Categorical Propositions
Categorical propositions are the backbone of traditional syllogistic logic. This domain tests standard form, the A/E/I/O scheme, quantity and quality, the subject-copula-predicate structure, and the traditional square of opposition.
Core rules
- Standard form: quantifier + subject term + copula + predicate term. All S are P is A; No S are P is E; Some S are P is I; Some S are not P is O.
- Quantity is universal in A and E, particular in I and O. Quality is affirmative in A and I, negative in E and O.
- A and O are contradictory; E and I are contradictory. A and E are contraries; I and O are subcontraries. Subalternation links A to I and E to O in the traditional square.
- Traditional Aristotelian logic often treats universals as having existential import; modern Boolean logic does not. State which interpretation you are using in an answer.
Worked example
No reptiles are warm-blooded. The subject is reptiles, the predicate is warm-blooded animals, the copula is are, and no makes it universal negative: E. Its contradictory is the I proposition Some reptiles are warm-blooded. If the E proposition is true, the I proposition must be false. The A proposition All reptiles are warm-blooded is a contrary, not a contradictory.
Traps
All S are not P is ambiguous in English; standardise it as No S are P or Some S are not P according to meaning. Only S are P is usually All P are S. Not all S are P is Some S are not P. Do not call a singular proposition universal merely because it names one definite object.