From Julian Hook:
Browsing some old Language Log posts recently, I came across "Prophylactic over-negation", 1/26/2012, featuring the phrase "It's not that I don't doubt…"
Something possessed me to hunt for other examples of the construction, which turned up a remarkable specimen in a piece about the personal life of Derek Jeter (Emily Shire, "Derek Jeter’s Lady-Killing Past Before Hannah Davis", 10/28/2015):
“It’s not that I don’t doubt that Jeter isn’t media-savvy.”
This sentence manages in ten and a half words to include one more negation than any of those in the LL post linked above. The context suggests that the intended meaning is something like “I concede that Jeter is media-savvy.” This might have been expressed using a common double-negative construction such as “I don’t doubt that Jeter is media-savvy” or “I don’t mean that Jeter isn’t media-savvy.” But here the writer couples “I don’t doubt” (2 negatives) with “isn’t” (3), and then ups the ante by negating the whole sentence via “It’s not that” (4). My suspicion is that it’s through nothing more than a stroke of luck that the negation parity seems somehow to come out correct in the end.
There are more like this one Out There:
[link] It's not that I don't doubt that certain key things weren't properly sterilized.
[link] Not that I don't doubt that advertising artists don't slip in naughty stuff…
[link] Not that I don't doubt that companies can't do altruistic, well-intentioned things;
[link] Not that I don't doubt that Prevost's reputation isn't warranted but I personally think the curved windows of the La Mirage are ghastly…
[link] not that I don't doubt that it couldn't happen.
I'll leave it to readers to determine whether all of these pass a logic parity check.
More important, I'm offering a prize (a year's free subscription to LLOG) for finding real-world examples with five or more negations in a dozen words, e.g. "Not that I don't doubt that his reputation isn't undeserved".
Some others that don't quite make it:
[link] I cannot deny that some of this negativity isn't deserved
[link] I won't deny that he isn't an undisputed documentary-maker
[link] I won't deny that the series isn't without its charms
[link] even the Spartans' head coach can't deny that Reid's style isn't necessarily bad
[link] Agree with me or not, you can't deny that it isn't a possibility he opts not to report after being drafted.
Anyhow, this one goes into the misnegations file, even if Julian's example comes out right in the end.