Inicio > Filosofía marxista, Psicología marxista > “The cultural-epistemological conditions of the emergence of algebraic symbolism”: Luis Radford

“The cultural-epistemological conditions of the emergence of algebraic symbolism”: Luis Radford

ABSTRACT
The main thesis of this paper is that algebraic symbolism emerged in the Renaissance as part of a new type of thinking − a new type of thinking shaped by the socioeconomic activities that arose progressively in the late Middle-Ages. In its shortest formulation, algebraic symbolism emerged as a semiotic way of knowledge representation inspired by a world substantially transformed by the use of artefacts and machines. Algebraic symbolism, I argue, is a metaphoric machine itself encompassed by a new general abstract form of representation and by the Renaissance technological concept of efficiency. To answer the question of the conditions which made possible the emergence of algebraic symbolism, I enquire about the cultural modes of representation of knowledge and human experience and look for the historical changes which took place in cognitive and social forms of signification.

1. Introduction

The way in which I wish to study the problem of the emergence of algebraic symbolism can easily lead to misunderstandings. Perhaps the most tempting misunderstanding would be to think of this paper as a historical investigation of the external factors that made possible the rise of symbolic thinking in the Renaissance. “External factors” have usually been seen as economic and societal factors that somewhat influence the development of mathematics. They are opposed to “internal factors”, which are seen as the true factors accounting for the development of mathematical ideas. The distinction between the internal and external dimensions of the conceptual development of mathematics rests on a clear cut distinction between the sociocultural on one side, and the “really” mathematical on the other. Within this context, the former is seen, as Lakatos suggested, as a mere complement to the latter. Viewed from this perspective, it may appear that the route I am taking to investigate the emergence of algebraic symbolism belongs to the sociology of knowledge. However, to cast my intentions in such a dichotomy is misleading.

The cultural-epistemological conditions of the emerge of algebraic symbolism

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