Appiah is sketching the world of experimental philosophy. As T notes, this discussion of a move from the armchair to the social-science interview and the hard-science lab parallels what's happened in linguistics: From an early generative world of introspective judgments about sentence structures, a lot of linguists have taken to using fMRI evidence and lots of other neuro- stuff, plenty of classic psych-type perceptual experiments and so on. T may be thinking specifically of the old divide between theoretical phonologists, once derided openly by lab folks as 'armchair linguists', and experimental phoneticians, once derided by phonologists as people 'who measure the bejesus out of everything with no interest in what it means.' The very name of the LabPhon movement — that's Laboratory Phonology, started back in the 1980s — highlights the effort to bridge precisely that divide. And it's been a tremendously productive ride, I'd say. (See here for one view of what's going on and what's at stake.)
Appiah uses the notion of the armchair, traditional symbol of the philosopher, to good effect. He concludes:
There always comes a point where the clipboards and questionnaires and M.R.I. scans have to be put aside. To sort things out, it seems, another powerful instrument is needed. Let’s see — there’s one in the corner, over there. The springs are sagging a bit, and the cushions are worn, but never mind. That armchair will do nicely.Well, kinda. But we've got the problem illustrated just below, in a sense, and he's already made the right basic point earlier in his article:
[A]lthough experiments can illuminate philosophical arguments, they don’t settle them.Isn't that the usual relationship between argumentation and experiments? Experiments are ways of providing data to test hypotheses we've come up with. Appiah is utterly right that experimental results have to be interpreted. But as I read his conclusion, he's saying that armchair work does settle philosophical arguments. I beg to differ: Those interpretations inevitably lead to sharper hypotheses and new rounds of experimentation. A lot of linguists are working on balancing these things today, including bridging that old phonetics/phonology gap.
And yeah, the cart-before-the-horse metaphor definitely breaks down – it's a cycle of interactions, of course.
Image from Punch, taken from here.