We know the sound of two hands clapping. But what is the sound of one hand clapping? – A Zen Kōan
This is the epigraph to Nine Stories, the 1953 collection that concludes with "Teddy." Together, these nine stories explore themes of innocence, youth, the psychological effects of war, and Eastern philosophies. In "Teddy," Eastern philosophies are discussed more explicitly than in any of the other eight stories.
A kōan is a short riddle of sorts that Zen masters give to Zen students. The idea is to meditate on the riddle and come up with a sort of answer. But the answer to the riddle isn't logical. If we ask you, "What is the square root of 435?", you can solve that question using the usual parts of your brain that are involved in mathematical calculations (or a handy calculator). The point is that there is a logical answer here. But kōans don't work that way. What is the sound of one hand clapping? If you meditate on this long enough, claim the Zen Buddhists, you will come up with an answer. But it's not a logical answer that you could explain to someone else. In other words, you can't look up the answer to this one. You have to intuit the answer on your own.
This is right on course with what Teddy discusses with Nicholson for much of "Teddy." He explains that we are so distracted and filled up with the trivial things we learn in school – like math and science and grammar and logic – that we don't open ourselves up to real spiritual truths. To get at those, you have to "empty yourself" of all the logical truths. Similarly, in Salinger's novel Franny and Zooey, college student Franny Glass complains that in school, all they learn is useless knowledge. Their goal is to amass as much of it as quickly as possible, which she finds no more noble than trying to amass wealth or fame or any material good. Knowledge is pointless, she says, unless it ultimately leads to wisdom.
So what we have is differentiation between logical or intellectual knowledge on the one hand, and spiritual truth on the other. Teddy is interested in the latter. The "answer" to this kōan belongs to the latter. Possibly, Salinger is advising us that the "answers" to his stories belong to the realm of spiritual truth as well, rather than to an intellectual domain.
Many of Salinger's nine stories – "Teddy" included – are confusing or ambiguous. In "Teddy," we wonder what to make of the death at the end of the story. In the collection's opening tale, "A Perfect Day for Bananafish," we are left wondering at the reasons behind a baffling suicide. If Salinger intends his stories in the kōan tradition, however, it means that we are not meant to "figure out" his works logically. We don't have to understand "Teddy," or the other stories in an intellectual way; instead, we're meant to understand them emotionally or spiritually.
One last note: Salinger definitely takes this idea seriously, but not so seriously that he can't have a little fun with it. In "A Reading of Salinger's 'Teddy'," scholar James Bryan points out this passage in the middle of the text:
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. (4.52)
This might very well be Salinger's "intellectual" answer to the kōan he places at the start of Nine Stories. One interpretation is that the author is playing around a bit, and having some fun at the expense of a serious Zen riddle. Another way to look at it is that Salinger maintains his gravity – he's just trying to show us how silly and useless it is to approach a kōan logically. Perhaps he's warning us: if you interpret "Teddy" logically or analytically, you're just clapping your own ear and pretending it's the answer to a difficult and ancient riddle.