| Quote #1 Thus much let me avow— (3) |
"Avow" is an important word here. The speaker wishes to make a strong declaration of fact, which suggests that he wants to be certain, rather than skeptical, about something.
| Quote #2 You are not wrong, who deem |
The speaker doesn't say that the woman is right, only that she is not wrong. The speaker seems unwilling to accept the skeptical position that life is all a big dream. There's a wee bit of hesitation there.
| Quote #3 All that we see or seem |
The speaker sure seems pretty convinced that life is just a dream within a dream. But skepticism is supposed to be about uncertainty, so this doesn't seem so skeptical to us. Can you really be certain about uncertainty?