The question about fair income inequality has been an important open question in economics and in political philosophy for over two centuries with only qualitative answers such as the ones suggested by Rawls, Nozick, and Dworkin. We provided a quantitative answer recently, for an ideal free-market society, by developing a game-theoretic framework that proved that the ideal inequality is a lognormal distribution of income at equilibrium. In this paper, we develop another approach, using the Nash Bargaining Solution (NBS) framework, which also leads to the same conclusion. Even though the conclusion is the same, the new approach, however, reveals the true nature of NBS, which has been of considerable interest for several decades.

José E. Muñoz-Negro, Juan F. Mula-Ponce, Josefa M. López-Pérez, José Pablo Martínez-Barbero, Jorge A. Cervilla Abstract: The object of study of Psychiatry is hybrid, that is, it is both natural and social. It combines the methods of natural Sciences and those of social Sciences. Currently, Psychiatry is the branch of Medicine where epistemological and hermeneutical conflicts are more than […]

Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had damaging effects on the fertility of science. I also suggest that recent important empirical results, such as the detection of the Higgs particle and gravitational waves, and the failure to detect supersymmetry where many expected to find it, question the validity of certain philosophical assumptions common among theoretical physicists, inviting us to engage in a clearer philosophical reflection on scientific method.

In this paper I raise some objections to Field’s characterization of applied mathematics, showing, by means of three examples, that it is too restrictive. While doing so, I articulate a different and wider account of applicability. I conclude with an argument supporting its compatibility with an anti-realistic view on the existence of mathematical entities.

During the early 1830’s Bernard Bolzano, working in Prague, wrote a manuscript giving a foundational account of numbers and their properties. In the final section of his work he described what he called `infinite number expressions’ and `measurable numbers’. This work was evidently an attempt to provide an improved proof of the sufficiency of the criterion usually known as the `Cauchy criterion’ for the convergence of an infinite sequence. Bolzano had in fact published this criterion four years earlier than Cauchy who, in his work of 1821, made no attempt at a proof. Any such proof required the construction or definition of real numbers and this, in essence, was what Bolzano achieved in his work on measurable numbers. It therefore pre-dates the well-known constructions of Dedekind, Cantor and many others by several decades. Bolzano’s manuscript was partially published in 1962 and more fully published in 1976. We give an account of measurable numbers, the properties Bolzano proved about them, and the controversial reception they have prompted since their publication.

In his Foundations of a General Theory of Manifolds, Georg Cantor praised Bernard Bolzano as a clear defender of actual infinity who had the courage to work with infinite numbers. At the same time, he sharply criticized the way Bolzano dealt with them. Cantor’s concept was based on the existence of a one-to-one correspondence, while Bolzano insisted on Euclid’s Axiom of the whole being greater than a part. Cantor’s set theory has eventually prevailed, and became a formal basis of contemporary mathematics, while Bolzano’s approach is generally considered a step in the wrong direction. In the present paper, we demonstrate that a fragment of Bolzano’s theory of infinite quantities retaining the part-whole principle can be extended to a consistent mathematical structure. It can be interpreted in several possible ways. We obtain either a linearly ordered ring of finite and infinitely great quantities, or a a partially ordered ring containing infinitely small, finite and infinitely great quantities.

El análisis de la rebelión estudiantil debe comenzar por una cuestión básica: la crisis de la universidad. Un nuevo grupo social ha emergido de las fuentes del neocapitalismo, de todo lo que se considera como su “adquisición” esencial: el mayor standard de vida, los adelantos en la tecnología y en la clase media, y los requerimientos de la automatización. Hay seis millones de estudiantes universitarios en Estados Unidos, dos millones y medio en Europa Occidental y casi un millón en Japón. Y se ha comprobado que es imposible integrar a este grupo al sistema neocapitalista tal como éste funciona en Europa Occidental, Estados Unidos y Japón

Les lignes qui suivent ne prétendent pas à l’originalité. Leur objectif est purement pédagogique. Elles visent avant tout à expliciter quelques notions de logique modale, jouant un rôle crucial dans les travaux récents de JeanPierre Dupuy, mais n’étant probablement pas familières à tous ses lecteurs. Par la même occasion, elles voudraient aussi montrer en quel sens ces travaux relèvent de la philosophie, en prenant celle-ci dans une acception rigoureuse, que nous croyons désormais bien établie, mais qui n’est pas non plus de notoriété publique. Comme ce second point est un peu plus délicat, nous l’aborderons en deux temps. Nous partirons d’un survol rapide de l’histoire de la pensée, pour en tirer une définition plausible de la philosophie. Puis, après avoir présenté quelques éléments de logique modale, nous préciserons cette définition à l’aide de l’aporie de Diodore Cronos et du défi qu’elle lance à toute pensée rationnelle.

Como lo anunciamos con anterioridad, los abordajes filosóficos requieren de un compromiso ontológico y gnoseológico en virtud del cual podamos ejercitar un análisis lo suficientemente potente para dar cuenta de lo tratado. En nuestro caso, el compromiso filosófico será con el sistema filosófico llamado Materialismo Filosófico. A continuación disponemos a explicar cuáles son los motivos que nos orillaron a decantarnos por este y no otros. Gustavo Bueno, principal autor del sistema, cuenta con una serie de doctrinas (teorías) de gran potencia para poder abordar la infinidad de categorías que se atraviesan en el momento de realizar un trabajo con las características de nuestras intenciones. Estamos hablando específicamente de su teoría política y su filosofía de la ciencia referidas a sus emblemáticos trabajos Teoría del Cierre Categorial y Primer ensayo sobre las categorías de las “ciencias políticas”. El primero nos permitirá poder clasificar el material que surja de los acercamientos científicos y determinar su estatuto gnoseológico mientras el segundo, estando resuelta la problemática gnoseológica tocante a las ciencias políticas en el trabajo anterior, será la plataforma desde la cual escudriñaremos el material político. A este arsenal sumaremos el Ensayo sobre las categorías de la economía política y trabajos que rebasan ya el arco de los dientes de Bueno tales como el Diccionario filosófico de Pelayo García Sierra.

Generalizing results of J’onsson and Tarski, Maddux introduced the notion of a pair-dense relation algebra and proved that every pair-dense relation algebra is representable. The notion of a pair below the identity element is readily definable within the equational framework of relation algebras. The notion of a triple, a quadruple, or more generally, an element of size (or measure) n>2 is not definable within this framework, and therefore it seems at first glance that Maddux’s theorem cannot be generalized. It turns out, however, that a very far-reaching generalization of Maddux’s result is possible if one is willing to go outside of the equational framework of relation algebras, and work instead within the framework of the first-order theory. In the present paper, we define the notion of an atom below the identity element in a relation algebra having measure n for an arbitrary cardinal number n>0, and we define a relation algebra to be measurable if it’s identity element is the sum of atoms each of which has some (finite or infinite) measure. The main purpose of the present paper is to construct a large class of new examples of group relation algebras using systems of groups and corresponding systems of quotient isomorphisms (instead of the classic example of using a single group and forming its complex algebra), and to prove that each of these algebras is an example of a measurable set relation algebra.