I've been trying to construct sentences using only Semantic Primes (i.e., from the Natural Semantic Metalanguage). However, I'm having a difficult time figuring out how to do so without "to" and "from". For example, how might a language say something like, "I move from this place to this place" without using using "to" and "from" and without changing the fundamental meaning of the sentence?
American Sign Language doesn't use "to" and "from". Instead, you would sign something along the lines of "PAST, I live Orlando. LAST-YEAR, I move Seattle." The word for "move" is directional, meaning that you would move your hands in the direction from Orlando to Seattle - or, northwest. So you might argue that "move" is more literally "move-to", but there still is no specific word for "to" in ASL.
What you are asking is a normal phenomenon in languages with noun cases.
So basically, in these languages your example sentence would be formed,
I move A-
The Ablative is much more widespread among the Indo-European languages, probably because it was one of the noun cases found in Sanskrit.
Note, however, that some languages still use particles along with certain noun cases, so it may not be a clear "without "to" and "from".
More than that! Some languages differ the movement toward an object (Lative) from movement into an object (Illative) or movement onto/under an object (Sublative),
and also a similar distinction with movement away from (Ablative) and movement from inside an object (Elative).