In my last post about generality, I tried to show how our ambition to discover ideas that are all-encompassing and eternal makes our worldview crumble, leaving us unable to think clearly even about simple issues with obvious solutions. Today, I want to discuss another instance of the same problem, in a simpler and more direct way. You can think of this essay as a prequel to “When Universality Breaks.”

What is boolean thinking

Every time someone asks you a yes/no question, you are being coerced into accepting a pattern of thought that we’ll call boolean thinking. The word “boolean” here is used in the sense of the Boolean logic, and the Boolean datatype in logic and programming — a type that admits only two values: true and false. By “boolean thinking,” I am referring to the precondition that every statement should necessarily be categorized as either true or false. This is a law in Boolean logic, known as the “law of excluded middle”).

“But every statement is either true or false,” some might object. This principle might not be entirely false, but it is also not entirely true (ba-dum-tss).

Context is key. By “context”, I mean the set of premises/postulates/axioms, which we presume in order to think. Depending on the context, a statement can be:

• Unknown or unknowable (if the context is incomplete)
• Senseless (if the question is meaningless)
• Both true and false (if the context varies)

You are probably aware of such situations, but you might still not see them as contradicting the Boolean doctrine (boolean thinking, as we shall see, is precisely that—a doctrine). It’s a mode of thought that, although not universally valid, is often useful. For instance, you can’t make plans with someone who says there’s a 40% chance they’ll go out tonight, or that the question doesn’t make sense. Thus, you might be tempted to treat all imperfections of the Boolean model as imperfections of the world — or of thinking agents themselves:

1. No statement is unknowable — somewhere out there, there must be an answer.
2. No statement is senseless — given enough effort, every statement can be interpreted.
3. A statement is both true and false only because we lack sufficient information.

People who think this way, I would say, suffer from a serious case of Boolean thinking. Fortunately, the condition is curable, provided that we understand its cause. As I mentioned, Boolean thinking always has to do with context. Generally speaking:

1. Each statement can be true in one context and false in another.
2. Every statement is senseless when presented without context.
3. Every statement is unknown when the context is incomplete.

The case against boolean logic

We’ve established that the truth or falsity of a statement depends on its context — that is, on the assumptions we take as true or false in order to justify it. Boolean thinking, boolean logic is applicable only if we agree on some universal context — a universal set of true statements on which every evaluation can rest.

Note that aside from being universal (valid for all statements) the context for boolean logic has to also be all-encompassing (relevant for every statement) i.e. the set of logical statements that form it should never, under no interpretation tell something invalid, and at the same time would let us deduce all that is valid. As I argue later, such context resembles what political philosophers call an authoritarian doctrine (although the phrase “authoritarian doctrines” is somewhat deceiving, because it isn’t the doctrines themselves that are authoritarian, but the role they play in people’s thinking patterns).

So, while boolean logic may be splendid when viewed by itself, when viewed in relation to the “real world” there is a huge issue with it, the namely that no logical context, no logical framework is strong enough to capture the things that we usually want to dissect, (the real world, if you must). Proving the claim above is a subject of a different text, for now it suffices to say that although it may not look logical or scientific, it is, however, very backed up by both logic and science. Rather than asking why this is the case, it is more appropriate to ask what makes us think the reverse, what makes us think that the real world may be captured by a boolean logical framework — I’d argue that the thought that it can be is an instance of the so called “is-ought fallacy” — the idea that something is true just because it will be good for us that it is true. But that’s a separate topic as well (see “When Universality Breaks”.

Now, we are ready to make the case against boolean logic:

Because boolean logic overlooks the importance of context (that each proposition can be true in one context, false in another, and also neither true nor false) it inspires dichotomous thinking, also known as black-and-white thinking.

i.e. boolean logic is apt for a world where there is a single unifying and also complete framework… a universal set of axioms. But that is not our world. Our world is a place where we constantly have to compare different frameworks and, different sets of axioms, which are all incomplete (here is the place where I should reference Godel’s theorem, but I am not going to do it, as it is too cliche, (pardon my lack of diacritics)).

In our world, we, for example, try to be happy with what we have, but at the same time strive to achieve more. We try to believe that people are good, but at the same time defend ourselves against evil etc. The boolean framework says it is either one and the other (e.g. people are either good or evil).

When we encounter something that doesn’t fit our Boolean framework, we have two options:

1. Pretend it didn’t happen (or twist our perception until it fits).
2. Declare that “the world isn’t logical” and stop trying to make sense of it.

Non-Boolean thinking, in contrast, allows multiple frameworks to coexist—without one diminishing the others.

Non-Boolean logic

Criticizing something is (nearly) pointless unless we offer an alternative and I will do my best to do just that.

Most people are aware of non-classical logics, but they tend to regard them as curiosities rather than real alternatives to traditional boolean logic. One branch of non-Boolean logic, however — intuitionistic or constructive logic — is increasingly relevant to many fields. It is, for example, the logic that is at the heart of the so called “proof assistants”. Boolean logic is also a special case of intuitionistic logic (the only difference is that it lacks the law of excluded middle).

Rather than resting on truth and falsehood, intuitionistic logic revolves around the concept of a proof. In contrast with classical logic, where a proof is primarily a process, intuitionistic logic treats a proof as an object: a construction that demonstrates the truth of a statement (you can see how this is related to programming — in intuitionistic logic, proving thing is similar to transforming some objects from one format to another).

Each proof depends on a context – a set of premises or other proofs we assume to exist. So, before evaluating any statement, intuitionistic reasoning asks: “What is the context?” i.e. “Give me the set of premises from which we are operating.”

From there, we proceed to manipulate the proofs of the premises in order to construct a proof of our statement.

You might say that this is much like “normal” logic. But there is a difference — intuitionistic logic makes us more acutely aware of the context in which we are operating. And if we start paying attention, we would observe that when trying to prove a statement, instead of the two truth values (true/false), there are actually three possibilities:

1. We might be able to construct a proof that a statement is true.
2. We might be able to construct a proof that it is false.
3. We might not be able to construct neither—the statement is neither true nor false.

And without the correct context, the statement might not make sense at all.

(Yes, in a perfect world, where we know everything, we would be able to prove or disprove every statement that we can formulate, but not in this world.

And with that realization, we are free from the Boolean prison — we realize that all thinking is relative there is no a single truth, (nor a single falsity).

For more on intuitionistic logic, see my book Category Theory Illustrated.

My reasons for criticising Boolean thinking are not merely academic. The way we think about logic shapes how we think about everything — and, ultimately, how we live our lives. This is why what I call “Boolean thinking” in logic has many names elsewhere. In philosophy, it’s called Platonism. In politics, it manifests as authoritarianism.

The second point is important. You might define authoritarian ideologies in many ways, but the key thing about them is that are based on a doctrine on which all people must abide to, in their thinking — a shared “context” or set of premises. The power of authoritarian rulers arises from the way they limit the things that people can think and say: rulers define what the premises are and from then on, then you are “free” to make the conclusions yourself. To rephrase Orwell’s famous slogan:

“Who controls the premises controls the conclusions.”

Authoritarian regimes rely on propaganda, and propaganda often uses Boolean thinking: the belief that if something doesn’t follow from the “official” premises, must be necessarily false (black and white thinking). Or that if two things seem opposed, one of them must be true and the other false (false dichotomies).

To combat such propaganda techniques always remember the two rules of the contexts:

1. There are many of them.
2. No-one gets to decide which is more important.

It began with a study. In December of 2025, Stanford researchers analyzed 2.2 billion social media posts looking for a pattern. They wanted to know what percentage of users posted severely toxic content. Not rudeness, not sarcasm, but speech that was so hateful that 90% of the world would flag it as being problematic.1

With this data in hand, they then asked thousands of people to answer a simple question:

They were surprised by the results. They had discovered an enormous reservoir of misperception that had been hidden in plain view.

The Bar

Here is the simplest version of the problem. Imagine walking into a bar with a hundred people inside.

Three of them are shouting — about politics, about each other, about whatever gets a reaction. The other ninety-seven are talking at a normal volume. But there's a bouncer at the door, and he gets paid by the minute you spend staring. So he's wired the three loudest people into the sound system and turned it all the way up.

You walk in, hear the roar, and conclude: this place is full of lunatics. Never hearing the 97 people having normal conversations a few feet away. You could leave, but all your friends are inside. You're stuck.

This is how social media deals with contentious topics. The bouncer is an algorithm. And whether you like it or not, you've been a bystander.

Pick a contentious topic. This is what your feed might look like.

Reading this feed, you might reasonably conclude that the country is split between unhinged extremes. It is not. And the gap between what Americans actually believe and what the feed suggests they believe may be the most consequential thing the platforms haven't shown you.

See the Room

Let's visualize this as a single room with 100 people inside. This is what it looks like:

This pattern repeats across platforms. On Twitter/X, toxic tweets receive ~86% more retweets and ~27% more visibility than non-toxic ones, 0.3% of users shared 80% of all contested news,14 and just 6% of users produce roughly 73% of all political tweets.16 On TikTok, 25% of users produce 98% of all public videos.15 The specific numbers vary. The dynamic is the same: a small minority of highly active users overwhelms the majority.

After a time consuming content in this room, your brain performs a kind of ambient demography. The feed becomes a sort of census. You conclude — logically — that the behavior must be widespread. The room might just be full of extreme people! Maybe most people do believe these crazy things.

This is not just about what we see on social media

If this were just about tone of our social posts, it wouldn't matter very much. But this distortion ends up causing some seriously bad patterns of behavior.

When the majority of people looks at the feed and assumes they're outnumbered, people will often self-censor.3 The dynamic replicates on social media17 — fear of social isolation suppresses opinion expression on platforms where it's perceived to be unwelcome. They go quiet, or they leave a platform entirely. They cede the space to users with more extreme politics.

The minority who aggressively post end up with their own distortion – believing they are part of the majority.5

A study of 17 extremist forums found the same pattern: the more someone posted, the more they believed the public agreed with them. More engaged participation bred false consensus.

Both sides develop wildly inaccurate beliefs about who the other side actually is.6 See how some of your own beliefs line up:

The distortion extends to policy beliefs. Step through to see the perception gap on the issue of immigration.

Elected officials are very good at sensing political sentiment. It's literally their job. (They are not elected to correct people's beliefs.)

Politicians who can build a coalition about a perceived belief are more likely to win. They position themselves against an opponent that doesn't exist, but their supporters think exists.

And remember: most of our politics now happens on social media. Candidates often read the same distorted feed. They are unlikely to change their minds.

The window of discourse shifts. Not because opinions changed, but because perceptions of opinions did.

When you believe the other side is extreme, you become more willing to treat them as a threat.7

Both Democrats and Republicans vastly overestimate how many on the other side support political violence. The result is a populace primed to assume the other side is ready to do horrible things.

Each step feeds the next. The distortion is self-reinforcing.

Knowing Isn't Enough

Okay. So now you know that a small minority dominates the feed.

You know that Republicans and Democrats actually have a far more nuanced set of opinions about contested issues.

Does that fix it? Not really. You also know that everyone else doesn't know it. And if the world continues operating as if the distortion is real, you should probably act the same — even though you know it's wrong. The room hasn't changed, even if you know people inside it are confused.

This is called a common knowledge problem.

Steven Pinker lays this out cleanly in his excellent recent book When Everyone Knows That Everyone Knows.8 Learning a fact changes what you know. Seeing it displayed publicly — where everyone else can see it too — where you know others can also see it, changes what everyone knows, and subsequently how they act.

Social media has no public square. It has 300 million private windows, each showing a different distortion of the same room. Illuminating the common thoughts between us has the potential to radically change it.

The Idea

So what can we do about this?

Fortunately, there's some good evidence showing how it can be fixed. Multiple studies show that when misperceptions are corrected in a public way, hostility drops. Mernyk et al. found that a single correction reduced partisan hostility for a full month.7 Lee et al. found that correcting overestimates of toxic users improved how people felt about their country and each other.1

We can do this today.

Imagine every post on a contested topic had a quiet link beneath it. Not a fact check, a label, or a warning. Instead — what if it had a Community Check?

A Community Check is an open-source design layer that could be deployed across social media, beneath contentious posts, to help users understand how other people on the platform (or the nation) actually feel about an issue.

It is a way of quickly adding context to the most hot-button viral issues, giving people more visibility into the opinions of the public.

The Idea in Action

Let's explore this intervention with a topic that cuts across political identity:

Money in Politics

On the surface, this seems contentious. But it's actually a supermajority issue: 81% are concerned about the influence of money on elections, including 78% of Republicans and 90% of Democrats. 75% say unlimited spending weakens democracy. Only 15% believe unlimited political spending is protected free speech.

And yet, very little changes, largely because everyone assumes the other side is fine with it. The feed is full of people defending their team's donors and attacking the other team's. It might look like a 50/50 partisan battle, but it's not. It's a majority consensus that cannot see itself.

What if you could see this consensus?

Community Check draws from a random sample of platform users + robust national polls, surveyed independently of the content. The sample is statistically representative. The results update continuously. And critically: everyone sees the same numbers.

Why This Isn't Fact Checking or Audience Polling

Traditional fact-checking is a top-down approach that often feels like it's dictating from above. This is hard for people to stomach. Content moderation for many years now has been perceived as removing speech. This simply adds context, much like the crowdsourced feature Community Notes (an inspiration for this project).

Nor is this just a user-poll under a post. Instead it's drawing from all platform users, coupled with statistically significant national surveys. It's an actual window into the views of the majority, not just the views of those looking at the post.

It Works for Video Too

Short-form video is the fastest-growing vector for political distortion. The same dynamic applies — a small minority of creators produce the vast majority of political content — but video bypasses the pause that text gives you. Community Check can adapt. Tap through to see how.

We Could Do This Now

Platforms already have a lot of these capabilities. They already survey users. They even know how to run sophisticated polls. There are a few technical details to work out (spec here), but this is not a hard problem to solve.

The unseen majority is the public. And the public deserves to know itself.

A tiny minority, dominating the feed. That's all it ever was. The rest of us were here the whole time, quiet and decent and waiting to be seen.

Follow my other work here