Logic and Critical Reasoning
This domain tests formal validity, informal argument analysis and fallacy identification. The distinguishing skill is separating validity (form) from truth (content) and from soundness (valid plus true premises).
Formal machinery
- Valid: it is impossible for the premises to be true and the conclusion false. Sound: valid and actually true premises.
- Propositional forms: modus ponens, modus tollens, disjunctive syllogism, hypothetical syllogism, contraposition. Invalid forms: affirming the consequent, denying the antecedent.
- Truth tables test validity: a counterexample row is a row with all premises true and the conclusion false.
- Quantifiers: universal and existential; watch scope, and remember that not-all does not entail none.
- Necessary and sufficient conditions: A is sufficient for B when A guarantees B; necessary when no B without A. Confusing them is the most common error in conditional reasoning.
Induction and argument analysis
Inductive arguments are strong or weak, cogent or not, never valid. Types: enumerative induction, analogical argument, inference to the best explanation. Evaluate by sample size, representativeness, base rates and alternative explanations.
- Informal fallacies: ad hominem, straw man, false dilemma, equivocation, begging the question, appeal to authority, slippery slope, hasty generalization, composition and division.
- Charity principle: reconstruct the strongest version before criticising.
Worked example
Argument: If it rained, the ground is wet. The ground is wet. Therefore it rained. Formalise: R implies W; W; therefore R. This is affirming the consequent. Counterexample row: R false, W true - a sprinkler ran. Premises true, conclusion false, so invalid. Repair: switch to modus tollens - if it rained the ground is wet; the ground is not wet; therefore it did not rain. That form is valid.
Traps that cost marks
- Calling an argument false instead of invalid, or rejecting a valid argument because you dislike a premise.
- Treating a fallacy name as a refutation without showing the defect.
- Missing equivocation when a term shifts meaning across premises.
- Confusing necessary with sufficient conditions in causal or legal reasoning.
- Assuming a strong inductive argument can be valid, or a valid one can be cogent.