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.

The study provides an insight into the structural features of the famous VIII century Buddhist treatise Tattvasaṅgrāha by Śāntarakṣita with regard to the text’s main purpose ( prayojana ) as it is treated in Kamalaśīla’s commentary Pañjikā. Any text along with its referential (representational) function of conveying message - meaning to the addressee, or its expressive function, reflecting the author's attitude to what is communicated, also performs the ‘appellative’ function, encouraging the recipient of the message to act. This function which (...) could also be called praxiological was always significant in Indian text culture, since from the times of Veda-s it was embedded in its very core. This function is of paramount importance in the case of Indian religious and philosophical texts, whose main aim is to convince and transform the consciousness of their percipients. Along with linear models of message transfer, Sanskrit texts could demonstrate non-linear semantic structures, transmitting the main idea of the text indirectly. It is exactly how one should perceive the message of Śāntarakṣita’s Tattvasaṅgrāha according to the suggested by Śāntarakṣita’s prominent student Kamalaśīla in his Pañjikā -commentary to the treatise. He proposes to consider Tattvasaṅgrāha not as a thematically heterogeneous encyclopaedic or doxographic work, whose main objective is to refute different non-Buddhist views (as it is often treated by scholars now), but as a text, which by its very design exposes one of the most important Buddhist principles - the law of the dependent origination ( pratītyasamutpāda ). The themes, discussed in a number of the chapters of Tattvasaṅgrāha, indeed, appear to have direct correlation with the characteristics of pratītyasamutpāda given to it in Śālistamba-sūtra - an early Mahāyāna text, which explains this universal law. Kamalaśīla suggests looking at Tattvasaṅgrāha as at one big unit-sentence - mahāvākya, with the exposition of pratītyasamutpāda as its unitary purpose-meaning ( abhidheya ). In this context, the treatise functions as a praxiological tool for the ‘installing’ into the consciousness of the text’s addressee the knowledge of ‘true principles’ (tattva-s) of pratītyasamutpāda. This interpretation of the main message of the text raises also a question of the adequate translation of the name of the treatise into other languages, because, according to Kamalaśīla, ‘ Tattvasaṅgrāha’ means the ‘Assembly of Principles-(tattva’-s)’ which specify precisely pratītyasamutpāda (pratītyasamutpāda-viśeṣaṇāni tattvāni). (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)

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)

This article discusses the connection between the ideas of Fyodor M. Dostoevsky and Vladimir S. Solovyov on the need for cultural and moral transformation of those who would claim to participate in...

My dear Aleksandr!I have finally found some quiet time for a slow and attentive read of your article “The Beginning of the Black Notebooks.”1 I very much liked the article, especially for your trul...

"This personification of wisdom with golden hair and a radiant aura echoes both the eternal feminine and the world soul. Rooted in Christian and Jewish mysticism, Eastern Orthodox iconography, Greek philosophy, and European romanticism, the Sophiology that suffuses Solovyov's philosophical and artistic works is both intellectually sophisticated and profoundly inspiring. Judith Deutsch Kornblatt brings together key texts from Solovyov's writings about Sophia: poetry, fiction, drama, and philosophy, all extensively annotated and some available in English for the first time (with assistance (...) from the translators Boris Jakim and Laury Magnus)."--Amazon website. (shrink)

This article defends the view that liars need not intend to deceive. I present common objections to this view in detail and then propose a case of a liar who can lie but who cannot deceive in any relevant sense. I then modify this case to get a situation in which this person lies intending to tell his hearer the truth and he does this by way of getting the hearer to recognize his intention to tell the truth by lying. (...) This case, and further cases that I develop from it, demonstrate that lying without the intention to deceive is possible. (shrink)