Thought experiment: Let's say that the Decleration of Independance were worded just a little differently.
In CONGRESS, July 4 1776
The unanimous Declaration of the thirteen United States of America,
When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
We hold these Truths to be self-evident, that all men are created equal, that they are endowed by Nature with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
That to secure these rights, Governments are instituted among Men, deriving their just Powers from the consent of the governed.
That whenever any Form of Government becomes destructive of these Ends, it is in the Right of the People to alter or abolish it, and to institute a new Government, laying its Foundation on such Principles, and organizing its Powers in such Form, as to them shall seem most likely to effect their Safety and Happiness. Prudence indeed, will dictate that Governments long established should not be changed for light and transient Causes; and accordingly all Experience hath shewn, that Mankind are more disposed to suffer, while Evils are sufferable, than to right themselves by abolishing the Forms to which they are accustomed. But when a long Train of Abuses and Usurpations, pursuing invariably the same Object, evinces a Design to reduce them under absolute Despotism, it is their Right, it is their Duty, to throw off such Government, and to provide new Guards for their future Security.
I made two subtle changes to the above passage (bolded). I removed an ambiguous and a direct reference to God. Now, if this document is, as Claus implies, dependant upon a supernatural Creator God, removal of that Creator God should fundamentally change the nature of the document. Does it?