En la IV República un alto porcentaje del ingreso petrolero se destinó a financiar el capitalismo rentístico con préstamos a bajas tasas de interés y largos plazos; la asignación de petrodólares baratos para importar maquinarías, insumos y tecnología; así como compras gubernamentales en condiciones muy favorables para la producción nacional. En la V República el mayor porcentaje de los ingresos petroleros se utilizó para financiar el neo-rentismo socialista como un modelo de dominación sustentado en el uso del ingreso petrolero para financiar la inversión social y crear una red clientelar que le sirve de apoyo político. El capitalismo rentístico y el neo-rentismo socialista son expresiones distintas del mismo modelo de acumulación extractivista. Los actores económicos, políticos y sociales se acostumbran a obtener ganancias e ingresos que no son fruto de su propia inversión ni de su trabajo productivo.

La dialectique hégélienne et marxiste a fait l’objet des années 50 aux années 70 de diverses tentatives de transpositions1 dans le langage de la logique formelle. Diverses raisons ont contribué à une telle entreprise. Tout d’abord il s’agissait de concilier deux secteurs de la logique qui avaient à l’époque le vent en poupe. Le formalisme logique s’était développé de façon fulgurante depuis le XIXe siècle et avait été identifié au langage même de la science, tandis que le marxisme jouissait dans l’après-guerre d’un prestige considérable, lui assurant les faveurs d’un grand nombre d’intellectuels. N’était-il pas tentant d’essayer de réconcilier les deux en passant outre aux réticences clairement exprimées dès leurs époques respectives par Hegel et Marx? D’autre part, un recours à la formalisation de la dialectique, s’il réussissait, aurait permis de savoir exactement en quoi consistait effectivement la logique hégélienne, mettant un coup d’arrêt définitif aux spéculations oiseuses fondées sur une définition trop floue de sa nature.

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.”

Abstract Although Alfred North Whitehead probably did not know of the new quantum theory of Heisenberg, Schr¨odinger and Dirac, there seem to be deep similarities between his idea of the process and the ideas of quantum theory. Both Whitehead’s metaphysics and quantum theory are theories of observations: The realities which quantum theory deals with are certain observations by scientists who use the theory. Finally, Whitehead’s speculative cosmology is an expansion and generalization of the British empiricists’ theory of perception. By characterizing the basic ideas of scientific development and their consequences for philosophy, Whitehead wants to unify different views of the nature of things and to overcome the dualistic tradition of Cartesianism in modernity. Four leading ideas have determined the theoretical sciences in the 19th century: Atomicity, continuity, energy preservation and evolution. According to Whitehead, the challenge to science was not to introduce these concepts but to fuse them together and expand their application. Therefore, the cell theory and Pasteur’s work were more revolutionary for him than the achievement of Dalton’s nuclear theory, “for they introduced the notion of organism into the world of minute beings. […] The doctrine of evolution has to do with the emergence of novel organisms as the outcome of chance.” [34, p. 95]

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns, or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty’s recent “r>g ” (return rate > growth rate) paradigmatic analysis of very-long-term wealth trends.

This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.

Almost two decades ago, Wattenberg published a paper with the title ‘Nonstandard Analysis and Constructivism?’ in which he speculates on a possible connection between Nonstandard Analysis and constructive mathematics. We study Wattenberg’s work in light of recent research on the aforementioned connection. On one hand, with only slight modification, some of Wattenberg’s theorems in Nonstandard Analysis are seen to yield effective and constructive theorems (not involving Nonstandard Analysis). On the other hand, we establish the incorrectness of some of Wattenberg’s (explicit and implicit) claims regarding the constructive status of the axioms Transfer and Standard Part of Nonstandard Analysis.

Abstract: Some models of set theory are given which contain sets that have some of the important characteristics of being geometric, or spatial, yet do not have any points, in various ways. What’s geometrical is that there are functions to these spaces defined on the ambient spaces which act much like distance functions, and they carry normable Riesz spaces which act like the Riesz spaces of real-valued functions. The first example has a family of sets, each one of which cannot be empty, but not in a uniform manner, so that it is false that all of them are inhabited. In the second, we define one fixed set which does not have any points, while retaining all of these geometrical properties.

Las distintas dimensiones de la investigación fenomenológica y su vínculo intrínse­co con las cuestiones de método llevan a prestar atención a la esfera de lo inaparente, y especialmente a la cuestión del acceso al plano trascendental. El inicio de la discusión se remonta al planteo sobre el abandono —o no— del cartesianismo en Husserl, tema que devino un tercer problema asociado con las vías de acceso a la reducción. En este trabajo estudiaremos este decurso con objeto de sugerir que los desarrollos sobre generatividad y filosofía de lo inaparente invitan a redefinir el problema en términos más generales, explorando qué accesos a lo trascendental se despliegan en las diversas dimensiones de investigación fenomenológica. En este sentido, seguiremos la deriva de las dos primeras discusiones para bosquejar finalmente las direcciones que surgirían en una labor de desarrollo de la tercera.

This discussion will further advance our argument that Badiou’s arguments against Deleuze are ultimately based upon an ontology (namely, his theory of the pure multiple) that does not appreciate the historicity of human and nonhuman entities, and hence it fails to think singularities, whereas Deleuze, along with Whitehead and Latour, do base their political philosophies upon an ontology that affirms the historicity of all identities. With this discussion in place we turn, in the final section, to Deleuze’s concept of a social multiplicity. This concept is integrally related to Deleuze’s further concepts, ‘becoming-imperceptible’ and ‘becoming-revolutionary.’