Another way de Botton's claim...
Erections and lubrication simply cannot be effected by willpower and are therefore particularly true and honest indices of interest. In a world in which fake enthusiasms are rife, in which it is often hard to tell whether people really like us or whether they are being kind to us merely out of a sense of duty, the wet vagina and the stiff penis function as unambiguous agents of sincerity.
Source: Psychology Today
...isn't, um, "particularly true and honest," let alone an "unambiguous agent of sincerity" would be that based on 3rd, 2nd, and lately 1st-hand evidence, it can be the case that no erection doesn’t mean not aroused. For some men some of the time, and almost all men as we age, the darn things aren’t up when you really, reallly, really want them to be.
Also, not to put too fine a point on it but not that long ago something like 27% of all email spam was for variations on erectile "dysfunction" remedies! How can he still make such a ridiculous assertion!?!?!? How can he not have made that connection?!?!?
Also, as another commenter, Crista, at Emily Nagoski's blog pointed out, vaginal lubrication can persist well after arousal has gone. And, of course, like erectile inconstancy, for some women some of the time, and most women as they age, vaginal lubrication can also "fail" to arrive either before or after orgasms, let alone arousal.
All of which just goes to show it would be an insult to sheep to call this guy de Button a mutton head.
I mean, look. I'm sure that for a privileged, cis, straight, white, high-income, younger than middle age, educated, non-medication-using, possibly non-sex-abused-or-abusing man from a developed country de Botton was just trying to make a philosophical point about how nice it is that there can be some confidence of certainty when your partner's shows genuine (if also highly typically indicated) arousal for you, as opposed to some other forms of communication that can be confused with, say, rote observances -- for instance anniversary "remembered" in your Outlook calendar, flowers orderd by her secretary, vaseline on the teeth to keep you smiling for in-laws, Lake Woebegone assurances of "no, it's fine, fine, really it's fine."