Since I've read many analytic philosophers (if not analytic metaphysicians) criticising not only the notion of “intuitions” - but also the philosophical reliance on them, I find it hard to make sense of Ladyman and Ross's stress on such a thing.
Sure, some philosophers have noted and even relied on intuitions; though many haven't. Though, as I argue later, it's almost impossible not to begin one's philosophical pursuits without utilising one's intuitions. And, it may follow from that, that if one's intuitions are acknowledged as a starting point, that starting point is bound to have an affect on much of what follows.
Having said that, it's indeed ironic, at least prima facie, 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 stress or even rely on intuitions?
A Case for Intuitions
There are many arguments in favour of intuitions... and not all of them use 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 (as it were) intuitions as well.
Bearing all that in mind, it's hardly a cardinal sin when metaphysicians begin by using phrases such as "it is intuitive that..." or "it is counter-intuitive that..." (the examples given by Ladyman and Ross) when, presumably, such people won't end their philosophical pursuits with such phrases.
So when Ladyman and Ross say that intuitions aren't scientific data, the metaphysician may simply say: “Yes, I know. And?”
On the one hand, it may be understandable to argue against intuitions regarding, say, quantum mechanics or the nature of DNA. However, many mathematicians and scientists (ranging from Kurt Godel 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 the guilty metaphysicians do.)
You can also defend the existence and utilisation of intuitions without using the phrase (which I noted in Ladyman and Ross's paper and elsewhere) “the faculty of intuition”. That sounds like the kind of reification that Gilbert Ryle warned against some seventy years ago. Indeed if people do believe in such a faculty, it will take on a role similar to that of Kant's a priori 'categories' or even the amygdala. 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 or biological point of view.
Though, again, our intuitions need not be seen as a priori, a-historical or even as constituting a faculty as such.
It would be wise to say, then, 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. Rather, they're simply using semi-rhetorical language; of which there are many other examples in analytic philosophy (such as "surely...", "it is obvious that...").