| 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?