Signo y representación del pensamiento matemático en la configuración del principio de población de Malthus

Abstract

This research is an approach to mathematical thinking from a sociocultural perspective and is located in the field of representation studies. It deals mainly with the role of the sign in the relations between symbolic forms and the social world. Under the conception of science as representational practice, it deals with the configuration space of the Population Principle in the first half of the nineteenth century. The objective is to describe the roles of the sign in the representations of mathematical thought that emerged in the configuration process of Malthus's Population Principle. The theoretical gaze assumes that the sign is a means for social interaction in the Vygotsky way. The methodological framework is taken from cultural history and works in the history of science that address the study of representation. Literary technologies are incorporated for the study of the text, considering it a tool for the production of knowledge to support the constitution of the data as part of the identified cultural artifacts. The literary technologies that emerged in the inquiry exercise are: the book, the replica, epistolary writing, travelers' memories, and number tables. The analysis shows that the approach from the cultural artifact to the dimension of the construction of scientific, social and political credibility shows the incorporation of specific instruments for the quantification of the population and the validation of Laws that sought to show a distance between the author and the knowledge produced. The recovered historical sources show that the sign manifested itself as a reflection and refraction of the social and natural world in the configuration of the Population Principle. The role of the refraction of the sign emerges when describing how the incorporation of the numerical tables in the scientific discourse of the time was related to the claim of truth by giving the value of mean sign to the mathematical proportion. From the reading of the textual corpus made up of the materials of the documentary archive, the representational practice emerged through the historical traces that evidence the reflexive and transitive forms, giving the possibility of studying the other representations that the pre-eminence of the empiricist method relegated. Finally, this approach to mathematical thinking shows how the epistemological role of the sign emerges, which is integrated into the space of negotiation of meaning, becoming a central part of the process of configuration of the Population Principle.