All, Some, and None

All, Some, and None

One major difference between Aristotle’s understanding of predication and modern (i.e., post-Fregean) logic is that Aristotle treats individual predications and general predications as similar in logical form:

he gives the same analysis to “Socrates is an animal” and “Humans are animals”.

However, he notes that when the subject is a universal, predication takes on two forms: it can be either universal or particular.

These expressions are parallel to those with which Aristotle distinguishes universal and particular terms, and Aristotle is aware of that, explicitly distinguishing between a term being a universal and a term being universally predicated of another.

Whatever is affirmed or denied of a universal subject may be affirmed or denied of it it universally (katholou or “of all”, kata pantos), in part (kata meros, en merei), or indefinitely (adihoristos).

| | Affirmations | Denials |
| Universal | P affirmed of all of S | Every S is P, All S is (are) P | P denied of all of S | No S is P |
| Particular | P affirmed of some of S | Some S is (are) P | P denied of some of S | Some S is not P, Not every S is P |
| Indefinite | P affirmed of S | S is P | P denied of S | S is not P |

via: http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/

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