Someone in the room says, "If the campaign were working, signups would be up, and signups are up, so the campaign is working." Heads nod. Budget gets renewed. The sentence sounds like logic, and it is shaped like logic, but it is one of the oldest broken shapes there is. Knowing why is a leadership skill, not a philosophy-class party trick.

The quick version

  • An argument has a structure, premises leading to a conclusion. Logic is about whether that structure holds, separately from whether the facts are true.
  • Valid = if the premises were true, the conclusion would have to follow. Sound = valid and the premises are actually true. You need both; people usually only check one.
  • A fallacy is a recurring broken move. Formal ones break the structure; informal ones smuggle in irrelevant content. Both pass for reasoning at speed.
  • The single best habit: make the hidden premise explicit, then ask what evidence would prove the claim wrong. Most weak arguments collapse the moment you do.

The idea in depth: validity is about shape, not truth

Formal logic studies arguments by their form, the pattern connecting premises to a conclusion, independent of subject matter. Its oldest and most useful distinction is between validity and soundness. An argument is valid when there is no possible situation in which the premises are all true and the conclusion is false; the conclusion is forced by the structure. It is sound when it is valid and its premises are in fact true. A valid argument can be built entirely on false premises and still be valid, the machine works, it has just been fed garbage.

The classic valid pattern is modus ponens: "If P then Q. P is true. Therefore Q." It is impossible for those two premises to be true and the conclusion false, which is exactly what makes it valid (see the standard treatment of modus ponens). The campaign argument at the top of this piece looks like that, but isn't. Its shape is "If P then Q. Q is true. Therefore P", which logicians call affirming the consequent, and it is a recognised formal fallacy: signups could be up for ten reasons that have nothing to do with the campaign. The Internet Encyclopedia of Philosophy gives the same shape its textbook example, "If she's Brazilian, then she speaks Portuguese; she speaks Portuguese; so she's Brazilian" (IEP, Fallacies), and the absurdity is obvious there precisely because the content is unfamiliar.

So the move is: when an argument matters, write it as premises and a conclusion, then ask two separate questions in order. First, if the premises were true, would the conclusion have to follow? (validity, the shape). Only then, are the premises actually true? (soundness, the facts). Keeping them separate stops the most common boardroom error: accepting a conclusion because the facts in the premises are real, without noticing the facts don't actually force the conclusion.

flowchart TD
    A(["An argument"]) --> B{"If the premises were true,
must the conclusion follow?"}
    B -->|No| C("Invalid, the shape is broken.
Stop here.")
    B -->|Yes| D("Valid shape")
    D --> E{"Are the premises
actually true?"}
    E -->|No| F("Valid but unsound,
built on bad facts")
    E -->|Yes| G("Sound, accept it")
Two questions, in order: check the shape first, the facts second. Leaders Loop

Taking a real argument apart: the Toulmin model

Pure formal logic is clean but narrow, almost no real workplace argument arrives as a tidy syllogism. The philosopher Stephen Toulmin made exactly that complaint in The Uses of Argument (1958), and offered a model built for practical, everyday reasoning instead. His layout names the parts of a real argument: the claim (what you want me to accept), the grounds (the data or evidence offered), and, the part people skip, the warrant, the usually-unspoken assumption that licenses moving from the grounds to the claim. He adds backing (support for the warrant itself), a qualifier ("probably", "in most cases", the honest strength of the claim), and the rebuttal (the conditions under which it would not hold).

The warrant is where most workplace arguments quietly fail. "Conversion dropped 8% (grounds), so we should redesign the checkout (claim)" hides a warrant, that the drop was caused by the checkout design, which, said out loud, is plainly an open question. The fix is the same discipline that powers hypothesis-driven problem solving: surface the assumption before you spend against it.

The warrant is the assumption nobody said out loud. Find it, and you've usually found the argument's weakest joint.

The practical move: for any recommendation with money behind it, force the three core parts onto the table, claim, grounds, warrant, and ask, "What would have to be true for the grounds to actually support the claim?" That single question drags the silent warrant into the open, and a warrant you can see is one you can test, qualify, or reject. It pairs naturally with knowing deductive, inductive and abductive reasoning, since the kind of warrant you need depends on whether you're claiming certainty or just the best available explanation.

flowchart LR
    G(["Grounds
(the evidence)"]) --> C(["Claim
(what to accept)"])
    W(["Warrant
(why grounds support claim)"]) -.licenses.-> C
    B(["Backing"]) -.supports.-> W
    R(["Rebuttal
(unless...)"]) -.limits.-> C
    Q(["Qualifier
(probably / usually)"]) -.tempers.-> C
Toulmin's layout. The dotted links are the parts people leave unspoken, and where arguments break. Leaders Loop

Fallacies: the broken moves that survive review

A fallacy is a pattern of reasoning that feels persuasive but doesn't actually support its conclusion. The useful split is between formal and informal. A formal fallacy can be spotted from the structure alone, affirming the consequent is one; so is denying the antecedent ("If P then Q; not P; therefore not Q"). An informal fallacy can't be caught by shape because the flaw lives in the content (IEP, Fallacies). The informal ones are the ones that survive a meeting, because they sound like ordinary debate:

  • Straw man, restating someone's position as a weaker version, then knocking that down ("So you're saying we ship with zero testing?").
  • Ad hominem, attacking the person to discredit the argument ("She's not technical, so ignore the concern") instead of the concern itself.
  • False dilemma, presenting two options as the only options ("We either freeze hiring or we go bankrupt") when a spectrum exists.

Here's the honest limitation, and it matters: knowing the fallacy names does not make you immune. Peter Wason's famous selection task (1966) showed that even motivated, intelligent people are strikingly bad at applying conditional logic in the abstract. In Wason's original study fewer than one in ten people picked the cards that could actually disprove a simple rule, and later studies of the abstract task rarely push that much past a fifth, because we instinctively reach for confirming cases instead of disconfirming ones (Wason selection task). The bug isn't ignorance of logic. It's that confirmation comes naturally and falsification doesn't.

Here the better move is a refusal: don't memorise a fallacy zoo and try to spot the animals live, because under time pressure you won't. Install one reflex instead, and it defeats the whole class at once, "What evidence would change my mind?" An argument that survives a real attempt to disconfirm it is worth keeping. One that can't was never reasoning; it was decoration. That's the same instinct behind good mental models and cross-disciplinary latticework: testing a belief from more than one angle before you trust it.

A worked example

A product lead opens the quarterly review: "Our enterprise tier is our future. Enterprise revenue grew 40% last quarter while self-serve was flat. We should move three engineers off self-serve and onto enterprise." (Figures here are illustrative.) The room is ready to nod, 40% is a real number, the engineers are real, the logic feels tight.

Run it through the toolkit. Toulmin first: the claim is "reallocate three engineers to enterprise"; the grounds are "enterprise grew 40%, self-serve was flat"; the unspoken warrant is that past growth rate predicts future return on added engineering. Said aloud, that warrant is contestable: enterprise may have grown 40% precisely because it was small (a base-rate effect), and self-serve may be flat because it's already mature and quietly funding everything else.

Then the formal check: "enterprise is growing, therefore enterprise is where investment pays off" is affirming-the-consequent territory, growth is consistent with "this is the right bet" but doesn't establish it; a dozen other causes fit the same data. Then the disconfirming question: "What would we expect to see if this were the wrong move?", perhaps that self-serve drives most enterprise leads, so starving it kills the very pipeline enterprise depends on. Nobody had checked. The decision that walked in as obvious walks out as a testable hypothesis with a number attached. That doesn't slow the decision down. It swaps a forty-percent story for one you could actually defend.

Frequently asked questions

Isn't this just being pedantic in meetings?

It's the opposite of pedantry if you do it silently and surface only the load-bearing flaw. You're not grading grammar; you're asking "what would have to be true for this to hold?" before money moves. The goal is a better decision, not a logic lecture, and you rarely need to say the word "fallacy" out loud to get there.

What's the difference between validity and soundness again?

Validity is about the shape: if the premises were true, would the conclusion have to follow? Soundness adds the second test: are the premises actually true? A valid argument with a false premise is valid but unsound, and unsound is what gets you. Check the shape first, because a broken shape means you can stop without litigating the facts at all.

Which fallacy should I learn first?

Affirming the consequent, because it's everywhere ("X is up, so our plan is working") and it hides inside data-driven arguments that feel rigorous. If you only ever catch one broken move, catch the leap from "the evidence is consistent with my claim" to "therefore my claim is true."

How is this different from intuition or experience?

It isn't a replacement, it's a check on it. Experience generates the hypothesis fast; logic stress-tests it before you commit. The two are complementary, which is also the heart of first principles vs heuristics vs analogical reasoning: heuristics propose, structure disposes.

If everyone's bad at formal logic (per Wason), why bother?

Because the failure is systematic and therefore beatable. You won't out-reason confirmation bias in your head, but you can install one process, "state the hidden assumption, then ask what would prove me wrong", that does the work your intuition won't. The discipline lives in the habit, not in raw cleverness.

Related in the Toolkit

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