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Logic

Logical Fallacies

Lesson

A fallacyis an argument form that looks persuasive but doesn’t actually guarantee the conclusion. Two of the most common confuse conditionals.

Affirming the consequent

From p→qp \to q and qq, conclude pp. Invalid.

“If rain, then wet. Wet. So it rained.” — could have been a sprinkler.

Denying the antecedent

From p→qp \to q and ¬p\neg p, conclude ¬q\neg q. Invalid.

“If rain, then wet. Not raining. So not wet.” — again, could be a sprinkler.

How to type your answer

1 = the argument is VALID, 0 = INVALID (fallacy).

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

p→q, p ∴qp \to q, \ p \ \therefore q

Problem 2

p→q, q ∴pp \to q, \ q \ \therefore p

Problem 3

p→q, ¬p ∴¬qp \to q, \ \neg p \ \therefore \neg q

Problem 4

p→q, ¬q ∴¬pp \to q, \ \neg q \ \therefore \neg p

Practice

Standard problems matching the lesson.

Problem 5

If rain, wet. Wet. So it rained.\text{If rain, wet. Wet. So it rained.}

Problem 6

If rain, wet. Raining. So wet.\text{If rain, wet. Raining. So wet.}

Problem 7

If rain, wet. Not raining. So not wet.\text{If rain, wet. Not raining. So not wet.}

Problem 8

If rain, wet. Not wet. So no rain.\text{If rain, wet. Not wet. So no rain.}

Problem 9

If A then B. B is true. So A.\text{If A then B. B is true. So A.}

Problem 10

If A then B. A. So B.\text{If A then B. A. So B.}

Problem 11

If A then B. Not A. So not B.\text{If A then B. Not A. So not B.}

Problem 12

If A then B. Not B. So not A.\text{If A then B. Not B. So not A.}

Problem 13

If bird, can fly. Can fly. So bird.\text{If bird, can fly. Can fly. So bird.}

Problem 14

If bird, can fly. Bird. So can fly.\text{If bird, can fly. Bird. So can fly.}

Problem 15

If bird, can fly. Cannot fly. So not bird.\text{If bird, can fly. Cannot fly. So not bird.}

Problem 16

If pass test, get A. Got A. So passed test.\text{If pass test, get A. Got A. So passed test.}

Problem 17

If pass test, get A. Failed. So no A.\text{If pass test, get A. Failed. So no A.}

Problem 18

If snow, ski. Skiing. So snowing.\text{If snow, ski. Skiing. So snowing.}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

p→q, ¬q ∴¬pp \to q, \ \neg q \ \therefore \neg p

Problem 20

p→q, q ∴pp \to q, \ q \ \therefore p

Problem 21

p→q, ¬p ∴¬qp \to q, \ \neg p \ \therefore \neg q

Problem 22

p→q, p ∴qp \to q, \ p \ \therefore q

Problem 23

p∨q, ¬p ∴qp \vee q, \ \neg p \ \therefore q

Problem 24

p→q,q→r∴p→rp \to q, q \to r \therefore p \to r

Problem 25

If lazy, fail. Not lazy. So pass.\text{If lazy, fail. Not lazy. So pass.}

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Quiz

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10 questions, no hints. About 5 minutes.