42 of 44 people found the following review helpful
This review is from: Infinity and the Mind (Paperback)
I've read a few of Rucker's other nonfiction books (his fiction is another topic entirely), and I think this one is still his best. I bought and read it when it was new and I'm about to buy a replacement copy.
The "book description" on this page touches briefly on one of Rucker's key points: "the transcendent implications of Platonic realism." This is well put, and the remarks above correctly relate this point to Rucker's "conversations with Godel." Godel was a mathematical Platonist -- that is, he believed that mathematical objects are real in their own right and that the mind has the power to grasp them directly in some way.
Rucker gets this right, unlike some other better-known interpreters of Godel who have co-opted his famous Theorems in the service of strong AI. Rucker, too, thinks artificial intelligence is possible, but for a different reason which he also here explores: he takes the idealistic/mystic view that _everything_ is conscious in at least a rudimentary [no pun intended] way, and so there's no reason to deny consciousness to computers and robots. Heck, even rocks are conscious -- just not very :-). (I don't know whether Rucker would still defend this idea today or not. At any rate, for interested readers, a more elaborate version of panpsychism is developed and defended in Timothy Sprigge's _The Vindication of Absolute Idealism_.)
These and other speculations are the jewels in a setting of solid exposition. Rucker is powerful in general on the topic of set theory, which he takes to be the mathematician's version of theology. And his discussions are a fine introductory overview of the various sorts of infinity, including but not limited to mathematical infinities. He is remarkably familiar with the literature of the infinite both inside and outside of mathematics, e.g. calling attention to certain neglected works by Josiah Royce (who discusses infinities in an appendix to _The World and the Individual_). He also discusses, quite accessibly, some of the paradoxes that arise from treating the set-theoretic "universe" as a completed, all-there-at-once set in its own right.
Rucker, a descendant of G.W.F. Hegel in both body and spirit, could be read profitably on this topic by a pretty wide audience. In particular he is a good cure, or at least the beginning of a cure, for certain philosophers who (more or less following Aristotle) would deny the real existence of actual infinities in particular and mathematical objects in general. (Also for interested readers: another, more technical defense of realism with regard to mathematical objects can be found in Jerrold Katz's _Realistic Rationalism_.)
My original copy of this book was published, with some justification, in Bantam's "New Age" series. I am glad to see the new edition is published by Princeton University Press.