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.

Based on Propostion 6 of his Principia, Newton’s geometrical derivation in Propositions 10 and 11 for the radial dependence of the two central forces that lead to elliptical orbits is notoriously difficult. An alternate and more transparent derivation is obtained by applying the affine transformation of a circle into an ellipse.

El objeto de este trabajo es analizar la estructura conceptual utilizada por Filón de Alejandría en la definición del término δικαιοσύνη (“justicia”) en Leyes particulares 4. 136-143. Examinaremos qué es la justicia según Filón y cuáles son los conceptos que son parte constitutiva del proceso racional que implica su definición. Indagaremos también cuáles son las influencias griegas y bíblicas que delimitan la idea filónica de la justicia en el ámbito legislativo. De esta manera, podremos demostrar que Filón entiende la justicia no solo como el fundamento de la normativa codificada en las disposiciones escritas en la legislación de Moisés, sino también como la virtud del conocimiento de las realidades divinas contenidas en las leyes del Pentateuco que tienen su origen en Dios.

Two theorems about the P versus NP problem be proved in this article (1) There exists a language L , that the statement L∈P is independent of ZFC. (2) There exists a language L∈NP , for any polynomial time deterministic Turing machine M , we cannot prove L is decidable on M .

A historical review of the problem of incompleteness in Mathematics since the 20th century is made. The Combinatorial Principle of Paris-Harrington is studied and the way in which it can be codified in the language of Arithmetic.

Este artículo expone la crítica de Ortega y Gasset al naturalismo y el fracaso de la razón naturalista, y muestra su nueva concepción de la razón vital, histórica y narrativa, como un paradigma alternativo, basándose en la dialéctica de las experiencias, la imaginación creativa del «animal fantástico» y en una nueva visión de la vida que proviene de Nietzsche, Dilthey y Goethe, que puede contribuir a afrontar el reto de los nuevos naturalismos en el contexto del pensamiento actual.

Dans l’avertissement de De la logique à la théologie, il demande à son lecteur de lui accorder quatre privilèges : « Le premier donne droit de raisonner. Lorsqu’un auteur avance une proposition, son critique considère donc qu’il avance en même temps l’ensemble des conséquences de cette proposition. …Le second donne droit de lire le texte étudié dans la langue des modernes. Il ordonne même d’être plus fidèle à l’esprit qu’à la lettre…Le troisième invite à considérer une philosophie comme un système et non comme un rhapsodie mal liée…Mon dernier privilège sera le droit d’être moi-même. L’histoire serait peine perdue si elle ne nous éclairait pas, et elle ne peut nous éclairer que par la distance que nous prenons par rapport à elle. »

First and foremost, it is necessary to define a terminological apparatus associated with the prospects of creating the Eurasian Union. It is impossible to miss the opportunity to expand the already existing terminological base by bringing distinctive innovations to political discourse which reflect deep structures of understanding. As Martin Heidegger said, language is the house of being. In formulating (and reproducing) a corresponding etymology, we participate in the process of not only creating new thoughts, but also new processes related to reorganizing the Eurasian region. In addition, it is necessary to overcome the positivist approach in which Latin and, consequently, Western-centric terminology imposes itself upon the subject. Moreover, it is necessary to work out a lexicon, mechanism, and culture of international relations which are appropriate to the third millennium not only for the region under consideration, but for other corners of the planet

The idea that subjectivity makes up the foundation or source of all objectivity applies to all transcendental idealists. Nevertheless, Husserl conceives of this relationship between subjectivity and objectivity in a radically different fashion than Kant. Husserl’s conception leads to a primacy of the noetic dimension of sense (Sinn) at the expense of the noematic dimension. In order to render this explicit, not only a closer look at Kant’s transcendental deduction is illuminating but also taking into account neo-Kantianism. In contrast to Husserl, Kant and the neo-Kantians grant primacy to the objective or noematic within the correlation between subject and object or noesis and noema.