Generally speaking, metaphysics seems to deal with questions that cannot be verified empirically, which are thus beyond the understanding of science. Because of this I'm wondering whether the answers metaphysics provides to these questions are in any way useful. Whether the substantivist or relativism account for space is correct, why is the answer useful?
Your question really has two parts: (1) what can we know about metaphysics? (2) given what we can know, how can that stuff be useful?
metaphysics seems to deal with questions that cannot be verified empirically, which are thus beyond the understanding of science
A few philosophers that I've read have made a distinction that seems to get lost here, the distinction between using empirical evidence and the scientific method. As one example: CS Lewis in Mere Christianity uses the example of certain personal experiences that we all share and tries to extrapolate metaphysical concepts about right and wrong. These personal experiences are the data upon which he builds the argument, but these experiences being personal are not "reproducible" in the scientific sense.
Taking CS Lewis's example also shows the potential use in metaphysics: it is a metaphysical, and not scientific question, whether morality is objective or relative, and so as a consequence what is and is not moral, and from that how a just society should (and should not) be structured. Seems useful to me.
Aristotle, who wrote a book which was later called metaphysics; and which then meant after the Physics, another book of his; said that this discipline explores the first principles of things. Physics in his sense is wider than the notion we have today; and its important that that this study comes after and not before; being more difficult, more abstract and much more uncertain; and this comes through in his discussion of the positions of different philosophers, as well as his own commentary on them.
Hume, who is often seen as the most severe of sceptics, defends in an Enquiry Concerning Human Understanding, the more difficult and profound study - Metaphysics against the friends of the 'easy philosophy' who are apt to pour scorn on it. Easy here, isn't a pejorative label - in fact Hume says the easy philosophy enjoys its fame for good reason; and nor should it be seen as easy, it too can be difficult in a different way.
You seem to claim that something that cannot be verified empirically is beyond the understanding of science and probably not useful.
Mathematics cannot be verified empirically, but is very helpful. Why do I think that mathematics cannot be verified empirically? First of all, it is an open question what mathematics is about. Whatever numbers are, a lot of them, indeed, infinitely many of them, are larger than the amount of stuff in the universe.
(Of course, there are philosophers, and especially metaphysicians, that work on those questions. Some think that mathematics can be verified empirically, see for example Maddy)
One branch of metaphysics is modality. Something is science, you seem to suggest, if it makes verifiable claims. Which is just to say that it has to be possible to verify it. The nature of possibility belongs in the realm of metaphysics. And working on modality helps us to pin down what is verifiable and what is not. If that is your demarcationline between science and non-science, working on metaphysics is useful.
Furthermore, I don't think that your claim is true in the first place. Science, for example theoretical physics, makes claims that are not empirically verifiable (at least not yet). Example: Theoretical Physics makes assumptions about what is in a black hole, but it is impossible for us to go into a black hole and make our observations. But theoretical physics is still useful I'd say.
I quite agree ( meaning, you seem to be doubtful about the usefulness of the metaphysics ), even though as Kant claims humans can never have direct access to reality, employing such a method like Edmund Husserl's phenomenology, which is the analysis like peeling the outside layer of the target object layer by layer, even though we can not have direct access to the object itself, we can scientifically analyze the nature or the subjective phenomenon as far as we can conduct the analysis. ( Thus we can reach to the object itself closer and closer. ) It is, actually, a branch of materialism in its nature, to me, personally. Metaphysics, on the other hand, are just difficult even to read their theories or whatever.
Feurbach also argued why Greek deity look like Greeks? He said it is because that Greeks at that age only were able to deduct their own image of God because they were able to look at the quite limited periphery. If then, should there be such a thing like Universal God, that would not be God, I think, but only a hole unknown which is unverifiable to anyone which nobody can put their faith in. I am sorry for my poor English.
A quote from Man A Machine I commented on Mozibur Ullah's answer.
To distrust the knowledge that can be drawn from the study of animated bodies, is to regard nature and revelation as two contraries which destroy each other, and consequently to dare uphold the absurd doctrine, that God contradicts Himself in His various works and deceives us.If there is a revelation, it cannot then contradict nature. By nature only can we understand the meaning of the words of the Gospel, of which experience is the only truly interpreter.
This is a speech from a 18th century's "philosopher", my friends!. How are we still "discussing" such a same issue. Personally, this is not related with the questioner's question, but we human beings have nod advanced so much from, to say, since latest around the early 20th century. Jaccues Derrida's Spectres of Marx, in which he claimed he "would like to?" be the inheritor of Marx, is, after having read, I thought it was a poem not a thesis or anything.
I'm not sure I understand the motivation for the question. The purpose of an answer is to answer the question. If the answer is 'beyond science' this doesn't mean it's beyond the understanding of scientists. Scientists are not necessarily any worse than philosophers at understanding metaphysics, given the same amount of effort to do so.
Assuming it is correct, how could an answer to a metaphysical question not be useful? Such questions are isomorphic and holographic thus (as Heidegger points out) the answer to one would be the answer to them all. How could it not be useful?
You cite two possible answers for questions about space and ask why they are useful. This is not a relevant question unless you can show one of the answers is correct.
I would suggest you have a false impression of metaphysics. Wrong answers are not useful, (albeit discovering they are wrong is), but correct answers will allow us to understand the world better. Surely it would be useful to know the origin of the laws of physics, the nature of space and time, the truth about consciousness and so forth.
We could probably agree that an incorrect answer to a metaphysical question will be useless but we cannot judge the usefulness of the correct answer until we know what it is. In Western thought it would be almost heretical to suggest that we could know the answer to a metaphysical question so you may be thinking only of this approach to metaphysics. Most of its champions insist that metaphysics does not produce answers so their usefulness is not investigated, discussed or known.
Speaking personally, taking up the study of metaphysics has turned out to be one of the most useful things I've ever done.
One can use the information contained in a map to assist in navigational activities within the territory the map is assumed to be a reliable representation of. One can use assembly instructions for the guidance required to piece together flat packed furniture. One makes a shopping list to alleviate the need to remember and to optimise expenditure. One uses signage to help find the location of the toilets in an unfamiliar shopping precinct. One uses the step-by-step procedure in the auto workshop manual to facilitate a coolant/oil/filter change on the car. One uses a recipe to cook an unfamiliar meal- the list is endless.
Generally speaking, If a representation R contains genuine and useful information about some target system E, then R can be used to ‘leverage’ (inform/guide/coordinate/instruct/organise/regulate/navigate/anticipate/prepare/etc.) one’s interactions with E (R is used to guide or correct for minor ‘cognitive deficits’ pertaining to E-interactions). If R doesn’t provide this, then R is redundant or worst impedimental. Metaphysics has no utility in this sense and I challenge anyone on this site to provide an obvious counter example that doesn’t trot out some clap trap about ‘understanding’. Pace Logical Positivism, I think the significance of what you might call “the social utility of representation” is however, hopelessly over looked.
Metaphysics seems to consist in little more than a pretence to ‘reality tracking’ when the only thing that’s really going on is ‘social coordination’ among only those privileged and versed enough to occupy the upper/inner echelons (much like the Catholic church for example). Think of the notion of ‘latent vs. manifest’ function from sociology. The manifest function here would be to get a grip on what reality is and does and to have that adequately communicated amongst ones interlocutors. The latent function is to reap the residual (perlocutionary, J.L. Austin) social benefits- to get along with this philosopher (camp), make each other feel good, solidarity, trust, inclusion, etc.; or the opposite -to antagonise, show defiance, annoy, exclusion, etc., tenure, grants, publishing notoriety and so on.
This ‘social’ phenomenon is rather ubiquitous. We’re all guilty of using a pretence to (or assumption of) reality tracking as a way (mode) of subserving social interaction on a quotidian basis: conversations involving putative topics, news, anecdotes, fables, hot and cold gossip, rumour/hearsay, jokes/comedy, conspiracy, propaganda, errant or extreme values, myths, superstition, religion, mysticism, spirituality, misconception, bigotry, ignorance, white lies, sub cultural norms…, much of what counts as philosophy, etc. It’s a group based (pragmatic) strategy that gets you access to all the latent goodies that come with being socially hooked up with people who are supposedly ‘on the same page’ and separated from those that aren’t.
“…, a merely random groping, and, what is worst of all, a groping among mere concepts.”- Immanuel Kant, (Critique of Pure reason).