I gave a paper yesterday at our weekly postgraduate seminar Eidos with the above title and I thought I might post about it here as well. The paper is available here. It is inspired by the recent Metametaphysics volume, edited by Chalmers, Manley and Wasserman. I’ve just reviewed the volume for our journal, Philosophical Writings. The volume is interesting and everyone working in metaphysics should take a look, but I’m not happy about one thing: the Quinean metaontology that nearly all of the contributors assume, with the exception of Kit Fine and Jonathan Schaffer. In my paper I discuss Fine’s contribution and Thomas Hofweber’s contribution; Hofweber criticises Fine and Schaffer and is generally opposed to the Aristotelian conception of metaphysics that they defend. Especially the positive part of the paper is very sketchy, so I would appreciate any comments as to how I should develop it. The problem is that it would become way too long if I included the full positive story. Maybe I should focus on a single example and show how we can settle it with the help of my proposed method?

Anyway, I thought I might briefly summarise what I find problematic about this topic. A common example that many of the authors use in one form or another concerns the existence of numbers. Now, the problem is that this seems like a very trivial question and metaphysics is not supposed to be trivial. There is an easy and rather irritating argument which supposedly establishes the existence of numbers:

(1) The number of elves is zero.
(2) There is such a thing as the number of elves.
(3) Hence, there are numbers.

If only metaphysics were this easy… The worry that one should have here is that if metaphysics is really about existence questions such as ‘Are there numbers?’ or ‘Are there tables?’, then it becomes either trivial, or metaphysical questions are handed over to science; after all, you might think that mathematicians should answer the question about the existence of numbers, and physicists about the existence of electrons, for instace. This is strictly a result of the Quinean understanding of ontological commitment: we commit ourselves to the existence of numbers when we quantify over them in the manner that we do in the premises of the above argument. Kit Fine and Jonathan Schaffer challenge this assumption, but I won’t go into the details of their suggestions here. I will, however, quote a splendid passage from Fine’s paper:

Quine’s approach to ontology appears to be based on a double error. He asks the wrong question, by asking a scientific rather than a philosophical question, and he answers the question he asks in the wrong way, by appealing to philosophical considerations in addition to ordinary scientific considerations. This marriage of a misguided methodology to an ill-conceived question produces the semblance of a question properly asked and properly answered, since the philosophical considerations to which he appeals are in many ways appropriate to the question he should have asked; and it [is] no doubt partly because the one error compensates for the other that philosophers have found it so easy to be oblivious to both. Perhaps something useful can come from following such a cockeyed procedure but true enlightenment can only be achieved by getting the question right and getting the methodology to fit the question. (p. 161.)

What is the right question, then? Well, I think that it has something to do with the nature or essence of the entity under investigation rather than its existence. In fact, I think that we have to assume that things like numbers exist in the traditional sense if we wish to have any debate at all. Accordingly, the real metametaphysical question is: how do we gain knowledge about the essences of entities? The answer to this question, which I have defended elsewhere, is that our epistemic access to essences is based on a priori reasoning. But not in any mysterious sense of ‘a priori’, or, at least, not any more mysterious than it is when scientists use the very same faculty of reasoning. I have a story about how this all works, basically I think that a priori reasoning deals with metaphysical modality and that metaphysical modality is grounded in essences pace Fine. See my paper ‘A New Definition of A Priori Knowledge: In Search of a Modal Basis’ for details.

Incidentally, I had a chat about this with Peter van Inwagen, who gave a paper here in Durham earlier today. He has also got a paper in the Metametaphysics volume, but van Inwagen is of course a hardcore Quinean. I asked him what he thought about Fine’s paper and his answer was: ‘bullshit’. But when I queried about the above argument concerning the existence of numbers and the threat of metaphysical questions being either trivial or handed over to science, I didn’t really get a satisfactory answer. This seems like a major challenge for Quinean metaontology and I would like to see how Quineans are supposed to cope with it. At the very least, I think that this problem calls for a re-assessment of Aristotelian metaontology, which does not seem to have such unfortunate consequences.