The small, the tiny, and the infinitesimal have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that written by Errett Bishop about Keisler’s book Elementary Calculus: an Infinitesimal Approach. In this skit we investigate both the argument itself, and some of its roots in Bishop George Berkeley’s criticism of Leibnizian and Newtonian Calculus. We also explore some of the consequences to students for whom the infinitesimal approach is congenial. The (...) casual mathematical reader may be satisfied to read the text of the five act play, whereas the others may wish to delve into the 130 footnotes, some of which contain elucidation of the mathematics or comments on the history. (shrink)

Qu'est-ce que la musique? Selon Jankélévitch, il y a dans la musique une double complication, génératrice de problèmes métaphysiques et de problèmes moraux. Car la musique est à la fois expressive et inexpressive, sérieuse et frivole, profonde et superficielle ; elle a un sens et n'en a pas. Il y a une ironique disproportion entre la puissance incantatoire de la musique et l'inévidence foncière du beau musical.

Introduction. The emerging paradigm of socio- cultural development of the Russian Federation’s local communities is conditioned by the trans- formation of production and economic practices based on the concept of a multi-layered economy and multifunctionality emerging under the pressure of globalization on the development of localities. The desire to preserve and maintain socio-cultural traditions, customs, and values is an axiological guideline for developing local communities. The growing social vulnerability of communities creates certain conditions for losing identity, ability for self-identification, and (...) leads to the destruction of socio-cultural identity. The purpose of the study. The article analyzes the problem of socio-cultural evolution when modern- izing production and economic activity generating factors causing the transformation of culture and sociality of local communities, thus determining the processes of integration and disintegration of socioculture. Methods. Sociocultural analysis provides an op- portunity to reveal the main directions of sociocul- tural development of local communities, to explain the essence of interaction, mutual influence and unification of local communities into an interactive socio-cultural space with compatible formations and components. Scientific novelty of the research. The author dis- plays the models of culture and sociality transfor- mation reflecting the processes of modification of the local communities’ lifestyle that determine the transition from the paradigm of sustainable tradi- tional socio-cultural development to the paradigm of innovative transformations. Results. The problem of sociocultural integration and disintegration is associated with globalization processes that generate contradictions of globality and locality. The processes of integration/disin- tegration of the local communities’ sociocultural development are conditioned by the culture and sociality evolution of the constructing model of socio-cultural behavior. The pressure of globaliza- tion plunges the socio-cultural space into a state of diffusion, instability. Historically established traditions, norms, values are transformed into intermediate forms that help to adapt to new living conditions, neutralize the negative consequences of modernization. Territorial sociocultural formations are being formed, within the framework of which attempts are being made to preserve the tradition- al socio-cultural environment. Conclusions. The dynamics of sociocultural pro- cesses determines the emergence of multidirec- tional poles of sociocultural life: from the desire to preserve the traditional socio-cultural environment, to the full acceptance of the meaningful qualities of liberal socio-culture, which destroys the sociocul- tural identity of local communities. (shrink)

This volume explores how Catholicism began and continues to open its doors to the wider world and to other confessions in embracing ecumenism, thanks to the vision and legacy of the Second Vatican Council. It explores such themes as the twentieth century context preceding the council; parallels between Vatican II and previous councils; its distinctively pastoral character; the legacy of the council in relation to issues such as church-world dynamics, as well as to ethics, social justice, economic activity. Several chapters (...) discuss the role of women in the church before, during, and since the council. Others discern inculturation in relation to Vatican II. The book also contains a wide and original range of ecumenical considerations of the council, including by and in relation to Free Church, Reformed, Orthodox, and Anglican perspectives. Finally, it considers the Council’s ongoing promise and remaining challenges with regard to ecumenical issues, including a groundbreaking essay on the future of ecumenical dialogue by Cardinal Walter Kasper. (shrink)

We propose that black holes may serve as a physical substratum for intelligent beings, based on(1) The descriptions of brain and psyche are complementary to each other, as internal and external observers of a black hole in the Susskind-t'Hooft's schema.(2) There is an aspect of the inner structure of a black hole that is isomorphic to the structure of the human subjective domain in the psychological model of reflexion.(3) Both black holes and the brain-psyche system have a facet that can (...) be represented using thermodynamic concepts.(4) Both lend themselves to a holographic description. (shrink)

I focus on the problem of whether a specific biologic basis exists for reinforcing the power of money. I argue in favor of its existence based on a new interpretation of data obtained in experiments with pigeons and rats in an experimental chamber. The experiments demonstrated that in the animals' behavior we can observe some features that had been considered pertinent to human beings only, such as making certain sources of utility “sacred.” (Published Online April 5 2006).

. We demonstrate that a comprehensive nonstandard set theory can be developed in the standard $\displaystyle{\in}$ -language. As an illustration, a nonstandard ${\sf Law of Large Numbers}$ is obtained.

In one of the first genetic screens aimed at identifying induced developmental mutants, Nadine Dobrovolskaïa-Zavadskaïa, working at the Pasteur Laboratory in the 1920s, isolated and characterized a mutation affecting Brachyury, a gene that regulates tail and axial development in the mouse. Dobrovolskaïa-Zavadskaïa's analysis of Brachyury and other mutations affecting tail development were among the earliest attempts to link gene action with a tissue-specific developmental process in a vertebrate. Her analyses of genes that interacted with Brachyury led to the discovery of (...) the t-haplotype chromosome of mouse. After 70 years, Brachyury and the multiple genes with which it interacts continue to occupy a prominent focus in developmental biology research. A goal of this review is to identify the contributions that Dobrovolskaïa-Zavadskaïa made to our current thinking about Brachyury and how she helped to shape the dawn of the field of developmental genetics. BioEssays 23:365–371, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

This article considers the contribution of Ernst Mally to the theory of objects, namely he introduced a distinction of two types of properties (determinations) — formal and extraformal, that allowed Meinongian theory of objects to provide a satisfactory response to the criticism of Bertrand Russell, related to the question of the existence of the golden mountain. According to Meinong, object's so-being (Sosein) is logically independent of its ontic status (Sein). In this case Russell asks, how the existent golden mountain can (...) be existent, golden and a mountain, because golden mountains do not exit (as well as round squares). So it was obvious that the independence of Sosein from Sein thesis should be revised. That's why Mally made a remark that the properties that make object's Sosein are extraformal. Later these ideas have formed the basis of the contemporary study of nonexistent objects, the basis of the theories of Terens Parsons, Richard Routley etc. In particular Parsons's distinction of nuclear and extranuclear properties is a revised version of Mally's distinction.In addition, the article analyzes Ernst Mally's critics of epistemological idealism and its connection with the famous psychologism dispute in logic and semantics in the late 19th and early 20th century. This dispute is more associated with the works of G. Frege and E. Husserl, which accused of psychologism many representatives of Brentano's School. Particularly Alexius Meinong was also called a psychologist. That's it's important to find out, which side was Mally on in this dispute. (shrink)

In the field of geographical limology, the new science of international borders, it is possible to distinguish several consecutive theoretical approaches that can be seen as either traditional or postmodern. At each consecutive stage new approaches have been applied together with, not in place of, the traditional, in order to continue to perfect the discipline (see, for instance, Minghi, 1963; Rumley and Minghi, 1991). Traditional approaches, such as historical mapping, the typological, the functional and the political, have been described in (...) previous theoretical works (e.g. Kolossov and O'Loughlin, 1998; Kolossov and Turovsky, 1998; Kolossov and Mironenko, 2001). Here we are concerned with the postmodern approaches, which have been emerging mostly during the 1990s and the present decade. (shrink)

This is the story of a textbook that students of developmental biology have used for 45 years. “An Introduction to Embryology” was released soon after a role for genes in the control of development became finally recognized but not yet well documented. Thus this book manifested the transition from embryology to developmental biology. The story of its author, Boris Balinsky, who against all odds survived to write this book, is remarkable on its own. He started his scientific career in the (...) USSR, but due to 20th century social and political upheavals, ended it in South Africa. This article will shed light on the life of Boris Balinsky, a scientist and writer and will explore the origins of his book. BioEssays 27:970–977, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

The author enters an already old dispute, that is, whether a countеrpart of the notion of philosophy could be encountered in the traditional India, upholds the view that the term ānvīkṣikī (lit. “investigation”) was nearest to it and traces its meaning along the texts on dharma, politics, poetics and philosophy properly. Two main avenues to the understanding of philosophy’s vocations in India have been paved in the Mānavadharmaśāstra, along with the commentaries thereon and by Kamandaki, the author of the Nītisāra (...) (as the knowledge of Ātman) and in the Arthaśāstra and the Nyāya texts composed by Vātsyāyana and Uddyotakara (as a metascience helping the other branches of knowledge bear their fruits). Therefore philosophy in India as well was regarded as the duality of ideological and methodological constituents, while the emphasis on analytic practice in the definitions of ānvīkṣikī (Wittgenstein’s conception of philosophy as a practice is also referred to in this context) paves a good promise for comparative philosophy. (shrink)

[Logical analysis and language as a code].

[The inscrutability of language and objectivity].

[On the objective and the still more objective].