Spoilers
When the computer is giving Logan his secret assignment it tells him there are 1056 unaccounted for runners. Next Logan says maybe some were renewed. Computer says no, then he says "so no one has ever been renewed?" How did he jump to that conclusion just from 1056 unaccounted for?
so, here is a stretch of a made up guess on my part... just filling in some POSSIBLE blanks here.
No movie ever explains absolutely everything, so you gotta be on board with just going for it sometimes.
As a DS MAN (Sandman), we might assume he has access to population data: people expired, "renewed", births, population... since they OFF all the runners they find, and most are "blown up into a renewed life", maybe he thinks the amount of people off grid was way to high. Maybe only like 3 that he knew of escaped, if any. So, 1056 seems like a really high number to him.
Next, the computer infers no one renews via surley tone "THE QUESTION HAS BEEN ANSWERED, LOGAN 5" (which, of course, is another plot hole: a computer with a "Tone" avoiding the question) so he sort of figures out that no one really renews when they blow up.
I think it flows okay. Probably not the tightest script from the 70's. I've watched worse. :)
EDIT: Just watched the scene on Youtube and it reminded me that I feel the number accounted was exposing a flaw in the computer's program counting population. >>Maybe<< the number was close to a number Logan had seen about people he went in for "Renewal", and that struck him to ask the question.
In any case, tis just another example of suspension of disbelief, how the story was told, we might not know exactly how his mind jumps to that - only that it does, and we are merely alonog for the ride.
Logan assumes anyone that ran did not escape as there is nothing outside and some must have reached renewal. His conclusion, maybe they weren't all runners and the calculation is a mistake, etc. The city computer's cold behavior was an effective way in conforming his (and ours) worst fears, quickly. It never came across to me Logan's dialogue jumped the gun. Maybe watch it again.
Earlier on the way to Carousel, Logan openly begins to question the way of things with Francis. A clear enough indication that Logan is 'wondering' somewhat and too much for a Sandman.
Expanding on the Scene
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Religious/Biblical:
The Birth (creation) of Adam to birth of Noah = 1056 years.
Fall of mankind to birth of Noah = 1056 years.
The domed city is an automated ark, similar to Noah's Ark from the Bible.
During the conversation before RETROGRAM, Logan states he is only Red 6. 1056 (10+56 = 66). The Number of the Beast is 666. The lifeclock/age crystal is possibly being likened to the Mark of the Beast.
PROCEDURE 033-03 (= 30 yrs. old): Jesus Christ lived for 33 years or 12060 days until Crucifixion in the year 33 A.D. on April the 3rd, Julian date. Carousel is possibly being likened to the Crucifixion.
Deleted Material:
A later deleted scene shows the last frozen runner labelled 1056. The robot Box intercepted and froze all unaccounted for runners. No one ever made it outside, nor to Sanctuary and Logan is aware of this fact.
Sanctuary:
https://en.wikipedia.org/wiki/Sanctuary
Ankh:
https://en.wikipedia.org/wiki/Ankh
70s Culture:
Sanctuary was the first notoriously gay disco in America (1969-72). It began as an underground secret-club and it epitomized the post-Stonewall era. A time when gays had won the right to dance intimately together without worrying about brutal police raids, putting an end to dancing in the dark. A scene of the film Klute (1971) was shot there. Location: 407 West 43rd St. & 9th Av, Manhattan, NY and former German Baptist Church.
In 1969, Jacqueline Susann began to popularize the Egyptian Ankh as a eternal life/love/sex symbol in the mainstream. And by using her novel The Love Machine, plus the trend-setting promotion surrounding it. For a while, people started wearing them around their necks and including Jessica 6. Virginia Ann Ford which appeared in a Logan's Run deleted scene (Beautiful Woman on Last Day), also was an uncredited extra in The Love Machine (1971) film.
Earlier in the movie Logan and Francis are talking about babies being born. They are all taught that when one dies another is born so the population is fixed. Francis says there will be two new sandmen babies because there are 2 sandmen in carousel tonight. Francis says that Sandmen always renew but Logan questions this saying, "How do you know?" Then Logan says "At least I wonder about it sometimes" Francis even says Logan wonders too much for a sandman and that he's too curious. Logan thinks his child will be a sandman but he isn't in carousel. Later in the movie he talks about "trying for renewal" like it's a gamble, not guaranteed. Seems like he just put the pieces together. He never saw or heard of a renewal. Runners and Jessica seem to say there is no renewal. If renewal were real, some percentage of the 1056 would be renewed but zero means no renewal. Logan says "But everyone believes that some..." but the computer insists zero.