Unit 2: Kinds of Proposition
Table of Contents
Kinds of Proposition
A proposition is the "building block" of an argument. It is a statement that asserts or denies something and can be either true or false. In logic, we classify propositions to understand their structure.
Traditional Classification (Categorical Propositions)
Aristotelian logic is built on Categorical Propositions. These are propositions that relate two classes (or categories) of things.
A "class" is a collection of all objects that have some common property (e.g., the class of "dogs," the class of "mammals").
A categorical proposition asserts that a class (the Subject class, S) is either included in or excluded from another class (the Predicate class, P).
The standard form of a categorical proposition has four parts:
- Quantifier: "All," "No," or "Some." (Tells us "how many" of the subject class).
- Subject Term (S): The class being talked about.
- Copula: "are" or "are not." (The linking verb).
- Predicate Term (P): The class being related to the subject.
Example: "All [Quantifier] dogs [Subject] are [Copula] mammals [Predicate]."
The Four-fold Scheme (A, E, I, O)
Propositions are classified in two ways:
- By Quality: Is it Affirmative (includes) or Negative (excludes)?
- By Quantity: Is it Universal (talks about the *whole* subject class) or Particular (talks about *part* of the subject class)?
This gives us the four standard forms:
| Type | Vowel | Form | Example | Quantity | Quality |
|---|---|---|---|---|---|
| Universal Affirmative | A | All S are P | All cats are mammals. | Universal | Affirmative |
| Universal Negative | E | No S are P | No cats are reptiles. | Universal | Negative |
| Particular Affirmative | I | Some S are P | Some cats are black. | Particular | Affirmative |
| Particular Negative | O | Some S are not P | Some cats are not black. | Particular | Negative |