As Bill Poser notes in the previous post, the inclusion of "under God" in the Pledge has long been controversial, but the interpretation of the phrase poses a particular linguistic problem, since as I noted once in a "Fresh Air" piece, the phrase is actually a hapax legomenon in this context.
"Under God" was taken from Lincoln's Gettysburg Address, but there it's used
as an adverbial: "...this nation, under God, shall have a new birth of freedom."
But in the Pledge, the phrase is used adjectivally, to modify nation.
As best I can tell, this is the only context in English where "under God"
is used in this way, which leaves its meaning up for grabs. Is it like "under
orders," "under a monarch," or "under heaven"? But then vagueness is
probably what commended the phrase in the first place -- what better way to
signal the doctrinal neutrality of the state?