Logical Reasoning and Critical Thinking
Logical Reasoning and Critical Thinking tests deductive validity, inductive strength and argument analysis. You must separate what an argument proves from what it merely suggests, and identify assumptions, weakeners and strengtheners.
Deductive reasoning
- Valid form: If P, then Q. Not Q, therefore not P. This is contrapositive and is valid.
- Invalid form: If P, then Q. Q, therefore P. This is affirming the consequent.
- Invalid form: If P, then Q. Not P, therefore not Q. This is denying the antecedent.
- Necessary condition: Q is necessary for P if P cannot occur without Q. Sufficient condition: P is enough for Q. Do not reverse them.
- In syllogisms, check whether the conclusion introduces a term or relation not licensed by the premises.
Inductive and argument analysis
- Inductive strength depends on sample size, representativeness and whether counterexamples are considered. A large but biased sample can be weak.
- Correlation is not causation. Alternative explanations include reverse causation, a common cause, or coincidence.
- To find an assumption, ask what must be true for the premises to support the conclusion. To weaken, attack that link; to strengthen, support it.
- Distinguish the conclusion from evidence. Words such as therefore, hence and so usually introduce the conclusion.
Worked example
Premises: If an officer completes crowd-control training, the officer is eligible for deployment. Officer A is not eligible for deployment. Can we conclude that A did not complete the training? Yes. Let P = completed training, Q = eligible. The premises give P → Q and not Q. By contrapositive, not Q → not P. The conclusion follows necessarily. By contrast, if the premise were A is eligible, we could not conclude A completed training, because eligibility may have other routes. That would be affirming the consequent.
Traps that cost marks
- Treating a sufficient condition as necessary, or vice versa.
- Accepting a conclusion because it is plausible rather than because it follows.
- Ignoring sample bias in survey or anecdote questions.
- Confusing an explanation of why a claim is attractive with evidence that it is true.
- Missing the word only, all, some or unless, which changes logical scope.
- Attacking the person rather than the argument.
Exam habit
Rewrite conditional statements in P → Q form. For weakening questions, state the assumption in one sentence, then look for the option that denies it.