The Cultural-Epistemological Conditions of the Emergence of Algebraic Symbolism
Proceedings of the 2004 History and Pedagogy of Mathematics Conference & ESU4, page 509-524. Uppsala, Sweden, (2006)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.