One idea: that A Strange Commonplace is essentially a form of picaresque novel –that it is nothing other than an interesting collection of unrelated vignettes– and the “repetitions” serve the same purpose as the hero/ protagonist of the typical picaresque novel, that of tying the various adventures together. In other words, the repetitions serve a structural purpose, and are what make A Strange Commonplace plausible as a single book. (Which may be close to the same as saying — the repetitions are Macguffins.)
Another idea: is that while, as in the forgoing, A Strange Commonplace is essentially a picaresque novel –one unrelated tale followed by another and having “repetitions” instead of a central protagonist– the repetitions were not added after the fact, to provide the structure, but were rather used before the fact, in order to create the vignettes in the first place — as part of a method of composition.
[In this view, Sorrentino, instead of saying, “I’m going to add a borsalino hat to this story so as to suggest a tie-in with this other story with a borsalino,” has established before writing the story, as a formal or informal rule of its composition, that it is to include one or more of these repeated elements. So they are essentially writing prompts for him: objects like the homburg hat and the gabardine dress located Sorrentino among the field of things he is capable of writing of, and so became his staring point.]
In what sense a symbol: I don’t entirely discount the idea of the repetitions serving a more traditional symbolic function, but would argue, first, they are more “signs” which we come to identify with certain ideas (the Grey Homburg, for example, with some sort of male sexual misdeed) than symbols of bottomless significance or “meaning.” And, second, that some sort of accounting needs to be made for the fact that human characters don’t seem to enjoy a privileged existence over objects with respect to their symbolism: that is, if the “grey homburg” is a symbol of something, so is “Claire.” One is not more or less symbol than the other, one is not more or less character than the other.
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Elsewhere on this site: a Commonplace concordance.