Since Euclid defined a point as “that which has no part” it has been widely assumed that points are necessarily unextended. It has also been assumed that this is equivalent to saying that points or, more properly speaking, degenerate segments, have length zero. We challenge these assumptions by providing models of Euclidean geometry where the points are extended despite the fact that the degenerate segments have null lengths, and observe that whereas the extended natures of the points are not recognizable (...) in the given models, they can be recognized and characterized by structures that are suitable expansions of the models. (shrink)

In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field${\mathbf {No}}$of surreal numbers was brought to the fore by the first author and employed to provide necessary and sufficient conditions for an ordered field (ordered$K$-vector space) to be isomorphic to an initial subfield ($K$-subspace) of${\mathbf {No}}$, i.e. a subfield ($K$-subspace) of${\mathbf {No}}$that is an initial subtree of${\mathbf {No}}$. In this sequel, analogous results are established forordered exponential fields, making use of a slight generalization of Schmeling’s conception of (...) atransseries field. It is further shown that a wide range of ordered exponential fields are isomorphic to initial exponential subfields of$({\mathbf {No}}, \exp )$. These include all models of$T({\mathbb R}_W, e^x)$, where${\mathbb R}_W$is the reals expanded by aconvergent Weierstrass system W. Of these, those we calltrigonometric-exponential fieldsare given particular attention. It is shown that the exponential functions on the initial trigonometric-exponential subfields of${\mathbf {No}}$, which includes${\mathbf {No}}$itself, extend tocanonicalexponential functions on theirsurcomplexcounterparts. The image of the canonical map of the ordered exponential field${\mathbb T}^{LE}$oflogarithmic-exponentialtransseries into${\mathbf {No}}$is shown to be initial, as are the ordered exponential fields${\mathbb R}((\omega ))^{EL}$and${\mathbb R}\langle \langle \omega \rangle \rangle $. (shrink)

We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer (...) than infinite lengths or temporal durations? We argue that the answer is surprisingly yes, and we outline the properties of a number system that could be employed to characterize such magnitudes. (shrink)

In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including $-\omega, \,\omega/2, \,1/\omega, \sqrt{\omega}$ and $\omega-\pi$ to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG, it may be said to contain (...) “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system ℝ of real numbers bears to Archimedean ordered fields. In Part I of the present paper, we suggest that whereas $\mathbb{R}$should merely be regarded as constituting an arithmetic continuum, No may be regarded as a sort of absolute arithmetic continuum, and in Part II we draw attention to the unifying framework No provides not only for the reals and the ordinals but also for an array of non-Archimedean ordered number systems that have arisen in connection with the theories of non-Archimedean ordered algebraic and geometric systems, the theory of the rate of growth of real functions and nonstandard analysis. In addition to its inclusive structure as an ordered field, the system No of surreal numbers has a rich algebraico-tree-theoretic structure—a simplicity hierarchical structure—that emerges from the recursive clauses in terms of which it is defined. In the development of No outlined in the present paper, in which the surreals emerge vis-à-vis a generalization of the von Neumann ordinal construction, the simplicity hierarchical features of No are brought to the fore and play central roles in the aforementioned unification of systems of numbers great and small and in some of the more revealing characterizations of No as an absolute continuum. (shrink)

More than a century ago, John Dewey challenged the education community to look to civic involvement for the betterment of both community and campus. Today, the challenge remains. In his landmark book, editor Thomas Ehrlich has collected essays from national leaders who have focused on civic responsibility and higher education. Imparting both philosophy and working examples, Ehrlich provides the inspiration for innovative new programs in this essential area of learning.

The innovative and revolutionary scholarship of the eminent Austrian legal theorist and professor of Roman law, Eugen Ehrlich, is of a very high..

In a number of works, we have suggested that whereas the ordered field R of real numbers should merely be regarded as constituting an arithmetic continuum (modulo the Archimedean axiom), the ordered field No of surreal numbers may be regarded as a sort of absolute arithmetic continuum (modulo NBG). In the present chapter, as part of a more general exposition of the absolute arithmetic continuum, we will outline some of the properties of the system of surreal numbers that we believe (...) lend credence to this mathematico-philosophical thesis. We will also provide an overview of No’s rich structure as a simplicity-hierarchical (or s-hierarchical) ordered field that recursively emerges from the interplay between its structure as an ordered field and its structure as a lexicographically ordered full binary tree. Finally, we will draw attention to how properties of the system of surreal numbers considered as an s-hierarchical ordered algebraic structure can be appealed to in conjunction with classical relations between ordered algebraic and geometric systems to help resolve, for the surreal case, one of the purported difficulties that lies at the heart of attempts to bridge the gap between the domains of number and of geometrical magnitude. In particular, we will explain how it is possible that despite the fact that every surreal number, considered as a member of an s-hierarchical ordered field, differs from every other in characteristic individual properties, the absolute (Euclidean) geometrical continuum, which is modeled by the Cartesian space over the ordered field No of surreal numbers, appears as an amorphous pulp of points that display little individuality. (shrink)

The article bears an implicit appeal to judge political programs not by ideological labels but rather by the criteria I call ‘decency.’ I enjoin Martin Buber’s concept of dialogue to argue that a politics of decency seeks to promote human well-being that reaches beyond mere material flourishing but is attentive to the full sweep of the regnant existential, social and politics realities that diminish fundamental human dignity. Such a political ethic, as Buber would put it, transcends the barriers of regarding (...) others as “It” – as perceived and conceived by the divisive categories of religious and cultural affiliation, age, sexual orientation, socalled race, and as inveterate political opponents. (shrink)

El objetivo de este artículo es estudiar la interacción entre la ocupación musulmana de ciudades y su desarrollo urbano durante este período. ¿Cómo gestionaron los musulmanes su integración como nueva élite gobernante en el funcionamiento de las estructuras urbanas sin destruir las iglesias y las sinagogas? Los musulmanes utilizaron una política uniforme y predeterminada, cuya manifestación física sobrevive en forma de la proximidad entre iglesias y mezquitas, sobre todo en los centros urbanos. Además, esta proximidad transformó los mercados de los (...) foros y cardisnes en aswāq. (shrink)

This study compares two local television newsrooms during sweeps ratings periods. Sweeps pose an ethical dilemma for newsworkers and their organizations in that the explicit goal of sweeps is to maximize audiences and profits, which strongly increases the pressure to produce sensationalistic or sleazy news to attract viewers. But sweeps also present the opportunity to produce more ethical and substantive news by giving reporters more time both off and on the air to explore issues. This study examines whether newsworkers and (...) their organizations can resolve this dilemma in such a way as to serve both market interests and the public interest. (shrink)

Contents/Inhalt: Preface. Vorwort. Abbreviations/Siglen. I. JASPERS ON WORLD PHILOSOPHY AND WORLD HISTORY OF PHILOSOPHY/JASPERS ÜBER WELT-PHILOSOPHIE UND WELTGESCHICHTE DER PHILOSOPHIE. Nekrolog von Karl Jaspers selbst verfaßt. Obituary by Karl Jaspers himself. Karl JASPERS: Weltgeschichte der Philosophie - Zweites Buch: Geschichte der Gehalte: Einleitung. Karl JASPERS: World History of Philosophy - Second Volume: History of the Substantive Contents of Philosophic Thought. Introduction. II. INTRODUCTION/EINLEITUNG. Leonard H. EHRLICH: Opening Remarks. Introduction of Jeanne Hersch, Honorary President of the Conference. Jeanne HERSCH: Von (...) der Wirkung einer "philosophia negativa". III. LEGACY AND TASK. VERMÄCHTNIS UND AUFGABE. Leonard H. EHRLICH: Ausblick: Vernunft, Geist, Geschichte. Sawako HANYU: the Concept of the "Encompassing" in World Philosophy. Andreas RINOFNER: Periechontologie und Weltgeschichte der Philosophie. Systematische Bemerkungen zu einem aufschlußreichen Verhältnis. Richard WISSER: Projekt und Vision einer "Weltgeschichte der Philosophie" und "Weltphilosophie" als Folgen der "Grundverfassung" von Karl Jaspers. IV. DIMENSIONS OF COMMUNICATION/RÄUME DER KOMMUNIKATION. Andreas CESANA: Grenzen der Rationalität und Kommunikation. Brenio ONETTO-BÄCHLER: Existentielle Kommunikation bei Jaspers. Czes_awa PIECUCH: Es ist gleichgültig, wer die Wahrheit ausspricht. Über die Uneigennützigkeit der existentiellen Kommunikation. Oswald O. SCHRAG: Existence, Existenz, and Social Organization. Vladimir KATASONOV: The Gadfly, Stinging the Sluggish Horse: The Socratic Mission of Jaspers's Philosophy. V. COMMUNICATIVE WORLD HISTORY OF PHILOSOPHY/KOMMUNIKATIVE WELTGESCHICHTE DER PHILOSOPHIE. Albrecht KIEL: Die Weisen des Umgreifenden, die der Mensch ist: Wege zu Jaspers' Periechontologie. Maria Luisa BASSO: K. Jaspers - N. Berdiaeff: une confrontation entre deux philosophies de l'histoire. Convergence et divergence d'affirmations. Inigo BOCKEN: Kommunikation und Mutmaßung. Versuch eines Vergleichs zwischen Jaspers' Idee einer Philosophie der Kommunikation und Nikolaus von Kues' Kunst der Mutmaßungen. Boles_aw ANDRZEJEWSKI: Jaspers' Stellung zur Romantik im Lichte seiner Sprachphilosophie. Endre KISS: Karl Jaspers' Auslegung Nietzsches als eines Metaphysikers der Immanenz. Danièle MOYAL-SHARROCK: Genie et Folie selon Jaspers. Milan UZELAC: The World and Existence. Pablo LÓPEZ-LÓPEZ: Das Studium der Philosophie als Studium der Weltgeschichte der Philosophie. VI. COMMUNICATIVE WORLD PHILOSOPHY: EAST AND WEST/KOMMUNIKATIVE WELTPHILOSOPHIE: OST UND WEST. Wonjae LEE: Karl Jaspers und das Weltproblem des interreligiösen Dialogs. Silvia MARZANO: Comunicazione mondiale, kantismo e frattura dell'essere in Karl Jaspers. Una "terza via" fra Occidente e Oriente? Indu SARIN: Jaspers's Quest for Existential Communication. Mohammed MARUF: Jaspers and Iqbal on Self, Freedom and Communication. Subhadr PANYADEEP: Ich und Nicht-Ich bei Jaspers und im Buddhismus. Kazuteru FUKUI: Das Wesen des Buddhismus und Jaspers' Philosophie. Yukio MASUBUCHI: Jaspers und Nishida. Eine Theorie des "Topos" in der Lehre von der Kommunikation. Hans SANER: Weltphilosophie und Globalkultur im interkulturellen Vergleich mit den Konzepten "Weltmusik" und "Weltkunst". Gerhard RAUCHE: The Paradox of " Das Scheitern " as a World Formula. VII. COMMUNICATIVE WORLD PHILOSOPHY: FREEDOM AND TOLERANCE/KOMMUNIKATIVE WELTPHILOSOPHIE: FREIHEIT UND TOLERANZ. Anna MASÓ-MONCLÚS: Libertad y autoridad en Hannah Arendt y Karl Jaspers. Otmar KLEIN: "Weltverabsolutierung" und Verantwortungsverlust. Kurt SALAMUN: Grenzen der Toleranz. Zum Offenheits- und Toleranzparadigma in der Philosophie von Karl Jaspers. Giorgio PENZO: Politik als Ethos und das Problem der Freiheit bei Jaspers. Gerhard KNAUSS: Von der Weimarer Republik zur Weltpolitik. Wandlungen in Jaspers' Auffassung und Wertung der Politik von der Heidelberger Frühschrift "Die geistige Situation der Zeit" bis zu den Basler Spätschriften. Hermann-Josef SEIDENECK: Freiheit und Wiedervereinigung auf dem Prüfstand. Prognose und Ergebnis unter dem Blickwinkel von existentieller Kommunikation im Welthorizont. Appendix/Anhang. (shrink)

Biodiversity studies comprise the systematic examination of the full array of different kinds of organisms together with the technology by which the diversity can be maintained and used for the benefit of humanity. Current basic research at the species level focuses on the process of species formation, the standing levels of species numbers in various higher taxonomic categories, and the phenomena of hyperdiversity and extinction proneness. The major practical concern is the massive extinction rate now caused by human activity, which (...) threatens losses in the esthetic quality of the world, in economic opportunity, and in vital ecosystem services. (shrink)

"Plato's Gift to Christianity is a book for all who seek to understand the beauty and depth of the Christian faith: for family discussions of values, virtues, and happiness; for educators who teach about the founding of Western Civilization and its basis of ethics; and especially for the Christian clergy who are not familiar with the Greek Classical and Platonic influence upon the making of Christianity. Dr. Ehrlich has presented here a most comprehensive study on the Platonic teachings adopted (...) by the New Testament and Early Church." --. (shrink)

Die Entwicklung eines philosophischen Systems ist für den Autor Folge der persönlichen Auseinandersetzung mit der Frage nach dem Lebenssinn und der Stellung des Menschen in der Welt. Die Frage nach dem Sinn des menschlichen Lebens ist die zentrale Frage des Menschen. Die zentrale Stellung bekommt diese Frage dadurch, dass der Mensch selbst - mehr unbewusst als bewusst - sie in seinem Verhalten, seinen Absichten und in seiner Lebensweise, in dem, was er vom Leben im Allgemeinen und von seinem persönlichen Leben (...) im Besonderen fordert und in ihm erreichen will, beantwortet. Diese Frage wird durch die Möglichkeit eines konkret bestimmten individuellen Lebensvollzugs gestellt und durch den Vollzug dieses individuellen, persönlichen Lebens beantwortet. Das eigentliche Problem eines jeden einzelnen Menschen ist seine Orientierung in der Welt. Den «Kompass» für die Orientierung in der Welt kann er nur in der Erkenntnis der Wirklichkeit finden. (shrink)

A few years ago, I wrote on the need for expansion of the environmental areas of bioethics, and covered some of the topics touched on here. Sadly, although it is possible to find some notable exceptions, bioethics does not provide much of an ethical base for considering human-nature relationships. Here I’m not going to deal with these philosophical issues or others about the nature of ethical decision-making. The rapid worsening of the human predicament means that applied ethical issues with a (...) significant environmental connection (what I call “ecoethics”), must be dealt with without waiting for the more interesting theoretical issues to be resolved. I define ecoethics very broadly to deal with dilemmas over a vast range of scales, and believe they now should penetrate virtually all areas of human activities. Ecoethics must struggle with issues of intra-generational (and interperson/group/nation) equity and the dilemmas of discounting by distance (valuing distant persons/events/costs/benefits less than those closer to the observer in physical or mental distance). Ecoethics also deals with the difficult dilemma of inter-generational equity—of discounting the future. That is especially troublesome when actions today can have significant environmental consequences 50 or more generations from now. Here I would like to highlight the ubiquity of those questions and the importance of seeking answers. (shrink)

Background Much like academic-industry partnerships, industry financial support of patient advocacy organizations has become very common in recent years. While financial conflicts of interest between PAOs and industry have received more attention in recent years, robust efforts to mitigate these conflicts are still limited. Main body The authors outline the possible benefits and ethical concerns that can result from financial interactions between biomedical companies and PAOs. They argue that the use of novel strategies, such as the creation of a standing (...) ethics committee, could be helpful in managing FCOIs and ensuring the warranted trust of PAO’s constituents. Although ethics committees to address FCOIs are common in the academic context, its use by PAOs is still limited. The authors conclude by describing the process of development and implementation of such an ethics committee at the Crohn’s & Colitis Foundation. Conclusions While collaborations with industry can result in conflicts of interest, PAOs can develop strategies to address those conflicts. One such strategy is the creation of a standing independent ethics committee to guide PAOs on new and/or existing programs and protocols as they pertain to their industry relationships. (shrink)