One of the distinguishing features of mathematics is the exceptional level of consensus among mathematicians. However, an analysis of what mathematicians agree on, how they achieve this agreement, and the relevant historical conditions is lacking. This paper is a programmatic intervention providing a preliminary analysis and outlining a research program in this direction.First, I review the process of ‘negotiation’ that yields agreement about the validity of proofs. This process most often does generate consensus, however, it may give rise to another (...) kind of disagreement: whether the original and new proof are effectively the same, leading to potential disagreement about the validity of the original proof.Second, I historicize the phenomenon of consensus. I show that in earlier European mathematics and other mathematical cultures, consensus about the validity of arguments was substantially weaker or conceived differently than it is today. This means that contemporary consensus about the validity of mathematical proofs should be explained by historical changes in mathematical practice.Finally, I conjecture what brought about the contemporary form of mathematical consensus. Since a sharp rise in consensus occurs around the turn of the 20th century, it makes sense to explain this consensus by the concurrent formalization of mathematics. However, this explanation has a major flaw: it explains a really existing phenomenon (consensus) by something that hardly ever happens (writing proofs in formal languages). I will therefore explain the ways in which formalization does enter mathematical practice so as to account for contemporary forms of mathematical consensus. (shrink)

Naturalism - the thesis that all facts are natural facts, that is the facts that can be recognised and explained by a natural science - plays a central role in contemporary analytical philosophy. Yet many philosophers reject the claims of naturalism. The essays in this anthology explore the difficulties of naturalism by revealing the ambiguities surrounding it, as well as the tensions that exist among its critics.

In this paper, we compare the two Global Reporting Initiative reporting standards, G3.1, and the most current version G4.0. We do this through the lens of political corporate social responsibility theory, which describes the broadened understanding of corporate responsibility in a globalized world building on Habermas’ notion of deliberative democracy and ethical discourse. As the regulatory power of nation states is fading, regulatory gaps occur as side effects of transnational business. As a result, corporations are also understood to play a (...) “political role” to fill regulatory gaps and contribute to a global governance system by voluntarily engaging in self-regulation. Such corporate political action, however, is not always legitimate as it suffers from a democratic deficit. Consistent with scholars in the field of political CSR, this paper argues that only by means of communication and discourse can this drawback be avoided. That is why CSR reporting and guidelines for standardizing the disclosed CSR information is key for political CSR. By comparing the GRI standards from a political CSR perspective, one can see whether these often-used reporting guidelines fulfill the communicative requirements and whether they are adequate tools to face the challenges of the twenty-first century. We present results from a theory-derived and criteria-driven comparison of the two guidelines. Indication of the effectiveness of voluntary self-regulation is, for example, important considering the 2014 directive of the European Union to make CSR reporting mandatory. We offer a guideline-based view on current CSR theory as well as CSR reporting practice. We discuss implications for CSR theory, particularly the appropriateness of deliberation in the Habermasian sense, which is the basis of political CSR theory. We do so by introducing the notion of “uncommitted deliberation” with regard to the refined concept of materiality in GRI 4.0, which induces subjectivity and reduces data-driven comparability. Finally, we address the limitations of this research as well as research questions for future studies. (shrink)

This paper studies Paul Cohen’s philosophy of mathematics and mathematical practice as expressed in his writing on set-theoretic consistency proofs using his method of forcing. Since Cohen did not consider himself a philosopher and was somewhat reluctant about philosophy, the analysis uses semiotic and literary textual methodologies rather than mainstream philosophical ones. Specifically, I follow some ideas of Lévi-Strauss’s structural semiotics and some literary narratological methodologies. I show how Cohen’s reflections and rhetoric attempt to bridge what he experiences as an (...) uncomfortable tension between reality and the formal by means of his notion of intuition. (shrink)

ArgumentThis paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law is reviewed (...) in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain. (shrink)

When young children first begin to ask 'why?' they embark on a journey with no final destination. The need to make sense of the world as a whole is an ultimate curiosity that lies at the root of all human religions. It has, in many cultures, shaped and motivated a more down to earth scientific interest in the physical world, which could therefore be described as penultimate curiosity. These two manifestations of curiosity have a history of connection that goes back (...) deep into the human past. Tracing that history all the way from cave painting to quantum physics, this book sets out to explain the nature of the long entanglement between religion and science: the ultimate and the penultimate curiosity. (shrink)

This article interprets Józef Maria Hoëné Wronski’s (1776–1853) use of actual infinities in his mathematical work. The interpretation places this usage, which undermined Wronski’s acceptance as a mathematician, in his contemporary mathematical and philosophical context and in the context of his own sociopolitical-philosophical project.

The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.

This paper explores the semiotic status of algebraic variables. To do that we build on a structuralist and post-structuralist train of thought going from Mauss and L vi-Strauss to Baudrillard and Derrida. We import these authors' semiotic thinking from the register of indigenous concepts (such as mana), and apply it to the register of algebra via a concrete case study of generating functions. The purpose of this experiment is to provide a philosophical language that can explore the openness of mathematical (...) signs to reinterpretation, and bridge some barriers between philosophy of mathematics and critical approaches to knowledge. (shrink)

"Roy Wagner is a one-of-a-kind anthropologist whose books provide intense intellectual stimulation. His way of connecting the world of New Guinea to the world of anthropology is unique and, well, mind-blowing.... He writes books that you actually want to and will read more than once."--Steven Feld, author of Sound and Sentiment "Wagner asks, daringly, what it would be like to imagine one of the most significant of human activities, the activity of description or representation, as a self-scaling phenomenon.... One begins (...) to glimpse a genuine 'alternative anthropology.'"--Marilyn Strathern, author of The Gender of the Gift. (shrink)

This text considers several case studies of subaltern silence as micro political resistance. Around these examples I thread a theoretical model to explain how performing silences could resist oppression without assuming an underlying well-articulated subjectivity. The article deals with the force of silence, its conditions of possibility, and its position with respect to representation.

This introduction to the Common Knowledge symposium titled “Comparative Relativism” outlines a variety of intellectual contexts where placing the unlikely companion terms comparison and relativism in conjunction offers analytical purchase. If comparison, in the most general sense, involves the investigation of discrete contexts in order to elucidate their similarities and differences, then relativism, as a tendency, stance, or working method, usually involves the assumption that contexts exhibit, or may exhibit, radically different, incomparable, or incommensurable traits. Comparative studies are required to (...) treat their objects as alike, at least in some crucial respects; relativism indicates the limits of this practice. Jensen argues that this seeming paradox is productive, as he moves across contexts, from Lévi-Strauss's analysis of comparison as an anthropological method to Peter Galison's history of physics, and on to the anthropological, philosophical, and historical examples offered in symposium contributions by Barbara Herrnstein Smith, Eduardo Viveiros de Castro, Marilyn Strathern, and Isabelle Stengers. Comparative relativism is understood by some to imply that relativism comes in various kinds and that these have multiple uses, functions, and effects, varying widely in different personal, historical, and institutional contexts that can be compared and contrasted. Comparative relativism is taken by others to encourage a “comparison of comparisons,” in order to relativize what different peoples—say, Western academics and Amerindian shamans—compare things “for.” Jensen concludes that what is compared and relativized in this symposium are the methods of comparison and relativization themselves. He ventures that the contributors all hope that treating these terms in juxtaposition may allow for new configurations of inquiry. (shrink)

This note opens with brief evaluations of classical foundationalist endeavors – those of Frege, Russell, Brouwer and Hilbert. From there we proceed to some pluralist approaches to foundations, focusing on Putnam and Wittgenstein, making a note of what enables their pluralism. Then, I bring up approaches that find foundations potentially harmful, as expressed by Rav and Lakatos. I conclude with a brief discussion of a late medieval Indian case study in order to show what an “unfounded” mathematics could look like. (...) The general purpose is to re-evaluate the desiderata of foundational programs in mathematics. (shrink)

Richard Wagner (1813-1883) zählt zu den herausragendsten Komponisten der Welt überhaupt und gilt aufgrund seiner musikalischen Interpretationen als ein Erneuerer der europäischen Musiklandschaft. Er fühlte eine enge Verbindung zu Ludwig van Beethoven, da eben sein Werk für die Entscheidung verantwortlich war, sich der Musik zuzuwenden. Das vorliegende Werk ist eine Hommage an den deutschen Künstler und erschien zu seinem einhundersten Geburtsjahr 1870. Es handelt sich hierbei um die englische Übersetzung der deutschen Originalfassung.

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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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 discusses the concept of mathematical metaphor as a tool for analyzing the formation of mathematical knowledge. It reflects on the work of Lakoff and Núñez as a reference point against which to rearticulate a richer notion of mathematical metaphor that can account for actual mathematical evolution. To reach its goal this article analyzes historical case studies, draws on cognitive research, and applies lessons from the history of metaphors in philosophy as analyzed by Derrida and de Man.

With Richard Wagner, opera reached the apex of German Romanticism. Originally published in 1851, when Wagner was in political exile, Opera and Drama outlines a new, revolutionary type of musical stage work, which would finally materialize as The Ring of the Nibelung. Wagner's music drama, as he called it, aimed at a union of poetry, drama, music, and stagecraft. ø In a rare book-length study, the composer discusses the enhancement of dramas by operatic treatment and the subjects that make the (...) best dramas. The expected Wagnerian voltage is here: in his thinking about myths such as Oedipus, his theories about operatic goals and musical possibilities, his contempt for musical politics, his exaltation of feeling and fantasy, his reflections about genius, and his recasting of Schopenhauer. ø This edition includes the full text of volume 2 of William Ashton Ellis's 1893 translation commissioned by the London Wagner Society. (shrink)

This article studies Ibn al-Haytham’s treatment of the common notions from Euclid’s Elements (usually referred to today as the axioms). We argue that Ibn al-Haytham initiated a new approach with regard to these foundational statements, rejecting their qualification as innate, self-evident, or primary. We suggest that Ibn al-Haytham’s engagement with experimental science, especially optics, led him to revise the framing of Euclidean common notions in a way that would fit his experimental approach.

This paper considers two models of embodied mathematical cognition, and analyses the image of mathematics that they support.

SECRETS OF THE TEMPLE : HOW THE FEDERAL RESERVE RUNS THE COUNTRY by William Greider New York: Simon and Schuster, 1987. 798 pp., $24.95 Greider pursues the theme that the Federal Reserve System promotes the interests of Wall Street?banks and bondholders?over those of Main Street?the rest of society. The wealth of fascinating observations he makes are, unfortunately, organized by a 1950s?style Keynesianism and a faith in unlimited, majoritarian democracy. Neither of these beliefs are at all adequate for remedying the deficiencies (...) of political control of the money supply, which is the real problem Greider has uncovered. (shrink)

Mitochondrial function and biogenesis depend on the transport of a large variety of proteins, ions, and metabolites across the two surrounding membranes. While several specific transporters are present in the inner membrane, transport processes across the outer membrane are less understood. Recent studies reveal that the number of outer membrane channels and their transport mechanisms are more diverse than originally thought. Four protein‐conducting channels promote transport of distinct sets of precursor proteins across and into the outer membrane. The voltage‐dependent anion (...) channel (VDAC) forms the major channel for small hydrophilic molecules. In addition, three channels with yet unknown substrate specificity exist in the outer membrane. In this review, we outline the emerging functional diversity, selectivity, and regulation of mitochondrial outer membrane channels. The presence of several channel‐forming proteins challenges the traditional view that the outer membrane forms an unspecific size‐exclusion filter for the flux of small hydrophilic molecules. (shrink)

Nowadays psychology as a scientific discourse and a positive practice finds itself in an epistemologically critical situation. The analysis of the actual state of the academic discussion in cognitive-behavioural psychology, the most representative and widespread theoretical-practical trend in European nations, reveals that it frequently is misunderstood as a exclusively technical proceeding, an amount of deficiently articulated operatory interventions, alienated from its underlying anthropological assumptions. This paper proposes to exam how far the gap between theoretical reflection and effective practice, a cleavage (...) frequently confirmed, may be reduced discussing the concept of Menschenbildannahmen, an idea firmly rooted in anthropological thinking. Actualmente, la psicología en tanto discurso científico y práctica positiva se encuentra en un estado epistemológicamente crítico. El análisis del estado actual de la discusión académica en la psicología cognitivo-conductual, la corriente teórico-práctica más representativa y más difundida en los estados europeos, devela que ésta frecuentemente es malentendida como un mero procedimiento técnico, un conjunto precariamente articulado de intervenciones operatorias, desentendidas de sus supuestos antropológicos subyacentes. Se propone examinar en qué medida la brecha entre reflexión teórica y práctica efectiva, una escisión ampliamente constatada, puede ser aminorada sometiendo a discusión el concepto de las Menschenbildannahmen, de extensa raigambre en el pensamiento antropológico. (shrink)

Actualmente, la psicología en tanto discurso científico y práctica positiva se encuentra en un estado epistemológicamente crítico. El análisis del estado actual de la discusión académica en la psicología cognitivo-conductual, la corriente teórico-práctica más representativa y más difundida en los es..

Nicholas Vriend asked whether F.A. Hayek was an “ace,” and answered affirmatively. By “ace,” Vriend meant someone who worked with agent-based modeling. To be sure, Hayek could not have worked with agent-based models because that platform did not exist when Hayek was developing his ideas about the distribution and use of knowledge in society. All the same, Vriend explained convincingly that Hayek could have made good use of the agent-based platform had it been available in the 1930s. To similar effect, (...) we argue in this paper that James Buchanan could have made good use of agent-based modeling to carry forward his ideas about the value of taking an emergent approach to the explanation of economic processes. (shrink)

Anzeige für das Litterarische Centralblatt, von E. Rohde.--Anzeige in der Norddeutschen Allgemeinen Zeitung vom 26. Mai 1872, von E. Rohde.--Zukunftsphilologie! Von U. von Wilamowitz-Möllendorff.--An Friedrich Nietzsche, von R. Wagner.--Afterphilologie, von E. Rohde.--Zukunftsphilologie! Von U. von Wilamowitz-Möllendorff.

A few years ago, a manuscript by Jost Bürgi (1552–1632) was brought to scholarly attention, which included an ingenious sine calculation method. The purpose of this paper is to discuss two aspects of this manuscript. First, we wish to improve the current understanding of Bürgi’s method of sine calculation, especially with respect to the calculation of sines at a resolution of 1 min. Second, we wish to suggest a possible transfer of knowledge between India’s Kerala School of mathematical astronomy and (...) Bürgi. The evidence for the latter seems to be stronger than the evidence for other available case studies, but still revolves mainly around analogies, and can therefore not be considered as conclusive proof of transmission. We also append a translation of the relevant chapter of Bürgi’s treatise. (shrink)

THE NIETZSCHE-WAGNER CORRESPONDENCE CHAPTER I. FIRST MEETING. MY brother writes in "Ecce Homo": "From the moment a piano edition of 'Tristan and Isolde* appeared (my compliments, ...

Contributors to this volume present methodological foundations for deductive modeling in policy analysis, applications to particular areas of public policy, and applications to the institutional framework within which particular policies are chosen.

It is nearly universally presumed that redistribution can be carried out effectively only at the national or even global level, because local redistribution will be negated through personal mobility: recipients will move to high-paying jurisdictions while taxpayers will move away from those jurisdictions. To avoid this situation requires redistribution to be concentrated at national and not at local levels. In contrast to this standard line of argument, we explore how redistribution might be carried out more effectively at local levels than (...) at the national level. To explain this reversal from standard analytical implications, we integrate three concepts that are not present in the standard analysis. These concepts are the Samaritan’s dilemma, co-production, and polycentricity. It is interaction among these three concepts that reverses the implications of the standard analysis of redistribution. (shrink)

"In the same period Wagner was deeply inspired by the works of Shakespeare, an influence that runs throughout this volume. The title essay, "Actors and Singers," is one of Wagner's most deliberate and philosophical writings. He wrote, "Art ceases, strictly speaking, to be Art from the moment it presents itself as Art to our reflecting consciousness. " He described how the unconsciousness of art, and thus art's power, connected natural genius to cultivate traditions.

Accountability in Education discusses the debate surrounding the accountability of teachers and questions the responsibility that parents, other groups and even children themselves have for their experience at school. In this book, Robert Wagner examines the assumptions underlying criticisms of major institutions for their lack of attention to the ethical and practical ramifications of their policies. Wagner questions the validity of this assumption by analyzing accountability relationships in schools, discussing the responsibility students have for the quality of their own experiences--as (...) well as the potential accountability of parents and other groups--and relating the issue of accountability in education to questions of moral and legal obligation in areas such as business, government and law. His book provides a cogent philosophical analysis of accountability and is invaluable to an understanding of a majour issue in the contemporary discussion of education. (shrink)

These six articles place conflicts in Asia within the context of peace psychology, catalogues the diversity of conflicts in Asia, describes the inspiring success Philippine citizens have had in effecting drastic change in political leadership through nonviolent protest, and examines stereotypes in Sino-Japanese relations. Research on two extremist groups in Pakistan-one endorsing and one not endorsing violent confrontation is then examined. The concluding article contributes to the argument that Asia can provide novel examples of conflict that broaden our perspective.

Contemporary fiscal theorizing largely assimilates the activities of government to that of some choosing agent. This paper explores an alternative approach where government is assimilated to an emergent process of complex interaction, as a form of complex adaptive system. Within this alternative vision, governments are treated not as objects of intervention into a market economy but as arenas of organized participation within it. While recent developments in computational modeling are starting to provide tools for probing such a vision, the roots (...) of that vision can be traced back to the spontaneous order theorists of the 18th century. After sketching some contours of this alternative vision, the remainder of the paper explores some possible implications of this change in vision for mapping the relationship among taxation, prosperity, and justice. (shrink)