7 min readConcept sheetSquare-of-opposition and distribution MCQs

Arguments and categorical propositions

An argument is premises supporting a conclusion. Categorical propositions come in four forms, A, E, I and O, linked by the square of opposition.

ArgumentPremises + a conclusion they support

Four formsA, E, I, O

DistributionA: S · E: S and P · I: none · O: P

Syllogism3 propositions, 3 terms (S, P, M)

The four categorical propositions

Code	Form	Quantity	Quality	Terms distributed
A	All S are P	Universal	Affirmative	Subject only
E	No S is P	Universal	Negative	Subject and predicate
I	Some S are P	Particular	Affirmative	Neither
O	Some S are not P	Particular	Negative	Predicate only

The classical square of opposition

Relation	Between	Rule
Contradictories	A and O; E and I	Always opposite: exactly one is true and the other false
Contraries	A and E	Cannot both be true; can both be false
Subcontraries	I and O	Cannot both be false; can both be true
Subalternation	A to I; E to O	If the universal is true, the particular is true. If the particular is false, the universal is false

Mood and figure of a syllogism

MoodLetters of the major premise, minor premise and conclusion, e.g. AAA

Figure 1M-P, S-M (middle: subject, then predicate)

Figure 2P-M, S-M (middle: predicate in both)

Figure 3M-P, M-S (middle: subject in both)

Figure 4P-M, M-S (middle: predicate, then subject)

Classic valid forms (figure 1)Barbara AAA, Celarent EAE, Darii AII, Ferio EIO

How NET asks this

How NET asks this: one proposition is given as true or false, and you decide which of the others are true, false or doubtful; or you name the terms a proposition distributes.

Exam angle

Typical MCQ: “If 'All teachers are honest' is true, which propositions must be false?” Its contradictory O ('Some teachers are not honest') and its contrary E ('No teachers are honest'). The I form is true by subalternation.

Typical MCQ: “Which terms does 'No S is P' distribute?” Both S and P. E distributes both terms; I distributes neither.

Remember it

"Unprepared Students Never Pass": Universals distribute the Subject, Negatives distribute the Predicate. Apply both rules and you get the distribution of A, E, I and O.