I wonder if the human genome -- or even the whole genetic program, from prokaryotes to humans -- is subject to Gödel's theorems? Is there something in the genetic program for which the program cannot account? How does the program even get to first base without a program to get there?
I shouldn't be abusing Gödel for my own demented purposes. However, I do have a couple books on him coming in the mail, and after digesting them I will presumably be in a more informed position to abuse his ideas.
But let's think this through with our rudimentary understanding. Everyone knows there is a genetic code responsible for our lives. How then do we do transcend this formal system? For if we didn't so escape its entailments we could never even know of it.
I touched on this in the book, but it is insufficiently fleshed out. But just as the mind cannot be reduced to any machine model, nor can Life be so reduced. Is DNA the secret of life, or Life the secret of DNA? Similarly, is the brain the secret of the mind, or vice versa?
Theoretical biologist Robert Rosen writes that one implication of Gödel's theorems is that a universe "consisting of pure syntax" is "too poor to do mathematics in."
From this he concludes that "contemporary physics is to biology as Number Theory is to a formalization of it," which means that there is always more to Life than can be contained in any reductive model: in short, semantics -- meaning -- can never be reduced to syntax -- order.
Could Life ever be exhaustively expressed in a formal program? Nah: "Gödel effectively demolished the formalist program," and "There is always a a purely semantic residue that cannot be accommodated by the syntactical scheme."
Rosen essentially affirms that reality is always more complex than the simple formalizations in which we try to enclose it. Again, something always escapes the formal system, model, or quantification.
Let's ponder some paradoxical implications.
Can we prove free will doesn't exist? Absolutely, but only if we are free to know the truth of our condition.
Can we prove that evolutionary biology is a complete explanation of man? Sure, but only if we transcend the explanation.
Can we prove that the mind is the product of random evolutionary changes? No doubt, but only from a position outside or above those changes.
I would tie this back to what Voegelin says about our being situated between immanence and transcendence. Because there is always transcendence, no immanent explanation will ever be complete.
Yesterday we touched on the need for revelation. What if -- just spiritballin' here -- the transcendent (Logos) becomes immanent (flesh) that the immanent may become transcendent?
That would be a pretty good answer to Klavan's question at the end of yesterday's post -- "if the human condition is the puzzle, which of the oldest solutions endure and what has Christianity added to them?"
There's still the dynamic space between immanence and transcendence, but instead of our perpetual reaching toward the latter pole, it reaches down into human nature, so our own reaching can finally get somewhere.
This would be an advance in our attempt to solve the puzzle of existence, like some kind of good news or something.
In fact, this morning Klavan's son Spencer addresses the questions posed by his father: our pre-Christian brethren -- stoics and the like -- took things pretty far in the direction of transcendence (↑). But "magnificent as they are," they
tend to exude a kind of weariness at their pinnacle. Heraclitus and Democritus, the weeping and the laughing philosopher, compassed between them the full range of human reactions to the natural world. Both of them concluded that it’s an endless flow of change -- everything always happens, so nothing ever really happens....
Those who grope their way up [↑] the mountain of human wisdom seem to reach the summit exhausted by the climb. If Christianity has something to add, it must be something you can’t work your way up to from below -- something that comes down [↓] onto the mountaintop from above, like thunder onto Sinai.
Something from totally outside the system definitively enters the system? Something radically unformalizable and irreducible? Something that cannot be modeled because it is the Model? The original Semantics that can never be reduced to syntax? The Way and the Life, only quite literally?
Like I said, I need to absorb these books on Gödel and figure out which one of us is more misguided.
Some similar thoughts to what we've said here:
ReplyDeleteThe left hemisphere of the human brain is attracted to certainty, logic, mechanism, the ability to articulate propositions clearly. It tends to grandiose optimism about a person’s capacities and to assert tyrannical dominance over the right hemisphere with the latter’s focus on lived experience, the organic, intuition, emotion, the body, music, the perception of depth, humor, poetry, nuance, irony and metaphor.
The fact that axioms are not provable seems like a point of entrance for right hemisphere intuition based on experience. Those who call themselves “empiricists” tend to want to limit experience to truths derived from the measurement of physical reality. Human experience includes a whole rich universe more than that; ranging from emotional and felt aspects of reality to religious experience. The ability to understand other human beings at all relies on these elements.
Gödel’s theorem proves that... an axiomatic system from which all mathematical truths can be shown to derive is not possible. This can only be done at the price of inconsistency. It is a common feature of LH writers like Richard Dawkins that they will suddenly introduce propositions that not only are not derivable from their axioms but are inconsistent with them. For instance, in The God Delusion he proposes that moral actions not derived from the biologically advantageous desire for a good reputation and reciprocity are nonetheless “good” mistakes. But, since, he has defined “goodness” as that which offers biological advantage, he is contradicting himself.
Aristotle recognized the provisional nature of axioms when he wrote that first principles are not provable. Now it turns out that no set of axioms are sufficient to capture all true statements no matter how the axioms are modified – at least when it comes to first-order logic....
... systems rely on axioms the truth of which must just be assumed and generate truths not provable within those systems either. It is as though no matter how hard the lid is shoved down on the pot, truths fly away into a broader context, the nature of which remains nebulous and poorly defined – exactly the context in which right hemisphere thinking comes into its own. It is that ability of the human mind that sets it apart from machines.