Jenkins has repeated asserted that, since there is ample historical evidence in the ancient Near East, one should expect to find similar quantities of evidence in the New World. Therefore, by analogy, we should expect ample evidence for the era of the Book of Mormon.
Alas, he is seriously misinformed.
For the ancient Near East we have literally hundreds of thousands of inscriptions and written texts. Contrast this with the New World, where there the inscriptions number in the hundreds, perhaps a couple thousand. Note there is probably several thousands times as much textual evidence from the ancient Near East as there is for the entire New World. And that, of course, ignores manuscript evidence such as the Bible, Jewish texts, Greek and Roman books, Egyptian papyri, etc.
When we look at the New World, we find perhaps several thousand written texts that survive from the Classic period (c. 200-1000 CE). Most are royal inscriptions and brief texts on royal ritual pottery. The vast majority date to the middle and Late Classic. There are no surviving books from this period. There are about a dozen codices from the Late Post-Classic period (1000-1600 CE).
But the Book of Mormon deals almost entirely with the Preclassic period (c 1800 BCE -200 CE). During that period there are perhaps a few dozen inscriptions. No books. The inscriptions are nearly all short, often marginally legible, fragmentary, and often can’t be read because of script and language issues.
I maintain that the only thing that could securely establish the historicity of Book of Mormon peoples would be written texts containing BOM personal names or place names. No other type of evidence would be conclusive. The problem is, there is insufficient data to undertake such a comparison. Furthermore, the personal and place names in Mesoamerican texts tend to be emblem glyphs (symbolic representations) rather than phonetic texts. Perhaps a half a dozen place names are known from Preclassic texts. The phonetic reading of almost all of these is unknown.
Jenkins asks about the question of falsifiability. I’ll set aside the problem that this is really a methodology issue for empirical experimental science, which doesn’t really work with non-empirical historical questions. But, the best test of “falsifiability” for the Book of Mormon would be the absence of BOM names in the corpus of Preclassic inscriptions. If we had, say, phonetic readings for several several thousand personal and place names in Preclassic Mesoamerica, and found no BOM names there, that would be problematic for the BOM. The problem is, there is no such data.
It is also faulty methodology to take Classic royal or place names, for which we have perhaps a couple hundred examples as a database for Preclassic times–again, many if not most cannot be read phonetically with certainty. First, place names change through time (e.g. Byzantium, Constantinople, Istanbul; Jerusalem, Aelia Capitolina, Quds), and second we would no more expect to find a Book of Mormon personal name in Classic Maya royal inscriptions than we should expect to find Augustine or Hannibal–the two most famous people of ancient Tunisia–in the corpus of Arabic-era royal inscriptions of Tunisia. (They’re not there.)
So, the problem is not that the Book of Mormon does not pass the test of finding personal or place names in Preclassic New World texts. The problem is that a meaningful test cannot be undertaken because there is not a sufficient database with which to compare Book of Mormon proper names.