Gödel's theorems mean that no matter how complete the formal system, it will always leave a semantic residue: semantics cannot be reduced to syntax, meaning to grammar, reality to mathematics, quality to quantity, etc. This seems intuitively obvious, but it's nice to have logic on one's side.
The bottom line is that man will never arrive at a theory of everything, but will be perfecting it until perishing from global warming in a few years.
At the moment, I'm cross-referencing our favorite logician, Gödel, with our favorite biologist, Robert Rosen.
As Gödel was a "meta-logician," I suppose we could say that Rosen was a meta-biologist, although he would no doubt object to the characterization, since it might imply an element of woo-woo or oogily-boogily.
Rather, he believed that he was the one pursuing hard science, while pulling no metaphysical punches. It's the reductionists who are the softheads. Rosen was a real scientist, proof of which is found in the fact that I don't understand half of what he says. I do, however, get the big picture.
Indeed, the big picture is the meta-picture, precisely. I won't say it's the only thing that interests me. Then again, it does seem to be my default setting, and indeed the default setting of any philosopher properly so-called. Now, to even call oneself a "philosopher" strikes me as unbearably pompous, for what is philosophy but error on a grandiose scale, with no hope of arbitrating between this doozy and that whopper?
If I actually believed that, I would despair, for it would mean that the bOb is pointless in a double sense, or nihilism squared. It would of course mean that life -- anyone's life -- is utterly meaningless. But it would also mean that my life in particular is not even meaningless, what with its meta-preoccupation with universal truths.
The moment I began studying psychology, I couldn't help thinking about metapsychology, i.e., the larger system of which one's psychological theories must be a part -- both the truths entailed in one's psychology, and the axiomatic truths it presupposes.
Moreover, without consciously realizing it, I was always on the lookout for logical and meta-logical inconsistencies in this or that system or paradigm. In general, the only way to harmonize such inconsistencies is with recourse to a higher truth in a vertical spectrum. Once you do this, you realize that, for example, mind cannot be a material process for the same reason that physics cannot describe reality. Again, there is always a semantic residue in such attempts at reducing one level to another.
For Rosen the duality of quantity and quality is not the same as that between hard and soft science, respectively. Rather, it rests on "presuppositions about the nature of material reality and on how we obtain knowledge about it." The duality between syntactics and semantics goes to "what is true by virtue of form alone, independent of any external referents, and what is not."
Which raises an interesting question: can formal truth be true in anything other than a trivial sense? In other words, is mathematics true only within its own system, or does it disclose real truth about the actual world? If one says Yes to the latter, this has enormous metaphysical (because meta-mathematical and trans-human) consequences.
The reductionist is guided by the conviction that "Qualitative is nothing but poor quantitative." Given this presupposition, "everything we call a quality or a percept is expressible in terms of numerical magnitudes, without loss or distortion.... therefore, every quality can be quantitated, and hence, measured or computed." Thus, "Everything else we call science is ultimately a special case of physics."
Put that way, it sounds almost like a straw man. And yet, it must be the metaphysical underpinning of science, so long as science is "true." If reductionism is not the case, then what is the foundation of the world? Not in some airy-fairy way, but precisely? What are the ultimate truths that must be and cannot not be, in order for mundane science to be true (at least as far as it goes)?
Now, some people couldn't care less about such questions: "most practicing mathematicians, like most practical (empirical) scientists, go on about their business, indifferent to such matters, convinced to the depths of their soul about the reliability of what they do."
Wait a minute -- depths? Soul? How did these contaminants get into the lab?! I suppose we can say that wherever the reductionist goes, he goes there too and spoils it.
In Hilbert's formalistic school of thought, semantics can "always be effectively replaced by more syntactic rules." That is to say, "any external referent, and any quality thereof, could be pulled into a purely syntactic system."
But a syntactic system is "a finite set of meaningless symbols" guided by a finite set of rules for combining them. Such a system is necessarily consistent, but is it complete? Yes, if you and I are machines. But if we were machines, could we ever know it? If math is just about more math, where's the inscape hatch? And if math is about the world, what is the world about?
Well, thanks to both Gödel and common sense, we know that whatever the mind is, it isn't a machine or computer.
But if reductionism is obviously wrong, does this imply that the opposite approach is the correct one? I don't think so. Rather, I suspect a kind of eternal complementarity between the extremes of empiricism-idealism, subjectivity-objectivity, quality-quantity, etc.
The ancients began at the other end -- the other end of reductionism -- in that for them
life simply was; it was a given; a first principle, in terms of which other things were to be explained.
To us this may seem naive, but is it any more naive than for a conscious lifeform to declare itself to be absolutely contingent? Whence this absoluteness? How did it sneak into the lab? Must have been smuggled in by Soul and Depth.
We are told that biology reduces to physics. But what if physics is an entailment of metabiology or something? Well, stranger things have happened.
On the one hand, biologists have convinced themselves that life is somehow the inevitable necessary consequence of underlying physical (inanimate) processes.... But on the other hand, modern biologists are also, most fervently, evolutionists; they believe wholeheartedly that everything about organisms is shaped by essentially historical, accidental factors, which are inherently unpredictable and to which no universal principles can apply.
In short, "they believe that everything important about life is not necessary but contingent."
That's what you call meta-irony, only without the self-awareness necessary to generate a guffah-HA! experience.
I'm running out of time, so I'll end with this thoughtlet: biology is indeed reducible to physics at one end, while referring to life at the other. But what does it mean to be "about" life? For that is life?
I'm going to go out on a limb and suggest that what we call life is ultimately rooted in the principle of Life Itself, just as the mind is grounded in the principle of Consciousness Itself, and persons in the principle of Divine Personhood. Above that it goes dark. Which is not to say that we can know nothing about it, only that it exceeds our puny models. Call it the principle of Divine Overflow.
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But if reductionism is obviously wrong, does this imply that the opposite approach is the correct one? I don't think so. Rather, I suspect a kind of eternal complementarity between the extremes of empiricism-idealism, subjectivity-objectivity, quality-quantity, etc.
Life doesn't reduce to physics - however, life can't exist without physics, either. It's a limitation without which the infinite cannot take hold, in a sense - like the rules for creating a work of art or a piece of music. There is an underlying structure and set of rules which, when followed, allow for an infinite set of variations, and without which the result can hardly be called "art" or "music."
Great post, very thought-provoking. Of course no discussion of meta-biology should neglect to mention the bi-partisan nature of the human condition.
We participate in the physical evolution of the human being, by inhabiting/riding a human body and consenting to reproduce and compete with other human beings and other organisms. And of course evolution as taught in science class rolls onwards.
At the same time we participate in the individual spiritual evolution of the soul as we inhabit a serial number of bodies from life to life, the soul remains integrated and grows more complex.
A world of many developed souls begins to be divinized in general, and that is the general spiritual evolution.
These are co-occurring tracks and no understanding of the human condition is possible without keeping both in mind. It is a daunting task.
-Tasurinchi by the River
Bob — I’m still struggling with Gödel. I sense that what he’s saying is very important but I feel as if I need a dummies’ guide. Can you please give me a few basic real-life examples that make its significance clear? I appreciate that it’s a ‘meta’ theory so perhaps practical examples aren’t possible. It’s just that I really want to understand it so would appreciate any remedial assistance! Thank you.
Hi Giles,
This seems like a decent breakdown of how the two statements of the theorem work, at a basic level. What are the implications?
Ironically, if you go to the main reference page for Gödel's theorem at Rational Wiki, it ends with a snarky comment about how terrible it is that anyone should apply the theorem to life. According to the rationalists, Gödel applies only to math, and how dare anyone notice it might have metaphysical applications as well.
Going back to this post's first paragraph, as I see it what Bob is getting at is ultimately that meaning - or existence, ultimately - requires intent; it's not enough that there is a supply of stuff which, when put together, create something more than just the sum of the things themselves. How did the stuff get put together and understood in the first place?
Example: some have argued that infinite monkeys pecking away at infinite typewriters for eternity would eventually produce the works of Shakespeare. What do they mean by this, really? What they're saying is randomness (monkeys banging away at typewriter keys), given raw materials and enough time to be expressed, will produce meaning. I wholeheartedly disagree; the silliness of the argument distracts from what is really being said. A better example lies in imagining that the white noise seen on a screen with no channel (i.e. no input signal) selected will occasionally depict the ceiling of the Sistine Chapel. Or that if one had a sufficiently large pile of Lego bricks, shaking them up for all eternity would yield, quite by accident, the shape of a house.
Back to Gödel. The pile of Lego bricks is certainly consistent, but without an intelligence to assemble the pieces into something other than a pile of bricks, that's all it will ever be. It is incomplete. It requires something outside of itself to be put to the purpose for which it was created. Or think of AOC's power strip plugged into itself for INFINITE POWER!!11!. All the pieces are in place, except the most important one.
In other, other words, all life is made of matter. But matter isn't sufficient to explain life. A human being disassembled into piles of his molecules, even if they are all kept neatly in piles together, is nothing but mud. And reassembled, the life would not be brought back, at least not outside the Resurrection. Matter is consistent but not enough on its own to explain even the simplest microbe, let alone a human consciousness.
Conversely, when Christ on the Cross stated, "It is finished!" that certainly implies that something has been made complete, but that something was certainly not consistent. In order for the meaning of existence to be completed, something from outside of the system had to enter in and make it so.
I don't know if it helps at all, or if I've just revealed how woefully stupid I am, but there's my thought, anyway. Not complete, by any stretch, but then I'm always only half-baked at best.
Great comment, interpreting Godel, by Julie. Thank you for that. Julie noted "all life is made of matter. But matter isn't sufficient to explain life." That is accurate.
The Indus Valley ancients thought long on the matter and decided there were realms corresponding to different aspects of the Cosmos, sort of like an onion.
Therefore life has its own life realm, sheath, plane, world, or what have you. When the life realm was intermixed with the matter realm, organisms resulted.
Mind, life, body, spirit. All with their own corresponding worlds. They all intersect in the human being, the most complicated creation in the Cosmos.
With heavy meditation, use of ganga, etc, one can experience and voyage into each of these worlds, and that's exactly what the ancients did.
Giles, to be honest, the entire edifice of European philosophy is very derivative and in often superficial, and the solid work of the ancients is always the gold-standard in philosophy.
The Indus Valley sages were sharp operators and nailed a lot of key concepts on mind-power alone, and also understood quantum mechanics to some degree, just by thinking about it long. Impressive.
Against that formidable intellectual tradition Godel somewhat pales in comparison.
-Regards, Interlocutor X
Giles:
I thought the book Incompleteness by Rebecca Goldstein was a good explanation.
As to real world examples, as Julie said, there are those who take a narrow, pedantic view and say the theorems *only* apply to formal mathematical systems, and those who take a broader view -- Gödel being among them. He would be the first to say that what we can prove is necessarily a subset of what is true.
All of which strikes me as common sense. I go back to what Schuon says in one of his most important books, Logic & Transcendence, for example,
"[W]hat completely escapes the notice of critical philosophy is that reason requires data if it is to function at all -- data which it cannot extract from itself and without which its activity is illusory."
Or,
"The position of science is exactly like that of a man who could grasp only two dimensions of space and denied the third because he was unable to imagine it; now what one spatial dimension is to another, so is the suprasensible to the sensible."
Moreover,
"rationalism itself starts fairly and squarely with a 'dogma,' namely, its gratuitous axiom that nothing exists except what is supplied to us by the reason in its service to sensible perceptions."
In reality,
"all thought has to start from an initial premise, which cannot come from thought itself but which must include an element of certainty whose soundness thought delineates."
This is a good description of those French philosophers who would deny the theorems:
"The rationalism of a frog living at the bottom of a well is to deny the existence of mountains: perhaps this is 'logic,' but it has nothing to do with reality."
And finally:
"Logic is perfectly consistent only when surpassing itself."
Kaboom.
By the way, in all of Schuon's books, I've never seen mention of Gödel. Rather, the above observations are a function of pure and unimpeded intelligence -- or intellect -- itself. In other words, they are self evident so long as one understands what intelligence is.
“Gödel had an obsessive fear of being poisoned; he would eat only food that his wife, Adele, prepared for him. Late in 1977, she was hospitalized for six months and could subsequently no longer prepare her husband's food. In her absence, he refused to eat, eventually starving to death.”
A classic death for a philosopher-logician.
He discovered the theorems at 25, and then had his first psychotic break several years later. I don't know anything about the quality of his work thereafter, when he was in and out of severe mental illness.
Thanks everyone — I greatly appreciate your trouble in explaining it further and now feel a little less stupid! Much appreciated.
The irreducibility of the particle and wave seem resonant with the quantitative and qualitative approaches. They're always there, always two, always one.
I definitely would not be popping back to read if it wasn't for Bob's playfulness, which might be an expression of the interplay between the two poles.
I like the intuition mention at the start. I feel it too, as perhaps everyone does, so consistently that it fades to ordinariness and bafflement at the impossibility of expression. The mystery astonishes and baffles one so thoroughly it becomes almost banal and tedious, like an impossible koan.
this wasn't the comment I was going to make.
Hello Andrew, I enjoyed the comment you weren't going to make. The banal, tedious, impossible koan that life sometimes becomes is noted by this writer as well.
But then, cutting through all banality, there are jubilant moments, like being dealt four aces on a big poker wager, or a really good sesh with a mate.
Now let us turn our attention to cryptocurrency. What do we know about it, and why is one type called "dogecoin" instead of just plain dogcoin? Is this a Scottish rendition of the word "dog?"
Do we need to get some dogecoin? Let us think on this.
-Wang Chung
Well, the lesson I learned from Gödel’s death is to never get paranoid dementia. In hindsight, one must do their best work in youth. So everybody have fun tonight. For tomorrow you could be a senile wackjob compulsively moaning along to The Smiths.
George Floyd, lord and savior.
Did Chavin’s history of playing a bit of Judge Dredd make Floyd innocent? Probably not. Will the verdict get the black community to research historic black crime rates enough to understand all the whys behind the disproportionate imprisonment of those on the margins of society and decide to work together to compensate, ala these Asians and them Mexicans (most Mexicans)? Probably not so much. Will they prefer to instead blame The Man, not knowing that Biden was The Man back when he voted to send their jobs away and build prisons for the new unemployed? Not as long as Obama is The Man (but their man).
Believe you me, I’ve tried many times to tell groups of young black urbans which I saw on the street to get off the street and go enroll in trade school or business school or any kind of school. Got my ass kicked every time. I then tried suggesting that they hang out with conservative white people, preferably of the evangelical Fox News watching variety. Same result. This may be more complicated than I thought.
Well, at least we can all agree the world's a better place without George Floyd running loose in it.
It's a low bar we set when the old "obey the law" Chris Rock skit is relied upon on to educate our black urban youth. Still, I can empathize that their grandparents leaving the chitlin homestead for better work in the cities, to then have that work disappear overseas so some Chinese can leave their own chitlin homesteads for their own cities, to then have their working man economy once so full of Cadillac car washes and afro-sheen barber shops that some halfway watchable movies were made about them, replaced by crack whores and burned out hoods.
Should inspirational movies be made about Detroit city hoods, transforming from blue collar factory workers to urban prairie, you may ask? "Intriguing idea" I might respond, though I think it'd take a bit of work to make it a comedy, let alone a cultural icon full of catchy songs and repeatable phrases with the true intention of educating and inspiring. Should Chris Rock be directing instead of Spike Lee, you may ask? "Intriguing idea" I might respond, though I think that Donald Trump having a cameo appearance might be a bit of a stretch.
Not very well known:
The large-scale enslavement of Africans in the New World from about 1450-1865 AD. was figuratively akin to a large asteroid strike on the earth.
The injury took about 400 years to inflict; the aftermath is felt strongly today.
Some people think "we've moved on."
We have barely moved on at all. The damage to society will take a full 5,000 years to completely heal.
Future historians have reported effects from the lesion of slavery lingered for millenia before becoming subtle and then undetectable.
The stigma on both sides of isle is heavy. There is white guilt and perception of whites being cruel, greedy, manipulative, and predatory. There is black shame and the perception of blacks being low, inferior, bestial, and subservient.
"We aren't responsible for what people did in the past." You may not be responsible but you will feel the effects.
This has played out in the Chauvin/Floyd incident. Each man portrays his stereotype perfectly.
The verdict rendered swims upstream from stereotypes and is a step towards erasing the stain of slavery. But we are less than 200 years into the healing process and the complete healing will take fully 20 times that duration. So buckle your seat belts.
Around 7,000 AD there will be no perceptible stigmas left. The whole thing will be over at last.
-White Water, Black Whole
There are more white slaves in the world today than there were black slaves in the U.S. in 1860. WHERE ARE MY REPARATIONS?!
Also, why isn't Africa paying reparations to U.S. blacks for capturing and selling their ancestors into slavery?
How do you repair an 85 IQ, anyway? There are ways to help, but they don't involve cash subsidies.
Dupree, genetic analysis reveals you are 50% of African descent. Have you ever wondered why you like jazz so much? Your other 50% is Yiddish. So you will not get any white reparations.
You are not missing much, as reparations for each white amounted to 40 Jelly Beans and a gerbil.
-White Water, Big Butt
Dupree is deeply buried in the stereotypes. He thinks he is white and therefore takes pains to be manipulative and predatory. Dupree believes Africans have low IQ's which can't be repaired. That is the straight out of the Goebbels handbook. Congratulations.
And we all know who Dupree is. Think about that.
BIPOC Good, White Man Baaaad
Let's all sing Beasts of America!.. wait, strike that...
Everybody sing Lift Every Voice and Sing!
Another aspect of America today is alcohol drinking.
As I understand it, buying and selling alcohol became illegal on 04/19/1920 at 12:00 AM. The constitution was amended (18th) to reflect that.
And yet we see alcohol sold and consumed everywhere in every state of the union. I've even seen adverts on TV for beer.
I've been told there was an addition constitutional amendment (21st) reversing the 18th amendment. However, this amendment was never ratified. I checked for the required signatures and they were short by one. It was never formally ratified and is not in effect.
I also see coffee sold everywhere. Coffee contains caffeine, an alkaloid virtually indistinguishable from cocaine (illegal, schedule 2). I'm told coffee houses bribe local officials to look the other way. They invent fanciful names for these bribes, such as sales tax.
Next to a coffee shop you might see a pot shop in many states. Now, I have been told pot is legal, but a check of the Federal regulations shows it is not. And state regulations do not super-cede Federal code. I have noted huge kick-backs to state coffers supposedly for "education" but it goes straight into the pockets of legislators for their mistresses and so forth.
Tobacco is a sacred herb used by the aborigines of North America and is not for Europeans to consume. Nevertheless you can see discarded filters from tobacco smoking littering the ground. A look at the regulations reveal the active ingredient of tobacco, nicotine, is regulated as a poison. The cigarette industry is completely unlawful in every sense of the word.
Now as for the first amendment: It states people have a right to bear arms (that is, an appendage with muscles, tendons, and joints, usually terminating in a hand with a prehensile thumb; most people possess two of these).
There is nothing in the amendment about any right of citizens to bear armaments (for instance muskets, pistols, shotguns and rifles). There has been a grave misunderstanding of this amendment. My staff is working hard to educate Congress so that this error can be ameliorated.
The founders intended each American could use their arms to engage in fisticuffs, and did not intend to have people shooting at each other.
Please support us in ensuring justice is achieved in America.
-Liberty Law Offices, Missoula, Montana.
So about our tragic population of 85 IQ blacks, Dupree might say: "Let em rot. Why should we care?"
To which I'd respond: "Because ten thousand blacks now stand between Frodo and Mount Doom. I've sent him (our little white friend Frodo) to his death."
Bob might wisely state: "No. There is still hope for Frodo. He needs time, and safe passage across the plains of Gorgoroth. We can give him that."
And then Dupree would agree: "Certainty of death... Small chance of success... What are we waitin' for?"
And so it would begin.
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