Categorical Logic - Quia



Categorical Logic

Categorical logic was first heavily explored by the ancient Greek thinker Aristotle.

He investigated the logical properties of four distinct sentence types.

The four sentence types:

A: All S are P (called an A type sentence)

E: No S are P (an E type sentence)

I: Some S are P (an I type sentence)

O: Some S are not P (an O type of sentence)

Each of these sentences has four components:

1) A quantifier (All, No, or Some)

2) A subject term (S)

3) A copula (are or are not)

4) A predicate term (P)

The quantifier specifies HOW MUCH of the subject term we are talking about. The “All” and “No” quantifiers are about every member of the subject class. The “Some” quantifier is defined as meaning “at least one (i.e., one or more).”

The only sentence with an “are not” copula is the O type of sentence. There never are any other sentences with an “are not” copula. If you wanted to say “All S are not P” you would just say “No S are P” instead in Aristotle’s system.

The QUANTITY of the four sentence types is either Universal or Particular. The A and E sentences (All and No) are Universal and the I and O sentences (Some) are particular.

The QUALITY of the four sentence types is Affirmative or Negative. The A and I sentences (All and Some are) are affirmative and the E and O sentences (No and Some are not) are negative.

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