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Reclaiming the Greek Heritage:  A Modern Mathematical Philosophy
Dr. Orville Boyd Jenkins
A review of the book by by Rudy Rucker
Infinity and the Mind:  The Science and Philosophy of the Infinite.  Boston:  Birkhaeuser, 1982  342p.
(Reissued by Princeton University Press, 1995; Current edition 2004. 368p.)

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Rudy Rucker deals with the concept of Infinity in regard to our mental conceptions and the structure of reality.  The question is whether or not the concept of Infinity makes sense, and how then the relation of finite thought and human consciousness relates to the possibility of infinites in the structure of reality.  

Rucker is a professor of Calculus and centres this discussion in the History of Mathematical Theory stemming from the ancient Greeks.  For the Greeks there was no distinction between mathematics and philosophy.  He takes a mathematical approach, but converses fluently in the disciplines of Quantum Physics and Philosophy.

I classified this book as Epistemology (the Philosophy of Knowledge) because the central concept is the meaning and definition of Human Consciousness.  In this regard Rucker probes the meaning of consciousness and the relationship of the individual mind to the concept of Universal Mind.

The title includes Infinity, because the investigation considers all aspects of the ultimate or Absolute.  So at the root of this is the question of whether it makes sense for anything to be Infinite.  Is there such a thing as Infinity?  Are there multiple infinities?  Involved is the question of whether the human mind can conceptualize an infinite thought, or is every human thought a finite thought?

The reason this is a question of Epistemology is that one must consider how we know, and what a finite mind can know.  Thus Rucker looks at the question in terms of many disciplines of knowledge.  Basically, we are asking whether it is possible for something in the universe (one mind, and its thoughts) to know the Absolute or Ultimate reality, of which it is a part!

Theory of Mind
Another term for the discipline commonly dealing with this problem is Theory of Mind.  Rucker looks at the concepts of Theory of Mind and the Philosophical question of the Absolute in a mathematical perspective.  He addresses the One-Many question of the relation of the individual to the Whole, or the partricle to the Universe.  This latter entails the concept of whether there is some ultimate unity to the universe, including the recent question of multiple universes, and whether the Absolute is sentient, as an active God or relatable entity.

Rucker points out that any ultimate question, posed in terms mathematical, theological or otherwise, is a mystical question.  He references concepts of Zen Buddhism as well as classical Western Philosophy and Christian theology.  He lays a firm foundation for the problem in a historical format by reviewing the ancient Greek concepts.

Mathematical Approach
I had never looked at these questions from a mathematical approach.  His discussion of set theory helps to see the issues involved in considering whether humans, as finite entities, can conceptualize the ultimate.  He deals with the relationship between thoughts and concepts and the external objective world.  Set theory and its refinements, which Rucker discusses in terms of the history of their development, provide a way of objectively evaluating whether there can be infinite.

Rucker lays out the formulas in geometry and calculus, but discusses the implications from practical and theoretical perspectives in science and theology.  I did not camp out in the mathematical formulas, but could generally follow the arguments.  The philosophical implications and the factors discussed in the practical and theoretical scientific disciplines were very helpful.  Rucker uses very practical life-situations and analogies to provide a reality for these concepts, which can seem ethereal and abstract.

Robot Souls?
One of the practical aspects is a whole chapter critically evaluating ideas of Artificial Intelligence, "Robots and Souls."  He asks whether an artificial intelligence can become self-developing to the stage comparable to human consciousness.  He ruminates on the relationship of artificial intelligences to human consciousness.

Rucker reviews the creative and ground-breaking theories and writings of Kurt Gödel, a mathematical philosopher in the 20th century.  Gödel conclusively established the concept of Infinity.  Rucker reports on personal discussions he had with Gödel, who was a mystic and philosopher.  They discussed the concept of Universal Mind and the existence of mind beyond body.

Cosmogony and the Absolute Mind
It was also interesting to see this perspective on the Theory of Mind, various concepts of the Absolute, and critical analysis of the possibilities and limitations of human conception, as written almost 25 years ago, and see that most of what is known and considered now was active knowledge back then.  The critical analysis Rucker provides was helpful for a fresh perspective on the methods mathematics brings to metaphysics involved now in Particle Physics and the Cosmogony now entailed by Theoretical physics on the astronomical level.

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First written and posted on Amazon 30 June 2006
Posted on Thoughts and Resources 27 November 2006
Last edited 5 November 2007

Orville Boyd Jenkins, EdD, PhD
Copyright © 2006 Orville Boyd Jenkins
Permission granted for free download and transmission for personal or educational use.  Other rights reserved.

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