God Is a Strange Loop, Part 4

Douglas Hofstadter's I Am a Strange Loop

In God Is a Strange Loop, Part 3, I continued showing the ideas worked out by Douglas Hofstadter in his recent book I Am a Strange Loop might play into a belief in God. It and its two predecessors, Part 2 and Part 1, dealt with "strange loops" of systems of mathematical logic wherein the systems unexpectedly turn right around and talk about themselves as axiomatic systems, while at the same time continuing to talk about whatever it was that they were intended to talk about in the first place.

An axiomatic system called Principia Mathematica, or PM, is set up to derive the laws of numerical computation, based on some simple axioms and rules of inference, as well-formed formulas consisting of strings of arcane symbols. If a well-formed formula is derivable — if it has a proof — it is called a theorem of PM.

PM has may theorems. One of them is (when translated into ordinary algebraic notation) "2+2=4". But "2+2=5" is not a theorem. While "2+2=4" is true, "2+2=5" is false. It cannot be derived, or proved.

Another theorem of PM — derivable, provable, hence true — is "There are infinitely many prime numbers." In fact, every true statement about numbers, or so it might be hoped, is mirrored by a theorem of PM.

But, no. As Austrian mathematician-logician Kurt Gödel showed, the following truth has a well-formed formula in PM which cannot be proven:

The formula that happens to have the code number g is not provable via the rules of Principia Mathematica.

I explained in my earlier posts what a "code number" —a.k.a. "Gödel number" — is. Suffice it to say that every formula of PM can be "arithmetized" to yield a single number which stands for the formula itself (!).

The above formula is stated in English translation, of course; inside PM, it appears in the form of a symbol string that is pretty much incomprehensible to the average eye. But never mind. We can still refer to the formula quite easily, amongst ourselves, by assigning it a name: KG, in honor of Kurt Gödel. Then we can ask, "What formula of PM happens to have g as its code number? And, for that matter, what number is g, and how is it computed?"

To answer the second question first, g does not really need to be computed per se! Gödel gave some "assembly instructions" for it by means of which it can be referred to within KG ... and that's all that is truly required.

The answer to the first question is that the formula which happens to have g as its code number is KG itself!

All of which means that the following is a "second-level meaning" of the original formula:

I am unprovable.

Whichever level of meaning you care to focus on, the formula in question is in fact unprovable. Which means it's true even though it can't be proven ... since if it were false, there would be a germ of inconsistency within PM that would spread to infect the whole system, rendering it useless.

Extrapolating from the above, we can see that it is not possible for mechanical systems of truth derivation to be "complete," in the sense that all truths about themselves are derivable. Oh, there are degenerate cases wherein the mechanical systems of truth derivation are so limited in their powers that they cannot even prove "2+2=4". But any system that can generate what mathematicians call number theory, in all its glory, is necessarily incomplete in a Gödelian sense.


The obvious conclusion we may draw is that truth is larger than provability. There is indeed in this world what Hofstadter calls a "true/false dichotomy." Yet he shows that

... the boundary line is so peculiar and elusive that it is not characterizable in any mathematical fashion at all. (p. 172)

Which means much of what is true has only "downward causality." All truth simply cannot be produced in a strictly mechanical fashion from the bottom up.

The formula KG discussed above can only be produced by a clever mind such as that of Kurt Gödel, working from the outside in, or from the top down. It cannot be generated in the "ordinary" way — from the bottom up, from the inside out — by applying PM's rules of mechanical inference.

KG's truth, likewise, can be known only by one who stands outside PM and peers in. Once KG has been oh-so-cleverly constructed by a great mind looking at PM from the outside, its truth is in a sense bestowed on it by the very mind of its constructor. Its original constructor was Gödel, of course, but he showed the rest of us (today, with Hofstadter's able help) how to construct this crucial formula of PM in such a way that we feel compelled to bestow truth upon it as well.

The argument which serves as our justification for bestowing truth on the unprovable is, once understood, irresistible. It crucially depends on the second-level meaning of KG, "I am unprovable," and on our seeing that a formula with such a second-level meaning simply must be true, even if unprovable ... or the entire system turns incoherent.

By analogy, truth bestowal — what Hofstadter calls "downward causation" — applies to the world as a whole, I would say. What works with respect to an axiomatic system like PM works equally for the cosmos we live in. There are things that are true about the universe that do not derive mechanically from the low-level workings of its particles and force fields. Some of its truth is bestowed from above.

But not, I would say, by a God who exists wholly outside the universe. Rather, God is an emergent property of the universe. God is the "I" who emerges from that which he bestows truth upon. That is why I call my philosophy a "God Is a Strange Loop" theology!

More later ...

God Is a Strange Loop, Part 3

Douglas Hofstadter's I Am a Strange Loop

In God Is a Strange Loop, Part 2, I enlarged upon my conjecture as to how the ideas worked out by Douglas Hofstadter in his recent book I Am a Strange Loop might play into a belief in God.

Hofstadter lays out an argument about how a human brain generates its symbolic "I" entity as a sense of self, a seat of consciousness, and even a soul. Details as to how the Hofstadter argument is couched can be read in the previous post and also in its predecessor, God Is a Strange Loop, Part 1. At this point, I would simply like to summarize the argument in a way that I dreamed up overnight.

Imagine, if you would, a T-shirt with the following message emblazoned across its front:

My Gödel number is not prim.

That's right ... that final word is "prim," not "prime." It applies to a number that, when suitably decoded using a standard recipe of algebraic computations, turns into a formula. This formula — one possible formula is simply "0=0" — consists of a string of symbols defined in a system of axioms and rules to be used for deriving the theorems of mathematical number theory.

Number theory is the theory underlying all the computations we (or our machines) do every day, including the computations by which the number that we wish to decode into a formula of this so-called "axiomatic system" is actually decoded. One theorem of the system that can derive mathematical number theory — or, actually, one axiom — is, of course, that zero equals zero.

If a number is "prim," it decodes into a symbol-string formula that our axiomatic system of number theory can derive, or "prove." But a number that is not "prim" — Hofstadter calls it a "saucy" number — decodes into a symbol string that is not provable within the axiomatic system.

By reversing the decoding process, one can encode any arbitrary string of symbols of the axiomatic system (which is called PM, after Principia Mathematica, a three-volume work by Bertrand Russell and Alfred North Whitehead — whence comes "prim"). The encoding process involves another computation, and it spits out a single number, called the string's "Gödel number." That name comes from Kurt Gödel, the Austrian mathematician/logician who, in 1931, figured out how to turn symbol strings of PM into numbers, and vice versa.

If the Gödel number of a string is prim, it means the symbol string is a well-formed formula of PM, and not just some hodgepodge of PM symbols thrown together at random. Furthermore, that particular well-formed formula, or "wff," happens to be one that PM can derive/prove — hence the "primness" of its Gödel number.

A wff such as "ss0+ss0=sssss0" is not provable, thankfully, because it means "2+2=5". ("ss0" stands for "the successor of the successor of zero," or 2; "sssss0" stands for the number which is fifth in the successor-to-zero sequence, or 5.)


Accordingly, when my hypothetical T-shirt says "My Gödel number is not prim," it's implying three things:

1. "I" have a Gödel number, which means "I" am in some sense like a PM symbol string
   
2. "My" symbol string is a wff, and not "symbol salad" — for if it were not a well-formed formula, the question of whether its Gödel number is prim would be totally irrelevant
   
3. The wff which "my" symbol string composes is, alas, not one whose Gödel number is prim
   

From those three implications can be derived a fourth, which is stenciled on the T-shirt's back:

I am not provable (therefore I am).

Any wff of PM which is not provable (not able to be derived by applying PM's rules to its axioms and previously derived theorems) is not a theorem of PM, and therefore presumably untrue. But, nominally, the theorems of PM are about numbers, not about theorems of PM. The theorem which Gödel derived whose English translation is "I am not provable" is an important exception. It's one which turns out to be among an infinite number of such exceptions ... but who's counting?

Even though "I am not provable" isn't obviously about a number, it has a Gödel number. For it to say, in effect, "My Gödel number is not prim" is merely to restate the selfsame "I am not provable" claim in different terms.


As an exception to the general rule that PM formulas are manifestly about numbers, this "My Gödel number is not prim" formula (which Hofstadter names KG, after Gödel's initials) has the same form as the non-exceptional "72900 is not prim". The latter formula happens to be false, since 72900 is the Gödel number of the PM theorem to the effect that "0=0". But "576 is not prim" is true, since 576 is the Gödel number of the PM formula "0=", which is not even well-formed, much less provable.

The "My Gödel number is not prim" formula, KG, is constructed like "72900 is not prim" or "576 is not prim", but with a twist. The hard-coded "72900" or "576" is replaced with a reference to the Gödel number of the very symbol string composing the KG formula itself!

When I speak of "a reference to" the Gödel number of KG itself, I mean the numerical or mathematical equivalent to our first-person pronoun "I" (or its variants such as "me" or "my").

This is why the KG formula can be translated as "I am not provable."


Now for an explanation of why I tacked "(therefore I am)" onto the end of the second T-shirt message.

Whether KG is expressed as "I am not provable" or as "My Gödel number is not prim," it simply cannot be false. It must be true. For if it were false, then it would be, in fact, provable ... and its Gödel number would accordingly be prim. But if provable, KG would be asserting a lie. Such a contradiction is inadmissible to any axiomatic system, since it would be like the one rotten apple that spoils the bunch. If any false assertion could be proved, then every false assertion could likewise be proved ... and the original intent of the axiomatic system to separate truths from falsehoods would crumble into dust.

So KG is true ... but not provable. Ergo, every axiomatic system (not just PM) lacks the ability to prove not just this but an infinite number of truths about itself.

Also, every axiomatic system that is at least as powerful as PM (i.e., it can derive the laws of standard number theory) is entitled to construct an internal symbolic reference to what amounts to an "I". The formulas that contain this symbolic "I" can typically not be proven ... yet the emergent phenomenon for which the English-language shorthand symbol is "I" has to be admitted to, in some sense, be in existence. It emerges, willy-nilly, from the fact that any PM-equivalent axiomatic system contains an infinitude of well-formed formulas — provable or not — each of whose Gödel number is that of the formula as a whole, and is also (by means of a proxy reference) a part of the formula.

Whenever that happens, the axiomatic system is entitled to tack on "(therefore I am)" to the tail end of its KG formula.


Hofstadter shows that the human brain is at some level precisely such an axiomatic system. It is a mechanical, computational machine, which is to say exactly the same thing about it. Yet, for the reason just given, it has an "I", and it is entitled to tack on "(therefore I am)" to the tail end of its KG formula and every other formula — every other thought — in which its "I" symbol necessarily appears.

Thus does each one of us possess legitimate certainty that he or she exists — never mind that none of our thoughts to this effect can be proven by rule-based derivations. If my "I" exists, it does so independently of provability.

When I imagine that "I" have on a T-shirt that says "My Gödel number is not prim" on its front and "I am unprovable (therefore I am)" on its back, what that really means is that such a T-shirt adorns my body — not my mind or soul. My "I" emerges from matter but is itself immaterial.

In my "God Is a Strange Loop" theology, I take that image and reapply it to the universe as a whole as if it were a body with a brain from which emerges an immaterial "I". The universe-as-a-body would, of course, need a "size cosmic" T-shirt, not the mere "size large" that I wear. Still, it makes sense to me to at least conjecture that God is the immaterial "I" of which the cosmic T-shirt speaks.

God Is a Strange Loop, Part 2

Douglas Hofstadter's I Am a Strange Loop

In God Is a Strange Loop, Part 1, I discussed my conjecture as to how the ideas worked out by Douglas Hofstadter in his recent book I Am a Strange Loop, notions about the genesis of the "I" in each human brain, might be extrapolated into an understanding of God as a sort of "world mind" or "world soul."

The human "I" is an emergent phenomenon, Hofstadter shows. Like all the "symbols" which the brain gives rise to, it springs forth from the workings of the lower-level components of the brain, the neurons and the signals they ceaselessly exchange. The "I" exists at the pinnacle of the human brain's rich symbol system. It potentiates self-awareness. It makes possible our conscious, subjective experience. It is the self. It is the soul.

Stripped to its barest essentials, the "I" represents the brain's ability to think about — to make and evaluate assertions about — its own thoughts. For example, if I think to myself, "I never think about pink elephants," the presence in my symbol system of an "I" symbol makes that thought possible.

But what makes the "I" symbol possible? After all, it is not intuitively obvious that a computer — a mere machine, even if it were to be programmed with all the artificial intelligence in the world — would, or could, generate an "I." Then again, it is not intuitively clear that it couldn't.

For what makes an "I" possible, Hofstadter says, has to do with what Austrian mathematician Kurt Gödel proved in 1931 with respect to any and all formal systems of logic. If the systems are at least powerful enough to derive the mathematical theory of numbers, there are, quite shockingly, some truths about numbers — and about themselves as systems — that they simply cannot derive.


To prove this, Gödel showed that all formal, rigorous, strictly mechanical systems of logical derivation — and by extension, all computers, even though computers hadn't yet been invented — can be "arithmetized." They can have their internal statements — their formulas, their candidate theorems — turned into numbers. The numbers are intrinsically subject to the laws of computation, which are actually theorems of number theory.

Gödel accomplished his feat by "arithmetizing" a formal system: one that had been designed to derive these very laws of computation as theorems of number theory. Specifically, it was the formal system developed by Bertrand Russell and Alfred North Whitehead in their series of books called Principia Mathematica. For example — and thankfully — Russell and Whitehead's PM system was capable of proving such theorems as (in symbols we recognize, not those used in PM) "2+2=4".

Gödel cleverly did all his "arithmetizing" in such a way as to be able to show that one possible candidate theorem in PM is the formula which can be loosely rendered as, "This very formula is unprovable in the PM system"!


The well-formed PM formula for which that sentence is just one possible English translation could just as well be translated more tersely as "I am unprovable" (with "in the PM system" being tacitly understood).

Thus, any general formal system of theorem derivation, as long at it is no less powerful than the number-theoretical PM system, is implicitly mirrored by an equally mechanical system of numerical computation. The fact that computations precisely mirror the formal system which derives the laws for doing those computations is key.

Moreover, Gödel showed that, in the PM-mirroring set of computations he devised, the so-called "Gödel numbers" that serve to "arithmetize" the well-formed formulas of the theorem-deriving system can be calculated independently of that system. You can take any counting number from the set 1, 2, 3, ... and determine whether the string of PM symbols it codes for is well-formed or not, according to the rules of PM.

For example, 72900 can be factored into 2² times 3⁶ times 5². The base numbers 2, 3, and 5 are successive prime numbers that can't be further factored. The exponents 2, 6, and 2 stand for, respectively, "0", "=", and "0" again. Thus, 72900 can be converted into "0=0", which is a well-formed formula in PM.

But 576 is not the Gödel number of a well-formed formula, or "wff." Its "prime factorization" reveals it to be equal to 2⁶ times 3². Hence, since 2 stands for "0" and 3 stands for "=", the exponents taken in sequence — 6, then 2 — translate the number 576 into the PM formula "0=". "0=" is a symbol string that is, shall we say, "ungrammatical" in PM.


To get back to Gödel's main goal: it was to prove that any such system as PM will have as one of its well-formed formulas the assertion "I (i.e., this formula) am unprovable."

Hence, any such system will have, in effect, an "I". If it didn't, all formulas of that general form would be sheer nonsense — which they aren't. They are as well-formed and as "grammatical" as "0=0".

The human brain, moreover, is presumably a general, powerful, PM-equivalent computational device. By "PM-equivalent" I mean that at some level of its inner operation the brain does exactly what PM or any other formal system does. It starts with some basic, unassailable rules of theorem derivation, a set of basic symbols, and some basic axioms which any fool can see are true, and proceeds to work out a huge set of further truths, beyond the axioms.

Accordingly, the operation of the brain itself mirrors PM, and every system like it. Furthermore, it cannot fail to do so in a Gödelian way, such that the brain's operation is also mirrored (however abstrusely) by numbers and the way numbers can be calculated, based on other numbers.

Like whatever formal system of logical derivation the brain may mirror in its Gödelian way, it is inherently truth-seeking. It wants to extend what it already knows — its axioms, plus those theorems it has already proven, so to speak — to derive in a strict, rule-bound way, more truths. It wants to know the truth, the whole truth, and nothing but the truth.

The whole truth, of course, includes what we know about ourselves: knowledge associated with our personal, individual "I" symbols. Given what Gödel proved about all formal systems and their arithmetical mirror images, it is not surprising that we can — indeed, we need to be able to — speak of ourselves in the first person, as an "I".


Gödel proved that any such system is "incomplete." To a mathematician, a computational system involving turning numbers into other numbers in lawful ways is incomplete if there is no way to tell for sure whether any given number actually belongs to a given well-defined set of numbers.

For example, take the set of prime numbers. A prime number is one that cannot be factored into smaller numbers which, when multiplied together, yield the original number. 11 is a prime number because the only multiplication of integers that yields it is 11 x 1. 12 is non-prime, or composite, because 4 x 3 = 12.

The set of prime numbers is infinite, it has been proved; there is no such thing as the highest prime number. Yet, because it is fairly easy to compute whether any candidate integer is prime, the set of prime numbers is considered complete.

In Gödel's proof of his so-called "Incompleteness Theorem," the well-defined set in question is not the set of primes, but instead the set of all Gödel numbers that represent theorems in PM. Gödel proved, crucially, that this particular set is incomplete.

In particular, the "I am unprovable" formula, expressed in terms of PM symbols, like all other formulas necessarily has a Gödel number: an inconveniently huge integer, unfortunately, which Gödel gave instructions for slimming down and plugging into the PM version of the "I am unprovable" formula, right in place of the "I". That hard-to-calculate number can be abbreviated g. g, in addition to forming a small part of the way this formula is expressed in PM, also is the Gödel number of the "I am unprovable" formula as a whole.

That, in a nutshell, is why g can have the pronoun "I" substituted for it in an English translation of the "I am unprovable" formula! The same formula could equally well be translated, "The formula whose Gödel number is g — which just so happens to be this very formula — is unprovable." Use of "I" makes the formula terser and a lot easier to state.


The fact that g is both a term in the formula and the Gödel number of the formula is what Hofstadter means by a "strange loop." Formal systems with no more than a modicum of theorem-generating power — just enough to derive the laws of number theory, in fact, and no more — all have strange loops. There is no way for such a system to be designed to avoid this kind of strange-loopiness, Gödel proved. There is no way for it to avoid having the ability to formulate first-person truths, truths which necessarily begin (in effect) with the pronoun "I".

Of course, it can likewise formulate first-person falsehoods. But the ability to formulate a falsehood — first-person or otherwise — is not the same as the ability to derive or prove that falsehood, as if it were somehow the truth.

The "I am unprovable" formula — Hofstadter dubs it "KG" in honor of the initials of its discoverer, Kurt Gödel — might conceivably be false. But if KG were false, then it would be provable, since "provable" is the logical opposite of "unprovable." But KG, a statement that says "I am unprovable," simply cannot be provable ... or there would be a contradiction lurking within the bounds of the PM system.

Hofstadter shows that this situation quite simply isn't allowable, for "if any false statement, no matter how obscure or recondite it was, were possible in PM, then every conceivable arithmetical statement, whether true or false, would become provable, and the whole grand edifice would come tumbling down in a pitiful shambles. In short, the provability of even one falsity would mean that PM had nothing to do with arithmetical truth at all" (pp. 163-164).

That would be unthinkable. The only other choice Gödel left us would seem, accordingly, to be inescapable. If they are not to be deemed inconsistent, then PM and all other formal systems like it with an "I" or strange loop lurking inside them have to be logically "incomplete."

Again, "incompleteness" means there are truths about the systems themselves that — although the systems can produce well-formed, "grammatical" formulas that express these truths — cannot be proven. One such well-formed formula is that whose English rendition is "I am unprovable." And there are an infinite number of other ones as well.


My "God Is a Strange Loop" conjecture is analogous to Hofstadter's belief that an "I" symbol is an emergent property of the human brain. Because the brain pretty much has to be is a formal, mechanical system of truth derivation with a numerical, computational Gödelian mirror image, it pretty much has to generate an "I".

My GISL conjecture is that the world as a whole is a formal, mechanical system of truth derivation with a numerical, computational Gödelian mirror image. Consequently, it too inescapably possesses a strange loop, an "I". The "I" of the world system is God.

God is the (absolutely necessary) emergent property of the world system who can meaningfully say, per the Old Testament, "I am that I am" (Exodus 3:14). By that odd construction, I think, God is describing himself as the quintessence of "I"-ness. God is the "I" greater than which no other "I" could conceivably be. (Perhaps the burning bush is analogous to the fact that trying to understand the logical "strange loop" at the heart of each and every "I"-ness can drive one totally bonkers!)


It is interesting that Hofstadter's argument about the relationship of every "I" to Gödelian strange-loopiness requires, at bottom, what the author calls "one article of faith" (p. 163). Namely, the requisite article of faith is the one referred to earlier in this post: the belief that the formal, mechanical, computational system from which the "I" emerges cannot contain an inconsistency.

All such systems have to be either inconsistent or incomplete, Gödel proved. Given the choice, the latter option simply has to be ruled out on its face. Otherwise, the system becomes incoherent and incapable of distinguishing truth from falsity.

It is not hard to find the same basic assumption about God carried explicitly or implicitly in the various theologies, be they liberal or conservative, of the Judeo-Christian faith communities. It just makes no sense whatsoever to talk of a God who makes no sense.

It makes no sense to think of God as the creator of the world, and of the cosmic order in the universe, if God were somehow even capable of making no sense. Coherence — a starting point of truth that forms the basis for any hope we humans may have for seeking and finding the whole truth — is simply taken as an article of faith in the Judeo-Christian worldview.

Accordingly, I assume it must also be taken as an article of faith in any theology deriving from my "God Is a Strange Loop" conjecture. Embracing such a commitment means that it may be possible to harmonize my "GISL theology" (as soon as I can work out what it is in full detail) with standard Judeo-Christian beliefs. But more on that in my next post ...

God Is a Strange Loop, Part 1

Having laid out what I intended to be a definitive theistic metaphysics in a series of five posts winding up with Genesis by Experience, Part 5, I now proceed blithely to contradict myself, if only to a degree.

"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

I woke up this morning to the realization that ideas put forth by Douglas Hofstadter in his most recent book, I Am a Strange Loop, and in its predecessor, Gödel, Escher, Bach: An Eternal Golden Braid, can bridge the dilemma's two horns.

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 ...

Genesis by Experience, Part 5

Genesis by Experience, Part 4 was my most recent post in this series in which I am trying to fashion a metaphysics I call genesis by experience, or GBE. In it, there is a God, and our own conscious minds are an echo or mirror image of God's consciousness. Just as our conscious acts of observation are capable of conferring factual coherence on quantum indeterminacy in our world, God's watching of the world confers grand coherence on the cosmos as a whole. An upshot of that is the reliability of worldly causality. In fact, the core principle of GBE is that causality is consciousness conferring coherence ... upon the cosmos, or upon any part thereof.

But GBE purports to be a metaphysics, not just an account of consciousness, causality, and coherence. A metaphysics is an account of existence per se. In order to extend what I have already said into a full-fledged account of existence, all I need to do is state an auxiliary principle that goes along with the core principle of GBE. The auxiliary principle is this: to exist is to be caused.

By that I mean that existence comes from being caused. If you exist, it is because you are caused.

If you exist, then it is because some consciousness has conferred coherence upon the stuff that you are made of, and has done so in such a way that you wind up having the particular qualities, properties, and characteristics by which you are accordingly are going to be able to be recognized as you by ... uh, well, recognized by any conscious mind!


You might think, if you disagree with me about the role of God in all this, that the causality that directly or indirectly puts your "stuff" together in a way that makes you and only you is something that happens in a sort of consciousness vacuum, such that your ineffable recognizability to other conscious minds, and to your own, arises only after the fact of your initial assembly at the hands of forces and laws of nature.

I reject that point of view — in part, because it makes it hard, if not impossible, to give an account of your existence-qua-existence. On the other hand, if existence is predicated on consciousness — God's consciousness, ultimately — then the problem solves itself. You exist, basically, because God sees you. As long as God sees you, you will always exist. And God has never not seen you. That is what the immortal soul is all about.


GBE is dualistic, as I said in the previous post, in that it finds mind and matter to be distinct. So it is fair to ask, does mind exist? If matter exists by virtue of being "seen" by mind, can the same be said of mind itself?

On this point I must admit to being a bit agnostic. On the one hand, we know that our conscious minds seem to be blind to any direct, observational awareness of those of other people. There is no way, except by analogy with my own introspection, for me to be certain that you are conscious. In fact, when each of us puts our own conscious mind under a powerful enough logical microscope, it seems to reveal to us that even our own consciousness may be but an illusion.

If I can't observe consciousness, can consciousness be said to exist? That seems to be the question.

On the other hand, perhaps all that is going on here is a limitation that applies to human consciousnesses, but not to divine consciousness. Perhaps God can "see" our conscious minds perfectly well ... and, accordingly, confer existence on them by way of imposing coherence on whatever "stuff" our conscious minds are made of. That's another way of looking at the situation. I don't know which one is right.


At any rate, now that I have failed to resolve the riddle of whether the thing which has the power to confer existence — this "thing" called consciousness — itself exists, I'd like to move on to another topic that interests me. It is the topic of intentionality.

For it seems to me that intentionality ranks with consciousness as a salient characteristic of mind. Minds not only have subjective experience, assuming they are conscious; they also have goals, intentions, desires, and the like. They try to arrange for certain outcomes to occur, and accordingly to suppress other possible outcomes.

In fact, it could be argued that God intentionally imposes coherence upon the world, thereby making for its reliably observable causal relationships, because he sees coherence as being his originative goal for the world. If there is to be a cosmos and not a chaos, it will be because God intentionally chooses that outcome instead of the other, and arranges for it to happen.

Out of that originative coherence, one could argue, emerges all the other facts about the world which God intends to see emerge — including the eventual evolution of beings called humans that themselves have conscious minds and can be said to be made in God's "image." Again, intent is meshed with consciousness: God's sees the world he intends to make. Intentionality and consciousness are two sides of the same mental coin.

Genesis by Experience, Part 4

"Causation is consciousness conferring coherence," I stated as the core principle of my incipient genesis-by-experience metaphysics, in my last post in this series, Genesis by Experience, Part 3. By that I meant that the aspect of mind we experience subjectively as consciousness is not just causally passive; it makes potentialities into realities, à la the quantum-theoretical paradox by which an observation of a photon's arrival at a human retina, through an intentionally aimed telescope, "fixes" the particular path the photon "chose" to take to us from a far-off quasar millions of years ago, before the first human walked the earth.

By implication — at least to this theistically inclined amateur philosopher — the consciousness religious believers attribute to God likewise turns potentialities into realities on a cosmic scale. This is what I take to be God's creative and sustaining role as founder of the universe. Thus do I arrive at the name I give my metaphysics: genesis by experience, which I abbreviate GBE.

David J. Chalmers's The Conscious Mind

GBE is an attractive theory to me for several reasons. One of them is that it collapses two hard-to-explain sets of facts into one. Philosopher of mind David Chalmers writes in The Conscious Mind that our possession of consciousness is not a slam dunk, given all the physical facts about our bodies and our world. Nor is the operation of causality, assuming causation is somehow more than just a reliable indicator of purely coincidental regularities occurring between so-called "causes" and so-called "effects." What is causality? What is consciousness? Why do they both exist? How can we be sure they exist? Tricky questions, all.

Chalmers attributes consciousness to "extra" laws of nature that, figuratively speaking — he says he has no particular belief in a divine creator — God put into the mix when he created the world. He takes a pass on the metaphysics of causality after noting that there may be an ineffable link between it and consciousness, preferring not to embrace any notion that leads to conclusions along the lines of "everything is conscious."

My GBE skirts the "everything is conscious" conclusion by virtue of its dualism. Mind and matter are different. Metaphysically, mind precedes matter. By that I mean that mind — consciousness, observation, sight in its purest sense — fixes the incoherent potentialities of matter into coherent actualities, thus making a world.

Thus, causation is consciousness conferring coherence. Philosophically, it's a "twofer." You get explanations for two mysteries for the price of one. The world is a coherent place. In that world, both consciousness and causation are not illusions or figments of the imagination but existentially real. They both stem from the intrinsic coherence of one single divine nature.


Another reason I like my genesis-by-experience metaphysics is that it contradicts both religious skepticism and religious fundamentalism in one fell swoop.

A great many philosophers today are religious skeptics — atheists, agnostics, freethinkers — who are ideological heirs to positivism, which holds that metaphysical propositions that cannot be verified by science are meaningless. They don't even rise to the level of being wrong.

Then there are the religious fundamentalists who seek to oppose atheism by affirming the "literal truth" of the Bible. Fundamentalism has taken the form of creationism, the idea that the stories of God's creating the world that are found in the Book of Genesis alongside the story of Noah's Flood and then the recitation of the generations of man leading up to the writing of the Old Testament are not fraught with poetic license. They are literally true, fundamentalists say, and if science thinks evolution happened, science has another think coming.

GBE metaphysics suggest that "In the beginning" — as in the Bible's assertion in Genesis 1:1, "In the beginning, God created the heavens and the earth" — refers to metaphysical precedence, not temporal precedence. There still could have been — and was — a process of biological evolution on earth over the course of billions of years of time. That poses no problem to religious belief; God exists metaphysically outside time.


GBE is a stereoptic metaphysics that converges the worldview of two separate "eyes" into one solid image. One eye is that by which we see the physical world itself, as if it were all that truly exists, and the other is the one by which we can "see" the metaphysical basis for the physical world: consciousness conferring causal coherence. God's consciousness confers causal coherence, and a world is born. Our consciousness echoes God's in observationally turning incoherent quantum potentialities into coherent concrete realities, and a world is affirmed.

Religious skeptics are accustomed to using just the first eye. Religious fundamentalists are wont to close that first eye in favor of the second one, which gives them "metaphysical vision." GBE humbly asks, "Why close either eye?"


Another way to look at the situation, philosophically speaking, is to ask what "facts" GBE takes for granted. In his book, Chalmers says he bypasses philosophical skepticism about how we know the physical world really exists, when we could just as well be "brains in vats" (p. 75). He does so by "giving myself the physical world for free," by which he means that he takes as given "all the facts about distribution of physical entities in space-time."

Doing that, he says, is tantamount to "fixing all physical facts about the world in the supervenience base" (pp. 75-76). He says facts about consciousness "supervene" on the "microphysical" properties of this world — the "supervenience base," in his way of looking at things — such that if our world lacked conscious beings, it would ipso facto have to be different in some way physically. Different subatomic particles in different arrangements in different force fields in our universe equal, to Chalmers, no consciousness. But, given all the microphysical facts of our universe as they actually exist, plus all the laws of nature including, he says, as yet undiscovered "psychophysical" laws, the universe is bound to have conscious beings in it. That's Chalmers' view in a nutshell.

My basic quarrel with Chalmers is that I don't agree that you can take the microphysical properties of this world as (even conceptually) given or known — "for free," as he characterizes his assumption.

Why not? Because, mainly, of quantum indeterminacy, the apparently necessary incompleteness in the description of a physical system that has become one of the characteristics of the standard description of quantum physics.

I know just enough about quantum theory to get myself in trouble ... so here goes nothing! I relate quantum indeterminacy to the paradox of Schrödinger's cat. Quantum-physics pioneer Erwin Schrödinger proposed a paradoxical thought experiment in which a cat would hypothetically be placed in a sealed box with a device that would release a lethal gas if and only if a radioactive particle decayed. The decay event would or would not occur in the period before the box was opened according to a probability function depending on the half-life of the particle. So, upon opening the box, the observer would find the cat either dead or alive. If the experiment were repeated many times, the ratio of dead cats to live ones would be expected to match that known probability.

The paradox was that, according to the laws of quantum mechanics, the life-death outcomes would remain indeterminate until the concluding acts of observation took place! Neither "the cat died" nor "the cat lives" would be a fact until the box was opened!

Hence, the set of physical facts which Chalmers takes as knowns or givens in his supervenience base has to be thought of as inevitably incomplete ... absent, that is, the requisite acts of observation which serve to "fix" those facts.


My genesis-by-experience metaphysics "fixes" that problem — pun intended — by flipping the "supervenience base" in such a way that physical "facts" now depend on two paired "facts" about God:

• God is conscious
• God observes the world

Thus do quantum indeterminacy and incompleteness give way to reliable causality and coherence in the world.

Chalmers treats consciousness and causality as the two major mysteries about our world, since it is not clear that either logically supervenes on the physical. It would not be totally nonsensical to imagine an alternate world in which consciousness is absent or causality works differently.

Well, in view of quantum indeterminacy and incompleteness, wouldn't coherence itself, at levels of organization above the quantum world, qualify equally as an explanandum in search of an explanation? Couldn't causality then be viewable as supervenient on coherence, with the latter supervenient on consciousness? That's the GBE view in a nutshell.


Oh, and ... does Schrödinger's cat accordingly die, if at all, before the box is opened? God only knows.

I don't mean that (entirely) as a joke. Literally, God, who sees all he wants to see, can know the outcome "in advance," and it would make sense to say that his observation of the cat inside the box "fixes" the outcome prior to our opening the box. On the other hand, how do we know he doesn't avoid "peeking" so as to allow our acts of conscious observation to complete the scenario? Here might begin a deep discussion of how God arranges for us to have free will.

Genesis by Experience, Part 3

In Genesis by Experience, Part 2, I continued sketching out my "genesis by experience" take on metaphysics. It is a theory of the existence of the human self or soul, a theistic theory that holds our — and the world's — existence to be caused, created, and constituted by "experience" taking place in the mind of God. Having such an experiential awareness of each and every one of us is what it means to say that God "sees" us: as the hymn goes, his eye is on the sparrow, and I know he watches me. It is by virtue of his never ceasing to watch us that each of us has an immortal soul.

Douglas Hofstadter's I Am a Strange Loop

My starting point in developing my "genesis by experience" philosophy of the soul is, as I said in the earlier post, Douglas Hofstadter's new book, I Am a Strange Loop. The book gives a explanation of how the human brain generates a sense of self or "I."

Hofstadter posits that the mind is populated with high-level "symbols" that emerge from the lower-level workings of the physical brain constituents, taken at the level of neurons, or atoms, or signals, or whatever. The self or "I" is simply the most crucial and most central of these emergent symbols, and Hofstadter accordingly identifies the emergent "I" with the consciousness we each harbor as well as with the soul we typically expect we have. (I personally think he is wrong about the soul having no independent existence outside the workings of the brain, and maybe about consciousness, too, but he's probably right about the emergence of the "I" symbol in the brain.)

David J. Chalmers's The Conscious Mind

My theory of genesis by experience depends, as I also said in that earlier post, on the notion that consciousness is causative. To borrow words from David J. Chalmers, author of The Conscious Mind: In Search of a Fundamental Theory, it is conceivable that consciousness itself — "subjective experience," "raw sensation" — is "a kind of causal nexus."

Our knowing "what is is like to be red," arising in response to the raw sensation we have of the color red when we see, say, a red tricycle, is what Chalmers means by consciousness. I consider it a kind of empathy. But it is more than that, I would quickly add. Consciousness is not only empathetic, it is also causative. I would, in fact, adopt the following as my philosophy's basic principle: causation is consciousness conferring coherence.

Chalmers finds consciousness and causality to be the two principal categories of facts in our world that do not supervene logically on physical facts. His book is primarily an argument that facts about consciousness do supervene on the facts and natural laws of our physical world ... but, for all logic has to say about it, the situation could be otherwise, and so the supervenience is "natural" and not "logical."

The natural/logical distinction can be put this way: unlike the logically necessary supervenience of biological facts on physical ones, the supervenience of consciousness on the physical realm in our world requires that God (figuratively speaking, in Chalmers' non-theistic worldview) had to do "extra work" or make "extra laws of nature" to make that happen.


Philosophers speak of "supervenience" when they want to to posit that one set of facts — or, actually, one set of properties — is unfailingly associated with another set that exists at a different conceptual level of organization. For example, living organisms' biological properties — for instance, their homeostasis, which is an organism's ability to regulate its internal environment to maintain a stable, constant condition — can be said to supervene on their physical properties such as the nature of the chemical reactions taking place inside their cells.

In I Am a Strange Loop, Hofstadter in effect shows how the mental constructs he calls "symbols" supervene on the electrochemical activity of neurons. When we want to talk about how the brain operates, we frequently need to take recourse to explanations involving the interactions of high-level symbols, he says, since trying to follow how low-level signals shunt about among the millions of neurons in the brain is a fool's errand. To reductively explain how, say, our seeing a cow triggers within us a feeling of nostalgia for a rustic past, we simply are forced to use the convenient "shorthand" of high-level symbols.


But Chalmers has it that not all supervenience is just a verbal shorthand that sidesteps the need to make impossibly detailed reductive explanations. In the case of consciousness, no reductive explanation is possible, Chalmers maintains. Hence, he says, consciousness is naturally supervenient on the physical, but it is not logically supervenient. In another imaginable world that is outwardly identical to this one, our "zombie twins" might wholly lack conscious experience.

Likewise, Chalmers shows that facts about causality in our world (as, for instance, how it is that we can know that "A causes B") supervene on "physical entities in space-time" in a mysterious way that we cannot logically say has to be that way.

David Hume and other philosophers, writes Chalmers (pp. 74-75), have claimed that

...external evidence only gives us access to regularities of succession between events; it does not give us access to any further fact of causation. So if causation is construed as something over and above the presence of a regularity (as I will assume it must be), it is not clear that we can know that it exists.

Put briefly, Chalmers simply assumes that causation beyond Hume's mere "regularities of succession" does in fact exist in our world, even if it's existence is mysterious and hard to confirm.

This problem concerning the uncertain existence of causality, says Chalmers, crops up also with respect to questions about consciousness. I can never know for sure that consciousness exists within you ... or, for that matter, within myself, since a zombie world is conceivable wherein my otherwise identical twin lacks consciousness, but is entirely unaware of that fact ... so how can I know for sure that I am who I claim I am, and not my blissfully ignorant zombie twin?

Concerning causality's hard-to-pin-down existence, Chalmers continues:

Once again, this skeptical problem goes hand in hand with a failure of logical [as opposed to natural] supervenience. In this case, facts about causation fail to supervene logically on matters of particular physical fact. Given all the facts about distribution of physical entities in space-time, it is logically possible that all the regularities therein arose as a giant cosmic coincidence without any real causation. At a smaller scale, given the particular facts about any apparent instance of causation, it is logically possible that it is a mere succession. We infer the existence of causation by a kind of inference to the best explanation — to believe otherwise would be to believe in vast, inexplicable coincidences — but belief in causation is not forced on us in the direct way that belief in biology is forced on us.

Chalmers accordingly believes that consciousness and causality are two separate categories of facts (and possibly the only two categories) that, out of other than strict logical necessity, spring forth from "the facts about distribution of physical entities in space-time" in our world.

True, he at one point (pp. 152-153) briefly considers, and then provisionally rejects, the possibility that these two sets of facts are ineffably related "so that there is a subtle sort of relevance for experience in causation." He says the main reason he spurns uniting the explanandum of causality with that of consciousness in such a way that one explanans serves to explain both is that "it seems to lead to a version of panpsychism, the view that everything is conscious, which many find counterintuitive."

My theory of genesis by experience, which builds a watchful divine consciousness into the description of our human situation, avoids panpsychism. It holds that Chalmers errs in assuming the existence of an independently determinable base of facts about the "distribution of physical entities in space-time" in our universe. It takes the fact that quantum phenomena such as which of two equiprobable paths a photon takes are fixed only by post-facto observation (see the earlier posts in this series and also Genesis by Observership) to imply that the distribution of physical entities in our world is not a given, knowable set of brute facts.

My idea of causation as "consciousness conferring coherence" sidesteps the problem of having to presume a set of independent physical facts by positing that a conscious divine being confers coherence on his created universe, and in so doing fixes certain physical facts that otherwise would not be fixed.

The coherence conferred by God's watchfulness — by his experience of the world he thus creates — is the same sort of coherence we confer when, by an act of observation, we eliminate the incoherence that would occur if we thought that a photon had arrived at our retina by Path B, even though we had been zeroed in on watching Path A at the time. Our act of observation likewise scotches the incoherence that would occur if we said that the unitary photon traveled along both paths at once.

In other words, when we zero in on Path A — say, by training a telescope on it, to the exclusion of Path B — our conscious act of observation "causes" Path A to have been the one actually used by the photon! Never mind that it seems wholly counterintuitive to think that our fixing of the photon's path happens after the fact, given that it was millions of years ago, long before humans even existed, that the photon set out upon its journey to our spot in the universe from a distant quasar. The scientists investigating the laws of quantum mechanics have shown that, as so often happens in science nowadays, our intuitions about this are simply wrong.

In fact, this would seem to be a case where counterintuitiveness and outright incoherence are at odds with one another ... and outright incoherence loses, to the detriment of intuitiveness. What the quantum physicist John Archibald Wheeler calls "genesis by observation" has to happen, no matter how counterintuitive it may seem to us, in order that the world we experience turns out to be a coherent one.

Genesis by Experience, Part 2

In Genesis by Experience, Part 1, I began laying out a theory of the existence of the human self or soul that I am for now calling "genesis by experience." It is a theistic theory in that it holds our existence to be caused, created, and constituted by "experience" that takes place within one particular conscious mind — specifically, the uniquely great mind of God.

Douglas Hofstadter's I Am a Strange Loop

My starting point in developing this theory is Douglas Hofstadter's new book, I Am a Strange Loop, giving his explanation of how the human brain generates a sense of self or "I." Hofstadter believes that the mind is populated with high-level "symbols" that emerge from the lower-level workings of the physical brain constituents, taken to be at the level of neurons, or atoms, or signals, or whatever. The self or "I" is simply the most crucial and most central of these emergent symbols, and Hofstadter accordingly identifies the emergent "I" with the "consciousness" we each think we harbor as well as with the "soul" we typically imagine we have.

I think Hofstadter is arguably right about how the "I" symbol emerges in, and from, the activity of a brain. However, I dispute his implication that the self or soul which that emergent phenomenon symbolizes lacks independent existence. I say it does exist, independently of our brain's emergent symbolization of it.

For example, there are brain-damaged or psychotic individuals whose "I" symbol never forms. Or, for that matter, the brains of embryos, fetuses, and very young infants as yet lack their "I" symbols. These human individuals still have a self or soul, say I, simply because God's conscious mind sees them.

David J. Chalmers's The Conscious Mind

My theory of genesis by experience depends on the notion that consciousness is causative. To borrow words from David J. Chalmers, author of The Conscious Mind: In Search of a Fundamental Theory, it is possible that "experience itself is a kind of causal nexus." "Experience" is for Chalmers, a professional philosopher of mind, a synonym for "consciousness" — in the sense of, say, our knowing "what is is like to be red." Such knowledge arises via our experience of the "raw sensation" associated with the color red that comes whenever we see, say, a red tricycle.

That sensation of experiencing "what it is like" to be X is separate and apart from the brain's physical workings in response to our perception of X, says Chalmers. In an imaginable "zombie world" that is just like ours in terms of what goes on there, event-wise, our "zombie twins" would simply lack that raw sensation. That lack would, however, produce no outwardly distinguishable change with respect to the events taking place in the zombie world.

I would further characterize our conscious experience as not unlike a form of empathy. Whenever we see, say, a red object, and when we accordingly experience the raw sensation which we associate subjectively with redness, we once again are automatically clued into "what it is like to be red." Manifestly, my knowing "what it is like to be you" is what we would both ordinarily mean by "empathy." So, extending that notion, I'd say that conscious experience constitutes "empathy" ... with, say, the redness of a tricycle. What is missing in our hypothetical zombie twins is precisely such "empathy."


Chalmers does not absolutely commit himself to the notion that conscious experience, so defined, is causative — he tends to think it is not — but he opens the door to that possibility when he says

... the very nature of causation is quite mysterious, and it is possible that when causation is better understood [by philosophers] we will be in a better position to understand a subtle way in which conscious experience may be causally relevant. (p. 150)

For, he says, there are two sets of facts that do not automatically emerge from physical facts in our world — emerge, that is, in the way Hofstadter says the "I" ineluctably emerges from the physical facts of a normal, mature human brain. One of the two sets of facts Chalmers thus singles out is the set of facts about human consciousness qua consciousness. And the other one is the set of facts concerning natural causality: what does it really mean to say "A causes B"? Both sets of facts are deeply mysterious, says Chalmers, so perhaps those "two mysteries might be more neatly wrapped into one" (p. 152).

My genesis-by-experience theory is an attempt to "wrap them into one," by bringing God into the picture.


Also in the picture, as I said in my prior post, is the idea, first broached by quantum physicist John Archibald Wheeler, of "genesis by observation." A thought experiment of Wheeler's devising — it concerned the selective observation of one of two equally likely paths which a photon might take from a distant quasar to arrive at our planet — yielded, by the laws of quantum mechanics, the counterintuitive result that the act of observation itself fixes the path chosen by the photon at some time in the distant past, before the eventual observer had even come into existence!

Subsequent real-life experiments have confirmed that quantum-level facts can indeed acquire their "genesis" by virtue of post-facto, time-delayed observation. Cosmologist Andrei Linde has even postulated that the crucial act of observation must be performed by a conscious being, though Wheeler himself has it that a purely mechanical "observer" would do just as well. In that dispute, I side with Linde, for I think "genesis" as spoken of in the Bible is a creative, constitutive, causative act on the part of the conscious mind of God.


That puts me in accord with the 18th-century Irish philosopher George Berkeley, who became a bishop in the Church of Ireland. Berkeley's thesis was esse est percipi: to exist is to be perceived. This is true, he said, for everything that exists ... except for minds, which cannot be directly perceived. It is minds which do the perceiving that confers existence on everything else. To avoid tying himself in a logical knot, Berkeley posited that there is in fact an original, uncreated, unperceived mind at work in establishing the existence of the world: God's.

I think Berkeley was spot on. And I think Chalmers misses the boat when he treats consciousness as if it were, to a first approximation, an "epiphenomenon" with no "causal efficacy."

My hunch is that human consciousness may arise as an emergent phenomenon from physical brain activity in just the way Hofstadter says it does. Or, it may even do so with the help of "extra," psychophysical laws of nature, as Chalmers suggests. Either way, I think it plays a role in the raw causality of the world — in a deep, counterintuitive, even paradoxical manner which Chalmers seems to deny outright, and which Hofstadter (at least in the early chapters of his book) seems to be blissfully unaware of, but which Wheeler and Linde have nevertheless twigged to. In so having a deep causal efficacy in the natural world, at least at the quantum level, our consciousness echoes the fundamental role that God's consciousness plays in the genesis of the world.

Genesis by Experience, Part 1

Douglas Hofstadter's I Am a Strange Loop

Douglas Hofstadter has a new book out, I Am a Strange Loop, giving his explanation of how the human brain generates a sense of self or "I." I've discussed the book to some extent in Douglas Hofstadter Is a Strange Loop. Now I'd like to present my counter-theory. Or, at least, I'd like to stake out the general territory it occupies in the realm of ideas, since I am by no means ready yet to answer all questions about my theory-in-the-making, much less meet all objections to it or fend off all misconceptions about it.

Hofstadter has it that the personal "I" is an epiphenomenon, by which he means it is real in the same sense that any thought pattern is real. Any thought pattern — or, as he calls it, any "symbol" in the human brain's vast repertory of symbols — is a phenomenon that emerges from entirely physical, wholly mechanistic workings that go on at the level of neurons or atoms or subatomic particles.

David J. Chalmers's The Conscious Mind

As such, the emergent "I" — which, at least in his early chapters, Hofstadter equates to the conscious mind and to the soul — is entirely a part of the material reality of the world, even if it is no solid, tangible thing. For a contrasting view of what it means for consciousness to be an epiphenomenon, one can read such philosophers of mind as David J. Chalmers, author of The Conscious Mind: In Search of a Fundamental Theory.

As I discussed in a great many of my earlier posts, beginning with Quickening to Qualia, or Taking Consciousness Seriously, Chalmers argues persuasively — though I now think he's wrong — that our conscious mind is at least to a first approximation epiphenomenal is a stricter sense than Hofstadter uses.

Specifically, Hofstadter's epiphenomenal "I" is capable of "pushing things around" in the physical world. For instance, when my "I" decides that my body needs to be fed, it arranges for me to (for example) stuff a hamburger into my mouth.

Chalmers' possibly epiphenomenal conscious mind — he's sure it is "naturally supervenient" on physical facts, less sure it is a true epiphenomenon according to the definition which he employs — pushes nothing whatsoever around. It lacks "causal efficacy" entirely (see p. 150 in the section "Is This Epiphenomenalism?").

He equates the conscious mind to "subjective experience," or just "experience." He says that our subjective experience is a nonphysical freebie that need not happen at all for the sum total of all the physical causality that takes place in the world to be exactly the same as it is.

If I stuff a hamburger into my mouth because I'm hungry, says Chalmers, that happens because of activity in my brain that is wholly physical. But my conscious experience of the hunger and of its satisfaction — whether or not it is truly epiphenomenal in the strictest sense — is a side show to all of that causal brain activity. "It seems to be a mere epiphenomenon, hanging off the engine of physical causation," writes Chalmers (p. 150).


My initial inclination when I first read the Chalmers book was to applaud his claim that human consciousness is immaterial and acausal — i.e., it exists in and of itself, but it does not intrude upon a "causally closed" physical world. I did this for reasons that have to do with my personal philosophical and religious biases. To wit, it seemed to me that establishing that we each have an immaterial component to our mind, the faculty which we call consciousness or subjective experience, makes it easier to maintain that we each have an immaterial soul.

I have since modified my views on questions of self, consciousness, and soul, but my philosophical and religious biases remain the same. I'd like to go into those biases now, if only because doing so will make it easier for me to get across what my new theory of the soul is all about.

I consider myself a Christian, and in my mind the "message" of my religion boils down to this: We are, each of us, equally and irrevocably precious in the sight of God, and we ought to treat one another — and ourselves — accordingly.

I bear in mind the passage in the Gospels where Jesus tells of the so-called Great Commandment and its sequel:

One of the scribes, when he came forward and heard them disputing and saw how well he had answered them, asked him, "Which is the first of all the commandments?" Jesus replied, "The first is this: 'Hear O Israel! The Lord our God is Lord alone! You shall love the Lord your God with all your heart, with all your soul, with all your mind, and with all your strength.' The second is this: 'You shall love your neighbor as yourself.' There is no other commandment greater than these." The scribe said to him, "Well said, teacher. You are right in saying, 'He is One and there is no other than he.' And 'to love him with your heart, with all your understanding, with all your strength, and to love your neighbor as yourself' is worth more than all burnt offerings and sacrifices." And when Jesus saw that he answered with understanding, he said to him, "You are not far from the kingdom of God." And no one had the courage to ask him any more questions. (Mark 12:28-34)

Here, love of God is juxtaposed here by Jesus with love of "neighbor" (and, not incidentally, of self) in such a way as to make it clear that we are to treat everyone, our own selves included, in the same way in which we are told to treat God himself: as a personal "Thou," rather than as a thing, an object, an "It."

When I say we are being told by Jesus in this passage to recognize," as we gaze upon one another, our mutual preciousness "in God's sight," I am I hope honoring Jesus's intentional juxtaposition of the Great Commandment with its equally great sequel. But my intent here is to dwell upon the phrase "in God's sight," because I think it is crucial.


My theory of consciousness incorporates the idea that it is "sight," in the sense of an exercise of observational powers from which emerge conscious experiences, which make things real. This is a sense of consciousness in which it cannot be considered as something separate from causality.

In coming up with my view of consciousness as profoundly causal in a way which does much more than "push things about," I am attempting to draw together several influences upon my thought. One of them is an idea I originally discussed in Genesis by Observership. Namely, there seems to be good scientific reason to be that there are events at the quantum level of the physical world that are ambiguous in nature — there are at least two possible ways in which such events could have transpired — until an act of observation made at a later time "fixes" one of those ways as "real" and discards all the others.

Several years ago, quantum physicist John Archibald Wheeler described a thought experiment in which a photon, a unit of light energy, is emitted by a far off quasar, somewhere across the broad vastness of space. It has two possible paths between there and here on Planet Earth, each path bent towards us by the gravity of a separate, conveniently positioned galaxy. Wheeler maintained that, according to the laws of quantum mechanics, which of the two paths the photon actually takes — or took — depends on which way we have decided to point our observational telescope!

Wheeler's conclusion could be summarized as, observation is required before certain "facts" become facts. It was later confirmed by real experiments performed on earth. He called the strongly counterintuitive phenomenon "genesis by observation."

The question arose whether the observation has to be done by a conscious being, with Wheeler answering in the negative. He said the mere registration of the event by a purely mechanical "observer" would suffice. Another scientist, the cosmologist Andrei Linde, disagreed. Linde posits that the observer has to be conscious.

I'm siding here with Linde, for reasons which I hope will become apparent as I lay out my theory.

Another train of thought which feeds into my incipient theory is one I broached in Esse Est Percipi. In that post, I talked about the philosophical stance of the Irish philosopher George Berkeley, who became a bishop in the Church of Ireland in the 18th century. Berkeley's thesis was esse est percipi, to exist is to be perceived.

By that he meant that all which exists — all except mind, which is the seat of perception — does so because it is perceived by a conscious mind. To avoid infinite regress, Berkeley posited that the great mind by virtue of whose conscious experience the universe comes to be in the first place is God's.


A third set of ideas which underpin my theory comes from the Chalmers book. In his "Is This Epiphenomenalism?" section, he looks for ways be which he might avoid identifying what he calls "naturally supervenient" consciousness as epiphenomenal, in the sense of lacking causal efficacy. One possible strategy which he considers for this is "the nonsupervenience of causation."

In an earlier chapter, Chalmers has already given the reasons why he finds the conscious mind to supervene — to emerge from — physical events naturally, not logically or metaphysically. He argues that there is no necessity of pure logic why what goes on in a brain must be associated with subjective experience. Likewise, it cannot be shown within the philosophical realm of metaphysics that consciousness must automatically accompany brain processes. Hence, given that consciousness does accompany brain states in the world we live in, the supervenience must be a natural one: i.e., by virtue of laws of nature which amplify those pertaining merely to physical matter.

Is there anything else we know about, he asks, that likewise supervenes on the physical world, but not for reasons of logic or metaphysics? Yes, he answers, there is in fact one other thing: causality itself. Consciousness and causality are the two main aspects of the world we live in that supervene naturally on physical facts.

To my mind, Chalmers is not entirely clear on what he means by "causality" — for the excellent reason that, as he shows, philosophers disagree as to precisely how our minds ought to deconstruct propositions such as "A causes B" to get to the bottom of what is meant by them. Chalmers writes:

... the very nature of causation is quite mysterious, and it is possible that when causation is better understood [by philosophers] we will be in a better position to understand a subtle way in which conscious experience may be causally relevant [after all]. (p. 150)

Again, one way in which conscious experience may be causally relevant is if causation itself, like consciousness, is "nonsupervenient" on physical reality, in the sense of not being either logically or metaphysically a slam dunk, given the physical facts. If, like consciousness, causation is only naturally supervenient, then perhaps those "two mysteries might be more neatly wrapped into one. Perhaps, for instance, experience itself is a kind of causal nexus ... " (p. 152).

"On this view," Chalmers adds a few sentences later, "causation needs to be realized by something in order to support its many properties, and experience is a natural candidate. If this is so, it may be that it is the very existence of [conscious] experience that allows for causal relations to exist, so that there is a very subtle sort of relevance for experience in causation."

Chalmers is not convinced that such a position is well-grounded, for reasons he mentions quite briefly. "The metaphysics of causation is as yet far from clear," he nonetheless says (p. 153), "and [accordingly] this proposal is certainly worth investigating."


My theory about consciousness-as-causation, then, draws from the notion of genesis by observership proposed originally by John Wheeler and modified by Andrei Linde to have it that the observer be conscious; from Berkeley's "immaterialism," a.k.a. "subjective idealism," which maintains that esse est percipi, to exist is to be perceived; and, thirdly, from Chalmers' hint that there may be "a very subtle sort of relevance for [conscious] experience in causation." At least for the moment, I'd like to call my theory that of "genesis by experience." By "genesis," I fully mean to imply that experience — observation, perception, sight — is directly implicated in God's creating and sustaining us and the universe we live in.

So, yes, my theory is as much a theological one as it is philosophical/metaphysical. It is also a scientific one, to the extent that it accords with Wheeler and Linde. Put all those adjectives together, and you can see why I feel my theory of consciousness-as-causation satisfies one of my deepest biases.

To be specific, I fully admit to being "biased to the bone" against two worldviews that are very much at loggerheads today, atheism and fundamentalism.

Atheists, agnostics, secularists, skeptics, freethinkers — these are all people who are reluctant to believe in God or religion, some of them quite outspokenly. Meanwhile, creationists, biblical literalists, advocates of so-called "intelligent design," and their ilk snipe at the atheistic elites, as they like to call them, in the name of a type of religion which repels me as much as atheism does.


"Conservative" Christians seem too often to be hate-filled Christians, which means they are no Christians at all. Not to speak ill of the dead, but some of the remarks of the late Jerry Falwell about gays and others epitomize what I am talking about:

"I really believe [said Falwell after the September 11 attacks] that the pagans, and the abortionists, and the feminists, and the gays and the lesbians who are actively trying to make that an alternative lifestyle, the ACLU, People For the American Way, all of them who have tried to secularize America. I point the finger in their face and say 'you helped this happen.'"

Such remarks (which Falwell later apologized for but said nonetheless that he stood behind) show how hate and fear go hand in hand — and how the idea that God sees each and every one of us as equally and irrevocably precious can get completely lost.

On the other side, when outspoken atheist Christopher Hitchens discusses religion as if it were poison (see In Search of Comity) I cringe. As I say, I believe a worldview such as the one I am outlining that ties creation and consciousness together in a deep way makes it clear that there is a God, and that we need to base how we treat each other on the preciousness we have in our Creator/Sustainer's eyes. What firmer basis for that sort of commitment could there possibly be?