Persuaded But Not Convinced?

Here’s one reason—as if people who’ve read my writings needed any more proof—that I’ll never be literary. In his interesting web article , Gerald Rusello quotes Jacques Barzun as saying, “the historian can only show, not prove; persuade, not convince.” I know other people get a lot out of a sentence like that; that, presumably, is why Russello quoted it. But when I read the sentence, I started wondering under what circumstances I might ever say, “Well, he showed it to me, but he didn’t prove it; I was persuaded, but not convinced.” Unsure when I—or indeed anyone—would ever say something like that, I’m left completely at sea.