 To see the problem, suppose that abstract objects, if they exist, exist necessarily, i.e., in all possible worlds. If physicalism is true, then the facts about such objects must either be physical facts, or else bear a particular relation (grounding, realisation) to the physical. But on the face of it, that is not so. Can one really say that 5+7=12, for example, is realised in, or holds in virtue of, some arrangement of atoms and void? Or can one say that it itself is a physical fact or a fundamental physical fact? If not, physicalism is false: the property of being such that 5+7=12 obtains the actual world but is neither identical to, nor grounded in or realized by, any physical property. (Sometimes the problem of abstracta is formulated as concerning, not abstract objects such as numbers or properties, but the grounding or realization facts themselves; see, e.g, Dasgupta 2015. We will set this aside here.)