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| Douglas R. Hofstadter's Gödel, Escher, Bach |
In Hofstadter's Chapter VI, "The Location of Meaning," he (without mentioning God by name) hints that the reality we each bear witness to is a message with an intrinsic meaning. If we call that meaning God, we do no violence to the truth.
Like all messages, reality or truth has three levels of "message-ness." The "frame message" signals that a meaning lies within, waiting for our intelligence to decipher it: it is not mere noise or static buzzing in our ears. Next, the "outer message" conveys, in a manner necessarily distinct from that in which the interior meaning is conveyed, clues to how to decipher the interior meaning. Finally, the "inner message" contains the interior meaning that the source of the message qua message wished to present to whoever receives and decodes the message.
As such, an inner message is like a genotype wherein is found all the requisite information as to how living cells are to proceed to build a canary, say, or how the mind is to construct the infinite Fibonacci sequence of numbers, in which every number is the sum of the previous two. The canary, or the expanded Fibonacci sequence, is the phenotype which the genotype internally codes for.
The relationship of the entire Fibonacci sequence, which is an endless stream of numbers, to their finite numeric "starter set" which acts as frame message, outer message, and inner message, all at once, is easy to see. It is straightforward and quite prosaic. The relationship of a canary or a tiger to its genotype is more exotic, tangled up as it is with the vast number of molecular reactions and biochemical pathways that serve to construct the finished product over time (if it can be said that a canary is ever finished).
The relationship of reality as a whole to its genotype, which I am calling God (and I hope Hofstadter would agree with the appellation), must be yet more exotic than that.
For one thing, a main point of Hofstadter's book is that no formal system (such as one that can manipulate logical symbol strings to generate a list of Fibonacci numbers "typographically"), if it is deemed to be internally consistent and if it is also of a generative power much more impressive than the relatively puny Fibonacci generator, is complete.
If the Fibonacci generator is expanded sufficiently, it can be turned into the entirety of what mathematicians call number theory. If that is done, the resulting formal system will be quite powerful, but it will perforce be unable to derive all the truths about number theory that the human intellect is capable of apprehending!
The Austrian mathematician Kurt Gödel demonstrated in 1931 that such systems cannot help but be incomplete. The theorems they are able to generate, and thus prove, map to true statements, but there are other true statements which do not have theorem-cognates internal to the system — to, that is, the number theory per se.
By extension, no matter what the formal system, if it is at all powerful, then "provability is a weaker notion than truth," writes Hofstadter (p. 19). Still, human intelligence can apprehend the "unreachable" truth beyond what the formal system can derive or prove.
This is a paradox: the human mind is housed in a brain which presumably operates "typographically," i.e., in the same mechanical way that any formal symbol system does its thing. Yet the mind can entertain and apprehend thoughts that properly lie outside its underlying system's power to prove.
Intelligence, accordingly, can reach supposedly unreachable truth. A man's reach exceeds his grasp, or what's a heaven for?
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