Modern though it may seem, the question of who wrote the Hebrew scriptures is actually discussed in ancient Jewish sources; in fact, the talmudic rabbis were well aware that books might have been written first in one form and then redacted by later editors. The standard account appears in the Babylonian Talmud, but an alternate version associated with the Masoretes, 10th-century scribes in northern Israel who preserved the old manuscripts of the Bible, appears in (among other places) a fragment found in the Cairo Geniza. Kim Phillips speculates as to which version might be the original:
A masoretic note [in the Geniza] shares numerous, obvious parallels with the [Talmud’s account]. . . .
In the talmudic passage, King Hezekiah [who ruled Judah in the 8th century BCE] and his associates are credited with writing (presumably the task we would refer to as editing) the books of Isaiah, Proverbs, Song of Songs, and Ecclesiastes. Regarding the attribution to Hezekiah and his associates of the last three works [whose own texts seem to ascribe authorship to King Solomon], it seems that the rabbis are relying on an extension of the sense of Proverbs 25:1: “These, too, are Solomon’s proverbs, which Hezekiah king of Judah’s men copied.”
In the masoretic version, Hezekiah and his associates have disappeared. These four books are all attributed to Isaiah’s authorial-editorial labors. It is quite understandable that Isaiah should be credited with having written [the book that bears his name], but what qualifications can he claim for editing the other three books? Is it just possible that these were appended to Isaiah’s CV on the basis of the various love-poetry and wisdom themes found in his prophecy (e.g. Isaiah 5:1–7 and 28:23–29)?
More likely is the hypothesis that the talmudic wording of the tradition lies somewhere in the pre-history of this masoretic tradition. At some point, Hezekiah and his associates were omitted from the wording (accidentally or otherwise), leaving Isaiah with the burden of editing Solomon’s works as well as writing his own book. Under the pressure of the fact that Joshua, Samuel, Jeremiah, and Ezra are claimed to have written the books that bear their names, it is easy to understand how such a mutation would credit Isaiah with writing his own book. That is to say: it makes sense to see the talmudic tradition as prior to the masoretic tradition in this case. It is harder to imagine the mutation occurring in the opposite direction.
Read more on Cambridge University Library: http://www.lib.cam.ac.uk/collections/departments/taylor-schechter-genizah-research-unit/fragment-month/fragment-month-4