Paradox: Figure that employs an apparent contradiction which, nonetheless, evokes some measure of truth; a statement which seems at one level to be nonsensical because it moves against a normalcy. At another level, however, the figure conjures a new way of seeing or understanding, a novel meaning.

Ex #1: "[Peacekeeping is] not a job for soldiers, but only soldiers can do it."

-- Dag Hammarskjöld

Ex #2: "Most important institutions are protected and empowered by esteem. To the cynic, a judge is an average woman in a robe; a general is a poser in a costume; a priest is a balding man with sweat staining his armpits. But however accurate these depictions, they are not true. Because of the institutions they serve, these people represent the rule of law, the triumph of duty, the presence of God."

-- Michael Gerson, 12 February 2018, Opinion Section, The Washington Post

Ex #3: "I don't hustle with people who are dishonest."

-- delivered by Woody Harrelson (from the movie White Men Can't Jump)

Ex #4: "Mexico is doing NOTHING to stop the Caravan which is now fully formed and heading to the United States. We stopped the last two -- many are still in Mexico but can’t get through our Wall, but it takes a lot of Border Agents if there is no Wall. Not easy!"

-- President Donald J. Trump, tweet on 1/19/19

(Which, of course, affirms President Trump's conclusion: "Not easy." Schrödinger, perhaps.)

Ex #5: "Purpose plays the long game -- easier to monetize than put a price on it." - M.E.

Further Examples

Michael Collins: They let us out of jail so we could do our best to be put inside again, Harry. Don't you see a certain paradox in that? Hmm?

Harry Boland: ....

Michael Collins: "Paradox -- a contradiction: where an immovable force meets an immovable object kind of thing.

Harry Boland: Zzzzzzz.

Michael Collins: Hey....

-- delivered by Liam Neeson and Aidan Quinn (from the movie Michael Collins)

-- Hubert Humphrey, 1964 Democratic National Convention Address

"Paradox has been defined as ‘Truth standing on her head to attract attention.’ But it must be admitted that writers, like other mendicants and mountebanks, frequently do try to attract attention. They set out conspicuously, in a single line in a play, or at the head or tail of a paragraph, remarks of this challenging kind; as when Mr. Bernard Shaw wrote: ‘The Golden Rule is that there is no Golden Rule’; or Oscar Wilde observed: ‘I can resist everything except temptation’; or as a duller scribe (not to be named with these and now doing penance for his earlier vices in the nobler toil of celebrating the virtues of Mr. Pond) said in defense of hobbies and amateurs and general duffers like himself: ‘If a thing is worth doing, it's worth doing badly.’  To these things do writers sink."

-- G.K. Chesterton, The Paradoxes of Mr. Pond (Audiobooksforfree.com)

Captain Ramsey: "I understand you two are contemplating a blitz-out. What sort of blitz were you contemplating?"

Captain Hilts: "Well, we sneak out at night to a spot I found near the wire -- a blind spot. Then we dig straight down three feet, take the dirt, spread it on top so it won't make a pile, and then straight out. Ives here is a tunnel man, so he digs in front, pushes the dirt behind him, and I stash it behind me. Then we just burrow right through the dirt like a couple of moles. Then, by dawn, we're under the wire, across the open space, into the woods -- and gone."

Squadron Leader Bartlett: "Hilts, how do you breathe?"

Captain Hilts: "Oh, we got a steel rod with hinges on it and we shove it up and make air holes as we go along."

Flight Lieutenant MacDonald: "Now, why didn't anybody think of that before? It's so stupid it's positively brilliant."

-- delivered principally by Steve McQueen, (from the movie The Great Escape)

"I am sending you out like sheep among wolves. Therefore, be as shrewd as snakes and as innocent as doves."

-- Mathew 10:16 (NIV)

"I think it can be said that he [John F. Kennedy] now stands with our other American martyrs in the cause of freedom and justice. His death is a terrible tragedy and sorrow -- first of all to his family, to our nation, and to our conscience. The criminal act that took his life brings shame to our country. An apostle of non-violence has been the victim of violence. The cause for which he marched and worked, I am sure, will find a new strength."

- Hubert H. Humphrey, Remarks on the Assassination of Martin Luther King, Jr.

Josiah Bartlett: So is he [Congressman Matt Santos] gonna step aside? 

Leo McGarry: I think so.

Abbey Bartlett: For Baker or Russell?

Leo McGarry: He's hard to read.

C.J. Cregg: Sitting VP should've kicked ass in the primaries. Vinick's gonna mop up the floor with Russell in November.

Josiah Bartlett: VPs are famous but unknown. He'll do better once he's outside my shadow.

- delivered by Martin Sheen, John Spencer, Stockard Channing, and Allison Janney (from the TV series The West Wing, Season 5, Ep. 22.

"The next time I have a daughter, I hope it's a boy."

-- delivered by Paul Lynde (from the movie Bye Bye Birdie)

George Herbert Walker Bush was America's last great Soldier-Statesman -- a 20th-Century Founding Father.

-- Jon Meacham, Memorial Remarks for President George H.W. Bush

  "We cannot stop the virus but working together we can slow it in its tracks and push it back. We all need to take steps to reduce close human contact. That's how the virus is spread -- not just at public gatherings or in public places but also in our own homes, places of leisure, and places of work. Large public gatherings are cancelled. All pubs and bars are shut. And we've asked people to curtail or cancel social gatherings like parties, weddings and other celebrations. In short, we're asking people to come together as a nation by staying apart from each other."

-- Taoiseach Leo Varadkar, St. Patrick's Day Address on the COVID-19 Pandemic

Note: Notable use of paradox in its delicate balance between measured directness and starkly offered compassion. Even so, the line could be polished by adding "as individuals" at the end for stylistic balance without any loss of rhetorical force. To wit: "In short, we're asking people to come together as a nation by staying apart from each other as individuals" Alternatively, "from each other" could simply be replaced by "as individuals."

Pippin: "If we go south, we can slip past Saruman unnoticed. The closer we are to danger, the farther we are from harm. It's the last thing he'll expect."

Treebeard: "Hmmmmm. That doesn't make sense to me. But then, you are very small. Perhaps you're right."

--  delivered by Billy Boyd and John Rhys-Davies (from the movie The Lord of the Rings: The Two Towers)

Sebastian: I get coffee five miles out of the way just so I can be near a jazz club.

Mia: Really?

Sebastian: Yeah, the Van Beek. Do you know it?

Mia: Uh-uh.

Sebastian: All the big swing bands used to play there -- Count Basie, Chick Webb. Anyway, it's a samba-tapas place now, so....

Mia: What's a "samba-tapas" place?

Sebastian: You know, it's like a Samba place where they serve tapas.

Mia: Oh.

Sebastian: Yeah, so the joke's on history? I don't know. That's L.A. They...worship everything and they value nothing.

-- delivered principally by Ryan Gosling (from the movie La La Land)

Note: Back story to the money quote.