Model-Based Reasoning in Science and Technology

TitleThe symbolic model for algebra: functions and mechanisms
Publication TypeBook Chapter (with title)
Year of Publication2010
AuthorsHeeffer, A
Secondary AuthorsMagnani, L, Carnielli, WA, Pizzi, C
Book TitleModel-Based Reasoning in Science and Technology
Volume314
Pages519–532
PublisherSpringer
ISBN Number9783642152221
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.

URLhttp://dx.doi.org/10.1007/978-3-642-15223-8\_29
Citation Key1217131
Download PDF (Author PDF)
PDF author (public):