Much of the mathematics with which Felix Klein and Sophus Lie are now associated (Klein’s Erlangen Program and Lie’s theory of transformation groups) is rooted in ideas they developed in their early work: the consideration of geometric objects or properties preserved by systems of transformations. As early as 1870, Lie studied particular examples of what he later called contact transformations, which preserve tangency and which came to play a crucial role in his systematic study of transformation groups and differential equations. (...) This note examines Klein’s efforts in the 1870s to interpret contact transformations in terms of connexes and traces that interpretation (which included a false assumption) over the decades that follow. The analysis passes from Klein’s letters to Lie through Lindemann’s edition of Clebsch’s lectures on geometry in 1876, Lie’s criticism of it in his treatise on transformation groups in 1893, and the careful development of that interpretation by Dohmen, a student of Engel, in his 1905 dissertation. The now-obscure notion of connexes and its relation to Lie’s line elements and surface elements are discussed here in some detail. (shrink)

RÉSUMÉDans ses écrits de Jena, Fichte tente de résoudre l’apparent conflit entre la nécessité de faire reposer la philosophie sur des principes scientifiques et celle de respecter sa nature de vocation autonome. Ce faisant, il a prétendu accomplir d’autres tâches, sur les plans métaphilosophique, pédagogique et polémique : justifier les questions qui l’occupaient, communiquer sa pensée correctement et répondre aux incompréhensions de ses adversaires. Cet article montre qu’à travers ces considérations, Fichte s’essaie aussi au problème plus vaste qui consiste à (...) préciser la relation entre la «lettre» de la philosophie comme doctrine et son «esprit» intersubjectif. (shrink)

This work examines the claim to scienific status made by supporters and practitioners of neoclassical economics. The approach taken is that of the history and philosophy of science. Analysis points to the conclusion that theories of economic choice are necessarily normative, essentially because of the nature of human behavior.

Carole Pearce's argument against African philosophy is founded on a set of factual flaws and the fallacious assumption that African philosophy is equivalent to ethnophilosophy, which she defines as a form of intellectual apartheid founded on irrational belief systems. I argue that African philosophy is in no way qualitatively different from, say, French or Chinese philosophy, and that ethnophilosophy is merely one aspect of it But ethnophilosophy could play the important role of critically evaluating African ethnic belief systems and the (...) interpretation of such by Western anthropologists. In general, African philoso phy is nothing more than the philosophical research (of whatever order) carried out by African philosophers in the context of African research paradigms. (shrink)

L. D. Harris; IV*—Solving the “Naval Battle”, Proceedings of the Aristotelian Society, Volume 78, Issue 1, 1 June 1978, Pages 45–62, https://doi.org/10.1093/ari.

L. D. Harris; IV*—Solving the “Naval Battle”, Proceedings of the Aristotelian Society, Volume 78, Issue 1, 1 June 1978, Pages 45–62, https://doi.org/10.1093/ari.

Provability logics with many modal operators for progressions of theories obtained by iterating their consistency statements are introduced. The corresponding arithmetical completeness theorem is proved.

In lieu of an abstract, here is a brief excerpt of the content:230 Feminist Studies 47, no. 1. © 2021 by Feminist Studies, Inc. Nneka D. Dennie The State and Future of Black Women’s Studies: The Black Women’s Studies Association and the National Women’s Studies Association in Conversation On February 25, 2021, the Black Women’s Studies Association (BWSA) and National Women’s Studies Association (NWSA) partnered for one of NWSA’s Kitchen Table Talks—a new initiative spearheaded by NWSA President Kaye Wise Whitehead (...) to foster dialogue between NWSA and other organizations. The event, titled “Space Making: State/Future of Black Women’s Studies,” featured three panelists and was moderated by Whitehead. The featured speakers were Stephanie Andrea Allen (BWSA conference chair), Jacinta R. Saffold (BWSA co-founder and treasurer), and Erica L. Williams (member of the NWSA Governing Council). Allen is a Black lesbian writer and publisher whose scholarship examines how lesbian literature and film responds to and resists the heteropatriarchal systems that invisibilize Black lesbians; she is a postdoctoral fellow and visiting assistant professor of gender studies at Indiana University. Saffold is an assistant professor of English at the University of New Orleans who researches twentieth- and twenty-first-century African American literature, hip hop studies, and digital humanities. Williams is an associate professor of anthropology at Spelman College, whose work has examined sex tourism and Black feminist activism in Brazil. Together, Whitehead, Allen, Saffold, and Williams explored their hopes for Black Women’s Studies and illuminated the challenges and joys of advancing the field. News and Views 231 The collaboration between BWSA and NWSA is a testament to how far Black Women’s Studies has come over the past fifty years and a promise of where it may continue to go in the future. NWSA was founded in 1977 and has since served as a hub for researchers, educators, and practitioners who interrogate questions of women and gender in their work. For decades, NWSA has been central to the nationwide US institutionalization of women’s, gender, and sexuality studies. By contrast, BWSA is a young organization that is continuing to grow. In 2018, Saffold and I co-founded BWSA in order to provide a community for scholars working in the field of Black Women’s Studies. BWSA is the only professional association specifically designed to bring scholars from a variety of disciplines into conversation about research that centers Black women. We launched BWSA with the goal of ensuring that future generations of scholars can readily access networks and mentorship from researchers who encounter a common question: when your work is simultaneously “too Black” and “too woman” for your field, department, or institution, what do you do? Drawing inspiration from well-established organizations in which we frequently participated, such as NWSA, the Association for the Study of African American Life and History (ASALH), the Association of Black Women Historians (ABWH), and the African American Intellectual History Society (AAIHS), Saffold and I sought to build a space that cultivated a Black feminist ethic of care for both the research and the researchers. In that spirit, BWSA provides resources to help scholars do their best work, including a mentorship program, a virtual writing community, a calls-for-papers list for publications, and article as well as graduate student paper prizes. It was an honor to join an organization as trusted and respected as NWSA for a dialogue about our shared visions for Black Women’s Studies. Three key themes emerged from the panelists’ conversation with each other. They repeatedly returned to the importance of making financial commitments to Black Women’s Studies, creating conditions to support Black women’s intellectual labor, and practicing self-care. Speakers explored the interplay between the responsibilities that institutions, communities, and individuals have to Black Women’s Studies and Black feminist scholars. They observed that in order for departments and universities to foster interdisciplinary work on Black women, they need to move beyond paying lip service to the idea that diversity, equity, and inclusion matter; there needs to be permanent funding for work on race, 232 News and Views gender, class, and sexuality. Panelists also emphasized that Black women being in community with each other and supporting one another have always been central to... (shrink)

A general equation is derived describing the concentration of all possible complexes of a central molecule with a set of ligands bound to the central molecule. This deduction allows the reaction rate constants for the binding of a given molecule to the central molecule to depend on the species of molecules already bound and the location of the molecules already bound. The model thus allows for structural alteration of the central molecule by binding. Functions describing the concentration dependence of any (...) effect whatever depending on the distribution of complexes are deduced. Possible applications and methods of application are indicated.II est dérivé une équation qui décrit la concentration des toutes les complexes d'une molécule centrale avec une collection de ligands connectés à la molécule centrale. La déduction montre comme les coefficients de la rapidité de reaction entre la molécule centrale et les molécules de la collection dépend de l'espèce et de la location des molécules déjà connectées.La modèle dérivée de l'équation montre les changements structurelles par la connection. Les functions qui décrivent la dependence de chaque effet à la concentration, sont dérivés. Ces effects dépendent aussi à la distribution des complexes. Des applications et des méthodes sont indiqués.Eine allgemeine Vergleichung hat man bekommen welche die Konzentration aller möglichen Komplexen eines zentralen Moleküles mit einer Reihe von „Ligands” verbunden mit dem zentralen Molekül beschreibt. Diese Folgerung gestattet dass die Reaktiongeschwindigkeit Konstanten für die Bindung eines gegebenen Moleküles mit dem zentralen Molekül abhÄngt von den Arten schon gegebenen Molekülen und die Ortsbestimmung der schon gebundenen Molekülen. Das Model zeigt die strukturelle Änderungen des zentralen Moleküls durch Bindung. Funktionen, die die Konzentrationband jedes Effektes beschreiben dass abhÄngt von der Distribution der Komplexen, sind abgeleitet.Mögliche Anwendungen und Methoden von Anwendung sind dargelegt. (shrink)

Clocks and Rulers Play Tricks. 6. Work Changes Mass. 7. Summing Up. Index. Unabridged republication of the edition published by Basic Books, Inc.