Common Logical Fallacies: Where Reasoning Goes Wrong

Common Logical Fallacies: Where Reasoning Goes Wrong | Ideasthesia

A fallacy is an argument that seems persuasive but violates the rules of logic.

The tricky part: fallacies often feel right. They exploit patterns in how we naturally think. That's why they persist — and why they're worth studying explicitly.

Knowing the fallacies is like having antibodies. Once you can name the error, you can resist it — in others' arguments and in your own.

Not every bad argument is a formal fallacy. Some are informal — they rely on rhetoric, emotion, or misdirection rather than structural invalidity. But the formal fallacies are where logic can definitively say: this pattern doesn't work.

Affirming the Consequent

The most common formal fallacy.

P → Q (If P then Q) Q (Q is true) ∴ P (Therefore P) — INVALID

"If it rained, the ground is wet. The ground is wet. Therefore, it rained."

Why it fails: The conditional says P guarantees Q. It doesn't say Q requires P. The ground might be wet from sprinklers, a burst pipe, or morning dew.

The valid move is modus ponens: P → Q, P, ∴ Q. The fallacy reverses the direction.

Denying the Antecedent

P → Q (If P then Q) ¬P (P is false) ∴ ¬Q (Therefore Q is false) — INVALID

"If it rained, the ground is wet. It didn't rain. Therefore, the ground isn't wet."

Why it fails: The conditional makes no claim about what happens when P is false. Other things could make Q true.

The valid move is modus tollens: P → Q, ¬Q, ∴ ¬P. The fallacy negates the wrong component.

Undistributed Middle

All A are B. All C are B. ∴ All A are C. — INVALID

"All dogs are mammals. All cats are mammals. Therefore, all dogs are cats."

Why it fails: A and C both fall under B, but that doesn't mean they overlap. B is the "middle term" and it's not distributed — we don't know if all of B connects A to C.

Illicit Major / Minor

Illicit Major: All A are B. No C are A. ∴ No C are B. — INVALID

"All roses are flowers. No tulips are roses. Therefore, no tulips are flowers."

Illicit Minor: All A are B. All A are C. ∴ All C are B. — INVALID

"All dogs are mammals. All dogs are animals. Therefore, all animals are mammals."

These fallacies draw conclusions about entire categories (B or C) from statements that only cover subcategories.

Existential Fallacy

All A are B. ∴ Some A are B. — INVALID if A might be empty

"All unicorns are magical. Therefore, some unicorns are magical."

Why it fails: If there are no unicorns, the universal statement is vacuously true, but the existential claim presupposes unicorns exist.

In classical logic with existential import, this inference works. In modern logic without existential import, it doesn't. Be explicit about whether your domain is nonempty.

Quantifier Shift Fallacy

∀x ∃y P(x, y) ∴ ∃y ∀x P(x, y) — INVALID

"Everyone has a mother. Therefore, someone is everyone's mother."

The first says each person has some mother (possibly different for each). The second says there's one universal mother. Quantifier order matters.

Four-Term Fallacy

A syllogism needs exactly three terms. Introducing a fourth breaks the logic.

"All banks are financial institutions. The river has a bank. Therefore, the river has a financial institution."

"Bank" has two meanings — financial institution and river's edge. Two different concepts, treated as one term. The argument has four terms in disguise.

This is also called equivocation — using a word with multiple meanings as if it meant the same thing throughout.

Informal Fallacies: A Brief Tour

These aren't structural errors but rhetorical tricks:

Ad Hominem: Attacking the person instead of the argument. "You can't trust his climate data — he drives an SUV."

Straw Man: Misrepresenting someone's position to make it easier to attack.

Appeal to Authority: Citing an authority outside their expertise. "This physicist thinks evolution is false."

Appeal to Popularity: "Everyone believes it, so it must be true."

False Dilemma: Presenting only two options when more exist. "You're either with us or against us."

Slippery Slope: Claiming one step leads inevitably to extreme consequences.

Circular Reasoning: The conclusion is hidden in the premises. "The Bible is true because it's the word of God, and we know it's the word of God because the Bible says so."

Why Fallacies Persist

Fallacies feel compelling because they exploit:

Pattern matching: Affirming the consequent looks like modus ponens.

Heuristics: "Most Bs are caused by A" makes A → B, B, ∴ A feel reasonable (and it's often good probabilistic reasoning, just not deductively valid).

Rhetoric: Arguments that attack opponents or invoke emotion bypass logical evaluation.

Complexity: In long arguments, a fallacious step can hide among valid ones.

Defending Against Fallacies

Identify the structure: Write out the argument form explicitly.
Check against valid forms: Does it match modus ponens, modus tollens, etc.?
Look for direction errors: Which way does the implication point?
Check quantifier scope: Are you sliding between "some" and "all"?
Watch for ambiguity: Does a word mean the same thing throughout?

The Positive Message

Fallacies aren't just errors to avoid — they illuminate how logic works by showing where it breaks.

Understanding why affirming the consequent fails teaches you what conditionals actually mean. Understanding the undistributed middle teaches you what syllogisms actually require.

Every fallacy is a lesson in logic, seen from the failure mode.

Part 8 of the Logic series.

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