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There is however a firm basis for the Republic in the rationality that we are all endowed with inalienable rights to life, liberty & property, regardless of how they originated.
And how did I contradict this? (I'm curious about your use of the word "however.")
You didn't; --- Chesterton did.
I was commenting on Chesterson's assumption that "dogma about the divine origin of man." is necessary for democracy. -- Could be, -- but I don't see that as needed in our Republic.
If you are talking about dogma in the sense of a (specific) religious doctrine, I agree. I would indicate that the DOI, as our establishing document is predicated on a non-specific but absolute belief in an eternal creator to which all nature, humans and human institutions are subordinate. If rights are inalienable, they must also be eternal and immutable. The creator that bestows them must then, be likewise. It's inescapable. Take away "Creator," from the DOI and the remainder of the premise on which this nation was founded crumbles.