The need for modification of the Huygens-Fresnel superposition principle arises even in the description of the free fields of massive particles and, more extensively, in nonlinear field theories. A wide range of formulations and superposition schemes for secondary waves are captured by Kirchhoff’s integral theorem. We discuss various versions of this theorem as well as its connection with the superposition principle and the method of Green’s functions. A superposition scheme inherent in linear field theories, which is not based on Kirchhoff’s integral theorem but instead relies on the completeness condition, is also discussed.

The subjects mathematics and mysticism come from my main scientific interests: logic and meditation phenomena. We will discuss two types of keys for these: the personal, through inner experience, and the transpersonal, described as an objective natural process. The two types of keys exist for both subjects.

Whitehead suele ser considerado como un filósofo oscuro y extrafío por su terminología, categorías, planteamientos.. . Pero su problemática es, en el fondo, similar a la de los grandes metafísicos. El tema de la creatividad es básico en su filosofía. Creatividad es el principio último que crea e impulsa el mundo. Dios mismo es creatura de la creatividad. Pero ella no es subsistente en sí. Radica en las entidades que crea. Sólo así es concebible un mundo en proceso de autocreación. Audaz posición y difícil de conjugar metafísicamente. Trato en este trabajo de estudiarla naturaleza y función de la creatividad y de juzgar su coherencia dentro de este sistema.

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 Lesnie ´ wski 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. Afterwards, Whitehead added to what was first a theory of the part-whole relation some definitions of topological notions such as junction. This would allow a first analysis of the concept of boundary. These topological reflections were then only reduced to mereological ones and it is only in Proces and Reality that Whitehead developed a directly topological theory in which the mereological concepts can be defined. Our purpose in this paper is to study these three mereo-topological theories and to set them out in a formalized way, in order to finally question about their possible axiomatization.

This is a short essay on the roles of Max Dehn and Axel Thue in the formulation of the word problem for (semi-)groups, and the story of the proofs showing that the word problem is undecidable.

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we distinguish between the graph theoretic (semantic) and the algebraic (syntactic) meaning of graph polynomials. We discuss how to represent and compare graph polynomials by their distinctive power. We introduce the class of graph polynomials definable using Second Order Logic which comprises virtually all examples of graph polynomials with a fixed finite set of indeterminates. Finally we show that the location of zeros and stability of graph polynomials is not a semantic property. The paper emphasizes a model theoretic view and gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the graph theoretic literature.

Progress in science has advanced the development of human society across history, with dramatic revolutions shaped by information theory, genetic cloning, and artificial intelligence, among the many scientific achievements produced in the 20th century. However, the way that science advances itself is much less well-understood. In this work, we study the evolution of scientific development over the past century by presenting an anatomy of 89 million digitalized papers published between 1900 and 2015. We find that science has benefited from the shift from individual work to collaborative effort, with over 90% of the world-leading innovations generated by collaborations in this century, nearly four times higher than they were in the 1900s. We discover that rather than the frequent myopic- and self-referencing that was common in the early 20 th century, modern scientists instead tend to look for literature further back and farther around.

El estudio de la obra de Aristóteles es imprescindible para acercarnos al modo en que Heidegger responde a la pregunta de qué es el tiempo1. El objetivo de la presente comunicación es, en primer lugar, analizar la peculiar radicalización del concepto de tiempo aristotélico efectuada por el joven Heidegger; en segundo lugar, mostrar la estrecha relación entre la comprensión vulgar del tiempo ofrecida por Aristóteles y el tiempo originario, centrándonos en el papel que tiene el momento temporal del futuro en la constitución de nuestro propio ser.

Deleuze’s philosophy constructs a unique and highly expressive poetics. In fact, it is the result of an intense work in writing, which may not be separated from his philosophy of conceptual creation. Current paper conceptualizes what would be a poetics of immanence in Deleuze´s terms, as a contrast to mimetic and representational poetics. The poetics of immanence proposes a mutual presupposition between concepts and affections, or between thought and its expression in words, instead of a transcendent relationship between the two terms. The essay investigates some features of this poetics to demonstrate its pertinence for certain modern and contemporary poetics. Samuel Beckett, one of the most important references to Deleuze, will be highlighted in the paper.

Countless differences between Hegel and Husserl notwithstanding, there is a common element in both of their accounts of the genesis of otherness. According to both, only if one delves into the interiority of self-consciousness, can one account for the rudimentary appearance of the Other. Following the Hegelian and Husserlian variants of such a strategy, this paper argues that: (1) at the primitive levels of self-consciousness, subjectivity is intersubjective through and through; (2) an irreducible distance separates the Other from the self, due to which plurality cannot be surpassed by totality. In contrast to the view which sees these claims as though they were irreconcilable with each other, this paper shows how each of them calls for its apparent opposite.