This post continues from earlier reflections on indexicals, but in a slightly different way. I want to offer a very strange theory of indexicals like "I", "now" and "this". They are not words at all. They are affixes, like the "-ing" in "walking" and the "in-" in "indoor". An affix is added to a root, and thereby yields a word. The affix indicates how the sentence makes use of the concept indicated by the root. In highly inflected languages, affixes may play a significant role in indicating whether a given noun is, say, the subject, direct object, indirect object, etc. of the sentence.
We might more accurately think of affixes as functions from partial words to words, remembering that adding an affix may force changes in the "root" part. Moreover, in my sense, an affix might not actually be contiguous with a word. Thus, in Polish the personal endings of past-tense verbs are sometimes allowed to float free of the verb and attach to something else. Thus, one can say: "My w domu bylismy" (="We at home were"), where "bylismy" is "byli" (=past tense of "to be" with a plural "-i" suffix) plus "-smy", the first personal plural ending for past-tense verbs, but one can also move the "-smy" to be after the "My" (="We"): "Mysmy w domu byli." One way—maybe not the way most Slavic grammarians will do it—to read this is as a sentence whose words are "My" (="We"), "-smy ... byli" (="were"), "w" (="at") and "domu" (="home"). The "-smy ... byli" is a scattered word there, written non-contiguously.
"I", "now" and "this" are such non-contiguous affixes. But where is the partial word to which the affix is attached? In ordinary-speech cases of "I" and "now", the answer is easy. With "I", the root is the speaker, and with "now", the root is the time of speech. In other words, when I say "I am now at home", the first word in the sentence is a scattered word consisting of two parts: me (the six-foot-tall guy having a body and a soul) and "I". The third word is a scattered word consisting of two parts: the actual time of speech (whatever the ontology there is—I do not think we need to insist on words or parts of words being something we take ontologically seriously, so we probably don't need to worry whether there are times) and "now". "This" is harder. My inclination is to take it as an affix attached to an activity of pointing at something, perhaps including just the pointing gesture (mental or physical, perhaps contextual), but perhaps including that which is pointed at. I don't have a very good analysis of that.
Fictional speech is puzzling for this view. When the narrator uses "I", if that is the affix, where is the root? I don't know what to say. But fictional speech is anyway problematic. Perhaps I can say that a "sentence" said by a fictional narrator is not really a sentence but a fictitious sentence, just as a "murder" committed by a fictional narrator is not really a murder but a fictitious murder.
And what about cases of "I" and "now" that do not really refer? For instance, you tell me: "The other day, George told me: 'I am not at home.'" But George is your imaginary friend. Whom does the "I" refer to? Well, there is no "I" in your sentence. There is only an "'I'". What is between quotation marks is not a sentence, and not even a candidate for a sentence, because it is incomplete, in the way "George Bush was -ing down the street" is.
This is a really revisionary view of language. Does it have any advantages? I think it does. For one, it makes indexicals not stand out as some disparate category. They are just affixes to a root that is often Lagadonian. Moreover, I think this is the sort of view at which one may end up if one has a general enough view of the possibilities for language—dropping any insistence on a linear structure, for instance, allowing Lagadonian languages, etc.[Edited to fix typo and remove an embarrassing slip.]