luhmann and Mitchell Dean – some indications are given as to how one might fruitfully elaborate on the problem of risk. Thus, rather than a mainly technology-driven new type of social reality, the ‘(world) risk society’ could perhaps better be seen as indicating a changing cultural self-understanding of late modern society, a new ‘semantics of crisis', or the emergence of new forms of governmentality in the contemporary welfare state. In conclusion, some indications are given as to how an analysis of more specific ‘risk logics' or ‘rationalities' could be elaborated on, and a terminology that reflects this more differentiated approach to risk in late modern society is suggested. (shrink)

Morality and economic rationality: integrative economic ethics as the rational ethics of economic activity; Part II. Reflections on the Foundations of Economic ...

While it might seem prima facie plausible that divine foreknowledge is all that is needed for prophecy, this seems incorrect. To issue a prophecy, God hasto know not just how someone will act, but how someone would act were the prophecy issued. This makes some think that Middle Knowledge is required.I argue that Thomas Flint’s two Middle Knowledge based accounts of prophecy are unsatisfactory, but one of them can be repaired. However the resources needed for repair also yield a sketch (...) of a foreknowledge-only account of prophecy. (shrink)

In this new book, Ulrich Beck develops his now widely used concepts of second modernity, risk society and reflexive sociology into a radical new sociological ...

Over the past decade, there has been a growing interest among analytic philosophers in life's meaning, but this surge of work is nearly all by naturalists theorizing from non-theistic starting points. To answer the need for a theistic philosophical perspective, God and Meaning features leading thinkers in analytic philosophy of religion and theology exploring important issues in metaphysics, epistemology, ethics, and biblical theology that intersect with life's meaning.

Epistemic arguments play a significant role in the foundations of market liberalism as exemplified, in particular, by the work of F. A. Hayek. Competition in free markets is claimed to be the most effective device both to utilize the knowledge dispersed throughout society as well as create new knowledge through innovation competition. The fast pace with which new economic opportunities are discovered and costs are reduced is considered proof of the benefits of free markets to the common good. However, with (...) its inherently unpredictable consequences, innovation competition is actually ambiguous in this respect. This feature raises questions over the stringency of market liberal pleas that oppose quests for redistribution and environmental concerns in an absolute fashion. (shrink)

The present study investigated whether individual differences between psychologists in thinking styles are associated with accuracy in diagnostic classification. We asked novice and experienced clinicians to classify two clinical cases of clients with two co-occurring psychological disorders. No significant difference in diagnostic accuracy was found between the two groups, but when combining the data from novices and experienced psychologists accuracy was found to be negatively associated with certain decision making strategies and with a higher self-assessed ability and preference for a (...) rational thinking style. Our results underscore the idea that it might be fruitful to look for explanations of differences in the accuracy of diagnostic judgments in individual differences between psychologists (such as in thinking styles or decision making strategies used), rather than in experience level. (shrink)

By assembling authors with a wide range of different disciplinary backgrounds, from philosophy, literature, political science, sociology to medical anthropology ...

For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist (...) can use the book as a source of references. Results and methods of many directions in propositional modal logic, from completeness and duality to algorithmic problems, are collected and systematically presented in one volume. (shrink)

This volume has its roots in two recent developments within mainstream analytic epistemology: a growing recognition over the past two or three decades of the active and social nature of our epistemic lives; and, more recently still, the increasing appreciation of the various ways in which the epistemic practices of individuals and societies can, and often do, go wrong. The theoretical analysis of these breakdowns in epistemic practice, along with the various harms and wrongs that follow as a consequence, constitutes (...) an approach to epistemology that we refer to as non-ideal epistemology. In this introductory chapter we introduce and contextualise the ten essays that comprise this volume, situating them within four broad sub-fields: vice epistemology, epistemic injustice, inter-personal epistemic practices, and applied epistemology. We also provide a brief overview of several other important growth areas in non-ideal epistemology. (shrink)

At the beginning of the 21st century the conditio humana cannot be understood nationally or locally but only globally. This constitutes a revolution in the social sciences. The `sociological imagination' so far has basically been a nation state imagination. The main problem is how to redefine the sociological frame of reference in the horizon of a cosmopolitan imagination. For the purpose of empirical research I distinguish between three concepts: interconnectedness, liquid modernity and cosmopolitization from within. The latter is a kind (...) of class analysis after class analysis, which takes on board globalization internalized. For the purposes of social analysis, therefore, it is necessary to distinguish systematically between the national manifestation on the one hand and cosmopolitan reality of `global flows', currents of information, symbols, money, risks, people, social inequalities, on the other. This internal involuntary and often unseen cosmopolitanization from below of the national sphere of experience is occurring, however, with the power of economic globalization. So what does inner `cosmopolitanization' mean? The key concepts and questions of a way of life, such as nourishment, production, identity, fear, memory, pleasure, fate, power and politics, can no longer be located and understood nationally, but only globally whether in the shape of globally shared collective futures, capital flows, impending ecological or economic catastrophes, global foodstuff chains, transnational power games, or the `Esperanto' of pop music. In this article I look at transformation in the understanding of space-time, of identity, of the production paradigms, as well as at the resulting consequences for key sociological concepts like class and power and, within this frame, point to certain dilemmas of cosmopolitanism. (shrink)

How we engage in epistemic practice, including our methods of knowledge acquisition and transmission, the personal traits that help or hinder these activities, and the social institutions that facilitate or impede them, is of central importance to our lives as individuals and as participants in social and political activities. Traditionally, Anglophone epistemology has tended to neglect the various ways in which these practices go wrong, and the epistemic, moral, and political harms and wrongs that follow. In the past decade, however, (...) there has been a turn towards the non-ideal in epistemology. This volume gathers new works by emerging and world-leading scholars on a significant cross section of themes in non-ideal epistemology. Articles focus on topics including intellectual vices, epistemic injustices, interpersonal epistemic practices, and applied epistemology. In addition to exploring the various ways in which epistemic practices go wrong at the level of both individual agents and social structures, the papers gathered herein discuss how these problems are related, and how they may be addressed. -/- Contributors: Alison Bailey, Olivia Bailey, Simon Barker, Heather Battaly, Havi Carel, Quassim Cassam, Charlie Crerar, Miranda Fricker, Trystan S. Goetze, Heidi Grasswick, Keith Harris, Casey Rebecca Johnson, Ian James Kidd, and Alessandra Tanesini. (shrink)

Les photos de ce portfolio ont été prises par Philippe Carta, Julien Goetz, Francis Guermann, Bernard Muscat et Michel Noirez. Projecteur et enrouleur 35 mm mobiles installés dans le vestibule de l’Opéra-Théâtre pour la projection de Moïse et Aaron – 24 mars 2011. Avant la projection de Moïse et Aaron, Jean-Marie Straub, debout face à l’écran de l’Opéra-Théâtre, vérifie la qualité de l’image et du son. François Narboni et Régine Palucci présentent Moïse et Aaron. A...