Hemeroteca del mes mayo, 2017

Introduction to Lambda Calculus

Por • 30 may, 2017 • Category: Leyes

Introduction Some history Leibniz had as ideal the following. (1) Create a ‘universal language’ in which all possible problems can be stated. (2) Find a decision method to solve all the problems stated in the universal language. If one restricts oneself to mathematical problems, point (1) of Leibniz’ ideal is fulfilled by taking some form of set theory formulated in the language of first order predicate logic. This was the situation after Frege and Russell (or Zermelo). Point (2) of Leibniz’ ideal became an important philosophical question. ‘Can one solve all problems formulated in the universal language?’ It seems not, but it is not clear how to prove that. This question became known as the Entscheidungsproblem. In 1936 the Entscheidungsproblem was solved in the negative independently by Alonzo Church and Alan Turing. In order to do so, they needed a formalisation of the intuitive notion of ‘decidable’, or what is equivalent ‘computable’. Church and Turing did this in two different ways by introducing two models of computation.

La machine mystique

Por • 29 may, 2017 • Category: Ciencia y tecnología

Peut-on opposer ou même séparer la foi avec les acquis de l’activité scientifique? Le théorème de Gödel a souvent été utilisé pour rendre compte de cette séparation. Le caractère abusif de cette utilisation a été bien analysé ([42], [11]). Nous nous proposons d’affiner cette analyse dans le cadre de l’hypothèse du Mécanisme Digital. Nous montrons que le Mécanisme Digital aboutit à une forme de concordisme spirituel ontologique, épistémologique et éthique. En effet, dans ce cadre, la théologie, dans le sens des (néo) platoniciens de la Grèce antique, devient ou redevient une science, et même la science la plus fondamentale en ce sens qu’elle devient capable de justifier, en principe et conceptuellement, toutes les autres. Une notion naturelle de théologie des machines, incluant la physique, est définissable, par les faits mêmes de l’incomplétude de Gödel, et de la non définissabilité de la vérité (Tarski) et de la connaissance (Kaplan-Montague [15]).

Constructive mathematics

Por • 29 may, 2017 • Category: Educacion

This text was published in the book “Penser les mathematiques: seminaire de philosophie et mathematiques de l’Ecole normale superieure (J. Dieudonne, M. Loi, R. Thom)” edited by F. Guenard and G. Lelievre, Paris, editions du Seuil, 1982, pp. 58-72. It is reproduced with the kind authorisation of Francois Apery.

La Filosofía y sus Lógicas

Por • 29 may, 2017 • Category: Educacion

El fin de siglo invita siempre a hacer un recuento de la centuria pasada en todas sus manifestaciones: políticas, militares, artísticas, científicas… La filosofía se hace también su pequeño hueco y cuenta el siglo –lo está haciendo ya en multitud de congresos y publicaciones– desde múltiples perspectivas:

Brouwer and Euclid

Por • 26 may, 2017 • Category: Ambiente

We explore the relationship between Brouwer’s intuitionistic mathematics and Euclidean geometry. Brouwer wrote a paper in 1949 called “The contradictority of elementary geometry”. In that paper, he showed that a certain classical consequence of the parallel postulate implies Markov’s principle, which he found intuitionistically unacceptable. But Euclid’s geometry, having served as a beacon of clear and correct reasoning for two millenia, is not so easily discarded. Brouwer started from a “theorem” that is not in Euclid, and requires Markov’s principle for its proof. That means that Brouwer’s paper did not address the question whether Euclid’s “Elements” really requires Markov’s principle. In this paper we show that there is a coherent theory of “non-Markovian Euclidean geometry.”

Uncertainty in Economic Growth and Inequality

Por • 25 may, 2017 • Category: sociologia

A step to consilience, starting with a deconstruction of the causality of uncertainty that is embedded in the fundamentals of growth and inequality, following a construction of aggregation laws that disclose the invariance principle across heterogeneous individuals, ending with a reconstruction of metric models that yields deeper structural connections via U.S. GDP and income data.

Mission nearly accomplished: Russia lives in a circle of simmering conflicts

Por • 24 may, 2017 • Category: Internacionales

Until recently, many experts have shared a different point of view on the state of affairs on the Korean Peninsula. They admitted a likelihood for a small or even a big war to break out in the region due to North Korea’s provocative activities or America’s attempts to stop them. Yet, they preferred to turn a blind eye on the fact that the crisis could carry a direct threat to Russia. Yet, the problem of North Korea and its nuclear missile weapons is not a problem for the USA, South Korea or China – this problem touches upon Russia in the first place.

Shaping the Future: Moscow and Beijing’s Multipolar World Order

Por • 24 may, 2017 • Category: Política

The main assumption Bobo Lo starts with to define relations between Moscow and Beijing is that the two countries base their collaboration on convenience and a convergence of interests rather than on an alliance. He goes on to say that the major frictions in the relationship concern the fate that Putin and Xi hold for Europe, in particular for the European Union, in addition to differences of opinions surrounding the Chinese role in the Pacific. In the first case, Lo states that Russia wants to end the European project while China hopes for a strong and prosperous Europe. With regard to the situation in the Pacific, according to this report, Moscow wants a balance of power between powers without hegemonic domination being transferred from Washington to Beijing.

Bajo el signo de la volatilidad

Por • 24 may, 2017 • Category: Economía

Con una fuerte deuda a cuestas, la fuentes de acceso a divisas por el suelo y la espiral de los intereses creciendo sin cesar, nuestros países debieron recurrir al Fondo Monetario Internacional. Éste conformaba la alcabala obligatoria para acceder al refinanciamiento bancario internacional, imponiendo las condiciones para ello. Tales condiciones implicaron, entre otras cosas, el desmantelamiento de las barreras arancelarias. Sin protección, las industrias regionales fueron arrasadas por la competencia extranjera. Fue así que la mayor parte de la región debió volver a concentrarse, como en tiempos coloniales, en los recursos naturales.

Whitehead’s mereotopology and the project of formal ontology

Por • 19 may, 2017 • Category: Leyes

Mereology is the theory of wholes and parts. The first formal mereology was developed by Husserl in his third Logical Investigation at the beginning of the twentieth century. In 1916 Stanisław Lesniewski gave the first axiomatization of a classical extensional formal mereology. That same year, Alfred North Whitehead also gave a sketch of a mereology in “La théorie relationniste de l’espace”. It was developed in the perspective of a theory of space in which the concept of point is no longer considered as primitive, but is built in terms of the relations between objects. This project was then taken up and amplified in the wider perspective of the method of extensive abstraction presented in An Enquiry Concerning the Principles of Natural Knowledge and The Concept of Nature.