The Starting Point: Lakoff and Núñez
摘要
This chapter starts by reviewing the model of mathematical cognition put forth by George Lakoff and Rafael Núñez in their classic 2000 book, Where Mathematics Comes From, including some of the chief critiques that were leveled initially at it. This chapter then looks at the implications of the Lakoff–Núñez approach for the study of math cognition and more specifically at the role of image schemas in this form of thought. These are recurring mental structures that establish, guide, and prefigure patterns of understanding and reasoning. Specific examples of how image schema theory can be enlisted to explain abstractions such as the number line and mathematical infinity will be discussed, followed by a consideration of the grounding and linking metaphors that supposedly underlie mathematical concepts. This chapter finally considers what may be the most controversial aspect of the Lakoff–Núñez approach—namely that mathematics and language are implanted in the same system of understanding.