Mathematical Metaphors Gone Wild

This chapter examines two case studies that illustrate the limitations of the cognitive theory of mathematical metaphor in accounting for the formation of actual historical mathematical life worlds. The first case study deals with four medieval and early modern examples of relating algebra to geometry. These examples show that when two mathematical domains are linked, what passes between them cannot be reduced to “inferences,” as assumed by the theory of mathematical metaphor. The second case study reviews notions of infinity since early modernity and demonstrates that these notions are far too variegated and complex to be subsumed under a single metaphor—namely, George Lakoff and Rafael Núñez's basic metaphor of infinity, which tries to read all mathematical infinities as metaphorically projecting final destinations on indefinite sequences.

Algebra over a field · Epistemology · George (robot) · Infinity · Linguistics · Mathematical structure · Mathematical theory · Mathematics education · Metaphor · Physics · Pure mathematics · Artificial Intelligence · Computer Science · Historical and Linguistic Studies · Historical and Literary Studies · Historical Philosophy and Science · Mathematics · Philosophy