This work may be defined as a modern philosophical approach to theoretical physics. Since ancient times science and philosophy evolved in parallel, thus renewing from time to time the epochal paradigms of human thought. We could not understand how the scientists of the past could have achieved so many goals, if we neglect the philosophical ideas that inspired their minds. Today, despite the spectacular successes of the Standard Models of Elementary Particles (SMEP) and Modern Cosmology (SMMC), theoretical physics seems to be run into a mess of contradictions that preclude the access to higher views. We are still unable to explain why it is so difficult to include gravitation into the SMEP, although General Relativity (GR) works so well in the SMMC, why it is so difficult to get rid of all the divergences of the SMEP, and «why there is something rather than nothing».

This short essay traces the conceptual history of micro- and macroscopicity in the context of physical science. By focusing on three distinct episodes spanning five centuries, we show the scientific and philosophical meanings of this antonym pair, despite never being far from «the small» and «the large,» have been evolving as the frontier of science advances. We analyze the intellectual and material impetus for these movements, and conclude that this conceptual history reflects the changing interaction between the natural world and humankind.

In this paper we argue against the orthodox definition of quantum entanglement which has been explicitly grounded on several «common sense» (metaphysical) presuppositions and presents today serious formal and conceptual drawbacks. This interpretation which some researchers in the field call «minimal», has ended up creating a narrative according to which QM talks about «small particles» represented by pure states (in general, superpositions) which –each time someone attempts to observe what is going on– suddenly «collapse» to a single measurement outcome. After discussing the consequences of applying ‘particle metaphysics’ within the definition of entanglement we turn our attention to two recent approaches which might offer an interesting way out of this metaphysical conundrum.

Capítulo I. Estudio de la universalidad semántica. §1. §2. §3. §4.

Capítulo II. Construcción del concepto de estructura metafinita. §5. §6. §7. §8. Esencia de los procesos dialécticos. §9. El metafinito, término de un proceso dialéctico.

Capítulo III. Tipología de las estructuras metafinitas. §10. Fundamento de una clasificación de las estructuras metafinitas. §11. Primer tipo de estructuras metafinitas: el metafinito connotativo. §12. Segundo tipo de estructuras metafinitas: el metafinito porfiriano. § 13. Tercer tipo de estructuras metafinitas: el metafinito conjuntual.

Capítulo IV. Presencia de las categorías metafinitas en las más diversas formas del pensamiento. §13. §14. §15. §16. §17. §18. §19.

In this manuscript we discuss the notion of (statistical) independence embedded in its historical context. We focus in particular on its appearance and role in number theory, concomitantly exploring the intimate connection of independence and the famous Gaussian law of errors. As we shall see, this at times requires us to go adrift from the celebrated Kolmogorov axioms, which give the appearance of being ultimate ever since they have been introduced in the 1930s. While these insights are known to many a mathematician, we feel it is time for both a reminder and renewed awareness.

Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratric strong law for the center of mass of the elephant random walk. The asymptotic normality of the center of mass, properly normalized, is also provided. Finally, we prove a strong limit theorem for the center of mass in the superdiffusive regime. All our analysis relies on asymptotic results for multi-dimensional martingales.

Weyl’s proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called Weyl geometry) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field theory of electromagnetism and gravity. After getting disillusioned with this research program and after the rise of a convincing alternative for the gauge idea by translating it to the phase of wave functions and spinor fields in quantum mechanics, Weyl no longer considered the original scale gauge as physically relevant. About the middle of the last century the question of conformal and/or local scale gauge transformation were reconsidered by different authors in high energy physics). In this context Weyl geometry attracted new interest among different groups of physicists

La dialéctica como un capítulo de lógica matemática El método dialéctico de razonamiento ha sido introducido de múltiples maneras por muchos autores, frecuentemente sin hacer mención de la palabra «dialéctica». En alguna de estas formulaciones la dialéctica ha violado la ley de contradicción, por ejemplo : «El Tathagata no puede ser reconocido por las treinta y dos marcas, porque lo que se dice que son las treinta y dos marcas, el Tathagata dice que son no-marcas, y en consecuencia que son las treinta y dos marcas»

The second edition of Volume I of Whitehead and Russell’s Principia Mathematica leaves the first edition intact (except for minor changes), but adds some new sections. The new sections—an introduction and three appendices—are chiefly devoted to a restatement of the logical theories of the authors in the light of the reduction in the number of primitives in the Principia by Sheffer and Nicod and in the light of the views of Wittgenstein (expressed in his remarkable Tractatus Logico-Philosophicus) on propositions and propositional functions.

We introduce neutrosophic choice functions, the neutrosophic counterpart of the Axiom of Choice, prove some results, and discuss how it effects the foundations of mathematics in a neutrosophic setting.