"Genesis by experience" was the name I gave my philosophy of the existence of the physical world, as well as of the conscious mind we each harbor and the immortal soul our religions tell us we, each of us, have. In my Part 5 post about GBE metaphysics, I brought up the fact that GBE proposes a dualism between mind and the physical world.
Specifically, it says that God's mind, in that it partakes of the same sort of conscious, subjective experience that our minds echo, confers coherence on the world and thus guarantees to us, God's creatures, the steady causal regularity that we marvel at in our scientific inquiries.
I extrapolated this idea from certain counterintuitive, even paradoxical results known to quantum physics, wherein the incoherence, uncertainty, and incompleteness that pervade quantum phenomena are replaced by a coherent knowability whenever observation enters the picture. At a macroscopic level, quantum uncertainty disappears. I attributed this genesis of worldly coherence to the ceaseless observation of the physical world by God.
I even went so far as to state that "to exist is to be caused," where causation is the conferring of (cosmic) coherence by virtue of conscious observation. But this led me to wonder if it would be inconsistent to claim that the mind whose consciousness confers coherence/existence upon the world is itself something that "exists." If that question is answered no, then how could God be said to "exist"?
Or, if that question of whether God "exists" is answered yes — for it looks as if consciousness per se can never be directly observed — what act of conscious observation, by what mind, could be said to confer "existence" on God?
I felt uneasy with both horns of that dilemma, so I quickly shunted it aside and went on to discuss the topic of intentionality as it applies to our minds and to God's. But the dilemma nagged at me overnight.
 |
| Douglas Hofstadter's I Am a Strange Loop |
 |
| Douglas Hofstadter's Gödel, Escher, Bach |
And so I'm undertaking the series of posts of which this one is the precursor of what will undoubtedly be many more yet to come. The general thrust of this series will be to modify GBE to remove the intrinsic mind-matter dualism that, as it stands now, GBE seems to require.
So modified, my GBE metaphysics will (I hope) become what I'll dub my "God Is a Strange Loop" theology — for short, GISL.
It will take me quite a while to lay out my GISL insight in all its glory. In fact, I'm going to sneak up on doing so gradually, because the subject is, I hate to say it, very much like the Hofstadter books in being conceptually challenging to the max.
Before I even begin stealthily approaching any sort of definitive statement of the inner kernel of my insight, I want to present a broad sketch of what I'm going for. The general idea of Hofstadter's books is to ask how the human brain gives rise to a mind that houses within itself a symbolized self or "I." Hofstadter's answer is that it happens by virtue of an intrinsically self-referential "strange loop."
Imagine the mind as, first of all, a machine, a computer — a vessel of "artificial" intelligence. Like all computing machines, it works just like a "formal system" works. That is, using a set of rules, it shunts symbols around to make well-formed symbol strings called formulas.
One formal system that mathematicians know is number theory, in which "0=0" ("zero equals zero") is a formula, because it is a well-formed symbol string. It is also a theorem (actually, an axiom, needing no proof) because it is true. On the other hand, "2+2=5", though well-formed, is false and hence is not a theorem. It cannot be proven — the rules of number-theoretical theorem derivation simply cannot be used to derive it.
About a century ago, Alfred North Whitehead and Bertrand Russell wrote a triptych of tomes called Principia Mathematica that tried to ground number theory in yet another formal system, set theory. It was their hope to do so in a fashion that guaranteed the PM system to be free of self-reference, because if a formal system's theorems can refer in any way to the system qua system, all hell breaks loose.
By all hell breaking loose is meant that what Hofstadter calls the Mathematician's Credo gets violated. According to the credo, every single true statement concerning the "stuff" the formal system deals with — numbers, in the case of number theory — corresponds to a derivable theorem within the system, while no false statement does so. If the first of those two assumptions is violated, the system is intrinsically incomplete. If the second is violated, the system is intrinsically inconsistent. Russell and Whitehead were on a mission to ground all of mathematics, via number theory, in set theory, in such a way as to avoid both incompleteness and inconsistency.
In 1931, along came 25-year-old Austrian mathematician-logician Kurt Gödel and upset Russell and Whitehead's apple cart. Gödel cleverly showed that there were, concealed within PM, well-formed symbol strings that, if false, rendered PM intrinsically inconsistent, while, if true, rendered it incomplete.
One such well-formed symbol string was the one which, loosely translated into English, reads "I am unprovable" (see I Am a Strange Loop, p. 138).
That bald statement needs some hasty elucidation. First of all, the "I" which is its first word refers to the statement itself (!). Second, "unprovable" means "unable to be derived within the PM system by means of applying the system's official rules of theorem derivation to well-formed symbol strings that have already been derived and/or to well-formed symbol strings which are taken to be axioms that don't need proof." So a statement which has the same import would be: This very wff — a "wff" is a well-formed formula within the system-at-hand — is not derivable within the system.
Standing back a way, one may twig to the fact that Gödel found a way to make wffs of PM talk about, not numbers like zero or two or 79,406, but wffs of PM! How he did takes Hofstadter two chapters to spell out Basically, Gödel figured out how to turn every conceivable symbol string of PM — well-formed or not, true or not — into a unique number. He devised a straightforward way of computing whether any given symbol string's "Gödel number" was in the set of numbers corresponding to all the wffs of PM. He demonstrated that the Gödel number of the "I am unprovable" symbol string was in the set. Hence, the PM-internal equivalent of "I am unprovable" is a wff.
Given that it is a wff, it cannot simply be thrown upon the trash heap as not even rising to the level of being a formula. So it must be either true (i.e., derivable) or false (i.e., not derivable).
Now — and this part of my discourse has to have a "to the best of my understanding" slapped conspicuously across it — it has not yet been determined which of these two possibilities is correct. For somewhat abstruse mathematical reasons, it is much, much harder to compute whether the number corresponding to a Gödel-arithmetized symbol string is in the set of numbers representing derivable theorems than it is to compute whether the number is in the wff set.
But never mind. It remains the case that the "I am unprovable" formula poses a double-barreled threat to the Mathematician's Credo. For if it does happen to be true, then there is at least one true statement of PM-extensible number theory that is — by its own self-implication! — unable to be derived within PM. In that case, PM would be intrinsically incomplete.
Or, if the "I am unprovable" formula happens to be false, then the formula is provable, and PM contains a contradiction.
Accordingly, PM is either incomplete or inconsistent.
Bertrand Russell could never accept that, according to Hofstadter. The hope of Russell and his co-author, Whitehead, was to constrain PM very carefully, in terms of its permissible symbols and rules, so that it was guaranteed to be both complete and consistent. To to that, Russell and Whitehead banned self-reference entirely, or so they thought. By not allowing sets, the theory of which was to serve as the rock-solid foundation for number theory, to "contain themselves," Messrs. R and W expected to forestall self-reference from ever cropping up within the PM system, no matter how elaborate it got.
What Gödel proved is that there simply is no way to banish self-reference from PM or any other equally rich formal system that mechanically shunts symbols around according to a fixed set of rules, thereby to produce scads of symbol strings that all qualify as being true.
But, says Hofstadter, the human brain is just such a symbol manipulator.
Accordingly, there is in effect no way that the brain — assuming it is elaborate enough, as the human brain surely is — could fail to be able to entertain as its own well-formed symbol strings such statements as (loosely translated into English) "I am this" or "I am not that."
Furthermore, that human capacity for self-referential "I"-ness has the ability to stand outside itself. It has what I am calling "externality."
A good example comes from Hofstadter's discussion of how Bertrand Russell judged his own Principia Mathematica system. Russell knew that at one level it was correct to say that PM was just a system that could derive certain wffs, but not other wffs. It was mechanical. The wffs had no "meaning." Neither, for that matter, had the derivable theorems. The latter were in some sense "true," but nonetheless they had no "meaning."
Yet at another level Russell was concerned lest, for instance, the wff which stood for "2+2=5" should turn out to be a derivable theorem. In the back of his head, Russell knew that the wff which stood for "2+2=5" did have a sort of "meaning" — by virtue, that is, of its being able to be "mapped" to "two plus two is five." Such a mapping — or, in technical lingo, such an "isomorphism" — indeed confers meaning on the wff by way of the wff's analogy with "two plus two is five." If the "2+2=5" wff turned out to be true within the system, whereas the analogous "two plus two is five" statement is clearly false outside the system, that would be a crushing blow.
Russell was, in fact, trying to "play God" by employing his own mind — a self-referential, "I"-generating formal system, in Hofstadter's view — to stand outside PM, another self-referential, "I"-generating formal system, and see how well the latter maps to a preconceived, PM-external standard of truth.
Thus, externality. The human mind, although it is itself a self-referential, "I"-generating formal system, is capable of standing outside other self-referential, "I"-generating formal systems of its own contrivance and judging the "meanings" of those systems' theorems against an external standard.
But here comes one of Hofstadter's "strange loops." The human mind can likewise judge itself — its own self, its "I" — and compare it to a preconceived, seemingly external standard of "truth." Indeed, I would hope my own self, my "I," to be as thoroughly self-consistent as Russell and Whitehead manifestly hoped their Principia Mathematica system to be. I would hope none of my self's "meanings" — none of the well-formed symbol strings that its rule system is capable of deriving; none of the thoughts which, upon due consideration, I believe to be "true" — turn out to be "false."
Stated by way of analogy with my religious understandings, I would hope that none of my beliefs contradict God's truth — for then I would be in sin.
One of the key facts about having a mind, accordingly, is that (assuming the mind arises from a sufficiently complex physical substrate) it turns out to be capable of standing outside itself and judging the truth value of its own "derivable theorems." It is an engine of theorem derivation, yes, but even as such, it is intrinsically incomplete. There is more to truth than it can mechanically derive — which doesn't faze it in the least!
The Gödelian alternative does faze it, though: that it is not (in a mathematical-logical sense) incomplete, but inconsistent.
Perhaps it is this preference for incompleteness over incoherence that underlies it's search for God — inasmuch as God, surely, possesses the one mind which is complete in the mathematical-logical sense. Or perhaps God is a stand-in for the mind's own externality: its ability to stand outside its own mechanical symbol-shunting process and attempt to judge how true the results of that process are.
My idea about God himself being a strange loop takes that thinking a step further. What if the whole world is conscious? What if, just as the complexity of a human brain is such that it is perforce a self-referential, "I"-generating formal system that can stand outside its own mechanical symbol shunting, the complexity of the world as a whole generates a "mind of its own."
This mind would, by strict analogy with ours, have the ability to transcend its own logical mechanics. Also by analogy with our own minds, it would be conscious — meaning that it would be able to confer coherence — nay, even "existence" — on what it consciously observes. That which it consciously observes would be ... what? Why, it would be the very physical substrate that gives rise to it: the world!
Furthermore, this "world mind" would be intentional, meaning that it is capable of goal-seeking behavior. The difference would be that, whereas our goal-seekingness can choose to manipulate things external to that which gives rise to it — things outside its body, that is — the "body" of the "world mind" would comprise everything in the physical world.
In ordinary religious language, the "goals" sought by the "world mind" would qualify as "God's will," and the process of bringing those goals about would represent "providence."
For, in my God-Is-a-Strange-Loop theology, GISL for short, the mind of God is this "world mind"!
More in my next post ...
No comments:
Post a Comment