The “Crisis of Foundations” in Math – and Psychology, Philosophy, Politics, Life…
Article by LiveReal Agents Grace and Thomas
Math went through a “crisis of foundations” several decades ago.
It was like an earthquake that cracked the foundation of a skyscraper.
Few of us really noticed or cared, aside from a few math geeks.
After all, it’s not like we forgot how to count, add, or multiply. Math still seemed to work just fine for most of us. 1+1=2.
In fact, math seemed to be the very definition of stability and certainty - more than chemistry, engineering, and even physics.
But those deep in the math scene noticed specific problems in the “skyscraper” of math. Those problems could be traced back to a cracked foundation, below ground, and mainly out of sight. Certain unresolved paradoxes became hazardous and seemed to threaten the foundations of math itself.
At the time, set theory served as the foundation of mathematics.
All mathematical proofs ultimately relied on it.
But Bertrand Russell (building on the work of others) noticed that set theory allows two contradictory statements to be proven, which is a no-no.
One version of this flaw became “Russell’s Paradox,” which pointed to unresolved problems in the foundations of math. That is one part of what led to the “crisis.”
Attempts to resolve this became an effort to establish a secure foundation for mathematics, and demonstrate that all of mathematics could ultimately rest on a solid and sturdy basis of logic.
The effort wasn’t successful at first.
Examining foundations isn't glamorous work. For example, Russell and Alfred North Whitehead wrote a book (Principia Mathematica) that spent a decent chunk of time proving that 1+1=2. (It was not a bestseller.)
But eventually, the crisis was mostly resolved.
The story had a happy ending. The result – the Zermelo/Frankl Set Theory – is stil the apparent solution today. The foundations of math seem stronger than before. (It might only be one battle in a larger war, but it was still a victory.)
The description above is a gross simplification of what happened and why. But still, it’s fair to ask:
What’s the point? Who cares?
Why does this matter to the rest of us?
Like every good horror movie, the crisis in math left a question or two:
Did the monster actually die, or will it come back? Will there be a sequel?
The answer seems to be “yes.”
There has been a sequel. Several, in fact. And in sequels, the monster often comes back stronger than before.
A similar “crisis of foundations” now seems to be taking place in other fields.
In psychology, philosophy, politics, theology, spirituality, and everyday life – to name a few – more crises are popping up.
These events aren’t in the highlands of academia. They involve ourselves and each other, our core ideas and beliefs, the codes we live by, our culture and society, ultimate matters that concern our very soul, and all the way down to mundane and everyday matters like dinner and driving to work.
These fields lie much closer to the heart of our day-to-day. This time, it’s personal.
There’s a common pattern. As Morris Kline described:
“…mathematicians had used an axiom unconsciously and much later not only realized that they were using it but had to consider the ground for accepting such an axiom.”
- (Mathematics: The Loss of Certainty by Morris Kline, p209).
When they examined and deconstructed ground as part of the effort to solve certain problems, they also deconstructed the same ground was also used in older, seemingly more well-established areas.
What we once took for granted – what seemed obvious – suddenly became up for grabs. What was once certain became uncertain.
Here are a few examples.
There’s the crisis of foundations in psychology.
One of the first jobs of a discipline is to define itself. (“What is this, anyway? What are we doing, exactly?”)
Psychology has had a notoriously difficult time defining itself. Some described it as the scientific study of the human mind. Others (behaviorists) have stated that “mind” isn’t a scientific term. Still other claimed that minds don’t even exist at all – and the better alternative is to define psychology as the study of behavior, and only behavior. But of course, others claimed that for us humans, “mind” or consciousness lies at the center of everything. (We perceive and understand behavior using our minds, after all.) “Cognitive science” entered the picture alongside others who hoped to ground psychology in biology. And so on. In case examining the origins of the word psychology itself could help: psyche (“soul”) and logos ("science") refer to the “science of the soul.” Yet many object to the word “soul” being near any part of a scientific discipline. Others (hand raised here) prefer defining psychology as simply “the study of human nature.” Yet that approach is hardly discussed anywhere, and some even claim that “human nature” doesn’t really exist.
Part of human nature seems to include disagreeing about human nature.
This might seem like tedious quibbling among narrow specialists. Yet the impact of this can be felt far and wide. From overprescribing medication (efforts to solve the happiness problem via pills) to widespread practices and methods in counseling, self-help, and personal development, psychology influences individuals and entire cultures (often behind the scenes) more than we’d sometimes like to admit.
Still, describing a crisis in the foundations of psychology might seem unfair because there’s hardly enough of a “foundation” even to have a crisis.
Psychology, in its current state, often seems more like an ongoing stream of research with no connective tissue. It produces scattered piles of data that lie about in disorganized heaps, soon to be pushed aside by fresh piles of scattered data. Some are more compelling than others. But even the most fascinating are only puzzle pieces, disconnected from the other puzzle pieces.
The single common denominator is a basic process: the effort to human beings scientifically. But commonalities end there. Beyond that point, everything is up for grabs. It becomes the wild west of the soul.
This leads to – putting it diplomatically – a sprawling mess. Entire schools within psychology have radically different premises, methods, and conclusions from one another. They can disagree with each other on nearly everything and hardly talk to each other. Behaviorists and psychoanalysts are classic rivals, for example. More recently, entire disciplines (the existential and transpersonal, for example) are largely ignored. Various experts arise and pass away, with many proclaiming “breakthroughs” that are soon forgotten, or laboring to produce elaborate systems or frameworks that are ignored and soon disappear. The DSM, the “Bible” of psychiatry and psychology, regularly undergoes major revisions (and so, is hardly “gospel”) and describes broad categories of “disorders” and seemingly arbitrary conditions (clusters of symptoms) with no underlying connecting framework. There’s no underlying model of human nature or consensus that “human nature” even exists.
The result is widespread disarray, even as the field continues to expand and seize turf from other domains.
The phrase “house of cards” comes up somewhat often on this topic. And this occurs in the field we often look to to understand what we feel, think, and do. Not unimportant things, those.
Perhaps this plays a role in our current state of mental health, or lack thereof?
This parallels a crisis of foundations in philosophy.
A core area of philosophy is epistemology, or asking, “How do I know?”
The effort to justify “how I know” certain things leads to the examination of basic beliefs, premises, axioms, or the starting points we assume as self-evident.
Yet today, clearly, there are widespread disagreements on these starting points or assumptions.
Two people can often discuss an issue starting from wildly different starting points, worldviews, or life philosophies. They might examine the exact same data, but interpret it very differently. They often disagree and eventually exit the conversation with no resolution in sight, without ever examining the reasons they’re interpreting the data so differently.
The debate over starting points (and how to justify them) rages on. And when nobody can agree on the nature of truth, reality, knowledge, good, or ultimate spiritual or metaphysical matters, the chaos that follows can become inevitable.
Meanwhile, there was a “death of metaphysics” (a “death of truth” or even “Death of God”) which mean old-school concepts like “truth” and “God” (much less metaphysics) also meant academic philosophers deciding to focus on the analysis of language and logic instead of the Big Questions. The result of this was, in some cases, philosophers essentially turning against philosophy itself.
Philosopher Leszek Kolakowski described it well:
“For well over a hundred years, a large part of academic philosophy has been devoted to the business of explaining that philosophy is either impossible or useless or both. Thus philosophy demonstrates that it can happily survive its own death: it keeps itself busy trying to prove that it has indeed died.”
- (Metaphysical Horror, p7)
One philosopher (Paul Arthur Schilpp), described “The Abdication of Philosophy,” where some professional philosophers essentially decided that philosophy itself was either impossible, misguided, or useless, and therefore opted to surrender and slink away, leaving a vacuum for others (non-professional philosophers, especially politicians) to fill the void. Yet the non-philosophers who stepped in to fill that void (including politicians, celebrities, and other intellectuals largely untrained in philosophy) didn’t exactly solve the problem. For example, Stephen Hawking saying that “…philosophy is dead” didn’t convince everyone to take their balls and go home. (The idea that “philosophy is dead” is a philosophical statement, after all. Great astrophysicists don’t automatically become great philosophers.)
Amid this, philosophy didn’t just shrink and disappear. Just the opposite, in fact.
When foundations become unstable, things don’t get quieter. They get louder. Far from settling things down, all of this seemed to lead to an exponential growth in arguments, alongside an exponential decline in the resolution of those arguments.
After all, if there is no truth or reality (much less Reality), if someone thinks “reality” is merely a social construction, that means we just “make it up.” And if you imagine that you can construct reality itself, then you can build anything you want – or try to. And anyone who gets in the way of that imagined utopia is seen as someone standing in the way of utopia.
Serious disagreements – and worse – easily ensue.
That has led to a crisis of foundations in politics.
When basic ideas that hold a society together deteriorate, opportunities suddenly appear for those who seem to have conviction or confidence in something, anything – especially if they’re smooth talkers.
Enter today’s chaotic political scene (as of 2024) and its many miseries.
While many document the political unrest and narrate the various events and disagreements, fewer trace the causes of these disagreements down to their origins. Disagreements are often rooted in deeper soil – that is, in lower-level disagreements about basic ideas (philosophy) and human nature (“psychology”).
Politicians thrive in this environment.
The situation recalls the predicament of math earlier, where the problem was that “set theory allows two contradictory statements to both be proven.” When there’s no common ground in society, politicians can essentially say anything. Psychological self-defenses are down. They’re able to make statements that arrive at wildly different conclusions because (again) they’re starting from wildly different premises.
This becomes fertile ground for an environment filled with gobs and gobs of contradictory statements.
This is often on full display during political debates.
During debates, participants hardly engage with each other. Instead of dialogues, they wind up performing dueling speeches or monologues. The result is what Thomas Kuhn in The Structure of Scientific Revolutions might describe as conflicting paradigms or different fundamental worldviews. They seem to be talking about specific issues, while under the surface, the real disagreements are about deeper ideas that often remain unspoken.
For citizens watching this, the effect can be disorienting. When entire worldviews seem contradictory, the world doesn’t seem to fit together. This can produce a sense of existential vertigo. A popular phrase is “feet firmly planted in mid-air.”
When citizens are ungrounded, they’re more easily dazzled by clever rhetoric and verbal sleight-of-tongue.
The media pretends to help by seeming to offer clarity. Yet instead of helping, it often makes things worse by acting as fight promoters instead of marriage counselors. Media figures often strive to heighten drama instead of clarity and resolution. Drama draws ratings, after all, while nuance and peaceful resolutions can defuse situations, which lessens drama – and loses ratings.
The logical result of this might be the end of a civilization or culture, which would be great for ratings at first.
But if those steering the ship in that direction don’t seem to care or can’t seem to stop themselves, the show will go on. Until it can’t.
This mirrors a crisis of foundations in spirituality.
Mental, emotional, political, and social confusion can make genuine spirituality impossible, or at least extremely difficult.
When our metaphysics is off – when our most basic ideas about the world and ourselves veers sideways – that can throw everything else off as well. (Most of our ideas are downstream from metaphysics).
If coherent spirituality becomes impossible, it doesn’t just quiet down.
It gets louder. Instead of settling down, it becomes more raucous. It goes underground, and usually returns in rougher forms. The core problem isn't sexual repression, but spiritual repression.
The result in these situations isn’t a lack of spirituality, but a distortion or warping of it.
In these circumstances, otherwise mundane disagreements can suddenly take on the intensity of a religious war.
Fanaticism, substitute religions, extreme fundamentalism, hardened and bitter atheism, religious rivalries, and so on ensue. The result can be tribalism where an earnest search for Truth can deteriorate into “my god can beat up your god.” The “spiritual but not religious” can battle the “religious but not spiritual,” which can bring out the worst in both. Instead of transforming humans into sages and saints, it brings out the worst in all of us.
But the plot gets even thicker.
Today, all of the world’s religions are practically at our fingertips. Yet ironically, the result often isn’t widespread spiritual literacy, but widespread confusion and friction. Instead of interreligious dialogue, there are culture wars. With so many different beliefs, opinions, practices, and cultures, many of which seem completely incompatible, how is it possible to sort it all out?
The result can seem like a chaotic sports league. Some fixate on the idea that their team is #1. Others don’t feel like their team is #1, and so, have vowed revenge. Still others aren’t fans of any particular team, and don’t see what all the fuss is about. They might even feel a little left out or homeless. Others see the whole scene as madness and launch crusades against sports altogether, or try to abandon and ignore the entire sports scene completely.
For some, the experience can be baffling. It can lead to throwing up hands, abandoning the problem altogether, and Netflx marathons or worse.
There are better solutions to the problem.
But sane answers are often drowned out by the noise.
The descriptions above–thumbnail summaries of math, psychology, philosophy, politics, and spirituality–are brief summaries that condense huge topics into a few sentences, and so are likely to enrage specialists who balk at broad, sweeping comments and “overgeneralizations.”
A popular fallacy today is that “specialists” are smart, credible, and rigorous thinkers while “generalists” aren’t.
But we’re living in the age of information overload. To become a specialist, areas of expertise are becoming narrower and narrower. The result of this means knowing more and more about fewer things. This creates a situation with hoards of experts on individual puzzle pieces but a shrinking number of those that can explain how the puzzle pieces fit together.
The result, for the rest of us, can be like a disorienting tour through an unending funhouse. Various specialists can offer hair-splitting corrections on minute details while ignoring the greater and more important problem. The overall experience is like trying to navigate a complex, life-sized labyrinth while only seeing through either a telescope or a microscope. We’re too zoomed in, and the perspective is almost always skewed.
And few seem to know why.
But what’s happening in front of us is the result of what’s happening several floors down. It’s all a result of our philosophy (our metaphysics, epistemology, psychology, teleology, and ethics) and even our souls sometimes being fragmented, disconnected, and out of alignment.
If the crisis of foundations in math wasn’t a single, one-time event, and if parallel versions of it are now echoing throughout psychology, philosophy, politics, and spirituality, then we could keep exploring how this extends even further into other fields – economics, theology, sociology, and so on – where other “foundations” might also be going wobbly.
But instead, let’s take a more intimate turn.
All of this can also play out in our personal lives.
If there’s widespread confusion on human nature (psychology), our basic beliefs about the world and ourselves (philosophy), our politics and the state of societal rest and unrest, ultimate matters including the point of it all (spirituality) and other existential riddles – it becomes impossible for it not to impact our personal lives.
Kolakowski called it “metaphysical horror.” Ken Wilber calls it “aperspectival madness.” It could also be understood as the idea that we’re now living through “The Death of God.”
Whatever we might call it, it can sometimes feel like living in the eye of a hurricane where the “hurricane” consists of contradictory ideas.
Being surrounded by a swarm of incompatible, impossible-to-digest ideas can feel disorienting. It can seem like we’re suffering from existential indigestion.
And this can quickly boil down to the level of everyday life. The simplest acts can suddenly become complex. For example, when put under scrutiny, even the simple act of eating dinner can lead to confusion. (“Processed foods or non-processed? Vegetarian or carnivore? Organic, or non-organic? Is meat murder? Is rabbit food fit for humans? Which diet is best?”) Even talking to friends can get complicated. (“Email, text, IM, phone, or face-to-face? Does social media count as real human interaction? Am I being recorded? Will every word of this conversation go down on my permanent record and be used against me in the court of law?”) And so on.
Mundane problems can eventually lead to profound problems if we follow them all the way. A missing button can become an “everything problem.”
As Nietzsche said, “Great problems are in the street.”
Yet, constantly wrestling with profound problems without relief can strain the load on our mental hard drive.
When our life philosophy or basic “map” of life gets shaky, we can experience an “existential crisis.” It’s the crisis of foundations in math, but on a personal level. It’s an inner earthquake.
When the ground gets shaky, everything above ground can feel uncertain and unstable. It can be disorienting. Radical uncertainty easily gives rise to anxiety, and the more anxiety-provoking things get, the more we tend to simply hunker down and focus on any immediate tasks at hand. This can help us survive the day, but it doesn’t necessarily solve the problem at the bottom that’s giving rise to it all.
In the book Reality Isn’t What it Used to Be, Walter Truett Anderson said that “we do not comprehend what a stunning – and yet still incomplete – upheaval of thought has occurred in the recent historical past.” (He wrote that around 1990.)
We still don’t seem to comprehend it fully.
So, what should we do?
What can us regular folks do through all this?
Should we ignore it? Give up? Wait for the experts to sort it out?
If a crisis of foundations really is happening on multiple fronts, what can those of us who just want to live lives with a degree of happiness, sanity, and meaning do to survive and thrive?
The outlook described above might seem bleak.
Yet there’s good reason for hope.
Again, we eventually resolved the crisis of foundations in math. Things got bumpy for a while, but apparently, math is no longer in crisis mode and is now on firmer ground.
There’s reason to believe that we’ll also resolve the crises in the other fields – and wind up stronger – as a result.
Philosophy, psychology, and so on might take some time to settle themselves out in academia, likely over several decades, at least.
But in the meantime, the rest of us have lives to live.
For those of us who can’t or don’t want to wait for The Experts to figure all this out, we can take matters into our own hands.
For us, the above situation can serve as a clarion call.
We can get in shape.
Luckily, our personal state doesn’t depend on experts resolving these crises. We’re on our own in some of these areas. And that’s fine. It’s always been the case, and always will be.
We can gear up and prepare ourselves. If the ride is bumpy and likely to get bumpier, we can train for bumps. We can upgrade our shock-absorbers, strap in tighter, scan the route for smoother paths, and look for causes of the turbulence.
We can work to become stronger.
“Getting stronger” along these lines isn’t just lifting weights. The strength we need here isn’t just physical.
It’s inside. It’s “existential fitness.”
A lifestyle of existential fitness is one that strengthens foundations. It means living away from fault lines. It can mean giving our life philosophy or worldview a checkup and makeover. It can mean working to harden up our bases of philosophical self-defense and psychological self-defense. It can mean getting genuine clarity on topics like anxiety, depression, and human nature in general toward the goals of basic sanity, happiness, and psychological health.
It can mean working toward no-nonsense spirituality that isn’t just a side-hobby but fully integrates with the rest of our lives. This might mean adopting a contemplative practice or running various spiritual experiments that are experiential and practical, with real-world effects.
And if enough people get aboard, it could even become a kind of Spiritual Renaissance.
There’s reason for hope. Even if the world floods with confusion and chaos, we can work toward building ourselves into an ark.
Surviving or thriving in a crisis of this sort isn’t any single magic bullet. It’s a “way of life.”
And in a crisis – or even without one – that “way” can be a good thing.