Matematikaren ikuspegi kategorialetik Gorpuztutako Matematikaren ikuspegira

Abstract

Saunders Mac Lane asked why mathematics has got the branches it has. The foundations of set theory do not explain properly the most important features of mathematical structure. We should not search on forms but on human activities and culture in order to explain that structure and its branches. In this way we can also answer why mathematics works so suitably in the understanding of reality: because it comes from the human activity in reality. Developing this view Lakoff and Nuñez have proposed a finer cognitive perspective of the issue, where mathematical reasoning is based in perceptual-motor and image schemas of the embodied mind. Thus Platonist philosophy of mathematics and its «dangerous consequences» are strongly attacked. I will finish this critical notice commenting some weaknesses of the view and the role diagrams play in connection with Embodied Mathematics.