distribution of terms - Logic

 In logic, "distribution of terms" refers to how a term in a categorical proposition relates to the entire class that it denotes. A term is considered distributed if it refers to all members of the category or class it represents. If it refers to only some members, it is undistributed.

Key Categorical Propositions

To understand distribution, we need to consider the four basic types of categorical propositions in logic:

1. Universal Affirmative (A):

All S are P.

Example: "All dogs are animals."

2. Universal Negative (E):

No S are P.

Example: "No dogs are cats."

3. Particular Affirmative (I):

Some S are P.

Example: "Some dogs are friendly."

4. Particular Negative (O):

Some S are not P.

Example: "Some dogs are not friendly."

Distribution of Terms by Proposition Type.

Each type of proposition distributes its terms differently:

1. Universal Affirmative 

(A: All S are P)

Subject (S): Distributed (because the proposition talks about all of S).

Predicate (P): Undistributed (it only refers to some of P, not all).

2. Universal Negative

(E: No S are P)

Subject (S): Distributed (talks about all of S).

Predicate (P): Distributed (since it's saying none of P applies to any of S).

3. Particular Affirmative

(I: Some S are P)

Subject (S): Undistributed (because "some" refers to only a part of S).

Predicate (P): Undistributed (since the proposition does not apply to all of P, only to some).

4. Particular Negative

(O: Some S are not P)

Subject (S): Undistributed (because "some" applies only to part of S).

Predicate (P): Distributed (because it denies the whole category of P to that part of S).

Summary of Term Distribution

Understanding term distribution helps in evaluating logical arguments and determining if they are valid, particularly in syllogisms, where the rules of distribution play a crucial role in determining whether the conclusion follows from the premises.