Laypersons and even many philosophers say that much of what's discussed and stated in analytic metaphysics is ridiculous and/or trivial. That may be true. Though we must have a wider and more historical vision here because isn't it also the case that this sort of thing has been said about many historical philosophical positions – both by laypersons and by philosophers?
Take the common reaction to Bishop Berkeley's "empirical idealism" (e.g., when Dr Johnson kicked the stone). Or the dismay at the seeming truism of Descartes' Cogito. And you don't even need to mention Martin Heidegger's “the nothing nots” (as translated by Rudolf Carnap) to elicit such responses. So, at least to the layperson, is analytic metaphysics really that different to what's gone before?
Perhaps we should also say that some old philosophical positions are now so well-known that it's therefore hardly surprising that many laypersons are no longer shocked or disgusted by them.
On the other hand, philosophical disgust at metaphysics goes back to Kant or further. As Craig Callender puts it:
“Kant famously attacked metaphysics as an assortment of empty sophistical tricks, a kind of perversion of the understanding.”
“Most of the controversies in traditional metaphysics appeared to me sterile and useless. When I compared this kind of argumentation with investigations and discussions in empirical science or [logic], I was often struck by the vagueness of the concepts used and by the inconclusive nature of the arguments."
Then again, so too did the just-mentioned Martin Heidegger – in his What is Metaphysics?  - at roughly the same time as Carnap. Not only that: Carnap spoke out against Heidegger's metaphysics – in his The Elimination of Metaphysics Through Logical Analysis of Language  - when Heidegger was himself speaking out against what he classed as “Western metaphysics”. Thus being against metaphysics – at least in the 1920s, 1930s, 1940s, and 1950s - became both a sport and a philosophical fashion.
As stated, many positions within analytic metaphysics (sometimes within the entire genus of metaphysics) are deemed by both laypersons and philosophers to be trivial, scholastic and/or oblivious to science.
This, for example, is Craig Callender (in his 'Philosophy of Science and Metaphysics') taking the piss out of analytic metaphysics:
“... when I bend my fingers into a first, have I thereby brought a new object into the world, a fist?”
Despite that, at least according to Callender, such views are nonetheless deemed to be “deep, interesting, and about the structure of mind-independent reality” by such metaphysicians.
Other philosophers have also had a go at analytic metaphysics.
David Chalmers, for example, thinks most of the disputes are primarily “verbal” in nature. Steven Yablo (who's written a lot on metaphysics – including about whether the Turin Shroud and the cloth it's made up of are two different objects) believes that there are no answers to many of the issues or disputes raised in analytic metaphysics. (See his 'Must Existence-Questions have Answers?'.)
When an analytic metaphysician (or indeed any metaphysician) says that metaphysics is concerned with problems which aren't (strictly speaking) scientific (as well as when he says that metaphysics uses analytical, philosophical and logical methods which aren't those of science), then some philosophers may give the obvious reply:
The problems, concepts and tools of metaphysics shouldn't be distinct from science – even if they aren't identical.
Though if you were to take this position too far, then metaphysics will simply become physics/science. Either that or, at the least, it will become a (subsidiary) part of science/physics.
The problem is that no only may such anti-metaphysical philosophers throw out all metaphysics with these demands (i.e., if you follow their logic to its conclusion), it may also be the case that much science will also be thrown out. (This point was famously made against certain positions advanced by the logical positivists in the 1920s and 1930s.)
For example, what about empirically-untestable string theory and multiverses? Are they examples of scientific “neo-Scholasticism”? What about some of the well-known mathematical and logical problems which can simply be seen as “intellectual puzzles” and nothing much more?
Again, the major criticism of analytic metaphysicians is that they more or less ignore science. In at least some cases, metaphysicians do so because they believe that metaphysics comes before physics. (Yes, despite the Greek translation of the word) Thus it doesn't make sense to consult science if science (or at least physics) comes after metaphysics. Nonetheless, Ted Sider (one of the best known analytic metaphysicians), for example, has a sophisticated view on metaphysics' relation to science. Put very simply, he doesn't believe that any metaphysician should ignore science. (However, at least at face value, that position may not amount to much.)
Indeed even when metaphysics does square with science (as 4-Dimensionalism, for example, is said to do), it may still be the case that this just adds to the cogency and value of the metaphysical theory or position. In other words, in terms of 4-D again, metaphysics could survive very well (thank you) without the help of Einstein's theories of relativity. In addition, positions on time in physics and cosmology are also deemed to be secondary to metaphysics by some analytic metaphysicians. It's even the case that such metaphysicians go further than that when they argue that physics and cosmology must be brought into line with metaphysics, not the other way around!
How can we respond to this Metaphysics First position?
It can be said that before the rise of modern science it was indeed philosophers who investigated “the fundamental structure and nature of physical reality” (as it's often put). However, after the rise of modern science, many philosophers now argue that metaphysicians shouldn't still be doing metaphysics without the help or findings of science.... at least not in 2017!
As a consequence of all that, such naturalistic philosophers are against what's often called “a priori metaphysics” or the search for “a priori truths”.
Prima facie, however, it's hard to believe that there's a 21st-century metaphysician who would claim to be engaged in an entirely a priori pursuit. (Though perhaps I'm wrong.) In fact I'm not even sure what the words “a priori metaphysics” (i.e., if taken literally) mean or whether it would be achievable even in principle.
Anyway, if such a priori metaphysics does exist, then the philosophers James Ladyman and Don Ross, for example, class it as “neo-Scholasticism”.
Thus I'll now concentrate on their position against analytic metaphysics.
Ladyman & Ross's Case Against Analytic Metaphysics
Sometimes Ladyman and Ross's (who are self-described “ontic structural realists”) main criticisms of analytic metaphysics seem a little rhetorical – at least as they stand. For example, in their book Everything Must Go: Metaphysics Naturalized, they argue/state:
i) That metaphysics "contributes nothing to human knowledge”.
ii) That metaphysicians are "wasting their talents”.
iii) That metaphysics “fails to qualify as part of the enlightened pursuit of objective truth, and should be discontinued”.
It's also the case that Ladyman and Ross are arguing that metaphysicians should be scientifically-literate holists who should attempt to show us “how everything fits together” (as Nelson Goodman once put it).
In other words, the “ontological structure” of the universe is the domain of physics and science generally. Metaphysics, on the other hand, should attempt to find a unified and “cross-disciplinary” philosophical synthesis of how the sciences tell us the universe/reality is structured. (Put that way, this is similar to Quine's position; though he didn't really emphasise cross-disciplinary unification as such.)
It's extremely ironic that in view of the counterintuitive positions advanced in analytic metaphysics that the enemies of such positions claim that metaphysicians rely too much on what they call “intuitions”.
I suppose that there may be a simple answer to that. Namely, intuitive positions – or intuitive beginnings (as it were) – can take one in very counterintuitive directions; just as the intuitively-true premises of logical arguments can take one to extremely counter-intuitive or even paradoxical conclusions.
In any case, it's notable how important the criticism of the analytic metaphysicians' reliance on intuitions is. It's also true that some philosophers have acknowledged - and then relied upon - intuitions; though many others haven't.
Having said all that, it's almost impossible not to begin one's philosophical pursuits without utilising one's intuitions to some extent - or even to a large extent. (All this, of course, entirely depends on the definition of the word 'intuition'.) And it may follow from this that if one's intuitions are acknowledged as a starting point, then that starting point is bound to have an affect on much of what follows (i.e., in terms of reasoning and actual philosophical conclusions).
On the other hand, it's also prima facie ironic that metaphysicians rely at all on intuitions. Isn't it far more likely that an epistemologist or a philosopher of mind (for reasons I hope are obvious) would (or even should) stress or rely on intuitions?
In any case, there are many arguments in favour of intuitions... and not all of them use intuitions to defend intuitions.
For example, you must start from somewhere. And the best - or even the only - place to start from in philosophy (as in most things) is from one's own intuitions. Indeed it's hard to even make sense of the idea of starting from anywhere else. And if you start from your own intuitions (I stress the word start), then it may be equally - or more - wise to take on board collective/social (as it were) intuitions too.
Bearing all that in mind, it's hardly a cardinal sin if metaphysicians begin their reasonings by using phrases such as "it is intuitive that" or "it is counter-intuitive that" when, presumably, such philosophers won't end their philosophical pursuits with such phrases (or, indeed, with a continued reliance on intuitions).
You can also defend the existence and utilisation of intuitions without using the phrase (which I noted in Ladyman and Ross) “the faculty of intuition”. That sounds like the kind of reification which Gilbert Ryle warned against (though he referred to intelligence, will, mental events, etc.) some seventy years ago. Indeed if people do believe in such a faculty, the it may well take on a role similar to that of Kant's a priori categories or even been seen as a module (or part) of the brain. In that case, just as philosophers could have asked Kant why he thought that the mind's concepts or categories were a-historical and universal; so a contemporary critic can ask why (some) metaphysicians think that our faculty of intuition is reliable and/or static from (say) an evolutionary/biological point of view.
However, our intuitions needn't be seen as a priori, a-historical or even as constituting a faculty as such.
It would be wise, then, to say that when contemporary metaphysicians appeal to intuitions, they don't (or, at least, they ought not to) refer to some magical ability which only they possess.
Others on Intuitions
If an “experimental” or “naturalist” philosopher says that intuitions aren't scientific data, then a metaphysician may simply say: “Yes, I know. And?”
On the one hand it may be understandable to argue against intuitions regarding, say, quantum mechanics, cosmology or the nature of DNA. On the other hand many mathematicians and scientists (ranging from Kurt Gödel and Alan Turing to Roger Penrose) have happily stressed the importance of intuitions in both mathematics and physics. (Though, admittedly, perhaps not in quite the same way these guilty metaphysicians do.)
In any case, what are now called “experimental philosophers” have a problem with (much) analytic metaphysics for this reason. As stated, they believe that they place too much emphasis on intuitions and their corresponding “thought experiments”. Of course speculation and even thoughts experiments are of vital importance in science too – especially in physics. However, experimental philosophers have something else in mind here. It's not that physical experiments are wrong: it's that thought experiments are wrong. In physics, speculations are eventually tested via experiment, observations, etc. This isn't the case when it comes to metaphysics. In analytic metaphysics, experiments or observations don't – or may not - make a blind bit of difference. Such metaphysical theories usually stand or fall regardless of experiments and even regardless of science taken more generally.
The other thing is that experimental philosophers are questioning the intuitions and thought experiments of analytic metaphysicians from a scientific or experimental point of view. That is, they use the empirical studies found in psychology and cognitive science to cast doubt on the efficacy or truth of human intuitions and philosophical thought experiments. Such empirical research on human subjects shows them that its very unwise to trust intuitions and what follows from them.
Of course metaphysicians and some philosophers aren't too keen on the views of these new kids on the block – the experimental philosophers (such as Jesse J. Prinz, etc.). Timothy Williamson (in his 'Philosphical intuitions and scepticism about judgement'), for example, believes that although intuitions can be taken as being very basic; they can also be - at least in some cases - the end result of previous high-level reasoning. This must mean that intuitions are actually the products of implicit/tacit prior knowledge. (They may also have value from an evolutionary point of view.) Even the imagination, according to Williamson, is a good guide to reality, at least if it's used correctly. (Of course Descartes said this about the mind and reason itself – i.e., if you use your mind and reason as God intended you to use them, then you can't go wrong.)
In the senses stated above, then, intuitions aren't really... well, intuitions at all. These judgements, positions or premises may simply have the phenomenological feel (as it were) of intuitions. However, this is also problematic in that it ties seemingly intuitive judgments, positions or even a priori premises to the subject's history and perhaps also to his/her sociological position within that history. Either way, we can ask whether intuitions come out well after all this contingency.
The metaphysical realism of (some/all?) analytic metaphysicians (though it's not necessary for an analytic metaphysician to be a metaphysical realist) has been challenged since the beginning of philosophy.
Take the position of John Locke.
John Locke believed that it may be permanently impossible for us to ascertain the true nature of the world or reality (i.e., his “something, I know not what”). In An Essay Concerning Human Understanding, Locke writes:
“…it is impossible for us to know, that this or that quality or Idea has a necessary connection with a real Essence, of which we have no Idea at all, whatever Species that supposed real Essence may be imagined to constitute.”
That's also partly why Bishop Berkeley turned towards empirical idealism; as well as away from scientific materialism and the scepticism it engendered. In his Three Dialogues between Hylas and Philonous, Berkeley wrote:
“.... the whole issue can be allowed to rest on a single question: is it possible to conceive of a sensible object existing independently of any perceiver? The challenge seems easy enough at first. All I have to do is think of something so remote—a tree in the middle of the forest, perhaps—that no one presently has it in mind. But if I conceive of this thing, then it is present in my mind as I think of it, so it is not truly independent of all perception.”
Then Kant brought noumena into the debate. The Kantian problem of noumena caused various later philosophers to embrace (Kantian) transcendental idealism once again – and so did many late 19th-century and early 20th century scientists (e.g., Mach, Helmholtz, Boltzmann, Hertz, early Einstein, etc.).
A semi-Kantian position is also offered – here in the 21st century - by Mauro Dorato. He writes (as quoted by Ladyman and Ross):
“.... the concept of unobservable entities that are involved in the structural relations always has some conventional element, and the reality of the entities is constituted by, or derived from, more and more relations in which they are involved.”
So why is this Kantian? Ladyman and Ross (again) write:
“... an epistemic structural realist may insist in a Kantian spirit... there being such objects is a necessary condition for our empirical knowledge of the world.”
This is a good description of the noumenal grounding of Kant's metaphysics and indeed his epistemology. You can sum it up with a simple Kantian question:
If there are no noumenal objects (which ground our representations, etc.), then what's it all about?
If we can now come up to date, Frank Jackson says that “we know next to nothing about the intrinsic nature of the world”. Indeed we “know only its causal cum relational nature”.
Scientific & Metaphysical Structuralism
One way out of this impasse (of noumena and the consequent embracing of idealism) is to become some kind of metaphysical or scientific structuralist. Thus Peter Unger, for example, argues that “our knowledge of the world is purely structural”. What's more, Peter Unger adds that
“things in themselves [i.e., noumena]... are idle wheels in metaphysics and the PPC imposes a moratorium on such purely speculative philosophical toys”.
However, there is indeed a major philosophical problem with this 21st century "anti-realism"; which may be highlighted by some metaphysical realists.
Even if our representations, models, "posited objects", etc. don't somehow “mirror” - or even represent - nature or reality (or if we didn't have the noumenal grounding in the first place), then surely we have precisely nothing. Or as Ladyman and Ross put it (almost quoting Kant word-for-word):
“...there being such objects is a necessary condition for our empirical knowledge of the world.”
So, again, we may not mirror nature or things; though we must capture something. Then again, how can we represent - let alone mirror - something as strange as Kantian noumena? How would that work?
This is when structuralists say:
Yes, we capture structure.
Yet that response won't quite work because metaphysical realists believe they're capturing (if not mirroring) determinate reality. Structuralists may not think that; though structure is real. That's why Ladyman and Ross, for example, appear to make what can be seen as the obvious conclusion when they write:
“.... we shall argue that in the light of contemporary physics... that talk of unknowable intrinsic natures and individuals is idle and has no justified place in metaphysics. This is the sense in which our view is eliminative...”
One can conclude that because we can't get at things and reality in their pristine metaphysically-realist state: then, if that's a necessary truth, we may as well say that “structure is all there is”. This ties in nicely with the structuralist position that Kantian noumena may as well also drop out of the picture. Or, as Wittgenstein put it in his Philosophical Investigations (though about something else), things or noumena are
“wheels which can be turned though nothing else moves with them is not part of the mechanism”.
To put the case very simply, there's an argument which one can adopt here:
i) There are things and a determinate reality, though we can never access them as they are “in themselves”.
ii) And if we can't access reality and things as they are in themselves, then why not drop the notion of a determinate reality completely from the philosophical picture?
It can be said that ii) follows from i); though it can't also be said (strictly speaking) to logically follow from i).