Logical Reasoning
Logical Reasoning
Paper I probes formal and informal reasoning: syllogisms, the square of opposition, series and analogies, coding–decoding, seating and ranking, assumption–conclusion, argument strength, and occasionally Indian logic (Nyāya's four pramāṇas).
Rules to work from
- Categorical propositions: A (All S are P), E (No S is P), I (Some S are P), O (Some S are not P).
- Square of opposition: A–O and E–I are contradictories (one true, one false). A–E are contraries (not both true). I–O are subcontraries (not both false). A implies I, and E implies O (subalternation).
- Valid conversions: E and I convert simply (No S is P ⇔ No P is S; Some S is P ⇔ Some P is S). A converts only by limitation (All S is P → Some P is S). O does not convert.
- Venn test beats intuition for two-premise syllogisms: draw the premises, then check whether the conclusion is already forced.
- Nyāya pramāṇas: pratyakṣa (perception), anumāna (inference), upamāna (comparison), śabda (testimony).
Worked example
Premises: All scholars are readers. Some readers are critics. Proposed conclusion: Some scholars are critics.
Draw it: the scholars circle sits inside readers; critics overlap readers, but the overlap may fall entirely outside scholars. The conclusion is therefore not valid - the fallacy is the undistributed middle, since "readers" is not distributed in either premise. Note also that no premise guarantees any critic is a scholar.
Traps that cost marks
- Illicitly converting an A proposition ("All S is P" ⇒ "All P is S" is invalid).
- Treating a possible conclusion as a necessary one.
- Rejecting a conclusion because it is not the only one, when the question asks what follows.
- Confusing "assumption" (unstated, necessary) with "inference" (drawn from stated evidence).