Is metaphysics worth doing? Answering such a question isn’t as easy as you might think, since like any branch of philosophy metaphysics is quite diverse, with, in my opinion, some good parts and some bad parts. But we can, and should, separate the good from the bas.
Let me start with bad metaphysics. Bad metaphysics is, in general, the study of concepts (a.k.a. essences), with the conclusions of such studies assumed to be a priori truths. For example, a philosopher might reflect on their concept of time and come to the conclusion that time is necessarily unbounded, this then would be an a priori truth, that time is unbounded (we should hope that no one actually comes to this conclusion). The problem with such studies is not that we are unable to reflect upon our concepts, but that reflection upon our concepts doesn’t tell us anything useful. The facts that such reflections reveal are simply facts about how our mind is working. It doesn’t prove that something corresponding to the concept exists independently of our conscious mind, or that the world is in agreement with our a priori conclusions from these concepts. Nor does it prove that the concept is present as given in the mind, only that it appears that way in our conscious experience. But perhaps examples of where this kind of metaphysics has gone wrong in the past would be more convincing. Two prominent blunders were Kant’s a priori “proof” that space was Euclidian (it turned out that it wasn’t), and a priori “proofs” that the mind is separate from the body (again, evidence points in the other direction). Conceptual analysis and phenomenology can both be seen as this kind of metaphysics, but I won’t go into detail about them here since I have already discussed their failings.
Some may attempt to defend metaphysics from the criticisms I have raised above by putting forward math as an example of metaphysics done right. But math is not about the world, math is about math. A theorem in mathematics is only true in the sense that given some set of axioms and proof rules it can be derived from them. It is not the case that it is a fact about the world. Given a different set of axioms and different proof rules and it might not be derivable, or its negation may be derivable. The fact that certain mathematical systems seem to reflect what is actually happening in the world (for example how classical logic seems to be a good model of truth preservation) is an a posteriori fact, and it is something that might turn out to be false (for example, how classical logic has been shown to be lacking in certain applications of the conditional). Math is useful because who knows when a mathematical system might turn out to be a good model of some part of the world, but math is just that, a model, not something that is itself part of the world and causing the effects that we say it is a good model of. But philosophy is supposed to be about the world, certainly its objects of study are (knowledge, language, mind, ect), and thus mathematics is not a good model for how we should do philosophy, we don’t want to construct philosophical theories and then simply hope that one of them reflects what is really going on.
Now that I have outlined what can go wrong with metaphysics let me elaborate on how it can be done right. Examining a concept, while relatively useless in its own right, can play an important role in larger philosophical investigations. Instead of discovering a priori facts about the concept such work can be taken as establishing working definitions for certain basic ideas. For example, a philosopher might put forward definition of person on which to build some theory. The definition he or she gives for personhood is not meant to be the last word on what people are, but rather picking out the objects the theory is about, they could have called them anything. Or we can examine concepts in order to create definitions that best fit our use of those words, so that the philosophical theories based upon them are about the same objects as our ordinary discourse. This way of forming definitions, unsurprisingly, also leads to a search for the “natural kinds” that underlie those everyday judgments, a search that may or may not be successful.
Obviously then I don’t think that we should abandon metaphysics; I have been known to dabble in it a bit myself. (see here) What is important is that metaphysics be engaged in with the knowledge that it can play only a limited role in philosophy, the answers to most interesting questions cannot be known a priori.