Logic and Critical Reasoning
The Logic and Critical Reasoning domain tests whether you can reconstruct and evaluate arguments, not whether you like their conclusions. GCE tasks usually ask you to separate validity from truth, test categorical syllogisms, apply truth-table methods, and identify informal fallacies by name.
Argument and evaluation
An argument has premises offered as support for a conclusion. Indicator words such as 'therefore', 'so', and 'hence' mark conclusions; 'because', 'since', and 'given that' mark premises. A deductive argument is valid when the conclusion cannot be false if the premises are true. Soundness adds actual truth of all premises. Inductive arguments are strong or weak, cogent or uncogent; they make the conclusion probable, not certain.
Categorical logic
A, E, I and O propositions have distribution patterns: A distributes its subject; E distributes both terms; I distributes neither; O distributes its predicate. For a valid syllogism, the middle term must be distributed at least once; no term may be distributed in the conclusion unless distributed in a premise; two negative premises cannot yield a conclusion; a negative premise requires a negative conclusion.
Propositional logic
Modus ponens (P→Q, P, therefore Q) and modus tollens (P→Q, ¬Q, therefore ¬P) are valid. Affirming the consequent (P→Q, Q, therefore P) and denying the antecedent (P→Q, ¬P, therefore ¬Q) are invalid. A truth table tests all assignments: a tautology is true on every row, a contradiction false on every row, and a contingency varies.
Worked example
Take: 'All philosophers are rational; some rational people are not logicians; therefore some philosophers are not logicians.' Let P = philosophers, R = rational, L = logicians. The premises are 'All P are R' and 'Some R are not L'; the conclusion is 'Some P are not L'. This is invalid. Counterexample: every philosopher is a logician, and some non-logician mathematicians are rational. Then both premises are true, but no philosopher is a non-logician. The middle term R is undistributed in both premises: the A proposition does not distribute its predicate, and the O proposition does not distribute its subject. The fallacy is undistributed middle.
Traps
Do not call an argument valid because its conclusion is true, or invalid because a premise is false. In traditional logic 'some' means at least one, not 'some but not all'. Do not confuse ad hominem (attacking the person) with criticism of an argument, or a straw man (misrepresenting an opponent) with a genuine counterexample. Check distribution before trusting a syllogism's surface plausibility.