I argue that the wave function ontology for quantum mechanics is an undesirable ontology. This ontology holds that the fundamental space in which entities evolve is not three-dimensional, but instead 3N-dimensional, where N is the number of particles standardly thought to exist in three-dimensional space. I show that the state of three-dimensional objects does not supervene on the state of objects in 3N-dimensional space. I also show that the only way to guarantee the existence of the appropriate mental states in the wave function ontology has undesirable metaphysical baggage: either mind/body dualism is true, or circumstances which we take to be logically possible turn out to be logically impossible.