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

The paper shows how to use the Husserlian phenomenological method in contemporary philosophical approaches to math-
ematical 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 onto-
logical 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.