In Uriel Simon's Four Approaches to the Book of Psalms: From Saadiah Gaon to Abraham Ibn Ezra, I read the Preface and Chapter Three: "Moses Ibn Giqatilah: The Psalms as Non-Prophetic Prayers and Poems".
The Preface was a useful summary of the four medieval Jewish approaches to the Book of Psalms that Simon discusses in the book. Simon mentions things that were also discussed in the chapters that I read yesterday, but I did not talk about them. I'll give a rough summary. As I said yesterday, Saadiah believed that the Book of Psalms was God's exhortations and commandments to human beings---a second Pentateuch, if you will. And, like the first Pentateuch, which was delivered by God to a single individual, so also (according to Saadiah) was the second Pentateuch given to a single person, namely, David. (But Saadiah still thought that God's revelation to Moses was special, for Numbers 12:8 distinguishes the revelation to Moses from that given to other prophets; for Saadiah, David received his revelation through an angelic intercessor.) Psalms that were le ("to") other personages were said by Saadiah to be about those personages, not written by them, for Saadiah believed that all of the Psalms were Davidic. Psalm 90:1, for example, labels a Psalm a prayer le-Moshe ("to Moses"), and Saadiah interprets that to mean that the Psalm was about Moses, not by him. Psalms that were "to" Asaph or the sons of Korah were said by Saadiah to be delivered to these people for performance, but they were composed by David. And, according to Saadiah, the Psalms were only to be performed in the Temple by the Levites. This was relevant to a dispute that Saadiah had with the Karaites, who claimed that Jews did not have to draw from the rabbinic Siddur of prayers, for they could use the Book of Psalms. For Saadiah, Jews needed to use the Siddur.
There were Karaites who believed that the Book of Psalms was a book of prayers from human beings to God, but these prayers were under the inspiration of the Holy Spirit, which was why they could predict the future and be relevant to it. Against Saadiah's claim that the Psalms could only be performed in the Temple, Karaites appealed to superscriptions of the Psalms and other biblical evidence that the Psalms were sung elsewhere as well. Simon notes in the Preface that, although Karaites' distinguishing mark was their rejection of rabbinic oral tradition, they actually overlapped with the Talmud in their conception of the Book of Psalms.
The third approach is what I read today: that of Moses Ibn Giqatilah, whom I will call "Rabbi Moses" for short. Rabbi Moses' view was that the Book of Psalms consisted of prayers that were non-prophetic, meaning that the Holy Spirit did not inspire them. At the same time, Rabbi Moses believed that the Psalms were composed by especially spiritual people, and so he was troubled by Psalms in which the Psalmist had a bad attitude towards God. Rabbi Moses dated certain Psalms to the exile, but, whenever a Psalm was associated with David, he tried his best to relate that Psalm to David's time, even if the Psalm appeared to mention a Temple or exile, things which existed after David. Rabbi Moses felt that he had to be faithful to the text, and yet he did not think that the Psalms could prophetically speak about future institutions or situations. Rabbi Moses said that the dedication of the house in Psalm 30:1 referred to David's house, not the Temple. Although Zion became a central mountain near the end of David's life, Rabbi Moses still thought that Psalms exalting Zion could be by David, for perhaps they were composed near the end of David's life, and David knew (on account of the prophet Gad) that Zion would become an important mountain for the sanctuary. For Rabbi Moses, David composed Psalms for the yet-to-be-built Temple. And, when Psalm 65:31 says that God will dwell on Zion and rebuild the cities of Judah, Rabbi Moses applies that sentiment, not to the exile, but rather to David's response to foreign enemies who insulted the Tabernacle that was sheltering the Ark.
Why Rabbi Moses had this particular view on the Psalms, I can only guess. Rabbi Moses, like Maimonides, liked to rationalize miracles---to attribute them to a natural cause. But, although he did tend to historicize prophecies---to relate their fulfillment to events in history rather than a Messianic future---he did not reject the notion of prophecy. Rabbi Moses thought, for instance, that Deuteronomy 30:3-4 concerned a future Messianic redemption, for its statement that the outcasts would be as far as the ends of the sky went beyond saying that there were Jewish exiles in Babylonia and Persia, showing that the prophecy related to a time beyond those particular exiles. Perhaps rationalism played some role in Rabbi Moses' aversion to the Psalms being prophetic, but another factor may be something that Abraham Ibn Ezra mentioned: that some thought Psalms about Zion had to come after the time of David because Zion was not important until the latter years of David's life. As we saw above, Rabbi Moses did not go this route, for he believed that Psalms about Zion that were associated with David were indeed by David. And yet, perhaps he thought that Psalms had to speak to their own times to be relevant to their audience, meaning that a reference to a far-off future event would make no sense to the people who first heard the Psalms, and thus was not likely.