Others have pointed out what the core argument of the book is, so I'll point to the spot where I believe the thesis is stated most clearly (p. 709 in my copy,
the 1980 Vintage Books paperback edition):
"My belief is that the explanations of 'emergent' phenomena in our brains--for instance, ideas, hopes, images, analogies, and finally consciousness and free will--are based on a kind of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time being itself determined by the bottom level. ...The self comes into being at the moment is has the power to reflect itself."
"My belief is that the explanations of 'emergent' phenomena in our brains--for instance, ideas, hopes, images, analogies, and finally consciousness and free will--are based on a kind of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time being itself determined by the bottom level. ...The self comes into being at the moment is has the power to reflect itself."