What do mathematicians dispute about, or on the ontological status of the objects of mathematics

摘要

In this article the author considers various conceptions concerning ontological status of the objectsof mathematics.The relation is show between these problems and a dispute over universals, and then Platonism,conceptualism and nominalism as the fundamental standpoints on the question o f mathematicalobjects are presented. Examples are given of concrete (specific) theories w ith in these standpointsand their implications (also epistemological ones) are shown.