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What manner of theories are there on the origin of Indo-European case-like prepositions (usually; they were originally postpositions, and a handful of languages still have postpositions)? They seem like a rather unusual breed of word, linguistically, in that they can seemingly act as both particles and adverbs as far back as PIE. This duality is especially evident in the fact that as particles they are free-standing words in all IE languages I know of, while in PIE and some modern IE languages (English being a counter-example) the adverbial forms are bound morphemes of the verb.

Thinking it over, I have two thoughts, though it's possible neither is correct (if the answer is known at all). First, they could have originally been free-standing verbs. This of course suggests that pre-PIE was a serial verb language, though I guess it's possible they could have been verbs of free-standing clauses (although that seems less probable).

The more complicated (and I think interesting) idea is they were originally bound derivational morphemes (possibly free-standing adverbs prior to fusion with the verb), and the object of the preposition was in fact the object of the verb itself. This implies that you could at one point only have up to two parameters of a verb, rather than the ability of modern languages to have many connected to a single verb by different prepositions or cases. As such something like "He brought it for her" would require something like "He brought it. [He] did-for her."

Of course this idea itself requires answering another question: how bound morphemes became free; usually free-standing words fuse to become bound morphemes, not the other way around. My example above sort of suggests how this might have happened: the deletion of an essentially semantically empty (and therefore redundant) verb such as "do", leaving the derivational morpheme standing on its own, and a resulting fusion of the two clauses into one.

Or I suppose a simpler possibility would be that the differentiation between adverb and particle occurred earlier than that, and at the time the adverb had not yet fused with the verb. Thus the free-standing adverb essentially split into two different words: the original adverb that subsequently fused with the verb to become a bound morpheme, and a particle that remained a distinct word.

Of course it's possible that that idea, while interesting, is entirely off base. Has this question been explored in more detail by other linguists?

Added 9/1: Actually, I can think of a third possibility just to throw out there. If we assume that pre-PIE was more hospitable to null anaphora than modern English, it's possible it had something like "prepositions" in Totonac. In Totonac, "prepositions" are actually bound morphemes of the verb (and there can be more than one such morpheme per verb), and the prepositional objects are themselves bare noun phrases. If the verb is intransitive, the (dipersonal) verb could agree with one of the prepositional objects based on a priority system, but otherwise prepositional objects were entirely unmarked and reference was left to the intuition. If such a system existed in pre-PIE it could have evolved into true particles by such morphemes coming to be bound to their objects rather than the verb, and evolved into adverbs by analysis of null anaphora as object-less.

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The only theory I know is that prepositions were originally adverbial in nature, and unbound. My professor of historical grammar of Greek suggested this. The idea is that it went something like this:

There was the house. Mother was already in. (Adverbial 'prepositions' aren't even always bound in English.)

Father came in through the front door.

Mother noticed the incoming noise, and now they are both in the hall.

The boundaries between regular adverb, adverb linked to a verb, particle, verbal prefix, and preposition are still fairly fluid in English. A few other suggestive features:

In many languages, there exist separable verbs, where the prefix is sometimes severed from the verb and relocated to a different position, without change in meaning. This occurs in Dutch, German, and Ancient Greek, for example.

Er soll aufstehen. — "He should stand up."

Steh auf! — "Stand up!"

In Ancient Greek, it is also possible to start a sentence with an adverbial preposition:

meta ton polemon — "after the war" (regular preposition governing the accusative).

Meta d' ho basileus eis oikon apêlthen. — "Afterwards, the kind went home." (Adverb used to introduce sentence.)

All this suggests that words like "in" and "after" once were (and still are, to a considerable degree) very flexible words. Their behaviour is still far more diverse than just as prepositions. Another interesting thing is prepositions that can take two (or more) different cases:

In horto ambulat. — "He walks in the garden." (garden is ablative)

In hortum vadit. — "He goes into the garden." (accusative)

Ich bin in der Kirche. — "I am in the church." (dative)

Ich gehe in die Kirche. — "I go into the church." (accusative)

Whenever the preposition in indicates a static being-in-a-place, it goes with the ablative (Latin) and dative (German), which are also the cases normally used for statically being in a place (as partially replacing the older locative inherited from Proto-Indo-European); that is, in Latin, you could under certain circumstances use the bare ablative without in to express the same. This also applies to the accusative, which is the normal case for a moving-towards, where English would stick -to on the preposition.

This suggests that the cases that are now commonly seen as determined by prepositions were probably already there when prepositions developed: it was perhaps once horto ambulat in, or something, where the ablative already suggested that one was walking within, not into the garden, and the preposition confirmed that, so to speak (the ablative can also be used to express "out of" without a preposition, and it is also the only possible case to be used with ex, "out").

If my English were poor and I said he came building out, you would immediately understand that I meant that he was coming out of a building; this shows that a preposition doesn't depend on its position in front of its noun as much as one might think.

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One thing to add on your examples is that the PIE locative case merged with the ablative in Latin, and dative in Germanic languages. Most of your examples of non-accusative objects are locative terms, which is why they take ablative/genitive case. –  Justin Olbrantz Sep 1 '12 at 22:39
    
@JustinOlbrantz: Added reference to locative. –  Cerberus Sep 3 '12 at 1:03

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