Answer and Explanation:
We have two quotiations to analyze:
- "The right to swing my fist ends at where your nose begins." and
- "To be free is not merely to cast off one's chains, but to live in a way that respects and enhances the freedom of others."
Both quotations are actually more similar to each other than they may look at first glance. They are both talking of being free. The first one does it metaphorically while the second one says the same thing in a more direct way.
What they basically mean is: we are all free. But, for our freedom to be worth something, we should respect the fact that other people are free as well. I do have the right to swing my fist, to cast off my chains. I can do anything I want... unless I begin to harm others. When I harm others - when I hit their nose or put chains around their limbs -, I'm making them prisoners, less free than myself. If I would not like that - being a prisoner, having my nose hit - for myself, I should not think of doing that to others.