Logic: Validity, Form, and Fallacies
What this domain asks
Logic tests formal reasoning and argument appraisal. Expect deductive validity versus inductive strength, soundness, truth tables, categorical syllogisms, propositional forms (modus ponens, modus tollens), quantifiers, and informal fallacies.
Concepts to hold firmly
- Validity: if the premises are true, the conclusion must be true. Soundness: valid plus true premises.
- Induction: strength comes in degrees; conclusions are probable, not guaranteed.
- Common forms: modus ponens (P→Q; P; therefore Q) and modus tollens (P→Q; not Q; therefore not P) are valid. Affirming the consequent and denying the antecedent are invalid.
- Fallacies: ad hominem, straw man, false dilemma, begging the question, equivocation, hasty generalization, post hoc.
- Counterexample method: one consistent scenario with true premises and false conclusion disproves validity.
Traps
- Confusing validity with truth: a valid argument can have false premises.
- Calling an argument "invalid" when it is merely unsound.
- Mistaking a strong inductive argument for a deductively valid one.
- Missing equivocation when a term shifts meaning between premises.
Rule of thumb
Translate the argument into symbols, then test: can you imagine a world where premises hold and the conclusion fails? If yes, invalid. If no, valid. For fallacies, name the specific structural error rather than the topic.
Worked example
"If it rains, the ground is wet. The ground is wet. Therefore it rained." This affirms the consequent and is invalid; a sprinkler would make the premises true and the conclusion false.