CHAPTER 28 ARE THERE MATHEMATICAL PHENOMENA?

摘要

SUMMARY A didactically relevant distinction in physics separates phenomena from experiments. Looking at the observer as the counterpart of both, concepts such as impression and percept can be considered useful, and we can subsume them under an approach of aesthetics as related to sensual perception. What seems to be plausible in the physical sciences might be less obvious in mathematics. However, several natural phenomena as well as certain artefacts can be associated with mathematical structures by an observer who sees the mathematics in them. The other way round, aesthetic production in mathematics and mathematics education is well established, and a comparison with the concept of the phenomenon could be interesting. I shall propose some definitions and analytical instruments and try to apply the categories of Firstness, Secondness, and Thirdness as introduced by Charles Sanders Peirce, and his idea of the Interpretant as a constituent of the triadic sign.