In 1847, a British mathematician named George Boole published a book. He made an audacious claim: human thought could be reduced to algebra. Not metaphorically, literally. The messy, intuitive, seemingly ineffable process of reasoning could be expressed as equations, manipulated like numbers, proven like geometry.

His contemporaries thought he was mad. Thought, after all, is fluid. It leaps, connects, wanders. Ideas arrive like sparks, sometimes illuminating, sometimes fleeting. How could you possibly capture that in symbols?

Boole’s answer changed everything. And you’re using it right now.

Every device you own relies on the system Boole invented. Every algorithm that predicts your preferences depends on it. Every decision a computer makes is based on the same system. This foundational system supports modern technology. What he discovered wasn’t just a curiosity for mathematicians. It was the blueprint for the digital age.

The system is called propositional logic, and it’s deceptively simple. It takes statements, claims about the world that are either true or false, and provides rules for combining them. If this is true, what must also be true? If that is false, what can we conclude?

Consider a detective reconstructing a crime. A witness says the suspect was at the bar at 9 PM. Security footage shows the robbery happened at 9:15 PM. The bar is thirty minutes away. Can the suspect have committed the crime?

You don’t need to be Sherlock Holmes to solve this; you need logic. If the suspect was at the bar at 9 PM, the bar is thirty minutes away. Therefore, the suspect couldn’t have been at the robbery at 9:15 PM. The conclusion follows necessarily from the premises.

This is what propositional logic does. It formalises the reasoning we do instinctively. Each step is made explicit and verifiable. Crucially, it is reproducible.

Here’s where it gets interesting. In the 1930s, a young mathematician named Claude Shannon was working on his master’s thesis at MIT. He was studying telephone switching circuits, the mechanical relays that routed calls through the network. These circuits were getting more complex, and nobody had a systematic way to design them.

Shannon had a realisation: what if he treated the switches like Boole’s logical propositions? A switch could be on or off, true or false. You could combine switches with AND gates (both must be on) or OR gates (at least one must be on). Suddenly, circuit design became a problem in formal logic.

His thesis, “A Symbolic Analysis of Relay and Switching Circuits“, is considered highly important. It is one of the most important master’s theses ever written. It showed that you could build circuits to perform any logical operation. And since logical operations could represent any computation, this meant…

You could build a thinking machine.

Not a machine that “thinks” in the human sense; computers don’t understand anything. But a machine that follows logical rules so precisely, so reliably, that it can execute any process you can formalise. This is the foundation of every computer ever built.

The elegance is in the restriction. Propositional logic doesn’t try to capture the full richness of human thought, metaphor, ambiguity, intuition. Instead, it strips thought down to its skeletal structure: statements and the relationships between them. If A is true, and if A implies B, then B must be true.

This creates something powerful: transparency. In natural thought, we leap from idea to idea, filling gaps unconsciously. We make assumptions we don’t realise we’re making. We see patterns that aren’t there and miss contradictions that are.

Logic insists that every step be explicit. Every assumption must be stated. Every inference must be justified. This doesn’t make logic “smarter” than intuition; it makes it checkable.

Think about for a second how Google Search works. When you type a query, the algorithm evaluates billions of web pages against thousands of logical conditions. Is this page relevant? Does it contain these keywords? Has it been linked to by trusted sources? Each question is a proposition – true or false. The answers combine through logical operations to produce a ranking.

The system isn’t “understanding” your query. It’s executing a massive chain of if-then statements, each link in the chain following necessarily from the one before. Logic at scale, compounding into something that feels almost intelligent.

This is the pattern everywhere in computation. Your phone’s GPS deciding which route to recommend. Netflix predicting what you’ll want to watch. A self-driving car determining whether to brake. Each decision point is a logical proposition. The relationships between them are governed by the same rules Boole formalised 180 years ago.

But here’s what makes logic genuinely profound: it exposes the limits of intuition.

Our gut feelings about what “must” be true are often wrong. We imagine consistency where none exists. We infer without justification. We’re confident about conclusions that don’t actually follow from our premises.

Logic is humbling. It shows, with ruthless precision, when our reasoning is valid. It also reveals when we’re just telling ourselves stories. If you can’t formalise an argument in logical terms, there’s a good chance the argument doesn’t actually hold together. It just feels like it does.

This is why computer science students spend so much time learning formal logic. It’s not because they’ll be writing proofs all day (though some will). It’s because it trains a particular kind of discipline. This includes the ability to think in steps that connect. It also involves building arguments that don’t leak. Lastly, it involves constructing systems that do what you intend rather than what you imagine.

The bridge between human reasoning and machine computation isn’t technological; it’s logical. Every app is a translation of human intention. Every algorithm is translated into formal propositions. Every piece of software involves propositions that a computer can execute.

And the remarkable thing is how far you can go with such simple tools. True, false, and, or, not, if-then. Six concepts, rigorously applied, are enough to build systems of breathtaking complexity.

Understanding propositional logic changes how you think about thought itself. It reveals that beneath the messy surface of human cognition, there’s a structure. The creativity, the leaps, and the sparks of insight reveal this structure. And that structure can be formalised. It can be tested and verified. If you’re clever enough, you can execute it billions of times per second. It can happen in a device that fits in your pocket.

Thought is no longer just a stream. It becomes architecture. Invisible, precise, powerful.

And in that architecture lies everything we’ve built in the digital age.