In the first paragraph of The American Crisis, what ideas does Paine use to justify the struggle of revolution?
I assume that you are asking about the first paragraph of the first pamphlet from the series that we now call The American Crisis. In this paragraph, Paine justifies the right of rebellion by saying that the British government is acting tyrannically to the point that it is enslaving the American people.
In this first paragraph, Paine asserts that the British government is establishing a tyranny over the American colonies. He says that the British have claimed that they have the right to tax the Americans in any and all situations. He says that the British have claimed the right “to Bind us” in all situations. That means that Britain has claimed the right to force Americans to do whatever Britain wants. This, he says, is tyrannical. In fact, he goes as far to say that this has made slaves of the Americans. He says that, if this “is not slavery, then is there not such a thing as slavery upon earth.”
Paine is implying here that he agrees with Thomas Jefferson’s words in the Declaration of Independence. Jefferson said that people have the right to rebel if their government fails to protect their rights to “life, liberty, and the pursuit of happiness.” Paine is saying that the British government is actively trying to take away at least the last two of these rights. Therefore, he is saying, the colonies have the right to rebel.
In this paragraph, where Paine famously announces that "these are the times that try men's souls," he goes on to define the stakes of the conflict by showing that it is, at bottom, a struggle against tyranny. He says that the British have sent an army to enforce their tyrannical rule over the colonies. Quoting the Declaratory Act, Paine observes that the British have asserted the right "to BIND us in ALL CASES WHATSOEVER," including the taxes that first provoked colonial ire. Paine goes on to say that if this is not "slavery," then there is "not such a thing as slavery upon Earth." By "slavery," Paine means that the colonists have been deprived of their liberty to the point that they can no longer control their own property. This condition was often described by republican writers as "slavery," and the arbitrary power claimed by the English was "impious," because it could only properly belong to God. The British had violated the rights of the colonists, both as British subjects, and, more importantly, as humans. In the face of this kind of tyranny, Paine proclaims, the Americans had no choice but to fight, and the struggle would not be easy. "Tyranny," Paine wrote, "like hell, is not easily conquered."