I noted before that I was surprised that John Quincy Adams circa 1814, when he had converted to an orthodox Calvinist understanding of Christianity endorsed a heterodox notion of the Bible's canon that sounded like something a unitarian rationalist (like his father) would endorse. JQA is open to the notion that some of the writings of John Milton, Homer and Virgil were divinely inspired along the same grounds he believed the inspired parts of the biblical canon were.
As I was rereading the elder Adams' letter to Thomas Jefferson dated Nov. 14: 1813, I noticed that he too is open to the notion that Virgil's writings constitute special revelation along the line of the parts of the biblical canon Adams believed were revealed by God.
As he wrote:
Blacklocks translation of Horace’s “Justum” is admirable; Superiour to Addisons. Could David be translated as well; his Superiority would be universally acknowledged. We cannot compare the Sybbiline Poetry. By Virgils Pollio we may conjecture, there was Prophecy as well as Sublimity. Why have those Verses been annihilated? I Suspect platonick Christianity, pharisaical Judaism, or machiavilian Politicks, in this case; as in all other cases of the destruction of records and litterary monuments. ...Did you notice that? In Virgil's Pollio, Adams conjectured there was "Prophesy," whose "[v]erses been annihilated" by "platonick Christianity, pharisaical Judaism, or machiavilian Politicks" coupled with "the destruction of records and litterary monuments."
One of the issues that John Adams had with fellow unitarian Joseph Priestley was Priestley not finding more "Christian principles" in words of Stoic figures like Cleanthes. One could argue that Christendom, the Roman Catholic Church in particular, but other traditions as well, have found ways to reconcile and incorporate the noble pagan teachings of the Ancient Greeks and to a lesser extent Romans into the faith.
But let's be clear on what they did. As the story goes, the canon constitutes special revelation. What Aristotle et al. offer is objective truths found in essences in nature discoverable by reason alone. When reason is used properly, these discoveries won't contradict special revelation and indeed, the findings of the two will support one another.
For instance, as it relates to the nature of sex, as the theory goes, the canon of special revelation neither forbids nor permits contraception between married couples. Aristotelian chains of reasoning relating to the nature of the sexual act demonstrate a law in nature that forbids contraception. This law doesn't contradict anything in the canon. Indeed if the same author of the canon is the author of nature, then it's simply a different channel to the same source. However, that channel comes from man's potentially flawed reason and is not in and of itself special revelation.
To the extent that the Church has the authority to make divine pronouncements, it can take what is discoverable from reason in the natural law and make it official dogma.
But that's not what John Adams (and later John Quincy Adams) did. Rather, what we see is being open to the notion that the writings of Virgil constitute special revelation, that if so should be added to the Bible, but that we can't presently (i.e. when he wrote the letter) be sure of because some corrupt, politicized churchy cabal destroyed the evidence.