How we cite our quotes: (Article.Sentence)
Quote #1
His Brittanic Majesty acknowledges the said United States, viz., New Hampshire, Massachusetts Bay, Rhode Island and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Maryland, Virginia, North Carolina, South Carolina and Georgia, to be free sovereign and independent states, that he treats with them as such, and for himself, his heirs, and successors, relinquishes all claims to the government, propriety, and territorial rights of the same and every part thereof. (1.1)
This is the big one. The first article of the treaty effectively creates the new country called the United States of America. Before this, there was a difference of opinion over whether the country existed. That was the whole reason for the war. Politics can't exist without acknowledging the different sides, and this does that, all while granting a formidable and non-negotiable, concession.
Quote #2
And also that the inhabitants of the United States shall have liberty to take fish of every kind on such part of the coast of Newfoundland as British fishermen shall use, (but not to dry or cure the same on that island) and also on the coasts, bays and creeks of all other of his Brittanic Majesty's dominions in America; and that the American fishermen shall have liberty to dry and cure fish in any of the unsettled bays, harbors, and creeks of Nova Scotia, Magdalen Islands, and Labrador, so long as the same shall remain unsettled, but so soon as the same or either of them shall be settled, it shall not be lawful for the said fishermen to dry or cure fish at such settlement without a previous agreement for that purpose with the inhabitants, proprietors, or possessors of the ground. (3.2)
This is part of Article 3: the fishing rights article. What you can see here is a small bit of politics being played with the language. Specifically, that while it's okay to fish pretty much anywhere, actually going to shore where the British control is a no-no. Granted, this is just to cure the fish (basically adding salt and stuff to preserve it), but it also stops a sneaky invasion. "We just landed here to cure these fish...with all these muskets and gunpowder."
Quote #3
It is agreed that Congress shall earnestly recommend it to the legislatures of the respective states to provide for the restitution of all estates, rights, and properties, which have been confiscated belonging to real British subjects; and also of the estates, rights, and properties of persons resident in districts in the possession on his Majesty's arms and who have not borne arms against the said United States. (5.1)
Ooh, layers. The treaty, a form of politics, is requesting more politics, to address the imbalance of power in other politics. Okay, so the war was, at least partly between the Patriots and the Loyalists. The Patriots win, so the treaty was doing its best to encourage the winning side to be magnanimous with the losing side. Acknowledging the internal politics in the external politics. It also sends a clear message to the Loyalists: your king has not forgotten you. Could be a deep game the British are playing.