<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Certain mathematical objects bear the name “pathological” (or “paradoxical”). They either occur as unexpected and (temporarily) unwilling in mathematical research practice, or are constructed deliberately, for instance in order to delimit the scope of application of a theorem. I discuss examples of mathematical pathologies and the circumstances of their emergence. I focus my attention on the creative role of pathologies in the development of mathematics. Finally, I propose a few reflections concerning the degree of cognitive accessibility of mathematical objects. I believe that the problems discussed in the paper may attract the attention of philosophers interested in concept formation and the development of mathematical ideas.</p>
</abstract>

Certain mathematical objects bear the name “pathological” (or “paradoxical”). They either occur as unexpected and (temporarily) unwilling in mathematical research practice, or are constructed deliberately, for instance in order to delimit the scope of application of a theorem. I discuss examples of mathematical pathologies and the circumstances of their emergence. I focus my attention on the creative role of pathologies in the development of mathematics. Finally, I propose a few reflections concerning the degree of cognitive accessibility of mathematical objects. I believe that the problems discussed in the paper may attract the attention of philosophers interested in concept formation and the development of mathematical ideas.

Domestication of Mathematical Pathologies

Department of Logic and Cognitive Science

Studies in Logic, Grammar and Rhetoric

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Domestication of Mathematical Pathologies"}

Certain mathematical objects bear the name “pathological” (or “paradoxical”). They either occur as unexpected and (temporarily) unwilling in mathematical...

Domestication of Mathematical Pathologies

Published Online: Dec 30, 2021

Page range: 709 - 720

DOI: https://doi.org/10.2478/slgr-2021-0043

Keywords
paradox, mathematical pathology, concept formation, mathematical intuition

© 2021 Jerzy Pogonowski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Domestication of Mathematical Pathologies

Published Online: Dec 30, 2021

Page range: 709 - 720

DOI: https://doi.org/10.2478/slgr-2021-0043

Keywordsparadox, mathematical pathology, concept formation, mathematical intuition

© 2021 Jerzy Pogonowski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
paradox, mathematical pathology, concept formation, mathematical intuition