The main aspect of the intuitionist ontology of mathematicsis the conception of mathematical objects as products (constructions) of the human mind. This paper argues that so long as the existence of mathematical objects is made dependent on thehuman mind (or even any physically realizable mind), the intuitionist ontology is refutable in that it is inconsistent with our well-confirmed beliefs about what is physically possible. At the same time, it is also argued that the intuitionistś attempt to remove this inconsistency by endowing the mind with various highly idealized features and capacities will erase any significant ontological difference between Intuitionism and Platonism.