However, I don't think the people using Latin for these purposes really think that logical precision is an important reason to do so. The Vatican Latinist I briefly studied with, Reginald Foster, doesn't seem to think that way -- he regularly made fun of people who acted as if "Latin came down from heaven in a gold box".
You might say that the use of Latin has a benefit of precision for the Catholic Church because there are some familiar theological and ecclesiological terms available whose meaning should be clear and which can be matched up with similar vocabulary in older Christian texts. Still, these texts are not using some kind of formal logic, and they don't do a more careful job of avoiding ambiguities than lawyers drafting legislation or contracts in modern languages do.
then these texts must be really horrible to read and no less bug ridden than any reasonably sized code-base, except that any bug is swiftly explained away as a feature by the commanding authority. Whether bear arms or it fell like scales from his eyes, this stuff doesn't age well, which is pretty much the point.
To be fair, though: The later bit is from Greek; but why not tomatoes, huh?
You might say that the use of Latin has a benefit of precision for the Catholic Church because there are some familiar theological and ecclesiological terms available whose meaning should be clear and which can be matched up with similar vocabulary in older Christian texts. Still, these texts are not using some kind of formal logic, and they don't do a more careful job of avoiding ambiguities than lawyers drafting legislation or contracts in modern languages do.