First of all, I love the M*********rs.

It's a trick IMO.
The first bit, "To believe is to know you believe" seems reasonable but is not. Believing is quite seperate from knowing. To know you believe "A" (for example) is a completely different process from the actual believing of "A"

The second bit "to know you believe is not to believe" is true, in fact it's what I just said, but when juxtaposed with the first bit (which is false) it seems to validate it, and the entire sentence.

It's a trick. Any others?