To a large extent, the philosophical underpinnings of the American colonists' revolt against Britain were provided by the work of the English philosopher John Locke.
Locke argued that governments existed to protect the natural rights of their citizens, most notably the right to own property. This functionalist view of government meant that individual governments could be judged against a set of abstract standards supposedly rooted in universal human nature.
If this weren't radical enough, Locke put forward the then quite revolutionary notion that if governments did not perform the tasks with which they had been charged—the defense and the protection of natural rights—then the people were perfectly entitled to overthrow them and replace them with governments that would do what they were supposed to do.
In essence, this is precisely what the American colonists did in relation to British rule. A majority of Americans came to believe that colonial rule constituted a threat to the rights and liberties to which they were entitled as British subjects.
As colonial rule became more authoritarian, Americans increasingly felt that their natural rights were under threat, and so a growing body of opinion held that it was time for America to break free from Great Britain and become an independent country.
The classic document of the independence movement, the Declaration of Independence, contains a famous passage which could easily have been written by Locke himself:
That whenever any Form of Government becomes destructive of these ends [that is to say, the securing of inalienable rights] it is the Right of the People to alter or abolish it, and to institute new Government.
This is pure Locke. The people feel that their rights and liberties are under threat and so have the right to abolish or alter the existing form of government and replace it with something better, a new arrangement that will protect their inalienable rights. And that's just what the American colonists did.