I just finished Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid. It is quite entertaining, no small feat for a book that revolves around Gödel's incompleteness theorems. Highly recommended, if you can tolerate a little bit of math and a lot of punning (Hofstadter is incredibly witty).
In GEB, Hofstadter builds up the argument that minds and machines are fundamentally the same, in the sense that both can be represented by mechanical/mathematical rules. In particular, he shows that a sufficiently complex formal system gains the ability to reason and make statements about itself.
On the way, Hofstadter takes a tour through music, art, logic, neurology, computer science, genetics, Zen... you name it. The scope of this book is astounding.
I think the most intriguing theme is the idea of taking a step back and making generalizations (or induction, if you like) about a system. This property is at the core of what we would call intelligence and is commonly believed to be one of the things that separates us from most animals (and from computers). Hofstadter relates an anecdote about the Sphex wasp to argue that animals are just hard-wired to handle a finite repertoire. But it is kind of chilling when you realize that the same is likely true of humans— the only thing that is different is the size of our repertoire:
[The Sphex wasp] has no ability to notice when the same thing occurs over and over and over again in its system, for to notice such a thing would be to jump out of the system, even if only ever so slightly. It simply does not notice the sameness of the repetitions. [...] Are there highly repetitious situations which occur in our lives time and time again, and which we handle in the identical stupid way each time, because we don't have enough of an overview to perceive their sameness?
Hofstadter concludes the book with some speculation about how the mind might be "implemented" in hardware, i.e. neurons (for example, how high-level pattern recognition happens, and how features in the mind might be represented in hardware) and how we might begin to understand the physical basis for high-level features of the mind (intentions, emotions, etc.). You might find this part interesting even if you skimmed over (or wanted to skim over) the more mathematical content of the book. GEB was written 30 years ago but much of it is still relevant— little of Hofstadter's speculation about neurology has been resolved since.