Who Owns the Goat? (Who Stole from Whom? Part VIII)

The goat belonged to either Farmer White, Farmer Brown, or Farmer Black. Farmer White claimed that the goat was his. Farmer Brown claimed that the goat did belong to Farmer White. Farmer Black either claimed that the goat belonged to him, or he claimed that it belonged to Farmer Brown, but, unfortunately, the court records are confused on this point. At any rate, at least two of the claims were correct.
Who owns the goat?

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

If Farmer Brown owned the goat, then Farmer Brown would be lying, as would Farmer White, leaving only one more claim to be possibly true, so Farmer Brown does not own the goat. If Farmer Black owned the goat, then Farmer Brown and Farmer White are still both lying. Therefore Farmer White owns the goat.