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According to this post, the active infinitive was formed as the locative of nouns based on verbal stems. Why was the locative used for the infinitive, rather than, say, the accusative?

The noun genos/genus "birth" had a locative like genesi/genere or similar, "in birth": I wonder what the semantic conexion and development was from there to an infinitive "being born".

The same applies to the dative ending -i turning a similar noun into a passive infinitive, although it seems this reconstruction is somewhat less widely accepted. What does the dative case have to do with (infinite) passivity?

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The Latin infinitive parallels Sanskrit and Ancient Greek, sec. Allen and Greenough. It appears that in Proto-Indo-European there was a "dative of purpose or consequence" idiom. The infinitive dative constructions competed with other datives. In Homeric times, the infinitive was not fully-fledged because it was not yet possible to add nouns and create a subordinate clause.

Only later, as seen in Latin, does the infinitive detach from the case system. Bortone 2002 pictures a grammaticalization of a previously purely concretely spatial system. Bortone also says the locative was an "old locative." Likewise for the dative. So the ending was already different in form and meaning. Being fossilized, it could not be updated to or needed to be dissimilated from accusatives of purpose like "ad proficiscendum."

genere is better connected to "multiply your pains in childbirth" and the uncommon "is birthing." "in birth" is active so it cannot develop into the passive "being born." But more natural is a rephrasing of the present progressive like "She is birthing" to a similar locative in English like "She is in the process of birthing."

Similar idioms exist in modern English. The locative case indicates an action's location, and the verb "go" forces that in "We will go shopping" = "We are planning to shop." The dative case is associated with the word "give," and that is seen in "I will not give myself up to temptation" = "I refuse to be tempted." To go to an extreme extent, also try replacing all instances of the English infinitive "to V [the N]" with "to go to a state of V-ness [of the N]" like "We need to bake the cake" with "We need to reach a state of bakedness of the cake," and the resulting sentence will sound weird but perfectly understandable.

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