The purpose of this paper is to provide a historical overview of some of the contemporary infinitesimalist alternatives to the Cantor-Dedekind theory of continua. Among the theories we will consider are those that emerge from nonstandard analysis, nilpotent infinitesimalist approaches to portions of differential geometry and the theory of surreal numbers. Since these theories have roots in the algebraic, geometric and analytic infinitesimalist theories of the late nineteenth and early twentieth centuries, we will also provide overviews of the latter theories and some of their relations to the contemporary ones.

This article is devoted to the development of the central ideas in the field of magnetism. The presentation is semi-technical in nature and it roughly follows the chronological order. The key contributions of Van Vleck, Dorfman, Pauli, Heisenberg, and Landau are presented. Then the advent of the field of itinerant electron magnetism starting with the investigations of Bloch and Wigner, and more successful formulation by Slater and Stoner is presented. The physical basis of the Slater-Stoner theory is discussed and its problems are summarized. Then, an overview of the debate between itinerant electron view of Stoner and localized electron view of Heisenberg is presented. Connected with this debate are the issues of exchange interactions.

The idea that there is a difference in principle between science and metaphysics, and not only a difference but an opposition, is about as old as science itself (and by ‘science’ we mean modem science as it has e:xisted for the last three or four hundred years). It became generally accepted by the men of science themselves in the seventeenth century, at least after the influence of the Cartesians had been broken. For Descartes could not, of course, accommodate such a delimitation as his whole philosophy was one great attempt to merge science and metaphysics into one. But he already had to reckol with contemporaries who thought differently.

The PLA officially took ownership of the first S-400 unit last week, according to Russian media reports. The Russian Ministry of Defense (MoD) and the Russian Federal Service for Military Technical Cooperation as well as the PLA have so far not publicly commented on either matter. Russia began delivering S-400 components, including launchers and mobile radar systems, to China in April. The last cargo shipment reportedly took place in early May. Russian personnel, specialized in operating the S-400 has been handing over the S-400 systems to the PLA over the past months, a process reportedly completed last week.

The Russian government’s and its military’s primary concern is to safeguard the Russian people’s welfare and security. They are not there to satisfy some people’s lust for blood. The Russian military is strong no doubt, but its function is the defence of Russian soil and that of the Russian nation. The S-300 may be one of the best anti-aircraft weapons around, but it’s not a nuclear weapon. By itself, it will not be enough to deter a determined adversary. A lot more will be needed to counter the retaliation that will surely come once such a weapon is used by the Syrians. Is the Syrian military and people, fatigued by years of fighting these proxy forces, in a position to handle an all out war with Israel and/or the US/NATO? And what would Russia’s response to such an eventuality be? Would they stand idly by and see an ally destroyed by the US and its minions? What happens if they DO get involved, if the Russians themselves start shooting down Israel and/or NATO planes? THINK

While the relation between visualization and scientific understanding has been a topic of long-standing discussion, recent developments in physics have pushed the boundaries of this debate to new and still unexplored realms. For it is claimed that, in certain theories of quantum gravity, spacetime ‘disappears': and this suggests that one may have sensible physical theories in which spacetime is completely absent. This makes the philosophical question whether such theories are intelligible, even more pressing. And if such theories are intelligible, the question then is how they manage to do so. In this paper, we adapt the contextual theory of scientific understanding, developed by one of us, to fit the novel challenges posed by physical theories without spacetime. We construe understanding as a matter of skill rather than just knowledge. The appeal is thus to understanding, rather than explanation, because we will be concerned with the tools that scientists have at their disposal for understanding these theories. Our central thesis is that such physical theories can provide scientific understanding, and that such understanding does not require spacetimes of any sort.

En el presente artículo pretendemos dar cuenta del valor e influencia incalculable que ejerció el filósofo británico A. N. Whitehead y su obra Process and Reality, en el pensamiento metafísico garcibaccquiano y que, hasta la fecha, ha sido comprensiblemente desatendida por los estudiosos de la obra garcibaccquiana. Trataremos de explicar las razones por las que, a nuestro parecer, la obra del filósofo británico supone una suerte de terremoto capaz de generar un cambio de paradigma filosófico y metafísico en el seno de la propuesta filosófica garcibaccquiana. Como trataremos de demostrar, la obra de Whitehead es capital no sólo par la comprensión de una fase concreta de obra garcibaccquiana. Nada más lejos de la realidad. La obra de Whitehead y su influencia en García Bacca determina el desarrollo y consolidación de un proyecto metafísico encaminado hacia la facticidad y la creación.

Florian Pausinger The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. The aim of these notes is to survey (some of) Henri’s contributions over the last four decades which considerably improved our understanding of one-dimensional van der […]

It is well known that several classical geometry problems (e.g., angle trisection) are unsolvable by compass and straightedge constructions. But what kind of object is proven to be non-existing by usual arguments? These arguments refer to an intuitive idea of a geometric construction as a special kind of an `algorithm’ using restricted means (straightedge and/or compass). However, the formalization is not obvious, and different descriptions existing in the literature are far from being complete and clear. We discuss the history of this notion and a possible definition in terms of a simple game

In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to F. W. Lawvere that illuminates and unifies the different perspectives on self-reference.