Unit 2: Categorical Propositions

The structure and classification of logical statements.

1. Sentence vs. Proposition

In logic, we do not study all sentences. We only study Propositions.

Sentence: A grammatical unit (Questions, Commands, Exclamations, or Statements).
Proposition: A sentence that is either True or False. Only "Declarative" or "Indicative" sentences are propositions.

Example: "Is it raining?" is a sentence, but not a proposition. "It is raining" is a proposition.

Every categorical proposition has three essential parts:

Subject (S): The term about which something is stated.
Predicate (P): The term that states something about the subject.
Copula: The link between S and P (always a form of the verb "to be" — is, are, is not, are not).

Example: "All [humans] (S) [are] (Copula) [mortal] (P)."

Aristotle classified propositions based on Quantity (Universal or Particular) and Quality (Affirmative or Negative).

Symbol	Type	Standard Form	Example
A	Universal Affirmative	All S is P	All cats are mammals.
E	Universal Negative	No S is P	No birds are dogs.
I	Particular Affirmative	Some S is P	Some students are hardworking.
O	Particular Negative	Some S is not P	Some fruits are not sweet.

A term is "Distributed" if the proposition tells us something about every member of that class.

Mnemonic: "ASEBINOP" (A distributes Subject, E distributes Both, I distributes Neither, O distributes Predicate).

Quantity vs. Quality: Be ready to identify these in any given sentence.
Logical Form: You will often be asked to convert "ordinary" sentences into "logical form."
Ordinary: "Every dog barks." → Logical (A): "All dogs are barking animals."
Distribution Rule: Universal propositions (A, E) always distribute the Subject. Negative propositions (E, O) always distribute the Predicate.