Formal Logic
The Argument That Can't Be Wrong — And Why That's a Problem
A perfectly valid argument can be built entirely from lies.
The Idea
Formal logic draws a sharp line between two things we instinctively blur: whether an argument is *valid* and whether it is *true*. Validity, in the technical sense, has nothing to do with truth. An argument is valid if the conclusion follows necessarily from the premises — if the structure holds, regardless of what the premises actually say about the world. Truth is about whether those premises correspond to reality. These two things can come apart completely. Consider: 'All fish can fly. Salmon are fish. Therefore, salmon can fly.' Every step of the reasoning is airtight. The conclusion follows with absolute necessity from the premises. The argument is perfectly valid. It is also, of course, nonsense — because the first premise is false. What logic gives you, then, is not a guarantee of truth but a guarantee of *transmission*: if your premises are true, and your argument is valid, your conclusion must be true. Logicians call this a *sound* argument — valid structure, true premises, reliable conclusion. This distinction matters far more than it might seem. Most bad arguments in everyday life aren't structurally broken — their logic is fine. The problem is that one premise is quietly false, unexamined, or smuggled in as obvious. The machinery of reasoning runs perfectly; it's just fed bad fuel. Formal logic trains you to separate these two questions — 'does this follow?' and 'is this actually true?' — and ask them one at a time.
In the World
In the early 1960s, Robert McNamara — US Secretary of Defense under Kennedy and Johnson — became notorious for running the Vietnam War like a logic problem. His team at the Pentagon were known as the 'Whiz Kids,' analysts who had modernised the US Air Force with quantitative methods and believed that rigorous, structured reasoning could solve any strategic challenge. Their arguments were, in a formal sense, coherent. If bombing sorties increase, enemy supply lines degrade. If supply lines degrade, enemy capacity falls. If enemy capacity falls, the war ends sooner. The logic tracked. The conclusions followed from the premises. But the premises were wrong — in some cases, fabricated. Body counts were inflated. Enemy resilience was miscalculated. The assumption that the North Vietnamese would respond to pressure the way a rational Western adversary might was never seriously examined. The structure of the reasoning was sound; the inputs were not. McNamara, late in life, came to understand this distinction painfully. In Errol Morris's documentary *The Fog of War*, he described his own failure in almost exactly these terms: they had been right about the reasoning and catastrophically wrong about the facts. A generation of formally valid arguments, built on premises nobody stopped to check, cost hundreds of thousands of lives. The machinery of logic had worked perfectly. It was just fed bad fuel.
Why It Matters
Once you internalise the valid/sound distinction, you start listening to arguments differently — including your own. The question shifts from 'does this make sense?' to 'wait, do I actually know that first part is true?' This is particularly useful in moments of strong conviction. When you feel certain a conclusion is right, it's tempting to reverse-engineer the argument — to reach for premises that get you where you already want to go. The reasoning feels watertight because you built it to be. But validity is cheap; any conclusion can be made to follow from something. Soundness is hard, because it requires you to turn your scrutiny toward the premises you least want to question. A more mindful engagement with any argument — your own or someone else's — involves pausing at each premise and asking: is this actually established, or am I just treating it as obvious? That pause, small as it is, is where a great deal of careful thinking lives. Formal logic, stripped of its symbolic notation, is really just the discipline of separating 'the reasoning works' from 'the facts are right' — and refusing to let one do the other's job.
A Question to Ponder
Think of something you're currently confident about — a belief, a plan, a judgment about a person or situation. Can you identify the premises your conclusion rests on, and when did you last actually check whether they're true?
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