| Title: | HOW DOES COMPLEX MATHEMATICAL THEORY ARISE? PHYLOGENETIC AND CULTURAL ORIGINS OF ALGEBRA |
| DOI No: | 10.1142/9789812707420_0021 |
| Source: | WORLDVIEWS, SCIENCE AND US
Philosophy and Complexity (pp 338-351)
|
| Author(s): | HELEN DE CRUZ
Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
|
| Abstract: | Algebra has emergent properties that are neither found in the cultural context in which mathematicians work, nor in the evolved cognitive abilities for mathematical thought that enable it. In this paper, I argue that an externalization of mathematical operations in a consistent symbolic notation system is a prerequisite for these emergent properties. In particular, externalism allows mathematicians to perform operations that would be impossible in the mind alone. By comparing the development of algebra in three distinct historical cultural settings - China, the medieval Islamic world and early modern Europe - I demonstrate that such an active externalism requires specific cultural conditions, including a metaphysical view of the world compatible with science, a notation system that enables the symbolic notation of operations, and the ontological viewpoint that mathematics is a human endeavour. I discuss how extending mathematical operations from the brain into the world gives algebra a degree of autonomy that is impossible to achieve were it performed in the mind alone. |
| Full Text: | View full text in PDF format (786KB) |
| TOC: | Back to Table of Contents |
|
|
