Categorical form
In Aristotelian logic, the categorical form of a categorical proposition is determined by its quality and quantity. The quality is affirmative or negative, the quantity is universal or particular. Thus there are four possible categorical forms, shown with their traditional codes.
- Universal affirmative' - every S is P (code 'A').
- Universal negative' - no S is P ('E').
- Particular affirmative' - some S is P ( 'I').
- Particular negative' - some S is not P. ('O').
The codes ‘A’ and ‘I’ are derived from the first two vowels of the Latin verb affirmo (I affirm), and the codes ‘E’ and ‘O’ from the two vowels of nego (I deny). This suggests that the codes are not derived from Aristotle (who spoke Greek, not Latin). They were certainly a medieval Latin innovation, but their origin is a mystery. Using these forms, it is possible to categorise and encode the three propositions of a syllogism into moods. For example, the syllogism 'every animal is a substance, every man is an animal, therefore every man is a substance' consists of three universal affirmatives, and therefore has the code AAA.
For the purposes of syllogistic logic, indefinite propositions such as 'a man (i.e. some man) is an animal' are treated as particular propositions, singular propositions such as 'Socrates is a man' are treated as universal propositions.
