La matemática mixta en las investigaciones de G. W. Leibniz

Para favorecer la interacción disciplinar y recuperar la dimensión práctica del conocimiento matemático en la escuela secundaria, Yves Chevallard plantea la necesidad de introducir en los programas de estudio la matemática mixta. La matemática mixta, cuyo apogeo tuvo lugar en Europa entre los siglos XVI y XVIII, se propone el abordaje de problemas surgidos por fuera de la propia matemática valiéndose de nociones mecánicas -como la de centro de gravedad y fuerza centrífuga- y del empleo de variados instrumentos para realizar las construcciones requeridas. En este trabajo consideramos a la matemática mixta en la cultura matemática de la segunda mitad del siglo XVII y, en dicho contexto, presentamos dos casos de la práctica matemática de G. W. Leibniz en los que la investigación matemática involucra el diseño de máquinas. La consideración de tales casos permite situar a la matemática mixta, siguiendo la terminología de Ian Hacking, en un terreno medio entre representar e intervenir. El terreno medio entre representar e intervenir es un valle fértil donde la matemática aporta a, y se nutre de, una multiplicidad de otros dominios. También es una vía de acceso para historizar el conocimiento matemático, destacando las condiciones materiales para su desarrollo y el importante rol de los problemas. Palabras clave: Práctica matemática, Resolución de problemas, Siglo XVII, Máquinas, Cultura material.

The creation of phenomena in interactive biorobotics

In so-called interactive biorobotics, robotic models of living systems interact with animals in controlled experimental settings. By observing how the focal animal reacts to the stimuli delivered by the robot, one tests hypotheses concerning the determinants of animal behaviour in social contexts. Building on previous methodological reconstructions of interactive biorobotics, this article reflects on the claim, made by several authors in the field, that this strategy may enable one to explain social phenomena in animals. The answer offered here will be negative: interactive biorobotics does not contribute to the explanation of social phenomena. However, it may greatly contribute to the study of animal behaviour by creating social phenomena in the sense discussed by Ian Hacking, i.e. by precisely defining new phenomena to be explained. It will be also suggested that interactive biorobotics can be combined with more classical robot-based approaches to the study of living systems, leading to a so-called simulation-interactive strategy for the mechanistic explanation of social behaviour in animals.

The Concept of Positive Law and Its Relationship to Religion and Morality

Can the concept of law be extended to other times and places in which the concept as understood in most countries and societies today—as a system of norms centred on a nation state, based on a constitution, formulated through codified legislation and judicial precedents, administered by lawmakers for its inception and judges for its implementation—simply did not exist? My contention is that such an extension is, at best, useless and, at worst, misleading. Producing an intelligible jurisprudence of the concept of law means keeping it within the reasonable boundaries of what is ordinarily understood by both lay and professional people when practising ‘the’ law. Developing a socio-historical jurisprudence of law, as distinct from other normativities, entails a threefold analysis: conceptual, historical, and praxiological. Following the ground broken by analytical philosopher Ludwig Wittgenstein, conceptual analysis engages in the exposition of the grammar through which concepts acquire their signification and are meaningfully used. In a manner inspired by philosopher of science Ian Hacking and by historian Reinhart Koselleck, historical analysis emphasizes the description of the birth, development, and use of concepts. Drawing on the work of sociologist Harold Garfinkel, praxiological analysis describes the practical methods used by people to make sense of their environment, to produce their local order, and to act accordingly. The three approaches converge in their insistence on adopting the endogenous/indigenous perspective towards social life and its production.

Investigación filosófica y emociones

Los estudios filosóficos sobre emociones se pueden dividir en dos grandes grupos: 1) aquellos que consideran que las emociones son naturales, resultado de nuestra evolución; 2) aquellos que, interesados en el pensamiento de autores concretos respecto a las emociones, no sostienen ninguna posición sustantiva acerca de ellas. En este artículo exploramos una tercera opción: entender que las emociones son históricas, contextuales y socialmente definidas. Abrimos así la posibilidad a una nueva forma de investigación filosófica, que partiría de la ontología histórica del filósofo Ian Hacking como herramienta desde la que abordar el estudio filosófico de las emociones en la historia. Emotions research in Philosophy could be classified into two main groups: 1) Those that considers emotions as a natural feature, the result of our evolutionary history; 2) Those that are interested in the study of what a particular philosopher said about the emotions, and, therefore, do not sustain any substantive claim about the nature of the emotions. I explore a third option: to understand emotions as historical, contextual, and socially constituted. This new approach opens up the door to a new form of philosophical inquiry on emotions in their historical contexts, based on Ian Hacking’s historical ontology.

Quantification and classification in education: What is at stake?

Histories of statistics and quantification have demonstrated that systems of statistical knowledge participate in the construction of the objects that are measured. However, the pace, purpose, and scope of quantification in state bureaucracy have expanded greatly over the past decades, fuelled by (neoliberal) societal trends that have given the social phenomenon of quantification a central place in political discussions and in the public sphere. This is particularly the case in the field of education. In this article, we ask what is at stake in state bureaucracy, professional practice, and individual pupils as quantification increasingly permeates the education field. We call for a theoretical renewal in order to understand quantification as a social phenomenon in education. We propose a sociology-of-knowledge approach to the phenomenon, drawing on different theoretical traditions in the sociology of knowledge in France (Alain Desrosières and Laurent Thévenot), England (Barry Barnes and Donald MacKenzie), and Canada (Ian Hacking), and argue that the ongoing quantification practice at different levels of the education system can be understood as cultural processes of self-fulfilling prophecies.

Espacios y emociones: una propuesta desde la ontología histórica

En este artículo proponemos una nueva aproximación al estudio de las emociones desde una aproximación transdisciplinar a la historia y a la filosofía. Para ello, cuestionamos lo que llamamos teoría del appraisal y apostamos por una definición social de las emociones, basada en la teoría de la emoción construida de Lisa Feldman Barrett. En concreto, proponemos considerar a las emociones como categorías humanas, lo que nos permitiría su estudio como parte de la ontología histórica. A partir de aquí, analizamos el problema acerca de la relación entre cultura material y experiencia emocional y proponemos el concepto de matriz, desarrollado por Ian Hacking, como una forma de ligar ambas. Apoyaremos esta aproximación con un estudio de caso: el del Hospital para Mujeres Incurables Jesús Nazareno, en Madrid, en la década de 1870. Este caso nos servirá para identificar y probar un conjunto de herramientas metodológicas que nos ayuden a analizar aquellos componentes materiales que construyen, determinan y condicionan nuestras experiencias emocionales.

Social Representations of Art in Public Places: A Study of Everyday Explanations of the Statue of ‘A Real Birmingham Family’

This article focuses on the social/cultural representations of the statue of A Real Birmingham Family cast in bronze and unveiled in Britain’s second city in October 2014. It reveals a family comprising two local mixed-race sisters, both single mothers, and their sons, unanimously chosen from 372 families. Three of the four families shortlisted for the statue were ‘mixed-race’ families. The artwork came about through a partnership between the sculptress, Gillian Wearing, and the city’s Ikon Gallery. A number of different lay representations of the artwork have been identified, notably, that it is a ‘normal family with no fathers’ and that it is not a ‘typical family’. These are at variance with a representation based on an interpretation of the artwork and materials associated with its creation: that a nuclear family is one reality amongst many and that what constitutes a family should not be fixed. This representation destabilizes our notion of the family and redefines it as empirical, experiential, and first-hand, families being brought into recognition by those in the wider society who choose to nominate themselves as such. The work of Ian Hacking, Richard Jenkins, and others is drawn upon to contest the concept of ‘normality’. Further, statistical data are presented that show that there is now a plurality of family types with no one type dominating or meriting the title of ‘normal’. Finally, Wearing’s statues of families in Trentino and Copenhagen comprise an evolving body of cross-national public art that provides further context and meaning for this representation.

Identifying the Explanatory Domain of the Looping Effect: Congruent and Incongruent Feedback Mechanisms of Interactive Kinds

Ian Hacking uses the looping effect to describe how classificatory practices in the human sciences interact with the classified people. While arguably this interaction renders the affected human kinds unstable and hence different from natural kinds, realists argue that also some prototypical natural kinds are interactive and human kinds in general are stable enough to support explanations and predictions. I defend a more fine-grained realist interpretation of interactive human kinds by arguing for an explanatory domain account of the looping effect. First, I argue that knowledge of the feedback mechanisms that mediate the looping effect can supplement, and help to identify, the applicability domain over which a kind and its property variations are stably explainable. Second, by applying this account to cross-cultural case studies of psychiatric disorders, I distinguish between congruent feedback mechanisms that explain matches between classifications and kinds, and incongruent feedback mechanisms that explain mismatches. For example, congruent mechanisms maintain Western auditory experiences in schizophrenia, whereas exporting diagnostic labels inflicts incongruence by influencing local experiences. Knowledge of the mechanisms can strengthen explanatory domains, and thereby facilitate classificatory adjustments and possible interventions on psychiatric disorders.

La injusticia testimonial como fabricación de personas: una lectura ontológica

El objetivo de este trabajo es desarrollar una lectura ontológica del fenómeno ético-epistémico que Miranda Fricker (2017) caracteriza como injusticia testimonial. Para hacer esto, recurriremos a las ideas desarrolladas por Ian Hacking (2001, 2002, 2006) respecto a las relaciones entre las clasificaciones sociales y las clases o tipos sociales. Por un lado, consideraremos los procesos que Hacking llama “fabricación de personas” (making up people), a saber, aquellos procesos mediante los cuales la articulación de ciertas clasificaciones hace posible la existencia de ciertos tipos de personas. Argumentaremos que los episodios de injusticia testimonial, que expresan los efectos de clasificaciones estereotípicas, pueden entenderse como parte de los procesos sociales de fabricación debido a que contribuyen a fabricar los atributos epistémicos, tales como la credibilidad, de ciertos tipos de personas. Por otro lado, con el fin de conceptualizar la situación ontológica bajo la cual el fenómeno de la injusticia testimonial se vuelve reconocible y reprochable, recurriremos a la idea de “clases interactivas” de Hacking. Sostenemos que el concepto de “clases interactivas” pone de manifiesto la naturaleza fundamentalmente inestable de las clases humanas y que enfatizar este aspecto dinámico permite iluminar las condiciones sociales bajo las cuales la injusticia testimonial aparece como éticamente culpable. En este sentido, argumentaremos que la injusticia testimonial puede devenir el objeto de un punto de vista normativo sólo en la medida en que las clases cuya existencia es posibilitada por las clasificaciones estereotípicas se encuentran ya atravesando un proceso de cambio.