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)

In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985 ). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989 ), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994 ) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this (...) paper we present the possible worlds semantics for partial meet multiple contractions. (shrink)

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.

The manuscript tradition of Seneca'sDialoguesconsists of one eleventhcentury manuscript, Ambrosianus C 90 inf., which is the main source for the text, and a ruck of later manuscripts of lesser and disputed worth. There are over a hundred of these, far more than has been supposed.

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)

This paper addresses the significance of the general class of diffeomorphisms in the theory of general relativity as opposed to the Poincaré group in a special relativistic theory. Using Anderson's concept of an absolute object for a theory, with suitable revisions, it is shown that the general group of local diffeomorphisms is associated with the theory of general relativity as its local dynamical symmetry group, while the Poincaré group is associated with a special relativistic theory as both its global dynamical (...) symmetry group and its geometrical symmetry group. It is argued that the two groups are of equal significance as symmetry groups of their associated theories. (shrink)

Integrating race and gender in a social constructionist framework, the authors examine the way that second-generation Asian American young women describe doing gender across ethnic and mainstream settings, as well as their assumptions about the nature of Asian and white femininities. This analysis of interviews with 100 daughters of Korean and Vietnamese immigrants finds that respondents narratively construct Asian and Asian American cultural worlds as quintessentially and uniformly patriarchal and fully resistant to change. In contradistinction, mainstream white America is constructed (...) as the prototype of gender equality. Hence, Asian American and white American women serve in these accounts as uniform categorical representations of the opposing forces of female oppression and egalitarianism. The authors consider how the relational construction of hegemonic and subordinated femininities, as revealed through controlling images that denigrate Asian forms of gender, contribute to internalized oppression and shape the doing of ethnicity. (shrink)

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

This study examined the role of key causal analysis strategies in forecasting and ethical decision-making. Undergraduate participants took on the role of the key actor in several ethical problems and were asked to identify and analyze the causes, forecast potential outcomes, and make a decision about each problem. Time pressure and analytic mindset were manipulated while participants worked through these problems. The results indicated that forecast quality was associated with decision ethicality, and the identification of the critical causes of the (...) problem was associated with both higher quality forecasts and higher ethicality of decisions. Neither time pressure nor analytic mindset impacted forecasts or ethicality of decisions. Theoretical and practical implications of these findings are discussed. (shrink)

In their paper, “Helpful Lessons and Cautionary Tales: How Should COVID-19 Drug Development and Access Inform Approaches to Non-Pandemic Diseases?” Holly Fernandez Lynch and colleagues have present...

Language provides rich social information about its speakers. For instance, adults and children make inferences about a speaker's social identity, geographic origins, and group membership based on her language and accent. Although infants prefer speakers of familiar languages, little is known about the developmental origins of humans’ sensitivity to language as marker of social identity. We investigated whether 9-month-olds use the language a person speaks as an indicator of that person's likely social relationships. Infants were familiarized with videos of two (...) people who spoke the same or different languages, and then viewed test videos of those two individuals affiliating or disengaging. Results suggest that infants expected two people who spoke the same language to be more likely to affiliate than two people who spoke different languages. Thus, infants view language as a meaningful social marker and use language to make inferences about third-party social relationships. (shrink)

'A mere metaphor', 'only symbolic', 'just a myth' - these tell tale phrases reveal how figurative language has been cheapened and devalued in our modern and postmodern culture. In God and the Creative Imagination, Paul Avis argues the contrary: we see that actually, metaphor, symbol and myth, are the key to a real knowledge of God and the sacred. Avis examines what he calls an alternative tradition, stemming from the Romantic poets Blake, Wordsworth and Keats and drawing on the thought (...) of Cleridge and Newman, and experience in both modern philosophy and science. God and the Creative Imagination intriguingly draws on a number of non-theological disciplines, from literature to philosophy of science, to show us that God is appropriately likened to an artist or poet and that the greatest truths are expressed in an imaginative form. Anyone wishing to further their understanding of God, belief and the imagination will find this an inspiring work. (shrink)

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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.

1. 4. 9. Fugite delicias, fugite enervantem felicitatem, qua animi permadescunt et, nisi aliquid intervenit quod humanae sortis admoneat, †velut perpetua ebrietate sopitif†. Although it is possible to produce a tolerable sentence by deleting et after permadescunt, it is generally agreed that a verb is missing in the last clause. Koch suggested sopiti, Gertz sopiti (...) manent Hermes, vivunt Schultess, languent Viansino. One would hesitate to add to the growing clutter of suggestions, did not one of Seneca's favourite verbs seem to meet all requirements, namely marcent. Cf. ben. 4. 6. 3 ‘quies in qua putrescis ac marces’; 4. 13. 1 ‘vobis voluptas est… securitatem sopitis simillimam adpetere e t … animi marcentis oblectare torporem’; dial. 1. 3. 10 ‘hunc voluptatibus marcidumet felicitate nimia laborantem’; 9. 2. 6; 10. 2. 2; epist. 74. 1; 89. 18 et al. (shrink)

Purpose: This paper intends to connect ideas from the radical constructivist approach to cognition and learning to ideas from the constraint-theoretic approach to social policy formulation. It then extends these ideas to a dialogic approach to social transformation and design. Method: After demonstrating a correspondence between von Glasersfeld's fit/match distinction and my constraint-oriented/goal-oriented distinction with respect to policy formulation, the paper evaluates the basic assumptions of radical constructivism and builds from them a framework for thinking and talking about a desirable (...) society and ways to participate in its realization. Findings: The ideas of von Glasersfeld's radical constructivism contribute significantly to the development of a conceptual base for applied research on social activism by raising new questions and stimulating new thinking. Practical implications: Social activism in everyday affairs can be a way of living in the "world." Conclusion: The work and thought of Ernst von Glasersfeld opens a path toward a rich array of concepts and ideas with the potential to inform efforts in a wide variety of human endeavors. (shrink)

The extant marketing literature provides little guidance for theory development or practice with regard to questions of ethical conformity and the resulting market response. To begin to bridge this research gap, we advance a theoretical framework of ethical conformity in marketing, appealing to marketing ethics, management strategy, and sociological foundations. We set the stage for our theoretical arguments by considering the role of normative expectations related to marketing practices and behaviors held by societal constituents. Against this backdrop, we propose drivers (...) of conformity in marketing, including practices consistent with both overconformity and underconformity. The framework allows us to advance testable research propositions by which questions of ethical conformity may be explored. We conclude by suggesting additional future research needed to develop the domain, specifically in the form of empirical inquiries uncovering firm strategic decisions with ethical implications. (shrink)