This post is my attempt to make Beckwith's argument more straightforward, and thus to see whether it has merit. I wont be able to offer much evaluation here; that would make the post even longer than it is. But I don't think I hide what I think about the idea.
Most of the main argumentation appears in Beckwith's ch.4, "The Structure of the Canon," pp. 110-66, with notes on pp. 166-80. It goes more-or-less like this:
1. The tripartite canon (Law, 5 books; Prophets, 8 books; Writings, 11 books = 24 books) was established by the second century BCE (pp. 111-18). Evidence:
(a) Sirach prologue (pp. 110-11), which mentions three times "Law, Prophets, Other Books," or some similar formula.
(b) Luke 24:44 (pp. 111-15), which mentions "Law, Prophets, Psalms." Beckwith spends some time arguing that "Psalms" = Writings, that is, that "Psalms" in Luke 24:44 refers not just to the Psalter but to the 11 books of the Writings as a unit. His argument for this is necessarily based on the idea that when Luke 24:44 refers to the "Prophets", it must mean the 8 books of the Prophets according to the current divisions of the Hebrew Bible. He does not even question this (on which, see Barton), and the same goes for his treatment of Sirach's prologue. His argument that "Psalms" can mean "Writings" goes as follows: (1) it would be odd for Jesus to omit the books of the Writings from his canon in Luke 24:44 since he quotes from Daniel and the like so frequently; (2) the prologue to Sirach does not have a set title for the third section of the canon; (3) Philo uses hymnoi as the title for some books beside the Law and Prophets, and this is probably also the third section of the canon; (4) the tenth-century Arabic writer al-Masudi spoke of the "Law, the Prophets, and the Psalms, which are the 24 books"; (5) some passages in rabbinic literature (t. Kelim 5.8; y. Meg. 2.3; Sepher Torah 2.3-4; Sop. 2.4) mention the "Fifths," which might mean the Psalter (divided into five books), which might stand for the entire collection of Writings.
(c) Matthew 23:35 // Luke 11:51 (p. 115), which implies, on Beckwith's interpretation, that Chronicles constituted the last book of the canon, which again might imply that the canon was tripartite.
(d) Philo, De vita contemplativa 25 (pp. 115-18), which mentions the Law, Prophets, and Hymnoi (and other books), and hymnoi means again the entire third section of the canon.
"It is thus a well-attested fact that, by the first century AD, the division of the canon into three groups of books was widespread in the Jewish world, and that it was familiar to Jesus" (p. 118).
2. The distribution of books between the Prophets and Writings was the same as in the modern Jewish canon and in the Talmudic baraita found in b. Baba Bathra 14b (pp. 118-27).
The sources discussed so far do not list the books in the different divisions of the canon, so for that we must rely on Josephus, Jerome, and the Talmudic baraita. Josephus (Against Apion 1.37-43) has a canon of 22 books, divided into 5 books of Law, 13 books of Prophecy, and 4 books of "hymns to God and precepts for the conduct of human life." On the other hand, Jerome (Prologus Galeatus) and the Talmud both distribute the books more-or-less the same (Jerome attests two ways of distributing books, both very similar to each other, one exactly equivalent to that in the Talmud). Beckwith favors Jerome & the Talmud over Josephus in terms of representing the earliest and best distribution because:
(a) Jesus (Matt. 23:35 // Lk. 11:51) implies that Chronicles concludes the canon, as it does in the Talmud, to which arrangement Jerome nearly attests, while Josephus is way off.
(b) The Sirach Prologue implies that late historical works (e.g., Daniel, Esther, Ezra-Nehemiah, Chronicles) are included in the third section of the canon, which is impossible in Josephus' arrangement. You'll have to read Beckwith's discussion for how he draws this inference from Sirach's prologue (p. 123).
(c) Josephus' arrangement can be explained as a modification of the Talmudic arrangement, but not vice versa.
3. Judas Maccabeus divided the canon into its three sections and distributed the books according to the manner of the baraita in Baba Bathra 14b (pp. 152-53).
Beckwith claims that the division of the non-Torah books into two distinct sections--Prophets and Writings--took place exactly in the mid-second century BCE, because while the Sirach prologue attests to its existence, the lack of an exact title for the third section--the prologue simply calls it 'the other books'--means that this third section cannot have long existed (p. 142, 152).
"The exact date of the division into Prophets and other Books was probably about 164 BC" (p. 152)For this surprisingly precise dating of the arrangement of the canon, Beckwith cites 2 Maccabees 2:13-15.
(13) The same things are reported in the records and in the memoirs of Nehemiah, and also that he founded a library and collected the books about the kings and prophets, and the writings of David, and letters of kings about votive offerings. (14) In the same way Judas [the Maccabee] also collected all the books that had been lost on account of the war that had come upon us, and they are in our possession. (15) So if you have need of them, send people to get them for you.How can Beckwith possibly see in this report the arrangement of the tripartite canon of scripture?
Judas knew that the prophetic gift had ceased a long time before (1 Macc. 9.27; cp. also 4.46; 14.41), so what is more likely than that, in gathering together the scattered Scriptures, he and his companions the Hasidim classified the now complete collection in the way which from that time became traditional, dividing the miscellaneous non-Mosaic writings into the Prophets and the other Books? (p. 152)And that is his argument. [Maybe you think I've left out part of it? No, I have not.] Beckwith further speculates that since Judas could not have collected all the scriptural books into a single volume, thus resulting in a fixed arrangement, he "must have done it primarily by compiling a list" (p. 153).
One last stage in the argument: though we now know that Judas Maccabeus divided the canon into three sections and assigned the books to the three sections precisely in accordance with the baraita of Baba Bathra 14b, we have not yet established that the exact sequence of books reported in the baraita derives from the action of Judas. But Beckwith can also prove this.
4. The internal order of the Prophets and Writings as reported in b. Baba Bathra 14b goes back to Judas Maccabeus (pp. 156-62).
(a) Beckwith asserts that "Judas's division of the miscellaneous non-Mosaic books"--which has in a few pages gone from a bizarre proposal to a fact of history, apparently--"was a deliberate and rational act," and so the order thus created should show signs of this, as the baraita does, Beckwith thinks (p. 156).
(b) The concluding position of Chronicles, to which Jesus attests (Beckwith thinks; see esp. pp. 211-22), corresponds to the order transmitted by the baraita (p. 156).
Beckwith attempts to illuminate the rationale for the division and sequence of books. He says that each section--Law, Prophets, and Writings--contains two types of books: history and another type. The Torah contains history and law; the Prophets, contain history and prophecy; and the Writings contain history and wisdom. The history books for each section narrate progressively later history. Beckwith then discusses what he perceives to be the problems to this account of things (pp. 158-62), which I do not feel like surveying right now.
But let me just note one of his points. The reason Ruth is in the Writings and not after Judges in the Prophets (as in other arrangements of the books, reflected now in the Christian arrangement of the OT) is because it serves as an introduction to the Psalter, since it ends with a genealogy of David. Also, the reason Chronicles is in the Writings rather than with the other history books in the Prophets (as in the Christian arrangement of the OT) is because it stands "at the end of the canon as a recapitulation of the whole biblical story, from the Creation [Adam] to the return" (p. 158). He goes on to say:
It follows that the presence of Ruth and Chronicles in the Hagiographa cannot be isolated from the order in which they stand in the Hagiographa, and that the same hand which divided the Hagiographa from the Prophets must also have determined the internal order of the two sections. It further follows that the hand responsible must have been later in date than the Chronicler, who apparently intended his work to precede Ezra-Nehemiah, not to follow it, while of course being earlier than the grandson of Ben Sira, who refers to the existence of the three sections of the canon in his prologue to Ecclesiasticus. (pp. 158-59)Strangely, some scholars would disagree with Beckwith by saying that he dates all of this too late, and instead it was the Chronicler himself, in the Persian era, who put the finishing touches on the canon (Julius Steinberg, his teacher Hendrik Koorevaar). Others (e.g. Georg Steins) would also attribute this action to the Chronicler, but would date him to the Maccabean date in line with Beckwith's timetable. More on them some other time.
Those are the fundamental points of Beckwith's argument that the baraita of b. Baba Bathra actually goes back to the second century BCE, nay, even to 164 BCE and the action by Judas Maccabeus. His next chapter--ch. 5, "The Order of the Canonical Books"--is mostly taken up with arguing against other ancient orders, such as reported in patristic lists and alternative Jewish orders. I might have more to say about this chapter some other time.