The notion of object (and with it ontology) in the foundations of quantum mechanics has been made both too easy and too hard: too easy, because particle distinguishability, and with it the use of proper names, is routinely assumed; too hard, because a number of metaphysical demands have been made of it (for example, in the notion of ‘primitive ontology’ in the writings of Shelly Goldstein and his collaborators). The measurement problem is also wrapped up with it. I shall first give an account of quantum objects adequate to the thin sense required of quantification theory (in the tradition of Frege and Quine); I then consider an alternative, much thicker notion that is strongly reminiscent of Leibniz’s monadology. Both apply to the Everett interpretation and to dynamical collapse theories (sans primitive ontology).