Despite the skepticism of many mathematicians and logicians as to the possibility of any test which will show conclusively the consistency or independence of the members of a postulate set, several methods have nevertheless been devised and employed, e.g., the empirical methods of Russell and Huntington, the internal method of Hilbert, and the reflective method of Royce. However, with the possible exception of Hilbert's method, these techniques require us to forsake the purely formal or abstract mode of analysis, and instead (...) to rely in some sense on “concrete representations” or “interpretations” or “modes of action” which are said to “satisfy” the postulates in question. In short, they are all interpretational methods—and here is the crux of the problem. “Is it possible,” queries Weiss, “that the only way we can determine whether a set is consistent is by seeing all the postulates actually exemplified in some object? If so, we must arbitrarily assume that the object is self-consistent, so that the proof of consistency must ultimately rest on a dogma. As independence rests on consistency there are therefore no satisfactory proofs as yet of either independence or consistency.” The question “is thus answered,” according to Young, “only by reference to a concrete representation of the abstract ideas involved, and it is such concrete representations that we wished especially to avoid. At the present time, however, no absolute test for consistency is known.” Moreover, “suppose,” says the late Dr. Eaton, “that the system has no interpretation: how can the consistency independence … of the postulates be shown? There should be some analytic way—purely in the realm of the abstract, without interpretation—of establishing these properties of a set of postulates. This is an important problem that awaits solution.”. (shrink)

I: Environmental aesthetics -- A phenomenological aesthetics of environment -- Aesthetic dimensions of environmental design -- Down the garden path -- The wilderness city : a study of metaphorical experience -- Aesthetics of the coastal environment -- The world from the water -- Is there life in virtual space? -- Is greasy lake a place? -- Embodied music -- II: Social aesthetics -- The idea of a cultural aesthetic -- The social evaluation of art -- Subsidization of art as social (...) policy -- Morality and the artist : toward an ethics of art -- Getting along beautifully : ideas for a social aesthetics. (shrink)

In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω 1.

By exploring principles found in psychology, math, physics, and shamanism, it becomes possible to link a cosmic perspective with ordinary life. This comprehensive work ventures into that challenging junction, journeying through the universe on paths of reason and magic, math and myth, bringing together humanity's traditional wisdom and shamanism with contemporary science.

The idea of aesthetic disinterestedness has been a central concept in aesthetics since the late eighteenth century. This exchange offers a contemporary reconsideration of disinterestedness from different sides of the question.

Abordaré la crítica de Axel Honneth a la primera Escuela de Frankfurt y su aparente omisión de Herbert Marcuse. Defenderé a Marcuse contra algunas de las críticas hechas por Honneth a la teoría crítica temprana de la Escuela de Frankfurt. Luego argumentaré que Marcuse siempre estuvo en busca de una subjetividad radical, incluso cuando advirtió contra los mecanismos unidimensionales en curso de producción de sujetos. Finalmente, mostraré que Honneth también construye su proyecto en torno a la búsqueda de una subjetividad (...) radical, pero aborda el problema a través de una teoría de la intersubjetividad que complementa el proyecto de Marcuse. (shrink)

From the earliest times art has been integral to human culture. Both fascinated and perplexed by the arts, people have tried, since the age of classical Greece, to understand how they work and what they mean. Philosophers wondered at first about the nature of art: what it is and how it relates to the cosmos. They puzzled over how art objects are created, and extolled human skills that seem at times godlike in their powers. But perhaps the central question for (...) such philosophers as Plato and Aristotle concerned our involvement with art: the response we have to beautiful things, the moral and salubrious powers of art, and perhaps most of all, the power of art to transform and transcend, leading us into a condition of enhanced perception that may be wondrous, dangerous, and at times overwhelming. The classical age displayed a richness of discussion that centered on art as an activity: an activity that is at once cosmic, social, and individual; an activity that brings understanding of a sort; an activity that may be salutary and even exalting, as in Aristotle's celebrated discussion of tragedy and its cathartic effects. Since the eighteenth century, however, this has changed. Questions about art have shifted to the idea of experience, paralleling the great change in the focus of philosophy from matters of ontology to those of epistemology. In place of starting from an examination of the nature of the universe and moving to the human position in the order of things, we have come to realize, since Descartes and Kant, that all inquiry has its inception in a human locus. Now, at the end of the twentieth century, we have finally recognized that the human factor in every kind of awareness and knowledge is structurally unavoidable. Art has become both a symptom of this change and a standard for grasping it. (shrink)

I explore how the notion of divine creation could be made understandable in a worldview dominated by empirical science. The crucial question concerns the empirical basis of belief in creation. Astronomical observations have changed our worldview in an exemplary manner. I show by an example from imaginative literature that human beings can perceive stars by means other than astronomical observation. This alternative mode may be described as “participatory perception,” in which a human experiences the world not by objectifying separation as (...) in science, but by personal involvement. I relate such perceptions to “embodied cognitive science,” a topical interdisciplinary field of research in philosophy, psychology, and neuroscience. Embodied cognitions initiate processes that can convey personal experiences of the stars. Such cognitions may involve religious apprehensions and give rise to sophisticated values. It is argued that the knowledge available through astrophysics and interpretation of the universe as divine creation represent two different ways of perceiving the same reality and should thus be seen as mutually complementary. (shrink)

The range of the aesthetic has expanded to cover not only a wider range of objects and situations of daily life but also to encompass the negative. This includes terrorism, whose aesthetic impact is central to its use as a political tactic. The complex of positive and negative aesthetic values in terrorism are explored, introducing the concept of the sublime as a negative category to illuminate the analysis and the distinctive aesthetic of terrorism.

Utopie und Tranzendenz.--Über Transzendenz und Symbol.--Der Einzelne und der Einsame.--Humanum und Exil.--Die phänomenologische Frage nach dem möglichen Menschen.