score:6
How to give useful directions
If someone unfamiliar with the Dallas-Fort Worth area asked the location of AT&T stadium (home of the Dallas Cowboys), the most informative answer would be in Dallas, Texas.
However, to an audience well-acquainted with the area, this answer would be inadequate. Everybody there knows AT&T stadium is not within the city limits of Dallas, but in nearby Arlington.
Alma’s referenced statement was made in approx. 83 BC (see Alma 4:11), among a group of people whose ancestors had left the Jerusalem area more than 500 years previously. They had never been there, nor had they ever met anyone who had been there. “Jerusalem”, the capital city of the land of their ancestors, is a name they would be familiar with. Both the name “Bethlehem”, and its physical proximity to Jerusalem, would be details lesser known to Alma and his audience, thousands of miles removed from the Middle East.
How many of us know the little towns and hamlets of the communities where our ancestors lived 500+ years ago?
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Objections
But wouldn’t the Nephites have known the name Bethlehem from their scriptures (which included the brass plates)?
The well-read among them may well have been familiar with the name, but that doesn’t mean they knew where it was or much about it. Your scriptures mention the river Pison (or Pishon)--do you know where it is located? Are you sure?
But Bethlehem is where the great King David was from! How could you not know about that city??
Do you know where Charlemagne was born?
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”At Jerusalem which is the land of our forefathers”
The verse does not say that Jesus will be born in Jerusalem. The phrase "which is the land of our forefathers” modifies “Jerusalem”, that is, “Jerusalem” was a useful shorthand for “the land of our forefathers”.
Indeed, since the Nephite knowledge of the Holy Land was based upon written records already centuries old, terms such as "Judea", or "Palestine" would be unknown to them. How would such a person refer to the region in general? Not as Israel--which they knew had been broken up. They could call it Judah...but they knew that Judah had fallen too (see 2 Nephi 1:4). It is indeed a real dilemma for historians even in the present day--what is a non-anachronistic neutral term for this region? The land of Jerusalem is a pragmatic choice. Even though the political name of the region changed many times over the centuries, the name Jerusalem remained reasonably consistent.
To someone far removed in time and space from the Middle East with no chance of booking a flight there, as Alma was, "Jerusalem" was a practical way to refer to the general area where his ancestors had lived.
For those interested in the relevant textual criticism for this verse, see here.
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Inverting the argument
Joseph Smith knew the name Bethlehem–this is where his critics try to have it both ways:
The double standard here is clear–Joseph’s account got intricate minor details of the geography of the Arabian peninsula right (see Book of Mormon Authorship: New Light on Ancient Origins pp. 143-156), but got the city of the Savior’s birth wrong???
(And not only would Joseph Smith have made this error, but Oliver Cowdery would have missed this detail in preparing the printer’s manuscript as well. The problem is only compounded if Sidney Rigdon or other alleged co-conspirators are introduced)
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Conclusion
In an ironic twist, this verse serves as evidence for the authenticity of the Book of Mormon. It is quite straightforward why a 1st century BC American prophet would refer to Jerusalem to describe a general area neither he nor anyone in his contemporary civilization had visited…but it is wildly implausible that a devious 19th-century religious mastermind–who had heard the New Testament Christmas stories told all his life–would fail to recall that Jesus was born in Bethlehem.
Returning to the original example:
Post-script re comments
Would God allow the author of holy writ to use an estimate?
Apparently yes. The remarkable frequency in Israelite tabulation & censuses with which the totals are an even multiple of 100 or 1000 provide prima facie evidence for rounding.
1 Kings 7:23 appears to estimate pi at 3 (there are other interpretations but this is the most common one). One can easily demonstrate with pencil & paper that pi does not equal 3, but in a civilization that did not have a decimal point, the concept of .14159265358979... would be meaningless. So God spoke to people's understanding (see 2 Nephi 31:3 for the relevant theology) and considered a rounding to 3 adequate for His purposes.
Alma's people had access to less detail about the geography of the Holy Land than people today have about the geography of the moon. I have no difficulty at all believing God was more interested in teaching them about the Savior's mission than He was about giving them a course on geography they didn't need and wouldn't understand.