Jerzy Pogonowski
Principia, Volume 67, 2020, pp. 87 - 118
https://doi.org/10.4467/20843887PI.20.004.13834Certain mathematical objects are called paradoxical or pathological. Such terms have negative connotations in common usage, in psychology, and in social science. However, the situation is different in mathematics. Emergence of mathematical paradoxes or pathologies always indicates a creative moment in the process of mathematical discovery. The paper contains reflections on this creative aspect of mathematical pathologies, the process of their domestication, and the cognitive accessibility of mathematical objects. The work on this paper was sponsored by the National Scientific Center research grant 2015/17/B/HS1/02232 Extremal axioms: logical, mathematical and cognitive aspects. The paper was presented during the 11th Polish Philosophical Congress in Lublin (2019).