The Art of Logic · Part 8 · Propositions · B2
All, No, Some: The Four Propositions A, E, I, O
Part 8 of The Art of Logic: every categorical proposition says something about all or some of a class, and says it or denies it. Four combinations, four letters: A, E, I, O. Quantifiers (all, every, no, none, some, not all) and the slippery scope of not, with Philo, Sophia, Marcos and Demetria.
Tonight, four letters that medieval students learned by heart: A, E, I, O.
A logic lesson in four vowels. All, no, some, and some… not.
Every categorical one. Let us try it on a basket of figs.
A categorical proposition has a quantity: it is universal (about all of the subject) or particular (about some of it). It also has a quality: it is affirmative or negative.
Together they make four forms. A: All S is P (universal affirmative). E: No S is P (universal negative). I: Some S is P (particular affirmative). O: Some S is not P (particular negative). Medieval teachers took the letters from the Latin AffIrmo, “I affirm”, and nEgO, “I deny”: A and I affirm, E and O deny.
In logic, some means “at least one, perhaps all”. In everyday English, “some figs are fresh” often suggests that others are not; in logic, it does not say so.
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