En este artículo analizamos conceptos fundamentales que sirven para entender mejor Das Kontinuum. Asimismo, defendemos la interpretación de Feferman —sobre todo, en lo referente al tratamiento de los conjuntos aritméticos, y al alcance del sistema que Weyl introdujo en el libro— como la más apropiada para entender la idea original, frente a la interpretación que Arnon Avron propuso recientemente.

En el presente artículo, introducimos el conjunto plitogénico (como generalización de conjuntos nítidos, borrosos, intuicionistas, borrosos y neutrosóficos), que es un conjunto cuyos elementos se caracterizan por los valores de muchos atrib utos. Un valor de atributo v tiene un grado correspondiente (difuso, intuicionista difuso o neutrosófico) de pertenencia d (x, v) del elemento x, al conjunto P, con respecto a algunos criterios dados. Para obtener una mejor precisión para los operadores d e agregación plitogénica en el conjunto plitogénico, (...) y para una inclusión más exacta (orden parcial), se define un grado de contradicción (disimilitud difusa, intuicionista difusa o neutrosófica) entre cada atributo del valor y el valor del atributo domina nte (el más importante). La intersección y la unión plitogénicas son combinaciones lineales de los operadores difusos t norm y tconorm, mientras que el complemento plitogénico, la inclusión (desigualdad), la igualdad está influenciados por los grados de co ntradicción (disimilitud) de los valores de los atributos. Por tal motivo el objetivo del presente trabajo es ofrecer algunos ejemplos y aplicaciones de los nuevos conceptos que se proponen, para su aplicación en la vida cotidiana. (shrink)

An arithmetical language, whose words are natural numbers written in hexadecimal numeration system, is defined and its applications for the representation, analysis and decision of formulae of some logical and normative systems are described and illustrated.The formulae, operations and relations of the represented system are associated as follows respectively to the numbers and the arithmetical operations and relations of the proposed language:1. Each well-formed-formula of the system is associated to a number of a set of natural numbers between zero (associated (...) to all tautologies and theses) and the binary supremum Φ of the set (Φ is associated to all contradictions and antitheses and his value is 2n-1, n depending on system’s dimensions and structure).2. Negation of a formula and disjonction and conjonction of t wo other more formulae of the system are associated respectively to the binary complement Φ-N(f) of the number associated to the first and to the binary infimun and supremum of the numbers associated to the last.3. The logical relations “f1 implies f2” (f1 -> f2), “f1 is incompat.ible with f2” (f1|f2), “f1 is the contradictory opposite of f2” (f1wf2) and “f1 is alternative to f2” (f1vf2) are true in the represented system if and only if the associated arithmetical relations, respectively “N(f1) absorbs arithmetically N(f2)”, “binary supremum of N(f1) and N(f2) is equal to Φ”, “sum of of N(f1) and N(f2) is equal to Φ” and “binary infimum of N(f1) and N(f2) is equal to 0”, are true.The applications of the proposed arithmetical language as very rapid and simplified tool of analysis and decision method are shown for the following systems: propositional logic, syllogistic, some deontic and alethic modal systems and some normative systems of statutory law:1. In the propositional logic, after fixing the maximum of variables considered, the numbers associated to these variables and to the contradictions are calculated. On this permanent basis, the evaluation of a farmula (especially in the case of many occurrences of many variables) is performed by the calculation of the associated number faster as in the traditional way.2. In the syllogistic, after the calculation of the number associated to each type of premise or conclusion, an arithmetical table of syllogisms shows that a proposed syllogism is valid if and only if the binary supremum of the numbers associated to the premises absorbs arithmetically the number associated to the conclusion. It is well-known that the search of this sort of arithmetization of syllogistic and the study of its possibilitiy has been a recurrent topic in modern logic, from Leibniz to Łukasiewicz and to-day.3. In a deontic equivalent:ial system who includes Von Wright’s deontic system of 1982 far norms of the first order, the calculation of the numbers associated to an types of permission and obligation sentences allows the im mediate arithmetical verification of an the classical relations between those sentences. The same is shown for an alethic modal system including the modlities of the first order of Lewis’s S5.4. For normative systems of statutory law, the arithmetical verification of the logical and normative relations is shown in precedent author’s papers -especially in recent “The ‘Ars Judicandi.’ Programme”-, though not yet in hexadecimal numeration system but only in binary and decimal ones.In all the represented systems, the arithmetical verification of the metalogical properties of the system -consistency and completeness- is performed in a very easy and rapid manner, after the arithmetic representation of the axiomatic basis of the latter by a system of equations. (shrink)

The present research studies with depth the mosque of Bāb Dukkāla at Marrakech, an architectural masterpiece created under the Saadian dynasty during the sixteenth century. The main aim of this study is to complete an accurate survey, by photogrammetry process, of the main building, but also of the related and adjoining buildings. These documentation and global analysis allow us to recognize a clearly religious complex designed to be well integrated in its urban context. In addition, spatial, constructive and ornamental aspects (...) of the complex are analyzed in order to understand the architecture developed during this historical period. (shrink)

This paper presents for the first time the IndetermSoft Set, as an extension of the classical (determinate) Soft Set, which operates on indeterminate data, and similarly the HyperSoft Set extended to the IndetermHyperSoft Set, where 'Indeterm' means 'Indeterminate' (uncertain, conflicting, non-unique result). They are built on an IndetermSoft Algebra which is an algebra dealing with IndetermSoft Operators resulting from our real world. Subsequently, the IndetermSoft and IndetermHyperSoft Sets and their Fuzzy/Fuzzy Intuitionistic/Neutrosophic and other fuzzy extensions and their applications are presented.

O presente trabalho visa analisar a possibilidade de se utilizar a ontologia matemática, conforme se pode observar na obra de Badiou, para conformar a estrutura lógica de teorias sociais. Trata-se de exemplificar como o conceito de multiplicidade sem unidade pode substituir a noção grega tradicional de que a unidade é anterior à multiplicidade. Para isso se apresentam as inovações matemáticas de Cantor, com a teoria dos conjuntos, e Paul Cohen, que apresenta as noções de “genérico” e “forçamento”, as quais (...) permitem a concepção de uma multiplicidade sem unidade. Por fim, aborda-se a analogia levantada por William Widen que aproxima o raciocínio lógico-matemático utilizado pela teoria dos conjuntos ao método de “subtração” utilizado por John Rawls para a formação de sua teoria da justiça. (shrink)

La introducción del grado de dependencia (y en consecuencia el grado de independencia) entre los componentes del conjunto difuso, y también entre los componentes del conjunto neutrosófico, se introduce por primera vez en la quinta edición del libro de Neutrosofía en el año 2006, basado en los elementos descritos en dicha edición del libro, se comienza a conocer conceptos de conjuntos neutrosóficos de los componentes borrosos así como los grados de dependencia e independencia, Por tal motivo el objetivo del (...) presente trabajo es extender el conjunto neutrosófico refinado, teniendo en cuenta la grado de dependencia o independencia de los subcomponentes que integran los conjuntos borrosos y neutrosóficos. (shrink)

Partiendo de la constatación husserliana de la crisis filosófica como crisis vital de una humanidad que se ha desviado de su _télos_ al implantar el modelo tecno-científico del dominio del mundo, el artículo investiga el lugar de la filosofía en el sistema educativo, explorando las reformas propuestas en Baviera y Prusia por Niethammer y Humboldt a principios del siglo XIX y que plantean, cada una a su modo, la necesaria incorporación de la filosofía a una educación de Estado que, frente (...) a las pretensiones utilitarias del filantropismo, logre elevar al hombre a su humanidad. En este sentido, retorna al concepto humanista de formación (_Bildung_) al que se consagran ambas reformas y que Gadamer recupera precisamente en _Verdad y método_ como un ideal para enfrentar la pretensión de universalidad de la ciencia moderna en relación a las nociones de conocimiento y de verdad, así como para pensar el horizonte ontológico de la experiencia hermenéutica. Es precisamente este ideal el que permite localizar el lugar de la filosofía en el conjunto del saber y conducir al hombre a su humanidad. (shrink)

A guerra civil iniciada no final de 2013 no Sudão do Sul causou, pela primeira vez na história das Nações Unidas, um afluxo gigantesco de deslocados internos para o interior de bases da Missão das Nações Unidas no Sudão do Sul, em busca de proteção. Assim, foram criados os Protection of Civilian Sites. Com a chegada de dezenas de milhares de pessoas em poucas semanas, houve um enorme crescimento nas demandas humanitárias e de segurança. Para prover a necessária proteção, foi (...) necessário o trabalho conjunto de militares, policiais e civis da UNMISS, que será apresentado nesse trabalho. (shrink)

En dos ocasiones, en sus “Homilías sobre los Salmos”, Basilio se vale da la noción griega de “systema” para designar a la Iglesia; el presente artículo procura indagar la posible proveniencia de tal expresión y algo de su alcance.

This article examines the role of gender in the culture of conjunto music, a Mexican American musical genre. It describes how gender is articulated with factors of ethnicity and class in the context of the conjunto setting and performance. The authors examine the structure of gender relations, socialization, and resistance, and they attempt to identify the effects within patriarchy on the forms of adaptation and power available to women in conjunto settings. Conjunto is an arena in which conventional gender identity (...) and gender inequality are reproduced, reinforced, and contested. (shrink)

Este artículo estudia la estructura lógico-matemática ligada a la mereo-topología de la teoría de conjuntos (MTTC), en cuanto esta estructura es el núcleo gnoseológico del neoliberalismo. En este contexto, analizamos los componentes lógico-matemáticos de tal estructura, a saber, la mereología, la topología y la teoría de conjuntos en oposición a la noción dialéctica de totalidad, como un medio para superar las consecuencias políticas y gnoseológicas derivadas de la asunción de tal aparato lógico-matemático. Asimismo, establecemos una relación entre la (...) MTTC y la fenomenología, lo cual permite analizar algunas inconsistencias relacionadas no solo con la estructura lógico-matemática de la MTTC, sino también con la implementación de la intencionalidad fenomenológica y la subsecuente ley eidética de dependencia. (shrink)

En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...) AE es la siguiente (B): “Existen ultraflitros sobre ℕ”. Se sabe que A implica B, pero se desconoce si B implica A. Di Prisco y Henle conjeturan en los artículos ([1], [2]) que esto no ocurre, es decir, conjeturan que B no implica A, en otras palabras, conjeturan que A es más fuerte estrictamente que B, que A es independiente de B, pero esto no se ha podido demostrar todavía aunque se ha intentado hacer desde hace aproximadamente 21 años. Una descripción detallada de este problema abierto puede encontrarse en esta ponencia (dictada en el marco del Día Mundial de la Lógica 14-01-2022) y en el artículo [3]. [1] C. Di Prisco y H. Henle. “Doughnuts, Floating Ordinals, Square Brackets, and Ultraflitters”. Journal of Symbolic Logic 65 (2000) 462-473. [2] C. Di Prisco y H. Henle. “Partitions of the reals and choice”. En “Models, algebras and proofs”. X. Caicedo y C.M. Montenegro. Eds. Lecture Notes in Pure and Appl. Math, 203, Marcel Dekker, 1999. [3] F. Galindo. “Tópicos de ultrafiltros”. Divulgaciones Matemáticas. Vol. 21, No 1-2, 2020. (shrink)

A indiscernibilidade das entidades quânticas é considerada como uma das noções centrais das teorias quânticas. Neste artigo expositivo, são apontadas algumas das razões para essa alegada importância, bem como as ideias básicas de uma teoria matemática que permite tratar de coleções dessas entidades. O artigo inicia com uma posição geral do autor sobre a filosofia da ciência.

ResumenEl estudio de las prácticas materiales de una sociedad requiere considerar los tipos de enmarcamiento epistemológico en que se desarrollan y sus efectos sobre éstas. Los modos de categorizar y distinguir y los modos organizar y agrupar son parte del enmarcamiento de las prácticas que este texto aborda. En particular, explora conceptualmente los modos de organización de conjuntos basados en la distinción agregativa entre lo singular y lo plural y los modos de organización enfocados en el efecto compositivo de (...) la diferencia entre molécula y masa. El ejercicio conceptual propone que ambos modos de organización sean empleados en conjunto, habilitando describir fenómenos de agregación y composición integrados sincrónica y diacrónicamente en la organización material de lo social.Palabras clave: agregación; composición; distinción; organización; prácticas materiales. (shrink)

Neste artigo, temos por objetivo analisar a hipótese de que o livro Aurora, no conjunto dos escritos de Friedrich Nietzsche, apresenta uma filosofia transitória. Nesse sentido, faremos ver que, justamente por causa de seu caráter transitório Aurora tem sido tão subestimada e obscurecida, principalmente quando comentada não a partir de seu quadro teórico transitivo, mas a partir de conceitos e projetos posteriores.In this article, we aim to examine the hypothesis that the book Daybreak, in all the writings of Friedrich Nietzsche, (...) presents a transitional philosophy. In this sense, we will see that, precisely because of its transitory Daybreak has been so overlooked and overshadowed, especially when commented not from their transitive theoretical framework, but from concepts and later projects. (shrink)

This essay aims to show that a phenomenological account of animal behavior can shed light on an ethological approach to alterity, and vice versa. The interface between ethology and phenomenology–which, as it is argued, is intelligible only with reference to a shared dimension of affection–is framed by means of the phenomenological concept of intentionality, which appears as a generative force of the organism, its behavior and surrounding world. This means that intentionality does not shape stable structures, but plastic and dynamic (...) processes that bound both the genesis of an organism and its surrounding world. Formation is thus understood as an epigenetic development, which suggests that natural forms are the result of a movement that goes from the general to the particular, from the most broad and regular structures of experience, to the multifarious proliferation of perspectives. (shrink)

In this paper I discuss some issues concerning the semantics of set theory. The set-theoretical nature of the semantics of axiomatic set theory raises a problem of circularity. It is well-known that when we adopt the model-theoretic point of view in the study of mathematical theories we decide to consider primarily structures in their relationship with languages. But for the fundamental structure adopted in a set-theoretic setting, namely the collection of all sets, together with the relation of membership, we would (...) have in that case a structure whose universe would be a set, and at the same time it would have the power of the collection of all sets. This is precisely the origin of the fundamental problem in the semantics of set theory. Apparently, the recourse to an intuitive or pre-theoretic semantics in terms of the iterative conception of sets is unavoidable. However, this strategy doesn´t seem to solve some basic philosophical topics involved and linked to the central semantic problem of set theory, namely, how to understand quantification over the totality of sets. Finally, I put forward some meta-philosophical considerations concerning the semantic problem I deal with. (shrink)

Este trabajo se propone mostrar que la noción de mundo circundante técnico [Werkwelt] elaborada por M. Heidegger no logra dar cuenta de la complejidad de la realidad técnica actual puesto que se basa en un modelo artesanal y cuasi-privado de producción. Sugerimos que, de ser consecuentes con las propuestas del mismo Heidegger, y descubrir en el medio técnico a la naturaleza y al mundo público, el Werkwelt debería expandirse hasta coincidir con un entramado pluri-sistémico en una soldadura de zonas funcionales (...) de muy diversa índole, es decir, un conjunto técnico, noción elaborada por G. Simondon. (shrink)

The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within (...) the framework of first-order logic, so this note is relevant; and the third note refers to the presence of mathematical platonism in the axioms of ZFC and in the axioms of "complete ordered field", it is known that the last axioms mentioned characterize (except isomorphism) the real number system and are currently used to develop the real Analysis in the context of set theory. It is hoped that this article will be of pedagogical utility for students interested in set theory and in the philosophy of mathematics (that are beginning in the subject). (shrink)

¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...) Matemática y Fundamentos de la Matemática (ver). También en la entrada "The Continuum Hypothesis" de la web de Enciclopedia de Filosofía de la Universidad de Stanford existe información importante y actualizada al respecto. En esta breve nota se comenta sobre el tema de una manera divulgativa. (shrink)

La investigación en educación histórica señala la necesidad de una transformación del proceso de enseñanza-aprendizaje de la historia. Se aboga por un cambio que promueva el desarrollo del pensamiento histórico y atienda tanto a la metodología como la epistemología del área. El objetivo de este artículo es presentar un programa de intervención gamificado para el desarrollo del pensamiento histórico en Educación Primaria, cuyo diseño ha sido validado por juicio de expertos, con la finalidad de que pueda servir de referencia para (...) el diseño de otras experiencias de aprendizaje gamificadas y contribuir así a la mejora de la educación histórica. (shrink)

Often ZF practice includes the use of the meta-theoretical notion of classes as shorthand expressions or in order to simplify the understanding of conceptual resources. NBG theory expresses formally the internalization of this feature in set theory; in this case, classes, before used metatheoretically, will also be captured by quantifiers of the first order theory. Never- theless there is a widespread opinion that this internalization of classes is harmless. In this context, it is common to refer to the conservativeness of (...) NBG in relation to ZF as a sufficient condition to understand those theories as “equivalent”, attributing a sense of virtuality to the use of classes quantified in NBG. We believe, however, that a technique used to estab- lish relationships between theories is not necessarily neutral in relation to its results - so a conservativeness established through models have different meaning and depth of that rela- tionship established by finitary interpretations. We believe, therefore, that the way in which relationships between theories are established influences the analysis result. In the case of the relationship between NBG and ZF, since NBG is finitely axiomatizible and ZF not, we believe that we have sufficient reasons to assert that the use of different analysis tools may re- veal differences such as expressiveness, ontological commitment and logical conservativeness. Therefore, this project aims to clarify the relationship between these two theories through triangulations between them and the different analysis tools. The use of finitary techniques, in this case, may prove greater expressiveness and ontological commitment of NBG in relation to ZF - relation obscured by an infinitary approach. We believe that, through this research, we can contribute to the debate on the basis of mathematics, denaturalizing the supposedly “equivalent” use of NBG and ZF for this purpose. (shrink)

El método de forcing usado (junto con el Método de "los constructibles" de Gödel) para probar la independencia de la hipótesis del continuo respecto de la axiomática de Zermelo-Fraenkel en los textos "Set Theory" de Kunen, y "Set Theory" de Jech, tiene entre sus fundamentos lógicos principales las propiedades de completitud y de Lowenheim -Skolem (hacia abajo). Por otro lado, se sabe por Lindström que no hay una lógica de mayor capacidad expresiva que la lógica de primer orden que satisfaga (...) simultáneamente ambas propiedades. Esto sugiere que no existe una lógica de mayor capacidad expresiva que la lógica de primer orden con la cual se pueda aplicar tal método. En este artículo se pretende argumentar a favor de tal sugerencia. (Nota: En mi ensayo "El Método de Forcing: Algunas aplicaciones y una aproximación a sus fundamentos metamatemáticos", publicado en el 2016, desarrollo con mayor rigurosidad y precisión matemática el tema, ver tal trabajo en la web o en esta página). The method of forcing used (along with Gödel's "constructibles" method) to prove the independence of the continuum hypothesis from the Zermelo-Fraenkel axiomatic system, in Kunen’s book "Set Theory" and in Jech's "Set Theory", is logically founded on the properties of completeness and Lowenheim-Skolem (downwards). On the other hand, Lindström has proved that there is no logic of greater expressive capability than the first order logic that is able to satisfy simultaneously both properties. This suggests that there is no logic of greater expressive capability than the first order logic with which this method can be wed. To provide a ground for this assertion is the purport of this paper. (Note: In my essay "The Forcing Method: Some applications and an approach to its metamathematical foundations", published in 2016, I develop with greater rigor and mathematical precision the topic, see such work on the web or on this page). (shrink)