No Magic: From Phenomenology of Practice to Social Ontology of Mathematics

Mirja Hartimo, Jenni Rytilä

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The paper shows how to use the Husserlian phenomenological method in contemporary philosophical approaches to mathematical practice and mathematical ontology. First, the paper develops the phenomenological approach based on Husserl's writings to obtain a method for understanding mathematical practice. Then, to put forward a full-fledged ontology of mathematics, the phenomenological approach is complemented with social ontological considerations. The proposed ontological account sees mathematical objects as social constructions in the sense that they are products of culturally shared and historically developed practices. At the same time the view endorses the sense that mathematical reality is given to mathematicians with a sense of independence. As mathematical social constructions are products of highly constrained, intersubjective practices and accord with the phenomenologically clarified experience of mathematicians, positing them is phenomenologically justified. The social ontological approach offers a way to build mathematical ontology out of the practice with no metaphysical magic.

Original languageEnglish
Pages (from-to)283-295
Issue number1
Early online date19 Jan 2023
Publication statusPublished - 2023
Publication typeA1 Journal article-refereed


  • Husserl
  • Mathematical practice
  • Metaphysical neutrality
  • Phenomenology
  • Social constructionism
  • Social ontology

Publication forum classification

  • Publication forum level 1

ASJC Scopus subject areas

  • Philosophy


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