So what are those three systems? One is indeed biblical Judeo-Christianity. The second is Enlightenment rationalism. And the third is a "noble-paganism," a Stoic sense of virtue that draws its inspiration from Greco-Roman antiquity. As Thomas Jefferson summed up the value synthesis regarding its inspiration on the Declaration of Independence:
All its authority rests then on the harmonizing sentiments of the day, whether expressed in conversation, in letters, printed essays, or in the elementary books of public right, as Aristotle, Cicero, Locke, Sidney, &c. ...
In that letter Jefferson also said: "All American Whigs thought alike on these subjects." It was the Whigs who synthesized these value systems into their own "Whig-republican" culture or worldview.
The original proposals for the Great Seal also well illustrate this dynamic. The "Judeo-Christian" promoters, obviously, often stress Franklin's original one:
"Moses standing on the Shore, and extending his Hand over the Sea, thereby causing the same to overwhelm Pharaoh who is sitting in an open Chariot, a Crown on his Head and a Sword in his Hand. Rays from a Pillar of Fire in the Clouds reaching to Moses, to express that he acts by Command of the Deity.
"Motto, Rebellion to Tyrants is Obedience to God."
However the Judeo-Christian defenders often ignore the other two pagan proposals. John Adams' allusion to Greco-Roman paganism:
John Adams chose the allegorical painting known as the "Judgment of Hercules" where the young Hercules must choose to travel either on the flowery path of self-indulgence or ascend the rugged, uphill way of duty to others and honor to himself.
And Thomas Jefferson's mixture of Old Testament Israel with Anglo-Saxon paganism:
Thomas Jefferson also suggested allegorical scenes. For the front of the seal: children of Israel in the wilderness, led by a cloud by day and a pillar of fire by night. For the reverse: Hengist and Horsa, the two brothers who were the legendary leaders of the first Anglo-Saxon settlers in Britain.
Overall I see these proposals as representing an enlightenment rationalist worldview that thought man's reason could pick and choose from the various tales of antiquity, be they biblical or pagan the "rational" parts that supported the Whig-republican worldview. As Noah Webster put it describing how this synthesis impacted the formation of the US Constitution:
IN the formation of our constitution, the wisdom of all ages is collected--the legislators of antiquity [Rowe: Webster names Fohi, Confucius, Solon, Lycurgus, Numa, Mango Capac, Zamolxis and Odin] are consulted--as well as the opinions and interests of the millions who are concerned. In short, in it an empire of reason.