Squares of Oppositions, Commutative Diagrams, and Galois Connections for Topological Spaces and Similarity Structures

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures

An explainable prediction method based on Fuzzy Rough Sets, TOPSIS and hexagons of opposition: Applications to the analysis of Information Disorder

This paper presents a novel approach for predicting and explaining instances of Information Disorder. The paper reports two significant findings: i) the use of structures of opposition to describe relationships between instances of Information Disorder, and ii) the development of an explainable prediction method that combines Fuzzy Rough Sets and TOPSIS with these structures. The findings have the potential to assist analysts and decision-makers in gaining a deeper understanding of the phenomenon of Information Disorder. The results are based on real data and demonstrate promising applications for future research

Casting the light of the theory of opposition onto Hohfeld's fundamental legal concepts

At the core of Hohfeld's contribution to legal theory is a conceptual framework for the analysis of the legal positions occupied by agents in intersubjective legal relations. Hohfeld presented a system of eight fundamental concepts relying on notions of opposition and correlation. Throughout the years, a number of authors have followed Hohfeld in applying the notion of opposition to analyze legal concepts. Many of these authors have accounted for Hohfeld's theory in direct analogy with the standard deontic hexagon. This paper reviews some of these accounts and extends them employing recent developments from opposition theory. In particular, we are able to extend application of opposition theory to an open conception of the law. We also account for the implications of abandoning the assumption of conflict-freedom and admitting seemingly conflicting legal positions. This enables a fuller analysis of Hohfeld's conceptual analytical framework. We also offer a novel analysis of Hohfeld's power positions.</p

From Analogical Proportion to Logical Proportions

International audienceGiven a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( a∧b and a¯∧b¯), or dissimilarity indicators ( a∧b¯ and a¯∧b) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the form “a is to b as c is to d”. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations (a¯,b¯,c¯,d¯)). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions

Color-Coded Epistemic Modes in a Jungian Hexagon of Opposition

This article considers distinct ways of understanding the world, referred to in psychology as Functions of Consciousness or as Cognitive Modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung's Simile of the Spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an Hexagon of Opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology

Multilemas y lógica hexagonal como herramienta para la creatividad social: sobre un caso de urbanismo participativo

Being the workshops inherent in participatory methodologies, these are determined as «a participatory process [that] entails the return of information to the same population, group or group, so that, duly supported by appropriate techniques, be these people who deepen, prioritize and plan their own strategies «(Red CIMAS, 2015). In this regard, one of the tools used by the CIMAS Network for these participatory returns are the so-called multilemmas or tetralemas (Villasante, 2006). From these, it is intended to make a group reflection on what has been said that comes out of the blocks that behave by promoting the emerging axes: the tension between the «is» and the «must be» (Colectio IOE, 2016). With this objective, they must follow three criteria of logical rigor (Villasante, 2006): take into account both the majority and minority positions, with the intention of avoiding discursive exclusion (Herzog, 2009) and keep in mind that «everything is relevant» (Montañés, 2002), look for friction points as oppositions –the dilemmas– (Conde, 2010) and look for contradictions in the social sense –the tensions– (Harvey, 2014), and listen to the questions to the questions that facilitate the subversión (Ibáñez, 1990).Siendo los talleres inherentes a las metodologías participativas, estos se definen como «un proceso participativo [que] conlleva la devolución de la información a la misma población, grupo o colectivo, para que, debidamente apoyada por técnicas adecuadas, sean estas personas las que profundicen, prioricen y planifiquen sus propias estrategias» (Red CIMAS, 2015). A este respecto, una de las herramientas generalmente utilizadas por la Red CIMAS para estas devoluciones participativas son los llamados multilemas o tetralemas (Villasante, 2006). A partir de estos se pretende realizar una reflexión grupal sobre lo dicho que salga de los bloqueos existentes mediante el fomento de los ejes emergentes: la tensión entre el «es» y el «debe ser» (Colectio Ioé, 2016). Con este objetivo, se deben seguir tres criterios de rigor lógico (Villasante, 2006): tener en cuenta tanto las posiciones mayoritarias como las minoritarias, con la intención de evitar la exclusión discursiva (Herzog, 2009), y tener presente que «todo es relevante» (Montañés, 2002), buscar los puntos de fricción como oposiciones —los dilemas— (Conde, 2010) y buscar las contradicciones en el sentido social —las tensiones— (Harvey, 2014), y escuchar las preguntas a las preguntas que faciliten la subversión (Ibáñez, 1990).Being the workshops inherent in participatory methodologies, these are determined as «a participatory process [that] entails the return of information to the same population, group or group, so that, duly supported by appropriate techniques, be these people who deepen, prioritize and plan their own strategies «(Red CIMAS, 2015). In this regard, one of the tools used by the CIMAS Network for these participatory returns are the so-called multilemmas or tetralemas (Villasante, 2006). From these, it is intended to make a group reflection on what has been said that comes out of the blocks that behave by promoting the emerging axes: the tension between the «is» and the «must be» (Colectio IOE, 2016). With this objective, they must follow three criteria of logical rigor (Villasante, 2006): take into account both the majority and minority positions, with the intention of avoiding discursive exclusion (Herzog, 2009) and keep in mind that «everything is relevant» (Montañés, 2002), look for friction points as oppositions –the dilemmas– (Conde, 2010) and look for contradictions in the social sense –the tensions– (Harvey, 2014), and listen to the questions to the questions that facilitate the subversión (Ibáñez, 1990)

The Stone and the Ivy: Music and Philosophy in Antagonisme by Xavier Darasse, on a Text by Alain Badiou

This thesis asks how music and philosophy interact in Antagonisme by Xavier Darasse. Antagonisme is a chamber work for piano, marimba, vibraphone, violin and narrator composed for the 1965 concours de composition at the Conservatoire de Paris on a text by Alain Badiou. Through the first ever study of correspondence, sketches and scores relating to the work, the thesis argues that Darasse responded to Badiou’s text through an unprecedented confrontation of serial procedures with Messiaen’s technique of interversion. Through original analyses of Messiaen’s writings on and uses of interversion, the thesis argues that Messiaen and Darasse used order, as sequence or ordinality, as a distinct musical parameter alongside the conventional serial parameters of pitch, duration, dynamics, timbre and articulation. By comparing Alain Badiou’s notion of a musical “situation” and Karl Popper’s “problem situation,” the thesis argues that the methodology best suited to studying the interaction of music and philosophy in Antagonisme takes into account both the immanent, musical problems at stake in the work and the broader contextual problems that Darasse and Badiou faced. This methodology integrates critical editing, music analysis and contextual criticism as distinct and equally important parts of the study. The thesis shows how Badiou’s text reflects its philosophical context, including structuralist debates around subjectivity and formal autonomy in serial works. The text also reflects the transition from Jean-Paul Sartre’s existentialism to the Marxist structuralism of Louis Althusser in Badiou’s early work and that of his contemporaries. Darasse’s musical response to Badiou’s text is first considered from a semiological perspective. After unravelling layers of ironic text-music relationships, it is argued that the relationship of text and music in Antagonisme must be considered as more than word-painting. Darasse’s innovative use of fundamental musical materials must be examined in its relationship to Badiou’s first theoretical article, completed in the same month as Antagonisme’s première, “Autonomy of the Aesthetic Process.” The issue of musical autonomy is both immanent to the work and essential to the tasks required in its study. The critical edition provided in an appendix of this thesis is an organ of thought in this regard. An edition representing the music’s most complete response to the text differs greatly from any extant version of the manuscript or the composer’s final intentions. The editor must make significant interventions, including material from the sketches that were never included in the manuscript or performance scores. In concluding the thesis, Badiou’s mature philosophy is convoked once more to argue that musicology can actively affirm the musical novelty of Darasse’s score