The Fourfold Classification: A, E, I and O
Chapter Twenty-Eight
Syllabus topic 2.2, "Traditional classification of proposition into categorical and conditional four -fold classification."
Pages 136 to 139 of 334
In one line
Categorical propositions are classified by quantity, universal or particular, and by quality, affirmative or negative, which gives four forms, called A, E, I and O.
In the wording a student can write in an examination: the traditional fourfold classification cross-divides categorical propositions by quantity and quality. A universal affirmative is called A, a universal negative E, a particular affirmative I and a particular negative O.
The two divisions being crossed
Quantity is settled by the quantifier and answers: how much of the subject class is being spoken about?
Universal propositions speak about the whole of it: "all", "every", "no", "none".
Particular propositions speak about part of it: "some", "certain", "a few", "most".
Quality is settled by the copula and answers: is the predicate being affirmed of the subject or denied of it?
Affirmative propositions affirm: "are", "is".
Negative propositions deny: "are not", "is not", and also "no", which carries the negative in itself.
Two divisions of two members each give four combinations, and there are no others. That is the whole of the classification.
The four forms
| Letter | Name | Form | Example |
|---|---|---|---|
| A | Universal affirmative | All S is P | All contracts are agreements |
| E | Universal negative | No S is P | No minor's agreement is enforceable |
| I | Particular affirmative | Some S is P | Some agreements are contracts |
| O | Particular negative | Some S is not P | Some agreements are not contracts |
Where the letters come from. They are taken from two Latin words. AffIrmo, "I affirm", supplies A and I for the two affirmatives, the first vowel for the universal and the second for the particular. nEgO, "I deny", supplies E and O for the two negatives in the same order. The mnemonic is old, it is asked, and it is worth one line in an answer.
Points that decide marks
"Some" means "at least one". It does not mean "some but not all", and it does not mean "a few". In logic "some contracts are void" is true even if every contract is void. This departs from ordinary usage, where saying "some" suggests "not all", and the departure is deliberate: the suggestion is a matter of conversational implication and not of what is asserted.
"No S is P" is universal, not particular. It is about the whole subject class, saying of every member that it is not P. The word "no" looks like a denial of quantity and is in fact a universal quantifier with negative quality.
"Some S is not P" is the O form and it is not the denial of "some S is P". Both may be true together: some agreements are contracts and some agreements are not contracts are both true, and both are true of the same class.
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