The symbolic model for algebra

functions and mechanisms

Albrecht Heeffer

pp. 519-532

in: Lorenzo Magnani, Walter Carnielli, Claudio Pizzi (eds), Model-based reasoning in science and technology, Berlin, Springer, 2010

Abstract

The symbolic mode of reasoning in algebra, as it emerged during the sixteenth century, can be considered as a form of model-based reasoning. In this paper we will discuss the functions and mechanisms of this model and show how the model relates to its arithmetical basis. We will argue that the symbolic model was made possible by the epistemic justification of the basic operations of algebra as practiced within the abbaco tradition. We will also show that this form of model-based reasoning facilitated the expansion of the number concept from Renaissance interpretations of number to the full notion of algebraic numbers.