9 Ambitious, Yet Modest, Metaphysics

There is a long history of worrying about whether or not metaphysics is a legitimate philosophical discipline. Traditionally such worries center around issues of meaning and epistemological concerns. Do the metaphysical questions have any meaning? Can metaphysical methodology lead to knowledge? But these questions are, in my opinion, not as serious as they have sometimes (historically) been taken to be. What is much more concerning is another set of worries about metaphysics, which I take to be the greatest threat to metaphysics as a philosophical discipline. These worries, in effect, hold that the questions that metaphysics tries to answer have long been answered in other parts of inquiry, ones that have much greater authority. And if they haven’t been answered yet then one should not look to philosophy for an answer. What metaphysics tries to do has been or will be done by the sciences. There is nothing left to do for philosophy, or so the worry. Let me illustrate this with two examples, one of which is our main concern here. 1.1 Two Examples The most striking examples where it seems that the question metaphysics tries to answer has been answered long ago outside of philosophy are examples from ontology. These will be our main concern in this paper. One of the central questions in the philosophy of mathematics is an ontological question: are there any mathematical objects? If there are then a certain story of mathematical truth and objectivity will have to be told, and if there are not then a completely different one has to be right. This is supposed to be a large-scale philosophical question about mathematics. It’s the question whether or not there are math-ematical objects. But it seems that this question is not a philosophical question at all. It is one that is easily answered within mathematics. Mathematics ha