Washington Irving's main purpose in A History of New York was to parody some of the essential moments in American history as well as to parody the common teachings of historians. In so doing, Irving relays many themes, but the most significant themes concern the wrongfulness of colonization and the treatment of Native Americans.
We particularly see Irving parody the colonization of the Native Americans early on in the book when he argues that killing the Indians was justified because they clearly had not used the same means Europeans use to cultivate farmland in order to cultivate their own land. The Indians, therefore, are poor stewards who had no rightful claim to the land. He further cites the Bible as a source of authority to justify slaughtering the Indians.
Later in the book, he further parodies the justification of colonization by repeating ideas commonly espoused by colonial empires. According to colonial empires, colonization is a good thing because it helps to educate savages and convert them to the Christian religion. We see Irving parody these common ideas when he himself refers to the Indians as savages and barbarians, such as in the following:
We have moreover found these miserable savages sunk into a state of the utmost ignorance and depravity ... Taking compassion, therefore, on the sad condition of these sublunary wretches, we have endeavored, while we remain on their planet, to introduce among them the light of reason and the comforts of the moon.