Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

level is determined by whether or not reality is mirrored in an isomorphic

(or looser) fashion on that level. So the fact that neurons always perform

correct additions (in fact, much more complex calculations) has no bearing

whatsoever on the correctness of the top-level conclusions supported by

their machinery. Whether one's top level is engaged in proving koans of

Boolean Buddhism or in meditating on theorems of Zen Algebra, one's

neurons are functioning rationally. By the same token, the high-level

symbolic processes which in a brain create the experience of appreciating

beauty are perfectly rational on the bottom level, where the faultless func-

tioning is taking place; any irrationality, if there is such, is on the higher

level, and is an epiphenomenon-a consequence-of the events on the

lower level.

To make the same point in a different way, let us say you are having a

hard time making up your mind whether to order a cheeseburger or a

pineappleburger. Does this imply that your neurons are also balking,

having difficulty deciding whether or not to fire? Of course not. Your

hamburger-confusion is a high-level state which fully depends on the

efficient firing of thousands of neurons in very organized ways. This is a

little ironic, yet it is perfectly obvious when you think about it. Nevertheless,

it is probably fair to say that nearly all confusions about minds and comput-

ers have their origin in just such elementary level-confusions.

There is no reason to believe that a. computer's faultlessly functioning

hardware could not support high-level symbolic behavior which would

represent such complex states as confusion, forgetting, or appreciation of

beauty. It would require that there exist massive subsystems interacting

with each other according to a complex "logic". The overt behavior could

appear either rational or irrational; but underneath it would be the per-

formance of reliable, logical hardware.

More Against lucas

Incidentally, this kind oflevel distinction provides us with some new fuel in

arguing against Lucas. The Lucas argument is based on the idea that

Codel's Theorem is applicable, by definition, to machines. In fact, Lucas

makes a most emphatic pronunciation:

Codel's theorem must apply to cybernetical machines, because it is of the

essence of being a machine, that it should be a concrete instantiation of a

formal system.^9

This is, as we have seen, true on the hardware level-but since there may be

higher levels, it is not the last word on the subject. Now Lucas gives the

impression that in the mind-imitating machines he discusses, there is only

one level on which manipulation of symbols takes place. For instance, the

Rule of Detachment (called "Modus Ponens" in his article) would b~ wired

into the hardware and would be an unchangeable feature of such a

machine. He goes further and intimates that if Modus Ponens were not an

Church, Turing, Tarski, and Others 577