The song starts with a lover-- he calls the woman he is addressing "my darling" and "my baby"-- promising his beloved wealth, or at least security, and a plan for heading out for the big city. He ends with what might be a proposal, if they are not already engaged.
The three songs that leap to mind (mine, anyway) are "Fast Car," by Tracy Chapman, which includes such wishes and hopes, "Atlantic City" by Springsteen, in which a man is willing to even commit crimes if it would mean some upward mobility for himself and his girl... and "Bicycle Built for Two," which is not a promise of "stick with me baby, 'cause I'm goin' places" but quite the opposite: "It won't be a stylish marriage/ I can't afford a carriage/ But you'll look sweet upon the seat/ of a bicycle built for two!" (spoiler alert: Daisy declines this proposal).
That verse of "Proof" sounded like a young man talking to his intended. The next fast-forwards to the senior years, and a more realistic outlook. The "tools of love" (i.e., the specifically male and female anatomical features) cease to function as reliably (and, as drug companies have discovered, "that is worth some money"). The mind loses its acuity, the eyes need "reading glasses," and even one's "smile" has lost some of its vibrancy.
The speaker responds to this discrepancy between the wild promises of the young and the resignations of the old by demanding "proof." Other examples of those from whom whom should require some collateral include those who "call you up/ Tell you something that you already know," which recalls the complaint about consultants who "borrow your watch to tell you the time," and people who back out of deals at the last second with no reprecussions to them.
Meanwhile, "faith" is no longer something accepted by most people-- it's an unconnected "island"; it belongs to the past, and the sun is setting on its relevancy.
In the next verse, the speaker elaborates on which demographic elements still "matter," with regard to the proof of someone's merit. While "race" used to be very significant, he posits, it no longer is. Now, gender is still significant, as is wealth-- although those two have opened (or shut) "doors" for all time.
The last verse seems to be an argument against all that, however. The lover from the first verse picks back up-- again addressing his "darling... baby"-- but trades his puffed-out-chest promises of materialistic success (talk of "silver") for a more poetic (and alliterative), nature-oriented philosophy:
Even though it is "hiding," at least half of the Moon is visible, he tells her. The sky bodes omens of "hope"; these "flecks" might be stars, long considered symbols of potential ("reach for the stars," "hitch your wagon to a star," etc.) Even if you can't fly in the "rain," you can still raise your wings to protect yourself "against" it. And if your head is sprouting a "tangled" thicket of self-doubt and imagined pains, try "washing" that anxiety away by thinking like a "gambler" and just trying your luck-- you can't win if you don't play.
In other words, have faith, but in the right things. Should the woman listening to the speech in the first verse have married this man, who promises that "soon," everything will be "silver"? No, she should ask after his bank statement, his diploma, and his job prospects. You know, proof.
But the second speech doesn't promise perfection. In fact, it acknowledges that there are "clouds" and "rain"... that people can get "weary" and situations "tangled." But it also promises that they will weather the worst times and always hope and work for better ones, and that he will always approach life with this sense of possibility. This is a more attractive offer, one more like Springsteen's speaker in "Thunder Road," who says, "I know it's late/ But we can make it, if we run."
So "proof" is the bottom line. But what gets proven, sometimes, is that you should have some faith... sometimes.
While not a huge hit, the song did have a popular video, as it featured both Chevy Chase (also prominent in the simple but silly "Call me Al" video) and Steve Martin. (The video mostly takes place on a parade float, but pauses to parody the video for "U Can't Touch This" by M.C. Hammer.)
Next song: Further to Fly