Traces the development of British philosopher Russell's (1872-1970) ideas on mathematics from the 1890s to the publication of his Principles of mathematics in 1903. Draws from Russell's unpublished manuscripts, correspondence, and published works to point out the influence of Hegel, Cantor, Whitehead, Peano, and others. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

Este ensayo es consecuencia de las reflexiones que desde hace años realizamos en el Instituto de Paz y Conflictos de la Universidad de Granada y que nos ha obligado a hacer una deconstrucción crítica de algunos aspectos del pensamiento pacifista. Bien es cierto que la supervivencia de la especie ha sido posible porque la respuesta a la conflictividad ha sido, mayoritariamente, la búsqueda de equilibrios dinámicos y de armonía. Pero, a pesar de todo, perviven muchas grietas, rupturas, dadas por la (...) propia contingencia y fragilidad humanas. Estamos ante unos entes humanos fragmentados, violentados, lo que hace más difícil la búsqueda de la armonía o la paz. Estas dificultades son razones de peso para trabajar en el camino de una «desfragmentación» ontológica que sea útil para liberar nuestras fuerzas emancipadoras y creativas. Construir la visión integrada y unitaria de la Ciencia de los Seres Humanos es una tarea conjunta que interesa sobremanera a la Investigación para la Paz.This essay is a consequence of the reflections we have been conducting for several years at the Instituto de Paz y Conflictos of the University of Granada. These reflections have obliged us to undertake a critical deconstruction of a few aspects of pacifist thought. Although the survival of the species has been possible because the response to conflicts has been, principally, the search for dynamic equilibrium and harmony; on the other hand there remain many fissures, ruptures brought about by the own human contingency and fragility. We find ourselves before a fragmented and distorted human being, which makes the search for harmony or peace even more difficult. These difficulties are convincing reasons for working towards an ontological “defragmentation” which is useful to liberate our emancipating and creative forces. To build the integrated and united view of Human Sciences is a collective task which is of great interest for Peace Research. (shrink)

I. WINCHESTER and K. BLACKWELL (eds.), Antinomies and paradoxes. Studies in Russell's early philosophy. Hamilton, Ontario: McMaster University Library Press, 1989. 248 pp. No price stated.

The main thesis of this paper is that some of the most important ideas and symbolic devices that made Russell's theory of descriptions possible were already present in writings by Frege and especially Peano that Russell knew well. The paper contains a detailed comparison between the relevant parts of Russell's theory--including manuscripts recently published--and some of Frege and Peano's insights, as well as a discussion of numerous possible objections that could be posed to the main claim. Even if Russell was (...) not actually influenced by those insights, the parallelism is close enough to be worth analyzing, especially in the case of Peano, whose writings are not very well known. (shrink)

In this article I try to show the philosophical continuity of Russell's ideas from his paradox of classes to Principia mathematica. With this purpose, I display the main results (descriptions, substitutions and types) as moments of the same development, whose principal goal was (as in his The principles) to look for a set of primitive ideas and propositions giving an account of all mathematics in logical terms, but now avoiding paradoxes. The sole way to reconstruct this central period in Russell (...) is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg. Thus the logical problems (doubts about propositions, matrices and functions) are parallel to the ontological (the searching for genuine logical subjects) and methodological ones (the status of eliminative reduction). Paradoxes were the cause that the kind of (constructive) definition already applied by Russell, as an inheritance of Moorean analysis, obtained a new trait: ontological elimination, which, beginning with a ?no classes theory? and the theory of descriptions, led to a new theory of judgment (already present in manuscripts from 1906), ?incomplete symbols, and logical constructions. (shrink)

Este artículo describe el reto que el protagonismo laical supone en los campos, inseparables y mutuamente referidos, de la misión, la comunión y la formación. La “teología del laicado”, en el orden teórico, y el apostolado seglar, en el práctico, se contemplan en el horizonte de una “eclesiología total”. La realidad de un “Pueblo de Dios en salida” solo será concretamente posible a través de la corresponsabilidad y la complementariedad de fieles y pastores.

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.

We expose the main ideas, concepts and results about Jakowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

If Unamuno had been able to choose how to be remembered, he would have wanted him to be a poet. This book wants to do justice to that happy possibility. But above all because Unamuno was a poet in the highest sense: he was while writing the same essay as a novel, or theater, letter or verse, and he was also a poet when he passionately lived all the facets of his intense existence. His intellectual work was poetic and his (...) personal relationships, as well as his political activity, also responded to that peculiar Unamunian aesthetic in which the vital horizon is inescapably confused with the tasks of thought." --Translated from back cover. (shrink)

Timelines is an inquiry into the nature of time, both as an apparent feature of the external physical world and as a fundamental feature of our experience of ourselves in the world. The principal argument of Timelines is that our coventional ideas about time are largely mistaken and that what we think of as independent physical time is actually our calibration of a certain relation between events. Namely, the relation between time-keeping events and the causal sequential differences of physical processes (...) which are real and independent of us. (shrink)

Viruses and related infectious genetic parasites are the most abundant biological agents on this planet. They invade all cellular organisms, are key agents in the generation of adaptive and innate immune systems, and drive nearly all regulatory processes within living cells.

This is a sketch of the basis and role of consciousness and the minimally required elements and constraints of any setting that may produce consciousness. It proposes that consciousness (as we know it) is a biologically-mediated product of evolved recursive and hierarchically nested representational systems that obey information theoretic principles and Bayesian (probabilistic) feedback and feedforward predictive modeling processes.