The Humble Axiom
What do religion, truth and lies, philosophy, fiction and math, intellectuals, journalism, propaganda, cults, politics and mental health have in common? The humble axiom. And its errant son, the profound insight.
All rationality, all reasoning, all the things that a human mind can think– are bounded. That means that they work only within the boundaries set by their axioms or central assumptions, and break down outside of it. This is itself an axiom.
Axioms are the fundamental basis of every field of human knowledge. They are statements that you consider as self-evidently true, that cannot be broken down into smaller parts and so do not require direct proof. For example, the entire field of Euclidean geometry is derived from just 5 of them:
1. A line can be drawn from a point to any other point.
2. A finite line can be extended indefinitely.
3. A circle can be drawn, given a center and a radius.
4. All right angles are ninety degrees.
5. If a line intersects two other lines such that the sum of the interior angles on one side of the intersecting line is less than the sum of two right angles, then the lines meet on that side and not on the other side
Axioms are used to generate “models” of a world. “Models” are abstractions or close-enough-approximate ideas of the world, of its systems or sub-systems, because humans can’t imagine worlds and systems in their full complexity. Models are always incomplete, waiting to be improved or replaced.
Models can be explored and tested in many ways, and the best ones produce insights, which are ideas that might provide a deeper, more accurate or more useful understanding of some aspect of the “real world.”
For example, the usefulness of the insights of Euclidean geometry were judged by how well it corresponded to and competed with other models of the world, and ultimately reality.
It helps you understand shapes and angles, it helps you farm, craft things with your hands, build homes and fight wars. Its insights were valid and useful across various ideas and real-world fields; so, they were “real” insights, now superseded by more advanced forms of geometry. These kinds of “real” insights are often found when mathematics is applied to material and practical problems, leading to the feeling of “the unreasonable effectiveness of mathematics”, as the physicist Eugene Wigner called it.
Science, more aptly called “the scientific method”, stands out in that it does not have “axioms” in the way that other fields do. That’s because it’s not a field. However, the philosophical and psychological frameworks that allow the scientific method to be considered valid and worthy do have foundational axioms. So, what the method results in are statements of probability about sets of data and observation, with numerous related ones coming together to form a “biology”, a “chemistry” or a “physics”.
Perhaps more controversially, the reason that atheists cannot “prove” that god does not exist is because their model of the world competes with religion’s model of the world; they can disprove specifics, they can highlight abuse and incoherent conclusions and practices, but they haven’t convincingly replaced the ancient, accessible axioms that lead to a religious mind and worldview. So one can deconstruct it to its foundations, but it will simply build itself back up again– differing only in those specifics that are dependent on the trends and whims of the time.
Philosophy, practical morality and law are also “man-made”, in the sense every moral and principle you know is derived from a few axiomatic morals or principles which may or may not be considered divine. As GK Chesterton put it, “Art, like morality, consists of drawing the line somewhere.”
A writer uses axioms to construct the world you will inhabit when reading their work, especially when it comes to magic systems in fantasy.
So, when they pull something out of their hat to write themselves out of a corner, we notice and are pulled out of the flow, even if the rules were only implicitly established.
We also see it in our narratives of ourselves. We have certain assumptions of our personality, borrowed in significant quantities from what others have told us, and we derive our opinions of our own actions from those core assumptions, for better or for worse. They all come together to form a complex gestalt of mental health.
So, it is the basis for sanity as individuals and societies — without it, reason is unbounded and circular.
Axioms do not prevent you from making mistakes in your reasoning. They are also not proof. Instead, they are a way to bring multiple parties on the same page, create a set-point in uncertainty, and illuminate some kind of path forward.
For example, “All men are born free and equal” is a foundational statement for modern democracy, and ““the universe was created by God” is one for many religions.
Humans are drawn to coherence and meaning, to finding the rules and principles that generate cause and effect and establish something as real, and to finding the metaphors that relate it to our actual lives and ambitions.
When you are following instructions or being guided by someone or something, the components of the world those instructions live in are constructed for you, and your imagination follows the rules set by the guide.
Within any such model, no matter how good or bad, a sudden insight can “feel” like enlightenment, revelation or mastery over a concept. However, that feeling is not reliable, it’s just the brain’s reward mechanism for figuring something out. And novelty, especially. In truth, if that insight and the model in which you derived it does not compete with other models, does not match reality, and is not useful, it’s probably a fake insight, to rudely co-opt a phrase from David Chapman’s Meaningness metablog. Your brain provides you with a heady little injection of “wow, this feels profound” juice, but we can call it “fake” because the actual insight is often utterly useless outside of that artificial model.
The mechanism of this “feeling” can be compared to Déjà vu, where one is certain that the present has happened before down to every detail, and though we know that is not possible, our mind convinces us that time is really repeating “again”. Then after the moment passes, we notice all the obvious and numerous differences, occasionally discover the trigger, and then soon forget the entire experience.
The mind has many such glitches in the matrix.
These features and flaws of the mind are exploited by sociopaths, narcissists, gaslighters and well-meaning suckers: to construct questions in a way that guide you to the answer they want, and create an emotional world around you that results in you feeling the emotions that they choose for you. This is so easy to do that it has almost certainly already happened to you in at least one subject of your interest, and probably more, and the subject most probably relates to your ideas about yourself and your political, religious or social beliefs. It is so easy to do that it has probably happened to these very people who do it others.
For instance, in a meditation, yoga session or Satsang conducted by such a teacher, or an article written by an intellectual or journalist skilled at fooling you and themselves, you might find yourself having multiple “breakthroughs”– shocks of clarity or profundity, recovered memories, release of tension, unexpected connections, the thrill of new knowledge slotting into place, a glimpse of god or chaos, overwhelming empathy, sadness or connectedness. It may shock and awe, and send shivers down your spine or spread prickly warmth along your limbs.
In truth, there’s a pretty good chance this is just “wow this is profound” juice. Many such insights are useless, evidenced by the fact that they almost never lead to tangible changes that others can perceive (and it is only others you trust who can judge whether you’re a “better person”) or tangible solutions that appeal to the various competing parties affected by a problem.
The more “complete” the experience around getting them– covering design, rhetoric, statistics, mystery, build-up and pay-off, charisma, emotion, eloquence, unusual sensations– the less likely we are to notice that the underlying model itself is nonsense.
A disturbing-yet-freeing realization is that we often do it to ourselves even when it is actually under our control: a hallmark of the depressed or anxious mind is to produce unsound axioms leading to unsound worldviews, resulting in even more unsound insights to which it attaches unwarranted importance.
Some of frustration and ill-temper debates cause in the last century are based in our skillful use of multi-layered abstract concepts and models built up over millennia, and in ignoring or being misled on their axiomatic foundations.
So naturally, our next questions are: “what do we do about it? How do I identify a real spiritual phenomenon, real knowledge and flashes of real insight?”
Well, if the universe could be generalized to a few “scientific” axioms, we wouldn’t be having this discussion. What we’re left with is a few different answers– a need to take things case-by-case, as much as possible.
The lofty, overarching answer is probably something like “honesty”. The practical one is perhaps to cultivate trusty, stable-minded, self-aware peers and rigour in testing our models across fields.
We aren’t talking about mistrusting every insight or idea. But if it came from a very specifically designed and constructed setting, it vastly increases the chance that it is useless outside that setting, and that you were prepped to get it.
But the same artificial construction becomes much more interesting if its self-aware and honest:
Can we build a world where even crazy experiments feel encouraged to be localized, honest and voluntary?
Would we have as much of a problem with a cult that tells us it’s a cult because it wants to see how far it can take its theories and does not harm its members on purpose– or are cults inherently incapable of such a structure? Would we object to a crazy dietary ideology whose members are voluntary self-experimenters and are famously transparent and rigorous about their results? Would we mind hardcore communism or unfettered free market capitalism if it is attempted as a voluntary experiment in a smaller area, localized as much as possible?
Don’t talented teachers use artificial thought experiments and simplified situations to build up to understanding a bigger subject? The key differentiator in actual results seems to be honesty. On the part of both the teacher and the taught, or the experimenter and the experimented on.
Luckily, sometimes we don’t even need to go as far as testing each and every thing.
Sometimes if we stare at a supposedly profound insight long enough, then like Déjà vu’s and mirrors in lucid dreams, you’ll find it simply melting away, revealing what you might have wrought upon yourself had you taken it to heart.
I borrowed the term “fake insights” from David Chapman’s excellent Meaningness article about them. You can read it here: https://meaningness.com/metablog/fake-insights
Originally published at http://the-gordianknot.com on October 14, 2020.
