 There are not very many alternatives to platonism. One can reject the existence of things like numbers and universals altogether. Or one can maintain that there do exist such things as numbers and universals, and instead of saying that they are abstract objects, one can say that they are mental objects of some sort (usually, the claim is that they are ideas in our heads) or physical objects of some sort. Thus, the four mainstream views here are as follows (and keep in mind that anti-platonists can pursue different strategies with respect to different kinds of alleged abstract objects, taking one view of, say, numbers, and another view of properties or propositions).