Getting rid of the apple of logic is an important concept in "Teddy." In fact, getting rid of stuff in general, emptying out your body, seems to be part of Teddy's multi-step program on the path to enlightenment. Check it out:
He [Teddy] sat forward abruptly, tilted his head to the right, and gave his right ear a light clap with his hand. "I still have some water in my ear from my swimming lesson yesterday," he said. He gave his ear another couple of claps, then sat back, putting his arms up on both armrests. […] He looked perfectly relaxed, even serene. (4.52)
He shifted in his seat and took out an eyesore of a handkerchief – a gray, wadded entity – and blew his nose. (4.81)
He's [Professor Peet is] teaching a lot of stuff right now that isn't very good for him […]. It stimulates him too much. It's time for him to take everything out of his head, instead of putting more stuff in. He could get rid of a lot of the apple in just this one life if he wanted to. (5.16)
Teddy not only condones emptying out for others – like Professor Peet – but he is also still in the process of emptying out his own body. When he gets rid of the water in his ear or blows his nose, it might be symbolic of the other, less tangible emptying out (i.e., getting rid of logic, material concerns, emotions, or intellectual interests) that Teddy is undergoing.
We should also keep in mind the image of the empty pool at the close of the story (yet another example of emptying out) as well as Teddy's fractured skull (the fatal injury is not mentioned in the ending itself, but is part of Teddy's prediction regarding his own death). Notice that he cracks his head open – the brain being, presumably, the source of all "logic and intellectual stuff" (4.99).
In his essay "A Reading of Salinger's 'Teddy'" in American Literature, scholar James Bryan makes the observation that, while "Teddy" is a story about emptying out, Salinger's "A Perfect Day for Bananafish" is concerned with just the opposite: the problems of filling yourself up. The protagonist of "Bananafish," Seymour Glass, uses the metaphor of the fantastical "bananafish" to explain the problems of stuffing oneself full of things like materialism. Seymour says:
"Well, they [the bananafish] swim into a hole where there's a lot of bananas. They're very ordinary-looking fish when they swim in. But once they get in, they behave like pigs. Why, I've known some bananafish to swim into a banana hole and eat as many as seventy-eight bananas. […] Naturally, after that they're so fat they can't get out of the hole again. Can't fit through the door."
Three facts make Bryan's connection between these two stories interesting and consequential. First, remember that "Bananafish" is the first tale in Salinger's Nine Stories collection, and "Teddy" is the last. The collection opens with the spiritual problem of gorging, and concludes with the spiritual solution of emptying oneself out.
Number two, note that both tales end in a death: Seymour's suicide in "Bananafish" and of course Teddy's death in our story. Seymour commits suicide – in one interpretation of the story anyway – in order to escape the disgusting gorging he describes in the passage above. Teddy's death, on the other hand, is the culmination of his emptying out. It's almost as though he has to empty himself out completely to get ready for the death that takes him closer to spiritual enlightenment.
Third, know that Salinger's fictional character Buddy Glass claims in another story ("Raise High the Roof Beam, Carpenters") to have written both "Bananafish" and "Teddy." He even hints that the character of Teddy is Seymour in disguise. If "Seymour" deals with the problem of gorging in "Bananafish" and escapes it with his death, then he successfully resolves that problem by emptying himself out in "Teddy" moving on to a better spiritual place. A small but intriguing bit of evidence is the fact that Seymour was quite a prolific poet, whereas Teddy believes poetry to be a distraction. It's as though this Seymour/Teddy character has advanced, and poetry is one of the things that got "emptied out" along the way from "Bananafish" to "Teddy."
(A brief note: we don't mean to imply that Teddy is literally the reincarnation of Seymour; there are several incongruities in the text that steer us away from this conclusion. Rather, Buddy presents a character with certain problems in "Bananafish" and explores the recovery from such problems in "Teddy.")