There's a problem, if I can use that word, with celebrating Independence Day on July 4. There's nothing wrong with celebrating the approval of the Declaration of Independence or the freedom of our nation, of course. But to simply celebrate July 4 and act like that was the day when America became independent -- well, it's a nice story, but it vastly oversimplifies a process that didn't end when the clock struck midnight on July 5.
Independence -- true independence -- was not won when a handful of brave men voted in Philadelphia to "dissolve the political bands which have connected them with another." It was not even won over the course of the war that brought that declaration about, though the blood of American soldiers fighting for America for the first time certainly did its part to found this nation.
But the real war to become an independent nation was fought over the months and years that followed that, as the Articles of Confederation government fell into chaos and another group of men went to Philadelphia and hammered out a new Constitution that has guided the country to this day. They were led by George Washington, who did something unheard of a decade later when he voluntarily gave up power that he could have held onto for his entire life.
The point of all that is that there's not really one "Independence Day" in American history. It took time to found this nation and figure out how to make it a country of free men and women. And while we're celebrating today, it wouldn't be a terrible idea to remember the other Independence Days, too.