Word Play Poetry

See if you can figure out what is going on in this outstanding poem I spotted on Farragoswainscot.com.

Argument With a Mirror
by Jeffrey Barnes

"Reality is what is."
"What is reality?"
"It is obvious."
"Is it?"
"There are observable laws."
"Observable? Are there?"
"Don't you see? I do."
"I see you don't."
"Science explains what we can know."
"Can we? What explains science?"
"It finds man what meaning life has."
"Has life meaning? What man finds it?"
"Anybody—for isn't it everywhere? Look—you see?"
"I see. You look everywhere. It isn't for anybody."
"How can you say that? Many know!"
"I know many that say you can? How?"
"How can we know? I know we can!"
"How?"
"Do you doubt 'I think, therefore I am?'"
"I, therefore, think I doubt you do."
"You are so contrary!"
"So are you."

In this "poem," every exchange of dialogue is palindromic at the word level—they read the same backwards as forwards. The man arguing with his reverse image sometimes intrudes into the other's domain, risking nasty cuts and seven years bad luck.